Merge pull request #805 from dimforge/dev

Release v0.23.2

CHANGELOG.md

@@ -4,6 +4,10 @@ documented here.
 
 This project adheres to [Semantic Versioning](https://semver.org/).
 
+## [0.23.2]
+In this release, we improved the documentation of some of the geometric types
+by applying changes similar to what we did in the version 0.23.1 for matrices.
+
 ## [0.23.1]
 In this release we improved the documentation of the matrix and vector types by:
 - Grouping `impl` bocks logically, adding a title comment to these impl blocks.

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name    = "nalgebra"
-version = "0.23.1"
+version = "0.23.2"
 authors = [ "Sébastien Crozet <developer@crozet.re>" ]
 
 description = "Linear algebra library with transformations and statically-sized or dynamically-sized matrices."

README.md

@@ -29,3 +29,11 @@
 </p>
 
 -----
+
+## Gold sponsors
+Rapier is supported by:
+<p>
+  <a href="https://embark-studios.com">
+    <img src="https://www.embark.dev/img/logo_black.png" width="301px">
+  </a>
+</p>

src/base/alias.rs

@@ -14,138 +14,242 @@ use crate::base::Matrix;
  *
  */
 /// A statically sized column-major matrix with `R` rows and `C` columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[deprecated(note = "This matrix name contains a typo. Use MatrixMN instead.")]
 pub type MatrixNM<N, R, C> = Matrix<N, R, C, Owned<N, R, C>>;
 
 /// A statically sized column-major matrix with `R` rows and `C` columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixMN<N, R, C> = Matrix<N, R, C, Owned<N, R, C>>;
 
 /// A statically sized column-major square matrix with `D` rows and columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixN<N, D> = Matrix<N, D, D, Owned<N, D, D>>;
 
 /// A dynamically sized column-major matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type DMatrix<N> = Matrix<N, Dynamic, Dynamic, Owned<N, Dynamic, Dynamic>>;
 
 /// A heap-allocated, column-major, matrix with a dynamic number of rows and 1 columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type MatrixXx1<N> = Matrix<N, Dynamic, U1, Owned<N, Dynamic, U1>>;
 /// A heap-allocated, column-major, matrix with a dynamic number of rows and 2 columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type MatrixXx2<N> = Matrix<N, Dynamic, U2, Owned<N, Dynamic, U2>>;
 /// A heap-allocated, column-major, matrix with a dynamic number of rows and 3 columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type MatrixXx3<N> = Matrix<N, Dynamic, U3, Owned<N, Dynamic, U3>>;
 /// A heap-allocated, column-major, matrix with a dynamic number of rows and 4 columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type MatrixXx4<N> = Matrix<N, Dynamic, U4, Owned<N, Dynamic, U4>>;
 /// A heap-allocated, column-major, matrix with a dynamic number of rows and 5 columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type MatrixXx5<N> = Matrix<N, Dynamic, U5, Owned<N, Dynamic, U5>>;
 /// A heap-allocated, column-major, matrix with a dynamic number of rows and 6 columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type MatrixXx6<N> = Matrix<N, Dynamic, U6, Owned<N, Dynamic, U6>>;
 
 /// A heap-allocated, row-major, matrix with 1 rows and a dynamic number of columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix1xX<N> = Matrix<N, U1, Dynamic, Owned<N, U1, Dynamic>>;
 /// A heap-allocated, row-major, matrix with 2 rows and a dynamic number of columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix2xX<N> = Matrix<N, U2, Dynamic, Owned<N, U2, Dynamic>>;
 /// A heap-allocated, row-major, matrix with 3 rows and a dynamic number of columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix3xX<N> = Matrix<N, U3, Dynamic, Owned<N, U3, Dynamic>>;
 /// A heap-allocated, row-major, matrix with 4 rows and a dynamic number of columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix4xX<N> = Matrix<N, U4, Dynamic, Owned<N, U4, Dynamic>>;
 /// A heap-allocated, row-major, matrix with 5 rows and a dynamic number of columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix5xX<N> = Matrix<N, U5, Dynamic, Owned<N, U5, Dynamic>>;
 /// A heap-allocated, row-major, matrix with 6 rows and a dynamic number of columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix6xX<N> = Matrix<N, U6, Dynamic, Owned<N, U6, Dynamic>>;
 
 /// A stack-allocated, column-major, 1x1 square matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix1<N> = Matrix<N, U1, U1, Owned<N, U1, U1>>;
 /// A stack-allocated, column-major, 2x2 square matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix2<N> = Matrix<N, U2, U2, Owned<N, U2, U2>>;
 /// A stack-allocated, column-major, 3x3 square matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix3<N> = Matrix<N, U3, U3, Owned<N, U3, U3>>;
 /// A stack-allocated, column-major, 4x4 square matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix4<N> = Matrix<N, U4, U4, Owned<N, U4, U4>>;
 /// A stack-allocated, column-major, 5x5 square matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix5<N> = Matrix<N, U5, U5, Owned<N, U5, U5>>;
 /// A stack-allocated, column-major, 6x6 square matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix6<N> = Matrix<N, U6, U6, Owned<N, U6, U6>>;
 
 /// A stack-allocated, column-major, 1x2 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix1x2<N> = Matrix<N, U1, U2, Owned<N, U1, U2>>;
 /// A stack-allocated, column-major, 1x3 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix1x3<N> = Matrix<N, U1, U3, Owned<N, U1, U3>>;
 /// A stack-allocated, column-major, 1x4 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix1x4<N> = Matrix<N, U1, U4, Owned<N, U1, U4>>;
 /// A stack-allocated, column-major, 1x5 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix1x5<N> = Matrix<N, U1, U5, Owned<N, U1, U5>>;
 /// A stack-allocated, column-major, 1x6 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix1x6<N> = Matrix<N, U1, U6, Owned<N, U1, U6>>;
 
 /// A stack-allocated, column-major, 2x3 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix2x3<N> = Matrix<N, U2, U3, Owned<N, U2, U3>>;
 /// A stack-allocated, column-major, 2x4 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix2x4<N> = Matrix<N, U2, U4, Owned<N, U2, U4>>;
 /// A stack-allocated, column-major, 2x5 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix2x5<N> = Matrix<N, U2, U5, Owned<N, U2, U5>>;
 /// A stack-allocated, column-major, 2x6 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix2x6<N> = Matrix<N, U2, U6, Owned<N, U2, U6>>;
 
 /// A stack-allocated, column-major, 3x4 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix3x4<N> = Matrix<N, U3, U4, Owned<N, U3, U4>>;
 /// A stack-allocated, column-major, 3x5 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix3x5<N> = Matrix<N, U3, U5, Owned<N, U3, U5>>;
 /// A stack-allocated, column-major, 3x6 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix3x6<N> = Matrix<N, U3, U6, Owned<N, U3, U6>>;
 
 /// A stack-allocated, column-major, 4x5 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix4x5<N> = Matrix<N, U4, U5, Owned<N, U4, U5>>;
 /// A stack-allocated, column-major, 4x6 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix4x6<N> = Matrix<N, U4, U6, Owned<N, U4, U6>>;
 
 /// A stack-allocated, column-major, 5x6 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix5x6<N> = Matrix<N, U5, U6, Owned<N, U5, U6>>;
 
 /// A stack-allocated, column-major, 2x1 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix2x1<N> = Matrix<N, U2, U1, Owned<N, U2, U1>>;
 /// A stack-allocated, column-major, 3x1 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix3x1<N> = Matrix<N, U3, U1, Owned<N, U3, U1>>;
 /// A stack-allocated, column-major, 4x1 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix4x1<N> = Matrix<N, U4, U1, Owned<N, U4, U1>>;
 /// A stack-allocated, column-major, 5x1 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix5x1<N> = Matrix<N, U5, U1, Owned<N, U5, U1>>;
 /// A stack-allocated, column-major, 6x1 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix6x1<N> = Matrix<N, U6, U1, Owned<N, U6, U1>>;
 
 /// A stack-allocated, column-major, 3x2 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix3x2<N> = Matrix<N, U3, U2, Owned<N, U3, U2>>;
 /// A stack-allocated, column-major, 4x2 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix4x2<N> = Matrix<N, U4, U2, Owned<N, U4, U2>>;
 /// A stack-allocated, column-major, 5x2 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix5x2<N> = Matrix<N, U5, U2, Owned<N, U5, U2>>;
 /// A stack-allocated, column-major, 6x2 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix6x2<N> = Matrix<N, U6, U2, Owned<N, U6, U2>>;
 
 /// A stack-allocated, column-major, 4x3 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix4x3<N> = Matrix<N, U4, U3, Owned<N, U4, U3>>;
 /// A stack-allocated, column-major, 5x3 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix5x3<N> = Matrix<N, U5, U3, Owned<N, U5, U3>>;
 /// A stack-allocated, column-major, 6x3 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix6x3<N> = Matrix<N, U6, U3, Owned<N, U6, U3>>;
 
 /// A stack-allocated, column-major, 5x4 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix5x4<N> = Matrix<N, U5, U4, Owned<N, U5, U4>>;
 /// A stack-allocated, column-major, 6x4 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix6x4<N> = Matrix<N, U6, U4, Owned<N, U6, U4>>;
 
 /// A stack-allocated, column-major, 6x5 matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type Matrix6x5<N> = Matrix<N, U6, U5, Owned<N, U6, U5>>;
 
 /*

src/base/alias_slice.rs

@@ -10,129 +10,207 @@ use crate::base::Matrix;
  *
  */
 /// A column-major matrix slice with `R` rows and `C` columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMN<'a, N, R, C, RStride = U1, CStride = R> =
     Matrix<N, R, C, SliceStorage<'a, N, R, C, RStride, CStride>>;
 
 /// A column-major matrix slice with `D` rows and columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceN<'a, N, D, RStride = U1, CStride = D> =
     Matrix<N, D, D, SliceStorage<'a, N, D, D, RStride, CStride>>;
 
 /// A column-major matrix slice dynamic numbers of rows and columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type DMatrixSlice<'a, N, RStride = U1, CStride = Dynamic> =
     Matrix<N, Dynamic, Dynamic, SliceStorage<'a, N, Dynamic, Dynamic, RStride, CStride>>;
 
 /// A column-major 1x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice1<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U1, SliceStorage<'a, N, U1, U1, RStride, CStride>>;
 /// A column-major 2x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice2<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U2, SliceStorage<'a, N, U2, U2, RStride, CStride>>;
 /// A column-major 3x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice3<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U3, SliceStorage<'a, N, U3, U3, RStride, CStride>>;
 /// A column-major 4x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice4<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U4, SliceStorage<'a, N, U4, U4, RStride, CStride>>;
 /// A column-major 5x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice5<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U5, SliceStorage<'a, N, U5, U5, RStride, CStride>>;
 /// A column-major 6x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice6<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U6, SliceStorage<'a, N, U6, U6, RStride, CStride>>;
 
 /// A column-major 1x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice1x2<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U2, SliceStorage<'a, N, U1, U2, RStride, CStride>>;
 /// A column-major 1x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice1x3<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U3, SliceStorage<'a, N, U1, U3, RStride, CStride>>;
 /// A column-major 1x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice1x4<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U4, SliceStorage<'a, N, U1, U4, RStride, CStride>>;
 /// A column-major 1x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice1x5<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U5, SliceStorage<'a, N, U1, U5, RStride, CStride>>;
 /// A column-major 1x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice1x6<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U6, SliceStorage<'a, N, U1, U6, RStride, CStride>>;
 
 /// A column-major 2x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice2x1<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U1, SliceStorage<'a, N, U2, U1, RStride, CStride>>;
 /// A column-major 2x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice2x3<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U3, SliceStorage<'a, N, U2, U3, RStride, CStride>>;
 /// A column-major 2x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice2x4<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U4, SliceStorage<'a, N, U2, U4, RStride, CStride>>;
 /// A column-major 2x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice2x5<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U5, SliceStorage<'a, N, U2, U5, RStride, CStride>>;
 /// A column-major 2x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice2x6<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U6, SliceStorage<'a, N, U2, U6, RStride, CStride>>;
 
 /// A column-major 3x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice3x1<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U1, SliceStorage<'a, N, U3, U1, RStride, CStride>>;
 /// A column-major 3x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice3x2<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U2, SliceStorage<'a, N, U3, U2, RStride, CStride>>;
 /// A column-major 3x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice3x4<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U4, SliceStorage<'a, N, U3, U4, RStride, CStride>>;
 /// A column-major 3x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice3x5<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U5, SliceStorage<'a, N, U3, U5, RStride, CStride>>;
 /// A column-major 3x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice3x6<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U6, SliceStorage<'a, N, U3, U6, RStride, CStride>>;
 
 /// A column-major 4x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice4x1<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U1, SliceStorage<'a, N, U4, U1, RStride, CStride>>;
 /// A column-major 4x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice4x2<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U2, SliceStorage<'a, N, U4, U2, RStride, CStride>>;
 /// A column-major 4x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice4x3<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U3, SliceStorage<'a, N, U4, U3, RStride, CStride>>;
 /// A column-major 4x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice4x5<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U5, SliceStorage<'a, N, U4, U5, RStride, CStride>>;
 /// A column-major 4x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice4x6<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U6, SliceStorage<'a, N, U4, U6, RStride, CStride>>;
 
 /// A column-major 5x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice5x1<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U1, SliceStorage<'a, N, U5, U1, RStride, CStride>>;
 /// A column-major 5x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice5x2<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U2, SliceStorage<'a, N, U5, U2, RStride, CStride>>;
 /// A column-major 5x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice5x3<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U3, SliceStorage<'a, N, U5, U3, RStride, CStride>>;
 /// A column-major 5x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice5x4<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U4, SliceStorage<'a, N, U5, U4, RStride, CStride>>;
 /// A column-major 5x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice5x6<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U6, SliceStorage<'a, N, U5, U6, RStride, CStride>>;
 
 /// A column-major 6x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice6x1<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U1, SliceStorage<'a, N, U6, U1, RStride, CStride>>;
 /// A column-major 6x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice6x2<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U2, SliceStorage<'a, N, U6, U2, RStride, CStride>>;
 /// A column-major 6x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice6x3<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U3, SliceStorage<'a, N, U6, U3, RStride, CStride>>;
 /// A column-major 6x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice6x4<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U4, SliceStorage<'a, N, U6, U4, RStride, CStride>>;
 /// A column-major 6x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSlice6x5<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U5, SliceStorage<'a, N, U6, U5, RStride, CStride>>;
 
@@ -183,21 +261,33 @@ pub type DVectorSlice<'a, N, RStride = U1, CStride = Dynamic> =
     Matrix<N, Dynamic, U1, SliceStorage<'a, N, Dynamic, U1, RStride, CStride>>;
 
 /// A 1D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSlice1<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U1, SliceStorage<'a, N, U1, U1, RStride, CStride>>;
 /// A 2D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSlice2<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U1, SliceStorage<'a, N, U2, U1, RStride, CStride>>;
 /// A 3D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSlice3<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U1, SliceStorage<'a, N, U3, U1, RStride, CStride>>;
 /// A 4D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSlice4<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U1, SliceStorage<'a, N, U4, U1, RStride, CStride>>;
 /// A 5D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSlice5<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U1, SliceStorage<'a, N, U5, U1, RStride, CStride>>;
 /// A 6D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSlice6<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U1, SliceStorage<'a, N, U6, U1, RStride, CStride>>;
 
@@ -209,129 +299,207 @@ pub type VectorSlice6<'a, N, RStride = U1, CStride = U6> =
  *
  */
 /// A column-major matrix slice with `R` rows and `C` columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMutMN<'a, N, R, C, RStride = U1, CStride = R> =
     Matrix<N, R, C, SliceStorageMut<'a, N, R, C, RStride, CStride>>;
 
 /// A column-major matrix slice with `D` rows and columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMutN<'a, N, D, RStride = U1, CStride = D> =
     Matrix<N, D, D, SliceStorageMut<'a, N, D, D, RStride, CStride>>;
 
 /// A column-major matrix slice dynamic numbers of rows and columns.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type DMatrixSliceMut<'a, N, RStride = U1, CStride = Dynamic> =
     Matrix<N, Dynamic, Dynamic, SliceStorageMut<'a, N, Dynamic, Dynamic, RStride, CStride>>;
 
 /// A column-major 1x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut1<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U1, SliceStorageMut<'a, N, U1, U1, RStride, CStride>>;
 /// A column-major 2x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut2<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U2, SliceStorageMut<'a, N, U2, U2, RStride, CStride>>;
 /// A column-major 3x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut3<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U3, SliceStorageMut<'a, N, U3, U3, RStride, CStride>>;
 /// A column-major 4x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut4<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U4, SliceStorageMut<'a, N, U4, U4, RStride, CStride>>;
 /// A column-major 5x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut5<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U5, SliceStorageMut<'a, N, U5, U5, RStride, CStride>>;
 /// A column-major 6x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut6<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U6, SliceStorageMut<'a, N, U6, U6, RStride, CStride>>;
 
 /// A column-major 1x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut1x2<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U2, SliceStorageMut<'a, N, U1, U2, RStride, CStride>>;
 /// A column-major 1x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut1x3<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U3, SliceStorageMut<'a, N, U1, U3, RStride, CStride>>;
 /// A column-major 1x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut1x4<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U4, SliceStorageMut<'a, N, U1, U4, RStride, CStride>>;
 /// A column-major 1x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut1x5<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U5, SliceStorageMut<'a, N, U1, U5, RStride, CStride>>;
 /// A column-major 1x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut1x6<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U6, SliceStorageMut<'a, N, U1, U6, RStride, CStride>>;
 
 /// A column-major 2x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut2x1<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U1, SliceStorageMut<'a, N, U2, U1, RStride, CStride>>;
 /// A column-major 2x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut2x3<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U3, SliceStorageMut<'a, N, U2, U3, RStride, CStride>>;
 /// A column-major 2x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut2x4<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U4, SliceStorageMut<'a, N, U2, U4, RStride, CStride>>;
 /// A column-major 2x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut2x5<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U5, SliceStorageMut<'a, N, U2, U5, RStride, CStride>>;
 /// A column-major 2x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut2x6<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U6, SliceStorageMut<'a, N, U2, U6, RStride, CStride>>;
 
 /// A column-major 3x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut3x1<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U1, SliceStorageMut<'a, N, U3, U1, RStride, CStride>>;
 /// A column-major 3x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut3x2<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U2, SliceStorageMut<'a, N, U3, U2, RStride, CStride>>;
 /// A column-major 3x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut3x4<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U4, SliceStorageMut<'a, N, U3, U4, RStride, CStride>>;
 /// A column-major 3x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut3x5<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U5, SliceStorageMut<'a, N, U3, U5, RStride, CStride>>;
 /// A column-major 3x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut3x6<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U6, SliceStorageMut<'a, N, U3, U6, RStride, CStride>>;
 
 /// A column-major 4x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut4x1<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U1, SliceStorageMut<'a, N, U4, U1, RStride, CStride>>;
 /// A column-major 4x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut4x2<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U2, SliceStorageMut<'a, N, U4, U2, RStride, CStride>>;
 /// A column-major 4x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut4x3<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U3, SliceStorageMut<'a, N, U4, U3, RStride, CStride>>;
 /// A column-major 4x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut4x5<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U5, SliceStorageMut<'a, N, U4, U5, RStride, CStride>>;
 /// A column-major 4x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut4x6<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U6, SliceStorageMut<'a, N, U4, U6, RStride, CStride>>;
 
 /// A column-major 5x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut5x1<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U1, SliceStorageMut<'a, N, U5, U1, RStride, CStride>>;
 /// A column-major 5x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut5x2<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U2, SliceStorageMut<'a, N, U5, U2, RStride, CStride>>;
 /// A column-major 5x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut5x3<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U3, SliceStorageMut<'a, N, U5, U3, RStride, CStride>>;
 /// A column-major 5x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut5x4<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U4, SliceStorageMut<'a, N, U5, U4, RStride, CStride>>;
 /// A column-major 5x6 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut5x6<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U6, SliceStorageMut<'a, N, U5, U6, RStride, CStride>>;
 
 /// A column-major 6x1 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut6x1<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U1, SliceStorageMut<'a, N, U6, U1, RStride, CStride>>;
 /// A column-major 6x2 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut6x2<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U2, SliceStorageMut<'a, N, U6, U2, RStride, CStride>>;
 /// A column-major 6x3 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut6x3<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U3, SliceStorageMut<'a, N, U6, U3, RStride, CStride>>;
 /// A column-major 6x4 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut6x4<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U4, SliceStorageMut<'a, N, U6, U4, RStride, CStride>>;
 /// A column-major 6x5 matrix slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixSliceMut6x5<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U5, SliceStorageMut<'a, N, U6, U5, RStride, CStride>>;
 
@@ -382,20 +550,32 @@ pub type DVectorSliceMut<'a, N, RStride = U1, CStride = Dynamic> =
     Matrix<N, Dynamic, U1, SliceStorageMut<'a, N, Dynamic, U1, RStride, CStride>>;
 
 /// A 1D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSliceMut1<'a, N, RStride = U1, CStride = U1> =
     Matrix<N, U1, U1, SliceStorageMut<'a, N, U1, U1, RStride, CStride>>;
 /// A 2D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSliceMut2<'a, N, RStride = U1, CStride = U2> =
     Matrix<N, U2, U1, SliceStorageMut<'a, N, U2, U1, RStride, CStride>>;
 /// A 3D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSliceMut3<'a, N, RStride = U1, CStride = U3> =
     Matrix<N, U3, U1, SliceStorageMut<'a, N, U3, U1, RStride, CStride>>;
 /// A 4D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSliceMut4<'a, N, RStride = U1, CStride = U4> =
     Matrix<N, U4, U1, SliceStorageMut<'a, N, U4, U1, RStride, CStride>>;
 /// A 5D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSliceMut5<'a, N, RStride = U1, CStride = U5> =
     Matrix<N, U5, U1, SliceStorageMut<'a, N, U5, U1, RStride, CStride>>;
 /// A 6D column vector slice.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type VectorSliceMut6<'a, N, RStride = U1, CStride = U6> =
     Matrix<N, U6, U1, SliceStorageMut<'a, N, U6, U1, RStride, CStride>>;

src/base/array_storage.rs

@@ -377,7 +377,7 @@ where
     where
         V: SeqAccess<'a>,
     {
-        let mut out: Self::Value = unsafe { mem::uninitialized() };
+        let mut out: Self::Value = unsafe { mem::MaybeUninit::uninit().assume_init() };
         let mut curr = 0;
 
         while let Some(value) = visitor.next_element()? {

src/base/conversion.rs

@@ -257,9 +257,8 @@ macro_rules! impl_from_into_mint_1D(
             #[inline]
             fn into(self) -> mint::$VT<N> {
                 unsafe {
-                    let mut res: mint::$VT<N> = mem::uninitialized();
+                    let mut res: mint::$VT<N> = mem::MaybeUninit::uninit().assume_init();
                     ptr::copy_nonoverlapping(self.data.ptr(), &mut res.x, $SZ);
-
                     res
                 }
             }
@@ -324,7 +323,7 @@ macro_rules! impl_from_into_mint_2D(
             #[inline]
             fn into(self) -> mint::$MV<N> {
                 unsafe {
-                    let mut res: mint::$MV<N> = mem::uninitialized();
+                    let mut res: mint::$MV<N> = mem::MaybeUninit::uninit().assume_init();
                     let mut ptr = self.data.ptr();
                     $(
                         ptr::copy_nonoverlapping(ptr, &mut res.$component.x, $SZRows);

src/base/interpolation.rs

@@ -56,6 +56,7 @@ impl<N: Scalar + Zero + One + ClosedAdd + ClosedSub + ClosedMul, D: Dim, S: Stor
     }
 }
 
+/// # Interpolation between two unit vectors
 impl<N: RealField, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
     /// Computes the spherical linear interpolation between two unit vectors.
     ///

src/base/unit.rs

@@ -15,7 +15,14 @@ use crate::{Dim, MatrixMN, RealField, Scalar, SimdComplexField, SimdRealField};
 
 /// A wrapper that ensures the underlying algebraic entity has a unit norm.
 ///
-/// Use `.as_ref()` or `.into_inner()` to obtain the underlying value by-reference or by-move.
+/// **It is likely that the only piece of documentation that you need in this page are:**
+/// - **[The construction with normalization](#construction-with-normalization)**
+/// - **[Data extraction and construction without normalization](#data-extraction-and-construction-without-normalization)**
+/// - **[Interpolation between two unit vectors](#interpolation-between-two-unit-vectors)**
+///
+/// All the other impl blocks you will see in this page are about [`UnitComplex`](crate::UnitComplex)
+/// and [`UnitQuaternion`](crate::UnitQuaternion); both built on top of `Unit`.  If you are interested
+/// in their documentation, read their dedicated pages directly.
 #[repr(transparent)]
 #[derive(Eq, PartialEq, Clone, Hash, Debug, Copy)]
 pub struct Unit<T> {
@@ -71,6 +78,7 @@ pub trait Normed {
     fn unscale_mut(&mut self, n: Self::Norm);
 }
 
+/// # Construction with normalization
 impl<T: Normed> Unit<T> {
     /// Normalize the given vector and return it wrapped on a `Unit` structure.
     #[inline]
@@ -140,6 +148,7 @@ impl<T: Normed> Unit<T> {
     }
 }
 
+/// # Data extraction and construction without normalization
 impl<T> Unit<T> {
     /// Wraps the given value, assuming it is already normalized.
     #[inline]

src/geometry/isometry.rs

@@ -14,14 +14,45 @@ use simba::scalar::{RealField, SubsetOf};
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1, U2, U3};
+use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::storage::Owned;
 use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
-use crate::geometry::{
+use crate::geometry::{AbstractRotation, Point, Translation};
-    AbstractRotation, Point, Rotation2, Rotation3, Translation, UnitComplex, UnitQuaternion,
-};
 
-/// A direct isometry, i.e., a rotation followed by a translation, aka. a rigid-body motion, aka. an element of a Special Euclidean (SE) group.
+/// A direct isometry, i.e., a rotation followed by a translation (aka. a rigid-body motion).
+///
+/// This is also known as an element of a Special Euclidean (SE) group.
+/// The `Isometry` type can either represent a 2D or 3D isometry.
+/// A 2D isometry is composed of:
+/// - A translation part of type [`Translation2`](crate::Translation2)
+/// - A rotation part which can either be a [`UnitComplex`](crate::UnitComplex) or a [`Rotation2`](crate::Rotation2).
+/// A 3D isometry is composed of:
+/// - A translation part of type [`Translation3`](crate::Translation3)
+/// - A rotation part which can either be a [`UnitQuaternion`](crate::UnitQuaternion) or a [`Rotation3`](crate::Rotation3).
+///
+/// Note that instead of using the [`Isometry`](crate::Isometry) type in your code directly, you should use one
+/// of its aliases: [`Isometry2`](crate::Isometry2), [`Isometry3`](crate::Isometry3),
+/// [`IsometryMatrix2`](crate::IsometryMatrix2), [`IsometryMatrix3`](crate::IsometryMatrix3). Though
+/// keep in mind that all the documentation of all the methods of these aliases will also appears on
+/// this page.
+///
+/// # Construction
+/// * [From a 2D vector and/or an angle <span style="float:right;">`new`, `translation`, `rotation`…</span>](#construction-from-a-2d-vector-andor-a-rotation-angle)
+/// * [From a 3D vector and/or an axis-angle <span style="float:right;">`new`, `translation`, `rotation`…</span>](#construction-from-a-3d-vector-andor-an-axis-angle)
+/// * [From a 3D eye position and target point <span style="float:right;">`look_at`, `look_at_lh`, `face_towards`…</span>](#construction-from-a-3d-eye-position-and-target-point)
+/// * [From the translation and rotation parts <span style="float:right;">`from_parts`…</span>](#from-the-translation-and-rotation-parts)
+///
+/// # Transformation and composition
+/// Note that transforming vectors and points can be done by multiplication, e.g., `isometry * point`.
+/// Composing an isometry with another transformation can also be done by multiplication or division.
+///
+/// * [Transformation of a vector or a point <span style="float:right;">`transform_vector`, `inverse_transform_point`…</span>](#transformation-of-a-vector-or-a-point)
+/// * [Inversion and in-place composition <span style="float:right;">`inverse`, `append_rotation_wrt_point_mut`…</span>](#inversion-and-in-place-composition)
+/// * [Interpolation <span style="float:right;">`lerp_slerp`…</span>](#interpolation)
+///
+/// # Conversion to a matrix
+/// * [Conversion to a matrix <span style="float:right;">`to_matrix`…</span>](#conversion-to-a-matrix)
+///
 #[repr(C)]
 #[derive(Debug)]
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
@@ -103,7 +134,7 @@ where
         }
     }
 }
-
+/// # From the translation and rotation parts
 impl<N: Scalar, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
@@ -131,6 +162,7 @@ where
     }
 }
 
+/// # Inversion and in-place composition
 impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
 where
     N::Element: SimdRealField,
@@ -178,6 +210,28 @@ where
         self.translation.vector = self.rotation.transform_vector(&self.translation.vector);
     }
 
+    /// Computes `self.inverse() * rhs` in a more efficient way.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use std::f32;
+    /// # use nalgebra::{Isometry2, Point2, Vector2};
+    /// let mut iso1 = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
+    /// let mut iso2 = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_4);
+    ///
+    /// assert_eq!(iso1.inverse() * iso2, iso1.inv_mul(&iso2));
+    /// ```
+    #[inline]
+    pub fn inv_mul(&self, rhs: &Isometry<N, D, R>) -> Self {
+        let inv_rot1 = self.rotation.inverse();
+        let tr_12 = rhs.translation.vector.clone() - self.translation.vector.clone();
+        Isometry::from_parts(
+            inv_rot1.transform_vector(&tr_12).into(),
+            inv_rot1 * rhs.rotation.clone(),
+        )
+    }
+
     /// Appends to `self` the given translation in-place.
     ///
     /// # Example
@@ -261,7 +315,14 @@ where
     pub fn append_rotation_wrt_center_mut(&mut self, r: &R) {
         self.rotation = r.clone() * self.rotation.clone();
     }
+}
 
+/// # Transformation of a vector or a point
+impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
+where
+    N::Element: SimdRealField,
+    DefaultAllocator: Allocator<N, D>,
+{
     /// Transform the given point by this isometry.
     ///
     /// This is the same as the multiplication `self * pt`.
@@ -377,224 +438,19 @@ where
     }
 }
 
-impl<N: SimdRealField> Isometry<N, U3, UnitQuaternion<N>> {
-    /// Interpolates between two isometries using a linear interpolation for the translation part,
-    /// and a spherical interpolation for the rotation part.
-    ///
-    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
-    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
-    ///
-    /// # Examples:
-    ///
-    /// ```
-    /// # use nalgebra::{Vector3, Translation3, Isometry3, UnitQuaternion};
-    ///
-    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
-    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
-    /// let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
-    /// let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
-    /// let iso1 = Isometry3::from_parts(t1, q1);
-    /// let iso2 = Isometry3::from_parts(t2, q2);
-    ///
-    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
-    ///
-    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
-    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
-    /// ```
-    #[inline]
-    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
-    where
-        N: RealField,
-    {
-        let tr = self.translation.vector.lerp(&other.translation.vector, t);
-        let rot = self.rotation.slerp(&other.rotation, t);
-        Self::from_parts(tr.into(), rot)
-    }
-
-    /// Attempts to interpolate between two isometries using a linear interpolation for the translation part,
-    /// and a spherical interpolation for the rotation part.
-    ///
-    /// Retuns `None` if the angle between both rotations is 180 degrees (in which case the interpolation
-    /// is not well-defined).
-    ///
-    /// # Examples:
-    ///
-    /// ```
-    /// # use nalgebra::{Vector3, Translation3, Isometry3, UnitQuaternion};
-    ///
-    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
-    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
-    /// let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
-    /// let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
-    /// let iso1 = Isometry3::from_parts(t1, q1);
-    /// let iso2 = Isometry3::from_parts(t2, q2);
-    ///
-    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
-    ///
-    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
-    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
-    /// ```
-    #[inline]
-    pub fn try_lerp_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
-    where
-        N: RealField,
-    {
-        let tr = self.translation.vector.lerp(&other.translation.vector, t);
-        let rot = self.rotation.try_slerp(&other.rotation, t, epsilon)?;
-        Some(Self::from_parts(tr.into(), rot))
-    }
-}
-
-impl<N: SimdRealField> Isometry<N, U3, Rotation3<N>> {
-    /// Interpolates between two isometries using a linear interpolation for the translation part,
-    /// and a spherical interpolation for the rotation part.
-    ///
-    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
-    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
-    ///
-    /// # Examples:
-    ///
-    /// ```
-    /// # use nalgebra::{Vector3, Translation3, Rotation3, IsometryMatrix3};
-    ///
-    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
-    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
-    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
-    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
-    /// let iso1 = IsometryMatrix3::from_parts(t1, q1);
-    /// let iso2 = IsometryMatrix3::from_parts(t2, q2);
-    ///
-    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
-    ///
-    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
-    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
-    /// ```
-    #[inline]
-    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
-    where
-        N: RealField,
-    {
-        let tr = self.translation.vector.lerp(&other.translation.vector, t);
-        let rot = self.rotation.slerp(&other.rotation, t);
-        Self::from_parts(tr.into(), rot)
-    }
-
-    /// Attempts to interpolate between two isometries using a linear interpolation for the translation part,
-    /// and a spherical interpolation for the rotation part.
-    ///
-    /// Retuns `None` if the angle between both rotations is 180 degrees (in which case the interpolation
-    /// is not well-defined).
-    ///
-    /// # Examples:
-    ///
-    /// ```
-    /// # use nalgebra::{Vector3, Translation3, Rotation3, IsometryMatrix3};
-    ///
-    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
-    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
-    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
-    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
-    /// let iso1 = IsometryMatrix3::from_parts(t1, q1);
-    /// let iso2 = IsometryMatrix3::from_parts(t2, q2);
-    ///
-    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
-    ///
-    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
-    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
-    /// ```
-    #[inline]
-    pub fn try_lerp_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
-    where
-        N: RealField,
-    {
-        let tr = self.translation.vector.lerp(&other.translation.vector, t);
-        let rot = self.rotation.try_slerp(&other.rotation, t, epsilon)?;
-        Some(Self::from_parts(tr.into(), rot))
-    }
-}
-
-impl<N: SimdRealField> Isometry<N, U2, UnitComplex<N>> {
-    /// Interpolates between two isometries using a linear interpolation for the translation part,
-    /// and a spherical interpolation for the rotation part.
-    ///
-    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
-    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
-    ///
-    /// # Examples:
-    ///
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::{Vector2, Translation2, UnitComplex, Isometry2};
-    ///
-    /// let t1 = Translation2::new(1.0, 2.0);
-    /// let t2 = Translation2::new(4.0, 8.0);
-    /// let q1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
-    /// let q2 = UnitComplex::new(-std::f32::consts::PI);
-    /// let iso1 = Isometry2::from_parts(t1, q1);
-    /// let iso2 = Isometry2::from_parts(t2, q2);
-    ///
-    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
-    ///
-    /// assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
-    /// assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);
-    /// ```
-    #[inline]
-    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
-    where
-        N: RealField,
-    {
-        let tr = self.translation.vector.lerp(&other.translation.vector, t);
-        let rot = self.rotation.slerp(&other.rotation, t);
-        Self::from_parts(tr.into(), rot)
-    }
-}
-
-impl<N: SimdRealField> Isometry<N, U2, Rotation2<N>> {
-    /// Interpolates between two isometries using a linear interpolation for the translation part,
-    /// and a spherical interpolation for the rotation part.
-    ///
-    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
-    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
-    ///
-    /// # Examples:
-    ///
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::{Vector2, Translation2, Rotation2, IsometryMatrix2};
-    ///
-    /// let t1 = Translation2::new(1.0, 2.0);
-    /// let t2 = Translation2::new(4.0, 8.0);
-    /// let q1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
-    /// let q2 = Rotation2::new(-std::f32::consts::PI);
-    /// let iso1 = IsometryMatrix2::from_parts(t1, q1);
-    /// let iso2 = IsometryMatrix2::from_parts(t2, q2);
-    ///
-    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
-    ///
-    /// assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
-    /// assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);
-    /// ```
-    #[inline]
-    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
-    where
-        N: RealField,
-    {
-        let tr = self.translation.vector.lerp(&other.translation.vector, t);
-        let rot = self.rotation.slerp(&other.rotation, t);
-        Self::from_parts(tr.into(), rot)
-    }
-}
-
 // NOTE: we don't require `R: Rotation<...>` here because this is not useful for the implementation
 // and makes it hard to use it, e.g., for Transform × Isometry implementation.
 // This is OK since all constructors of the isometry enforce the Rotation bound already (and
 // explicit struct construction is prevented by the dummy ZST field).
+/// # Conversion to a matrix
 impl<N: SimdRealField, D: DimName, R> Isometry<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
 {
     /// Converts this isometry into its equivalent homogeneous transformation matrix.
     ///
+    /// This is the same as `self.to_matrix()`.
+    ///
     /// # Example
     ///
     /// ```
@@ -621,6 +477,33 @@ where
 
         res
     }
+
+    /// Converts this isometry into its equivalent homogeneous transformation matrix.
+    ///
+    /// This is the same as `self.to_homogeneous()`.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use std::f32;
+    /// # use nalgebra::{Isometry2, Vector2, Matrix3};
+    /// let iso = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_6);
+    /// let expected = Matrix3::new(0.8660254, -0.5,      10.0,
+    ///                             0.5,       0.8660254, 20.0,
+    ///                             0.0,       0.0,       1.0);
+    ///
+    /// assert_relative_eq!(iso.to_matrix(), expected, epsilon = 1.0e-6);
+    /// ```
+    #[inline]
+    pub fn to_matrix(&self) -> MatrixN<N, DimNameSum<D, U1>>
+    where
+        D: DimNameAdd<U1>,
+        R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
+        DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    {
+        self.to_homogeneous()
+    }
 }
 
 impl<N: SimdRealField, D: DimName, R> Eq for Isometry<N, D, R>

src/geometry/isometry_alias.rs

@@ -2,16 +2,33 @@ use crate::base::dimension::{U2, U3};
 
 use crate::geometry::{Isometry, Rotation2, Rotation3, UnitComplex, UnitQuaternion};
 
-/// A 2-dimensional direct isometry using a unit complex number for its rotational part. Also known as a rigid-body motion, or as an element of SE(2).
+/// A 2-dimensional direct isometry using a unit complex number for its rotational part.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Isometry`](crate::Isometry) type too.**
+///
+/// Also known as a 2D rigid-body motion, or as an element of SE(2).
+
 pub type Isometry2<N> = Isometry<N, U2, UnitComplex<N>>;
 
-/// A 3-dimensional direct isometry using a unit quaternion for its rotational part. Also known as a rigid-body motion, or as an element of SE(3).
+/// A 3-dimensional direct isometry using a unit quaternion for its rotational part.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Isometry`](crate::Isometry) type too.**
+///
+/// Also known as a rigid-body motion, or as an element of SE(3).
 pub type Isometry3<N> = Isometry<N, U3, UnitQuaternion<N>>;
 
-/// A 2-dimensional direct isometry using a rotation matrix for its rotational part. Also known as a rigid-body motion, or as an element of SE(2).
+/// A 2-dimensional direct isometry using a rotation matrix for its rotational part.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Isometry`](crate::Isometry) type too.**
+///
+/// Also known as a rigid-body motion, or as an element of SE(2).
 pub type IsometryMatrix2<N> = Isometry<N, U2, Rotation2<N>>;
 
-/// A 3-dimensional direct isometry using a rotation matrix for its rotational part. Also known as a rigid-body motion, or as an element of SE(3).
+/// A 3-dimensional direct isometry using a rotation matrix for its rotational part.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Isometry`](crate::Isometry) type too.**
+///
+/// Also known as a rigid-body motion, or as an element of SE(3).
 pub type IsometryMatrix3<N> = Isometry<N, U3, Rotation3<N>>;
 
 // This tests that the types correctly implement `Copy`, without having to run tests

src/geometry/isometry_construction.rs

@@ -11,12 +11,13 @@ use simba::scalar::RealField;
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, U2, U3};
+use crate::base::dimension::{DimName, U2};
 use crate::base::{DefaultAllocator, Vector2, Vector3};
 
 use crate::geometry::{
-    AbstractRotation, Isometry, Point, Point3, Rotation, Rotation2, Rotation3, Translation,
+    AbstractRotation, Isometry, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, Point,
-    Translation2, Translation3, UnitComplex, UnitQuaternion,
+    Point3, Rotation, Rotation3, Translation, Translation2, Translation3, UnitComplex,
+    UnitQuaternion,
 };
 
 impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
@@ -112,8 +113,8 @@ where
  *
  */
 
-// 2D rotation.
+/// # Construction from a 2D vector and/or a rotation angle
-impl<N: SimdRealField> Isometry<N, U2, Rotation2<N>>
+impl<N: SimdRealField> IsometryMatrix2<N>
 where
     N::Element: SimdRealField,
 {
@@ -151,7 +152,7 @@ where
     }
 }
 
-impl<N: SimdRealField> Isometry<N, U2, UnitComplex<N>>
+impl<N: SimdRealField> Isometry2<N>
 where
     N::Element: SimdRealField,
 {
@@ -190,10 +191,8 @@ where
 }
 
 // 3D rotation.
-macro_rules! isometry_construction_impl(
+macro_rules! basic_isometry_construction_impl(
-    ($RotId: ident < $($RotParams: ident),*>, $RRDim: ty, $RCDim: ty) => {
+    ($RotId: ident < $($RotParams: ident),*>) => {
-        impl<N: SimdRealField> Isometry<N, U3, $RotId<$($RotParams),*>>
-        where N::Element: SimdRealField {
         /// Creates a new isometry from a translation and a rotation axis-angle.
         ///
         /// # Example
@@ -236,7 +235,11 @@ macro_rules! isometry_construction_impl(
         pub fn rotation(axisangle: Vector3<N>) -> Self {
             Self::new(Vector3::zeros(), axisangle)
         }
+    }
+);
 
+macro_rules! look_at_isometry_construction_impl(
+    ($RotId: ident < $($RotParams: ident),*>) => {
         /// Creates an isometry that corresponds to the local frame of an observer standing at the
         /// point `eye` and looking toward `target`.
         ///
@@ -373,8 +376,34 @@ macro_rules! isometry_construction_impl(
             Self::from_parts(Translation::from(trans.coords), rotation)
         }
     }
-    }
 );
 
-isometry_construction_impl!(Rotation3<N>, U3, U3);
+/// # Construction from a 3D vector and/or an axis-angle
-isometry_construction_impl!(UnitQuaternion<N>, U4, U1);
+impl<N: SimdRealField> Isometry3<N>
+where
+    N::Element: SimdRealField,
+{
+    basic_isometry_construction_impl!(UnitQuaternion<N>);
+}
+
+impl<N: SimdRealField> IsometryMatrix3<N>
+where
+    N::Element: SimdRealField,
+{
+    basic_isometry_construction_impl!(Rotation3<N>);
+}
+
+/// # Construction from a 3D eye position and target point
+impl<N: SimdRealField> Isometry3<N>
+where
+    N::Element: SimdRealField,
+{
+    look_at_isometry_construction_impl!(UnitQuaternion<N>);
+}
+
+impl<N: SimdRealField> IsometryMatrix3<N>
+where
+    N::Element: SimdRealField,
+{
+    look_at_isometry_construction_impl!(Rotation3<N>);
+}

src/geometry/isometry_interpolation.rs

@@ -0,0 +1,210 @@
+use crate::{Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, RealField, SimdRealField};
+
+/// # Interpolation
+impl<N: SimdRealField> Isometry3<N> {
+    /// Interpolates between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, Translation3, Isometry3, UnitQuaternion};
+    ///
+    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
+    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
+    /// let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    /// let iso1 = Isometry3::from_parts(t1, q1);
+    /// let iso2 = Isometry3::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
+    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.slerp(&other.rotation, t);
+        Self::from_parts(tr.into(), rot)
+    }
+
+    /// Attempts to interpolate between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Retuns `None` if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined).
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, Translation3, Isometry3, UnitQuaternion};
+    ///
+    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
+    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
+    /// let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    /// let iso1 = Isometry3::from_parts(t1, q1);
+    /// let iso2 = Isometry3::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
+    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn try_lerp_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.try_slerp(&other.rotation, t, epsilon)?;
+        Some(Self::from_parts(tr.into(), rot))
+    }
+}
+
+impl<N: SimdRealField> IsometryMatrix3<N> {
+    /// Interpolates between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, Translation3, Rotation3, IsometryMatrix3};
+    ///
+    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
+    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
+    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    /// let iso1 = IsometryMatrix3::from_parts(t1, q1);
+    /// let iso2 = IsometryMatrix3::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
+    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.slerp(&other.rotation, t);
+        Self::from_parts(tr.into(), rot)
+    }
+
+    /// Attempts to interpolate between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Retuns `None` if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined).
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, Translation3, Rotation3, IsometryMatrix3};
+    ///
+    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
+    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
+    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    /// let iso1 = IsometryMatrix3::from_parts(t1, q1);
+    /// let iso2 = IsometryMatrix3::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
+    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn try_lerp_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.try_slerp(&other.rotation, t, epsilon)?;
+        Some(Self::from_parts(tr.into(), rot))
+    }
+}
+
+impl<N: SimdRealField> Isometry2<N> {
+    /// Interpolates between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::{Vector2, Translation2, UnitComplex, Isometry2};
+    ///
+    /// let t1 = Translation2::new(1.0, 2.0);
+    /// let t2 = Translation2::new(4.0, 8.0);
+    /// let q1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
+    /// let q2 = UnitComplex::new(-std::f32::consts::PI);
+    /// let iso1 = Isometry2::from_parts(t1, q1);
+    /// let iso2 = Isometry2::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
+    /// assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);
+    /// ```
+    #[inline]
+    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.slerp(&other.rotation, t);
+        Self::from_parts(tr.into(), rot)
+    }
+}
+
+impl<N: SimdRealField> IsometryMatrix2<N> {
+    /// Interpolates between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::{Vector2, Translation2, Rotation2, IsometryMatrix2};
+    ///
+    /// let t1 = Translation2::new(1.0, 2.0);
+    /// let t2 = Translation2::new(4.0, 8.0);
+    /// let q1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
+    /// let q2 = Rotation2::new(-std::f32::consts::PI);
+    /// let iso1 = IsometryMatrix2::from_parts(t1, q1);
+    /// let iso2 = IsometryMatrix2::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
+    /// assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);
+    /// ```
+    #[inline]
+    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.slerp(&other.rotation, t);
+        Self::from_parts(tr.into(), rot)
+    }
+}

src/geometry/mod.rs

@@ -21,6 +21,7 @@ mod rotation_alga;
 mod rotation_alias;
 mod rotation_construction;
 mod rotation_conversion;
+mod rotation_interpolation;
 mod rotation_ops;
 mod rotation_simba; // TODO: implement Rotation methods.
 mod rotation_specialization;
@@ -58,6 +59,7 @@ mod isometry_alga;
 mod isometry_alias;
 mod isometry_construction;
 mod isometry_conversion;
+mod isometry_interpolation;
 mod isometry_ops;
 mod isometry_simba;
 

src/geometry/point.rs

@@ -19,7 +19,25 @@ use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::iter::{MatrixIter, MatrixIterMut};
 use crate::base::{DefaultAllocator, Scalar, VectorN};
 
-/// A point in a n-dimensional euclidean space.
+/// A point in an euclidean space.
+///
+/// The difference between a point and a vector is only semantic. See [the user guide](https://www.nalgebra.org/points_and_transformations/)
+/// for details on the distinction. The most notable difference that vectors ignore translations.
+/// In particular, an [`Isometry2`](crate::Isometry2) or [`Isometry3`](crate::Isometry3) will
+/// transform points by applying a rotation and a translation on them. However, these isometries
+/// will only apply rotations to vectors (when doing `isometry * vector`, the translation part of
+/// the isometry is ignored).
+///
+/// # Construction
+/// * [From individual components <span style="float:right;">`new`…</span>](#construction-from-individual-components)
+/// * [Swizzling <span style="float:right;">`xx`, `yxz`…</span>](#swizzling)
+/// * [Other construction methods <span style="float:right;">`origin`, `from_slice`, `from_homogeneous`…</span>](#other-construction-methods)
+///
+/// # Transformation
+/// Transforming a point by an [Isometry](crate::Isometry), [rotation](crate::Rotation), etc. can be
+/// achieved by multiplication, e.g., `isometry * point` or `rotation * point`. Some of these transformation
+/// may have some other methods, e.g., `isometry.inverse_transform_point(&point)`. See the documentation
+/// of said transformations for details.
 #[repr(C)]
 #[derive(Debug, Clone)]
 pub struct Point<N: Scalar, D: DimName>

src/geometry/point_alias.rs

@@ -3,14 +3,26 @@ use crate::base::dimension::{U1, U2, U3, U4, U5, U6};
 use crate::geometry::Point;
 
 /// A statically sized 1-dimensional column point.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
 pub type Point1<N> = Point<N, U1>;
 /// A statically sized 2-dimensional column point.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
 pub type Point2<N> = Point<N, U2>;
 /// A statically sized 3-dimensional column point.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
 pub type Point3<N> = Point<N, U3>;
 /// A statically sized 4-dimensional column point.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
 pub type Point4<N> = Point<N, U4>;
 /// A statically sized 5-dimensional column point.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
 pub type Point5<N> = Point<N, U5>;
 /// A statically sized 6-dimensional column point.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
 pub type Point6<N> = Point<N, U6>;

src/geometry/point_construction.rs

@@ -6,12 +6,17 @@ use rand::distributions::{Distribution, Standard};
 use rand::Rng;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1, U2, U3, U4, U5, U6};
+use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::{DefaultAllocator, Scalar, VectorN};
+use crate::{
+    Point1, Point2, Point3, Point4, Point5, Point6, Vector1, Vector2, Vector3, Vector4, Vector5,
+    Vector6,
+};
 use simba::scalar::ClosedDiv;
 
 use crate::geometry::Point;
 
+/// # Other construction methods
 impl<N: Scalar, D: DimName> Point<N, D>
 where
     DefaultAllocator: Allocator<N, D>,
@@ -79,7 +84,7 @@ where
     /// assert_eq!(pt, Some(Point3::new(1.0, 2.0, 3.0)));
     ///
     /// // All component of the result will be divided by the
-    /// // last component of the vector, here 2.0.
+    /// // last component of the vector, here 2.0.
     /// let coords = Vector4::new(1.0, 2.0, 3.0, 2.0);
     /// let pt = Point3::from_homogeneous(coords);
     /// assert_eq!(pt, Some(Point3::new(0.5, 1.0, 1.5)));
@@ -158,45 +163,55 @@ where
  * Small points construction from components.
  *
  */
+// NOTE: the impl for Point1 is not with the others so that we
+// can add a section with the impl block comment.
+/// # Construction from individual components
+impl<N: Scalar> Point1<N> {
+    /// Initializes this point from its components.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::Point1;
+    /// let p = Point1::new(1.0);
+    /// assert_eq!(p.x, 1.0);
+    /// ```
+    #[inline]
+    pub fn new(x: N) -> Self {
+        Vector1::new(x).into()
+    }
+}
 macro_rules! componentwise_constructors_impl(
-    ($($doc: expr; $D: ty, $($args: ident:$irow: expr),*);* $(;)*) => {$(
+    ($($doc: expr; $Point: ident, $Vector: ident, $($args: ident:$irow: expr),*);* $(;)*) => {$(
-        impl<N: Scalar> Point<N, $D>
+        impl<N: Scalar> $Point<N> {
-            where DefaultAllocator: Allocator<N, $D> {
             #[doc = "Initializes this point from its components."]
             #[doc = "# Example\n```"]
             #[doc = $doc]
             #[doc = "```"]
             #[inline]
             pub fn new($($args: N),*) -> Self {
-                unsafe {
+                $Vector::new($($args),*).into()
-                    let mut res = Self::new_uninitialized();
-                    $( *res.get_unchecked_mut($irow) = $args; )*
-
-                    res
-                }
             }
         }
     )*}
 );
 
 componentwise_constructors_impl!(
-    "# use nalgebra::Point1;\nlet p = Point1::new(1.0);\nassert!(p.x == 1.0);";
-    U1, x:0;
     "# use nalgebra::Point2;\nlet p = Point2::new(1.0, 2.0);\nassert!(p.x == 1.0 && p.y == 2.0);";
-    U2, x:0, y:1;
+    Point2, Vector2, x:0, y:1;
     "# use nalgebra::Point3;\nlet p = Point3::new(1.0, 2.0, 3.0);\nassert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0);";
-    U3, x:0, y:1, z:2;
+    Point3, Vector3, x:0, y:1, z:2;
     "# use nalgebra::Point4;\nlet p = Point4::new(1.0, 2.0, 3.0, 4.0);\nassert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0);";
-    U4, x:0, y:1, z:2, w:3;
+    Point4, Vector4, x:0, y:1, z:2, w:3;
     "# use nalgebra::Point5;\nlet p = Point5::new(1.0, 2.0, 3.0, 4.0, 5.0);\nassert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0 && p.a == 5.0);";
-    U5, x:0, y:1, z:2, w:3, a:4;
+    Point5, Vector5, x:0, y:1, z:2, w:3, a:4;
     "# use nalgebra::Point6;\nlet p = Point6::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);\nassert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0 && p.a == 5.0 && p.b == 6.0);";
-    U6, x:0, y:1, z:2, w:3, a:4, b:5;
+    Point6, Vector6, x:0, y:1, z:2, w:3, a:4, b:5;
 );
 
 macro_rules! from_array_impl(
-    ($($D: ty, $len: expr);*) => {$(
+    ($($Point: ident, $len: expr);*) => {$(
-      impl <N: Scalar> From<[N; $len]> for Point<N, $D> {
+      impl <N: Scalar> From<[N; $len]> for $Point<N> {
           fn from(coords: [N; $len]) -> Self {
               Self {
                 coords: coords.into()
@@ -206,4 +221,4 @@ macro_rules! from_array_impl(
     )*}
 );
 
-from_array_impl!(U1, 1; U2, 2; U3, 3; U4, 4; U5, 5; U6, 6);
+from_array_impl!(Point1, 1; Point2, 2; Point3, 3; Point4, 4; Point5, 5; Point6, 6);

src/geometry/rotation.rs

@@ -23,6 +23,36 @@ use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
 use crate::geometry::Point;
 
 /// A rotation matrix.
+///
+/// This is also known as an element of a Special Orthogonal (SO) group.
+/// The `Rotation` type can either represent a 2D or 3D rotation, represented as a matrix.
+/// For a rotation based on quaternions, see [`UnitQuaternion`](crate::UnitQuaternion) instead.
+///
+/// Note that instead of using the [`Rotation`](crate::Rotation) type in your code directly, you should use one
+/// of its aliases: [`Rotation2`](crate::Rotation2), or [`Rotation3`](crate::Rotation3). Though
+/// keep in mind that all the documentation of all the methods of these aliases will also appears on
+/// this page.
+///
+/// # Construction
+/// * [Identity <span style="float:right;">`identity`</span>](#identity)
+/// * [From a 2D rotation angle <span style="float:right;">`new`…</span>](#construction-from-a-2d-rotation-angle)
+/// * [From an existing 2D matrix or rotations <span style="float:right;">`from_matrix`, `rotation_between`, `powf`…</span>](#construction-from-an-existing-2d-matrix-or-rotations)
+/// * [From a 3D axis and/or angles <span style="float:right;">`new`, `from_euler_angles`, `from_axis_angle`…</span>](#construction-from-a-3d-axis-andor-angles)
+/// * [From a 3D eye position and target point <span style="float:right;">`look_at`, `look_at_lh`, `rotation_between`…</span>](#construction-from-a-3d-eye-position-and-target-point)
+/// * [From an existing 3D matrix or rotations <span style="float:right;">`from_matrix`, `rotation_between`, `powf`…</span>](#construction-from-an-existing-3d-matrix-or-rotations)
+///
+/// # Transformation and composition
+/// Note that transforming vectors and points can be done by multiplication, e.g., `rotation * point`.
+/// Composing an rotation with another transformation can also be done by multiplication or division.
+/// * [3D axis and angle extraction <span style="float:right;">`angle`, `euler_angles`, `scaled_axis`, `angle_to`…</span>](#3d-axis-and-angle-extraction)
+/// * [2D angle extraction <span style="float:right;">`angle`, `angle_to`…</span>](#2d-angle-extraction)
+/// * [Transformation of a vector or a point <span style="float:right;">`transform_vector`, `inverse_transform_point`…</span>](#transformation-of-a-vector-or-a-point)
+/// * [Transposition and inversion <span style="float:right;">`transpose`, `inverse`…</span>](#transposition-and-inversion)
+/// * [Interpolation <span style="float:right;">`slerp`…</span>](#interpolation)
+///
+/// # Conversion
+/// * [Conversion to a matrix <span style="float:right;">`matrix`, `to_homogeneous`…</span>](#conversion-to-a-matrix)
+///
 #[repr(C)]
 #[derive(Debug)]
 pub struct Rotation<N: Scalar, D: DimName>
@@ -111,6 +141,44 @@ where
     }
 }
 
+impl<N: Scalar, D: DimName> Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
+{
+    /// Creates a new rotation from the given square matrix.
+    ///
+    /// The matrix squareness is checked but not its orthonormality.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::{Rotation2, Rotation3, Matrix2, Matrix3};
+    /// # use std::f32;
+    /// let mat = Matrix3::new(0.8660254, -0.5,      0.0,
+    ///                        0.5,       0.8660254, 0.0,
+    ///                        0.0,       0.0,       1.0);
+    /// let rot = Rotation3::from_matrix_unchecked(mat);
+    ///
+    /// assert_eq!(*rot.matrix(), mat);
+    ///
+    ///
+    /// let mat = Matrix2::new(0.8660254, -0.5,
+    ///                        0.5,       0.8660254);
+    /// let rot = Rotation2::from_matrix_unchecked(mat);
+    ///
+    /// assert_eq!(*rot.matrix(), mat);
+    /// ```
+    #[inline]
+    pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Self {
+        assert!(
+            matrix.is_square(),
+            "Unable to create a rotation from a non-square matrix."
+        );
+
+        Self { matrix }
+    }
+}
+
+/// # Conversion to a matrix
 impl<N: Scalar, D: DimName> Rotation<N, D>
 where
     DefaultAllocator: Allocator<N, D, D>,
@@ -225,39 +293,13 @@ where
 
         res
     }
-
-    /// Creates a new rotation from the given square matrix.
-    ///
-    /// The matrix squareness is checked but not its orthonormality.
-    ///
-    /// # Example
-    /// ```
-    /// # use nalgebra::{Rotation2, Rotation3, Matrix2, Matrix3};
-    /// # use std::f32;
-    /// let mat = Matrix3::new(0.8660254, -0.5,      0.0,
-    ///                        0.5,       0.8660254, 0.0,
-    ///                        0.0,       0.0,       1.0);
-    /// let rot = Rotation3::from_matrix_unchecked(mat);
-    ///
-    /// assert_eq!(*rot.matrix(), mat);
-    ///
-    ///
-    /// let mat = Matrix2::new(0.8660254, -0.5,
-    ///                        0.5,       0.8660254);
-    /// let rot = Rotation2::from_matrix_unchecked(mat);
-    ///
-    /// assert_eq!(*rot.matrix(), mat);
-    /// ```
-    #[inline]
-    pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Self {
-        assert!(
-            matrix.is_square(),
-            "Unable to create a rotation from a non-square matrix."
-        );
-
-        Self { matrix }
 }
 
+/// # Transposition and inversion
+impl<N: Scalar, D: DimName> Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
+{
     /// Transposes `self`.
     ///
     /// Same as `.inverse()` because the inverse of a rotation matrix is its transform.
@@ -361,6 +403,7 @@ where
     }
 }
 
+/// # Transformation of a vector or a point
 impl<N: SimdRealField, D: DimName> Rotation<N, D>
 where
     N::Element: SimdRealField,

src/geometry/rotation_alias.rs

@@ -3,7 +3,11 @@ use crate::base::dimension::{U2, U3};
 use crate::geometry::Rotation;
 
 /// A 2-dimensional rotation matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Rotation`](crate::Rotation) type too.**
 pub type Rotation2<N> = Rotation<N, U2>;
 
 /// A 3-dimensional rotation matrix.
+///
+/// **Because this is an alias, not all its methods are listed here. See the [`Rotation`](crate::Rotation) type too.**
 pub type Rotation3<N> = Rotation<N, U3>;

src/geometry/rotation_construction.rs

@@ -8,6 +8,7 @@ use crate::base::{DefaultAllocator, MatrixN, Scalar};
 
 use crate::geometry::Rotation;
 
+/// # Identity
 impl<N, D: DimName> Rotation<N, D>
 where
     N: Scalar + Zero + One,

src/geometry/rotation_interpolation.rs

@@ -0,0 +1,78 @@
+use crate::{RealField, Rotation2, Rotation3, SimdRealField, UnitComplex, UnitQuaternion};
+
+/// # Interpolation
+impl<N: SimdRealField> Rotation2<N> {
+    /// Spherical linear interpolation between two rotation matrices.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::geometry::Rotation2;
+    ///
+    /// let rot1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
+    /// let rot2 = Rotation2::new(-std::f32::consts::PI);
+    ///
+    /// let rot = rot1.slerp(&rot2, 1.0 / 3.0);
+    ///
+    /// assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);
+    /// ```
+    #[inline]
+    pub fn slerp(&self, other: &Self, t: N) -> Self
+    where
+        N::Element: SimdRealField,
+    {
+        let c1 = UnitComplex::from(*self);
+        let c2 = UnitComplex::from(*other);
+        c1.slerp(&c2, t).into()
+    }
+}
+
+impl<N: SimdRealField> Rotation3<N> {
+    /// Spherical linear interpolation between two rotation matrices.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::geometry::Rotation3;
+    ///
+    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    ///
+    /// let q = q1.slerp(&q2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(q.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let q1 = UnitQuaternion::from(*self);
+        let q2 = UnitQuaternion::from(*other);
+        q1.slerp(&q2, t).into()
+    }
+
+    /// Computes the spherical linear interpolation between two rotation matrices or returns `None`
+    /// if both rotations are approximately 180 degrees apart (in which case the interpolation is
+    /// not well-defined).
+    ///
+    /// # Arguments
+    /// * `self`: the first rotation to interpolate from.
+    /// * `other`: the second rotation to interpolate toward.
+    /// * `t`: the interpolation parameter. Should be between 0 and 1.
+    /// * `epsilon`: the value below which the sinus of the angle separating both rotations
+    /// must be to return `None`.
+    #[inline]
+    pub fn try_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
+    where
+        N: RealField,
+    {
+        let q1 = Rotation3::from(*self);
+        let q2 = Rotation3::from(*other);
+        q1.try_slerp(&q2, t, epsilon).map(|q| q.into())
+    }
+}

src/geometry/rotation_specialization.rs

@@ -21,6 +21,7 @@ use crate::geometry::{Rotation2, Rotation3, UnitComplex, UnitQuaternion};
  * 2D Rotation matrix.
  *
  */
+/// # Construction from a 2D rotation angle
 impl<N: SimdRealField> Rotation2<N> {
     /// Builds a 2 dimensional rotation matrix from an angle in radian.
     ///
@@ -48,7 +49,10 @@ impl<N: SimdRealField> Rotation2<N> {
     pub fn from_scaled_axis<SB: Storage<N, U1>>(axisangle: Vector<N, U1, SB>) -> Self {
         Self::new(axisangle[0])
     }
+}
 
+/// # Construction from an existing 2D matrix or rotations
+impl<N: SimdRealField> Rotation2<N> {
     /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
     ///
     /// This is an iterative method. See `.from_matrix_eps` to provide mover
@@ -150,35 +154,6 @@ impl<N: SimdRealField> Rotation2<N> {
         crate::convert(UnitComplex::scaled_rotation_between(a, b, s).to_rotation_matrix())
     }
 
-    /// The rotation angle.
-    ///
-    /// # Example
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::Rotation2;
-    /// let rot = Rotation2::new(1.78);
-    /// assert_relative_eq!(rot.angle(), 1.78);
-    /// ```
-    #[inline]
-    pub fn angle(&self) -> N {
-        self.matrix()[(1, 0)].simd_atan2(self.matrix()[(0, 0)])
-    }
-
-    /// The rotation angle needed to make `self` and `other` coincide.
-    ///
-    /// # Example
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::Rotation2;
-    /// let rot1 = Rotation2::new(0.1);
-    /// let rot2 = Rotation2::new(1.7);
-    /// assert_relative_eq!(rot1.angle_to(&rot2), 1.6);
-    /// ```
-    #[inline]
-    pub fn angle_to(&self, other: &Self) -> N {
-        self.rotation_to(other).angle()
-    }
-
     /// The rotation matrix needed to make `self` and `other` coincide.
     ///
     /// The result is such that: `self.rotation_to(other) * self == other`.
@@ -227,6 +202,38 @@ impl<N: SimdRealField> Rotation2<N> {
     pub fn powf(&self, n: N) -> Self {
         Self::new(self.angle() * n)
     }
+}
+
+/// # 2D angle extraction
+impl<N: SimdRealField> Rotation2<N> {
+    /// The rotation angle.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::Rotation2;
+    /// let rot = Rotation2::new(1.78);
+    /// assert_relative_eq!(rot.angle(), 1.78);
+    /// ```
+    #[inline]
+    pub fn angle(&self) -> N {
+        self.matrix()[(1, 0)].simd_atan2(self.matrix()[(0, 0)])
+    }
+
+    /// The rotation angle needed to make `self` and `other` coincide.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::Rotation2;
+    /// let rot1 = Rotation2::new(0.1);
+    /// let rot2 = Rotation2::new(1.7);
+    /// assert_relative_eq!(rot1.angle_to(&rot2), 1.6);
+    /// ```
+    #[inline]
+    pub fn angle_to(&self, other: &Self) -> N {
+        self.rotation_to(other).angle()
+    }
 
     /// The rotation angle returned as a 1-dimensional vector.
     ///
@@ -236,31 +243,6 @@ impl<N: SimdRealField> Rotation2<N> {
     pub fn scaled_axis(&self) -> VectorN<N, U1> {
         Vector1::new(self.angle())
     }
-
-    /// Spherical linear interpolation between two rotation matrices.
-    ///
-    /// # Examples:
-    ///
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::geometry::Rotation2;
-    ///
-    /// let rot1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
-    /// let rot2 = Rotation2::new(-std::f32::consts::PI);
-    ///
-    /// let rot = rot1.slerp(&rot2, 1.0 / 3.0);
-    ///
-    /// assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);
-    /// ```
-    #[inline]
-    pub fn slerp(&self, other: &Self, t: N) -> Self
-    where
-        N::Element: SimdRealField,
-    {
-        let c1 = UnitComplex::from(*self);
-        let c2 = UnitComplex::from(*other);
-        c1.slerp(&c2, t).into()
-    }
 }
 
 impl<N: SimdRealField> Distribution<Rotation2<N>> for Standard
@@ -292,6 +274,7 @@ where
  * 3D Rotation matrix.
  *
  */
+/// # Construction from a 3D axis and/or angles
 impl<N: SimdRealField> Rotation3<N>
 where
     N::Element: SimdRealField,
@@ -325,60 +308,6 @@ where
         Self::from_axis_angle(&axis, angle)
     }
 
-    /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
-    ///
-    /// This is an iterative method. See `.from_matrix_eps` to provide mover
-    /// convergence parameters and starting solution.
-    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
-    pub fn from_matrix(m: &Matrix3<N>) -> Self
-    where
-        N: RealField,
-    {
-        Self::from_matrix_eps(m, N::default_epsilon(), 0, Self::identity())
-    }
-
-    /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
-    ///
-    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
-    ///
-    /// # Parameters
-    ///
-    /// * `m`: the matrix from which the rotational part is to be extracted.
-    /// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
-    /// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
-    /// * `guess`: a guess of the solution. Convergence will be significantly faster if an initial solution close
-    ///           to the actual solution is provided. Can be set to `Rotation3::identity()` if no other
-    ///           guesses come to mind.
-    pub fn from_matrix_eps(m: &Matrix3<N>, eps: N, mut max_iter: usize, guess: Self) -> Self
-    where
-        N: RealField,
-    {
-        if max_iter == 0 {
-            max_iter = usize::max_value();
-        }
-
-        let mut rot = guess.into_inner();
-
-        for _ in 0..max_iter {
-            let axis = rot.column(0).cross(&m.column(0))
-                + rot.column(1).cross(&m.column(1))
-                + rot.column(2).cross(&m.column(2));
-            let denom = rot.column(0).dot(&m.column(0))
-                + rot.column(1).dot(&m.column(1))
-                + rot.column(2).dot(&m.column(2));
-
-            let axisangle = axis / (denom.abs() + N::default_epsilon());
-
-            if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, eps) {
-                rot = Rotation3::from_axis_angle(&axis, angle) * rot;
-            } else {
-                break;
-            }
-        }
-
-        Self::from_matrix_unchecked(rot)
-    }
-
     /// Builds a 3D rotation matrix from an axis scaled by the rotation angle.
     ///
     /// This is the same as `Self::new(axisangle)`.
@@ -488,67 +417,13 @@ where
             cp * cr,
         ))
     }
+}
 
-    /// Creates Euler angles from a rotation.
+/// # Construction from a 3D eye position and target point
-    ///
+impl<N: SimdRealField> Rotation3<N>
-    /// The angles are produced in the form (roll, pitch, yaw).
-    #[deprecated(note = "This is renamed to use `.euler_angles()`.")]
-    pub fn to_euler_angles(&self) -> (N, N, N)
 where
-        N: RealField,
+    N::Element: SimdRealField,
 {
-        self.euler_angles()
-    }
-
-    /// Euler angles corresponding to this rotation from a rotation.
-    ///
-    /// The angles are produced in the form (roll, pitch, yaw).
-    ///
-    /// # Example
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::Rotation3;
-    /// let rot = Rotation3::from_euler_angles(0.1, 0.2, 0.3);
-    /// let euler = rot.euler_angles();
-    /// assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
-    /// assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
-    /// assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);
-    /// ```
-    pub fn euler_angles(&self) -> (N, N, N)
-    where
-        N: RealField,
-    {
-        // Implementation informed by "Computing Euler angles from a rotation matrix", by Gregory G. Slabaugh
-        //  https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.371.6578
-        if self[(2, 0)].abs() < N::one() {
-            let yaw = -self[(2, 0)].asin();
-            let roll = (self[(2, 1)] / yaw.cos()).atan2(self[(2, 2)] / yaw.cos());
-            let pitch = (self[(1, 0)] / yaw.cos()).atan2(self[(0, 0)] / yaw.cos());
-            (roll, yaw, pitch)
-        } else if self[(2, 0)] <= -N::one() {
-            (self[(0, 1)].atan2(self[(0, 2)]), N::frac_pi_2(), N::zero())
-        } else {
-            (
-                -self[(0, 1)].atan2(-self[(0, 2)]),
-                -N::frac_pi_2(),
-                N::zero(),
-            )
-        }
-    }
-
-    /// Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated
-    /// computations might cause the matrix from progressively not being orthonormal anymore.
-    #[inline]
-    pub fn renormalize(&mut self)
-    where
-        N: RealField,
-    {
-        let mut c = UnitQuaternion::from(*self);
-        let _ = c.renormalize();
-
-        *self = Self::from_matrix_eps(self.matrix(), N::default_epsilon(), 0, c.into())
-    }
-
     /// Creates a rotation that corresponds to the local frame of an observer standing at the
     /// origin and looking toward `dir`.
     ///
@@ -656,7 +531,13 @@ where
     {
         Self::face_towards(dir, up).inverse()
     }
+}
 
+/// # Construction from an existing 3D matrix or rotations
+impl<N: SimdRealField> Rotation3<N>
+where
+    N::Element: SimdRealField,
+{
     /// The rotation matrix required to align `a` and `b` but with its angle.
     ///
     /// This is the rotation `R` such that `(R * a).angle(b) == 0 && (R * a).dot(b).is_positive()`.
@@ -727,6 +608,123 @@ where
         Some(Self::identity())
     }
 
+    /// The rotation matrix needed to make `self` and `other` coincide.
+    ///
+    /// The result is such that: `self.rotation_to(other) * self == other`.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::{Rotation3, Vector3};
+    /// let rot1 = Rotation3::from_axis_angle(&Vector3::y_axis(), 1.0);
+    /// let rot2 = Rotation3::from_axis_angle(&Vector3::x_axis(), 0.1);
+    /// let rot_to = rot1.rotation_to(&rot2);
+    /// assert_relative_eq!(rot_to * rot1, rot2, epsilon = 1.0e-6);
+    /// ```
+    #[inline]
+    pub fn rotation_to(&self, other: &Self) -> Self {
+        other * self.inverse()
+    }
+
+    /// Raise the quaternion to a given floating power, i.e., returns the rotation with the same
+    /// axis as `self` and an angle equal to `self.angle()` multiplied by `n`.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::{Rotation3, Vector3, Unit};
+    /// let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
+    /// let angle = 1.2;
+    /// let rot = Rotation3::from_axis_angle(&axis, angle);
+    /// let pow = rot.powf(2.0);
+    /// assert_relative_eq!(pow.axis().unwrap(), axis, epsilon = 1.0e-6);
+    /// assert_eq!(pow.angle(), 2.4);
+    /// ```
+    #[inline]
+    pub fn powf(&self, n: N) -> Self
+    where
+        N: RealField,
+    {
+        if let Some(axis) = self.axis() {
+            Self::from_axis_angle(&axis, self.angle() * n)
+        } else if self.matrix()[(0, 0)] < N::zero() {
+            let minus_id = MatrixN::<N, U3>::from_diagonal_element(-N::one());
+            Self::from_matrix_unchecked(minus_id)
+        } else {
+            Self::identity()
+        }
+    }
+
+    /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This is an iterative method. See `.from_matrix_eps` to provide mover
+    /// convergence parameters and starting solution.
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    pub fn from_matrix(m: &Matrix3<N>) -> Self
+    where
+        N: RealField,
+    {
+        Self::from_matrix_eps(m, N::default_epsilon(), 0, Self::identity())
+    }
+
+    /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    ///
+    /// # Parameters
+    ///
+    /// * `m`: the matrix from which the rotational part is to be extracted.
+    /// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
+    /// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
+    /// * `guess`: a guess of the solution. Convergence will be significantly faster if an initial solution close
+    ///           to the actual solution is provided. Can be set to `Rotation3::identity()` if no other
+    ///           guesses come to mind.
+    pub fn from_matrix_eps(m: &Matrix3<N>, eps: N, mut max_iter: usize, guess: Self) -> Self
+    where
+        N: RealField,
+    {
+        if max_iter == 0 {
+            max_iter = usize::max_value();
+        }
+
+        let mut rot = guess.into_inner();
+
+        for _ in 0..max_iter {
+            let axis = rot.column(0).cross(&m.column(0))
+                + rot.column(1).cross(&m.column(1))
+                + rot.column(2).cross(&m.column(2));
+            let denom = rot.column(0).dot(&m.column(0))
+                + rot.column(1).dot(&m.column(1))
+                + rot.column(2).dot(&m.column(2));
+
+            let axisangle = axis / (denom.abs() + N::default_epsilon());
+
+            if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, eps) {
+                rot = Rotation3::from_axis_angle(&axis, angle) * rot;
+            } else {
+                break;
+            }
+        }
+
+        Self::from_matrix_unchecked(rot)
+    }
+
+    /// Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated
+    /// computations might cause the matrix from progressively not being orthonormal anymore.
+    #[inline]
+    pub fn renormalize(&mut self)
+    where
+        N: RealField,
+    {
+        let mut c = UnitQuaternion::from(*self);
+        let _ = c.renormalize();
+
+        *self = Self::from_matrix_eps(self.matrix(), N::default_epsilon(), 0, c.into())
+    }
+}
+
+/// # 3D axis and angle extraction
+impl<N: SimdRealField> Rotation3<N> {
     /// The rotation angle in [0; pi].
     ///
     /// # Example
@@ -837,103 +835,59 @@ where
     /// assert_relative_eq!(rot1.angle_to(&rot2), 1.0045657, epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn angle_to(&self, other: &Self) -> N {
+    pub fn angle_to(&self, other: &Self) -> N
+    where
+        N::Element: SimdRealField,
+    {
         self.rotation_to(other).angle()
     }
 
-    /// The rotation matrix needed to make `self` and `other` coincide.
+    /// Creates Euler angles from a rotation.
     ///
-    /// The result is such that: `self.rotation_to(other) * self == other`.
+    /// The angles are produced in the form (roll, pitch, yaw).
-    ///
+    #[deprecated(note = "This is renamed to use `.euler_angles()`.")]
-    /// # Example
+    pub fn to_euler_angles(&self) -> (N, N, N)
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::{Rotation3, Vector3};
-    /// let rot1 = Rotation3::from_axis_angle(&Vector3::y_axis(), 1.0);
-    /// let rot2 = Rotation3::from_axis_angle(&Vector3::x_axis(), 0.1);
-    /// let rot_to = rot1.rotation_to(&rot2);
-    /// assert_relative_eq!(rot_to * rot1, rot2, epsilon = 1.0e-6);
-    /// ```
-    #[inline]
-    pub fn rotation_to(&self, other: &Self) -> Self {
-        other * self.inverse()
-    }
-
-    /// Raise the quaternion to a given floating power, i.e., returns the rotation with the same
-    /// axis as `self` and an angle equal to `self.angle()` multiplied by `n`.
-    ///
-    /// # Example
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::{Rotation3, Vector3, Unit};
-    /// let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
-    /// let angle = 1.2;
-    /// let rot = Rotation3::from_axis_angle(&axis, angle);
-    /// let pow = rot.powf(2.0);
-    /// assert_relative_eq!(pow.axis().unwrap(), axis, epsilon = 1.0e-6);
-    /// assert_eq!(pow.angle(), 2.4);
-    /// ```
-    #[inline]
-    pub fn powf(&self, n: N) -> Self
     where
         N: RealField,
     {
-        if let Some(axis) = self.axis() {
+        self.euler_angles()
-            Self::from_axis_angle(&axis, self.angle() * n)
+    }
-        } else if self.matrix()[(0, 0)] < N::zero() {
+
-            let minus_id = MatrixN::<N, U3>::from_diagonal_element(-N::one());
+    /// Euler angles corresponding to this rotation from a rotation.
-            Self::from_matrix_unchecked(minus_id)
+    ///
+    /// The angles are produced in the form (roll, pitch, yaw).
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::Rotation3;
+    /// let rot = Rotation3::from_euler_angles(0.1, 0.2, 0.3);
+    /// let euler = rot.euler_angles();
+    /// assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
+    /// assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
+    /// assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);
+    /// ```
+    pub fn euler_angles(&self) -> (N, N, N)
+    where
+        N: RealField,
+    {
+        // Implementation informed by "Computing Euler angles from a rotation matrix", by Gregory G. Slabaugh
+        //  https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.371.6578
+        if self[(2, 0)].abs() < N::one() {
+            let yaw = -self[(2, 0)].asin();
+            let roll = (self[(2, 1)] / yaw.cos()).atan2(self[(2, 2)] / yaw.cos());
+            let pitch = (self[(1, 0)] / yaw.cos()).atan2(self[(0, 0)] / yaw.cos());
+            (roll, yaw, pitch)
+        } else if self[(2, 0)] <= -N::one() {
+            (self[(0, 1)].atan2(self[(0, 2)]), N::frac_pi_2(), N::zero())
         } else {
-            Self::identity()
+            (
+                -self[(0, 1)].atan2(-self[(0, 2)]),
+                -N::frac_pi_2(),
+                N::zero(),
+            )
         }
     }
-
-    /// Spherical linear interpolation between two rotation matrices.
-    ///
-    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
-    /// is not well-defined). Use `.try_slerp` instead to avoid the panic.
-    ///
-    /// # Examples:
-    ///
-    /// ```
-    /// # use nalgebra::geometry::Rotation3;
-    ///
-    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
-    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
-    ///
-    /// let q = q1.slerp(&q2, 1.0 / 3.0);
-    ///
-    /// assert_eq!(q.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
-    /// ```
-    #[inline]
-    pub fn slerp(&self, other: &Self, t: N) -> Self
-    where
-        N: RealField,
-    {
-        let q1 = UnitQuaternion::from(*self);
-        let q2 = UnitQuaternion::from(*other);
-        q1.slerp(&q2, t).into()
-    }
-
-    /// Computes the spherical linear interpolation between two rotation matrices or returns `None`
-    /// if both rotations are approximately 180 degrees apart (in which case the interpolation is
-    /// not well-defined).
-    ///
-    /// # Arguments
-    /// * `self`: the first rotation to interpolate from.
-    /// * `other`: the second rotation to interpolate toward.
-    /// * `t`: the interpolation parameter. Should be between 0 and 1.
-    /// * `epsilon`: the value below which the sinus of the angle separating both rotations
-    /// must be to return `None`.
-    #[inline]
-    pub fn try_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
-    where
-        N: RealField,
-    {
-        let q1 = Rotation3::from(*self);
-        let q2 = Rotation3::from(*other);
-        q1.try_slerp(&q2, t, epsilon).map(|q| q.into())
-    }
 }
 
 impl<N: SimdRealField> Distribution<Rotation3<N>> for Standard

src/geometry/swizzle.rs

@@ -6,23 +6,23 @@ use typenum::{self, Cmp, Greater};
 macro_rules! impl_swizzle {
     ($( where $BaseDim: ident: $( $name: ident() -> $Result: ident[$($i: expr),+] ),+ ;)* ) => {
         $(
-            impl<N: Scalar, D: DimName> Point<N, D>
-            where
-                DefaultAllocator: Allocator<N, D>,
-                D::Value: Cmp<typenum::$BaseDim, Output=Greater>
-            {
             $(
                 /// Builds a new point from components of `self`.
                 #[inline]
-                    pub fn $name(&self) -> $Result<N> {
+                pub fn $name(&self) -> $Result<N>
+                 where D::Value: Cmp<typenum::$BaseDim, Output=Greater> {
                     $Result::new($(self[$i].inlined_clone()),*)
                 }
             )*
-            }
         )*
     }
 }
 
+/// # Swizzling
+impl<N: Scalar, D: DimName> Point<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
     impl_swizzle!(
         where U0: xx()  -> Point2[0, 0],
                   xxx() -> Point3[0, 0, 0];
@@ -63,3 +63,4 @@ impl_swizzle!(
                   zzy() -> Point3[2, 2, 1],
                   zzz() -> Point3[2, 2, 2];
     );
+}

src/geometry/unit_complex.rs

@@ -7,7 +7,26 @@ use crate::geometry::{Point2, Rotation2};
 use simba::scalar::RealField;
 use simba::simd::SimdRealField;
 
-/// A complex number with a norm equal to 1.
+/// A 2D rotation represented as a complex number with magnitude 1.
+///
+/// All the methods specific [`UnitComplex`](crate::UnitComplex) are listed here. You may also
+/// read the documentation of the [`Complex`](crate::Complex) type which
+/// is used internally and accessible with `unit_complex.complex()`.
+///
+/// # Construction
+/// * [Identity <span style="float:right;">`identity`</span>](#identity)
+/// * [From a 2D rotation angle <span style="float:right;">`new`, `from_cos_sin_unchecked`…</span>](#construction-from-a-2d-rotation-angle)
+/// * [From an existing 2D matrix or complex number <span style="float:right;">`from_matrix`, `rotation_to`, `powf`…</span>](#construction-from-an-existing-2d-matrix-or-complex-number)
+/// * [From two vectors <span style="float:right;">`rotation_between`, `scaled_rotation_between_axis`…</span>](#construction-from-two-vectors)
+///
+/// # Transformation and composition
+/// * [Angle extraction <span style="float:right;">`angle`, `angle_to`…</span>](#angle-extraction)
+/// * [Transformation of a vector or a point <span style="float:right;">`transform_vector`, `inverse_transform_point`…</span>](#transformation-of-a-vector-or-a-point)
+/// * [Conjugation and inversion <span style="float:right;">`conjugate`, `inverse_mut`…</span>](#conjugation-and-inversion)
+/// * [Interpolation <span style="float:right;">`slerp`…</span>](#interpolation)
+///
+/// # Conversion
+/// * [Conversion to a matrix <span style="float:right;">`to_rotation_matrix`, `to_homogeneous`…</span>](#conversion-to-a-matrix)
 pub type UnitComplex<N> = Unit<Complex<N>>;
 
 impl<N: SimdRealField> Normed for Complex<N> {
@@ -40,6 +59,7 @@ impl<N: SimdRealField> Normed for Complex<N> {
     }
 }
 
+/// # Angle extraction
 impl<N: SimdRealField> UnitComplex<N>
 where
     N::Element: SimdRealField,
@@ -115,24 +135,28 @@ where
         }
     }
 
-    /// The underlying complex number.
+    /// The rotation angle needed to make `self` and `other` coincide.
-    ///
-    /// Same as `self.as_ref()`.
     ///
     /// # Example
     /// ```
-    /// # extern crate num_complex;
+    /// # #[macro_use] extern crate approx;
-    /// # use num_complex::Complex;
     /// # use nalgebra::UnitComplex;
-    /// let angle = 1.78f32;
+    /// let rot1 = UnitComplex::new(0.1);
-    /// let rot = UnitComplex::new(angle);
+    /// let rot2 = UnitComplex::new(1.7);
-    /// assert_eq!(*rot.complex(), Complex::new(angle.cos(), angle.sin()));
+    /// assert_relative_eq!(rot1.angle_to(&rot2), 1.6);
     /// ```
     #[inline]
-    pub fn complex(&self) -> &Complex<N> {
+    pub fn angle_to(&self, other: &Self) -> N {
-        self.as_ref()
+        let delta = self.rotation_to(other);
+        delta.angle()
+    }
 }
 
+/// # Conjugation and inversion
+impl<N: SimdRealField> UnitComplex<N>
+where
+    N::Element: SimdRealField,
+{
     /// Compute the conjugate of this unit complex number.
     ///
     /// # Example
@@ -166,42 +190,6 @@ where
         self.conjugate()
     }
 
-    /// The rotation angle needed to make `self` and `other` coincide.
-    ///
-    /// # Example
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::UnitComplex;
-    /// let rot1 = UnitComplex::new(0.1);
-    /// let rot2 = UnitComplex::new(1.7);
-    /// assert_relative_eq!(rot1.angle_to(&rot2), 1.6);
-    /// ```
-    #[inline]
-    pub fn angle_to(&self, other: &Self) -> N {
-        let delta = self.rotation_to(other);
-        delta.angle()
-    }
-
-    /// The unit complex number needed to make `self` and `other` coincide.
-    ///
-    /// The result is such that: `self.rotation_to(other) * self == other`.
-    ///
-    /// # Example
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::UnitComplex;
-    /// let rot1 = UnitComplex::new(0.1);
-    /// let rot2 = UnitComplex::new(1.7);
-    /// let rot_to = rot1.rotation_to(&rot2);
-    ///
-    /// assert_relative_eq!(rot_to * rot1, rot2);
-    /// assert_relative_eq!(rot_to.inverse() * rot2, rot1);
-    /// ```
-    #[inline]
-    pub fn rotation_to(&self, other: &Self) -> Self {
-        other / self
-    }
-
     /// Compute in-place the conjugate of this unit complex number.
     ///
     /// # Example
@@ -237,25 +225,13 @@ where
     pub fn inverse_mut(&mut self) {
         self.conjugate_mut()
     }
-
-    /// Raise this unit complex number to a given floating power.
-    ///
-    /// This returns the unit complex number that identifies a rotation angle equal to
-    /// `self.angle() × n`.
-    ///
-    /// # Example
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::UnitComplex;
-    /// let rot = UnitComplex::new(0.78);
-    /// let pow = rot.powf(2.0);
-    /// assert_relative_eq!(pow.angle(), 2.0 * 0.78);
-    /// ```
-    #[inline]
-    pub fn powf(&self, n: N) -> Self {
-        Self::from_angle(self.angle() * n)
 }
 
+/// # Conversion to a matrix
+impl<N: SimdRealField> UnitComplex<N>
+where
+    N::Element: SimdRealField,
+{
     /// Builds the rotation matrix corresponding to this unit complex number.
     ///
     /// # Example
@@ -290,7 +266,13 @@ where
     pub fn to_homogeneous(&self) -> Matrix3<N> {
         self.to_rotation_matrix().to_homogeneous()
     }
+}
 
+/// # Transformation of a vector or a point
+impl<N: SimdRealField> UnitComplex<N>
+where
+    N::Element: SimdRealField,
+{
     /// Rotate the given point by this unit complex number.
     ///
     /// This is the same as the multiplication `self * pt`.
@@ -376,7 +358,13 @@ where
     pub fn inverse_transform_unit_vector(&self, v: &Unit<Vector2<N>>) -> Unit<Vector2<N>> {
         self.inverse() * v
     }
+}
 
+/// # Interpolation
+impl<N: SimdRealField> UnitComplex<N>
+where
+    N::Element: SimdRealField,
+{
     /// Spherical linear interpolation between two rotations represented as unit complex numbers.
     ///
     /// # Examples:
@@ -392,7 +380,6 @@ where
     ///
     /// assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);
     /// ```
-
     #[inline]
     pub fn slerp(&self, other: &Self, t: N) -> Self {
         Self::new(self.angle() * (N::one() - t) + other.angle() * t)

src/geometry/unit_complex_construction.rs

@@ -13,6 +13,7 @@ use crate::geometry::{Rotation2, UnitComplex};
 use simba::scalar::RealField;
 use simba::simd::SimdRealField;
 
+/// # Identity
 impl<N: SimdRealField> UnitComplex<N>
 where
     N::Element: SimdRealField,
@@ -32,7 +33,13 @@ where
     pub fn identity() -> Self {
         Self::new_unchecked(Complex::new(N::one(), N::zero()))
     }
+}
 
+/// # Construction from a 2D rotation angle
+impl<N: SimdRealField> UnitComplex<N>
+where
+    N::Element: SimdRealField,
+{
     /// Builds the unit complex number corresponding to the rotation with the given angle.
     ///
     /// # Example
@@ -100,6 +107,30 @@ where
     pub fn from_scaled_axis<SB: Storage<N, U1>>(axisangle: Vector<N, U1, SB>) -> Self {
         Self::from_angle(axisangle[0])
     }
+}
+
+/// # Construction from an existing 2D matrix or complex number
+impl<N: SimdRealField> UnitComplex<N>
+where
+    N::Element: SimdRealField,
+{
+    /// The underlying complex number.
+    ///
+    /// Same as `self.as_ref()`.
+    ///
+    /// # Example
+    /// ```
+    /// # extern crate num_complex;
+    /// # use num_complex::Complex;
+    /// # use nalgebra::UnitComplex;
+    /// let angle = 1.78f32;
+    /// let rot = UnitComplex::new(angle);
+    /// assert_eq!(*rot.complex(), Complex::new(angle.cos(), angle.sin()));
+    /// ```
+    #[inline]
+    pub fn complex(&self) -> &Complex<N> {
+        self.as_ref()
+    }
 
     /// Creates a new unit complex number from a complex number.
     ///
@@ -165,6 +196,50 @@ where
         Rotation2::from_matrix_eps(m, eps, max_iter, guess).into()
     }
 
+    /// The unit complex number needed to make `self` and `other` coincide.
+    ///
+    /// The result is such that: `self.rotation_to(other) * self == other`.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::UnitComplex;
+    /// let rot1 = UnitComplex::new(0.1);
+    /// let rot2 = UnitComplex::new(1.7);
+    /// let rot_to = rot1.rotation_to(&rot2);
+    ///
+    /// assert_relative_eq!(rot_to * rot1, rot2);
+    /// assert_relative_eq!(rot_to.inverse() * rot2, rot1);
+    /// ```
+    #[inline]
+    pub fn rotation_to(&self, other: &Self) -> Self {
+        other / self
+    }
+
+    /// Raise this unit complex number to a given floating power.
+    ///
+    /// This returns the unit complex number that identifies a rotation angle equal to
+    /// `self.angle() × n`.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::UnitComplex;
+    /// let rot = UnitComplex::new(0.78);
+    /// let pow = rot.powf(2.0);
+    /// assert_relative_eq!(pow.angle(), 2.0 * 0.78);
+    /// ```
+    #[inline]
+    pub fn powf(&self, n: N) -> Self {
+        Self::from_angle(self.angle() * n)
+    }
+}
+
+/// # Construction from two vectors
+impl<N: SimdRealField> UnitComplex<N>
+where
+    N::Element: SimdRealField,
+{
     /// The unit complex needed to make `a` and `b` be collinear and point toward the same
     /// direction.
     ///

src/lib.rs

@@ -15,7 +15,7 @@ Simply add the following to your `Cargo.toml` file:
 
 ```.ignore
 [dependencies]
-nalgebra = "0.21"
+nalgebra = "0.23"
 ```
 
 

tests/core/serde.rs

@@ -3,9 +3,10 @@
 use na::{
     DMatrix, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, Matrix3x4, Point2, Point3,
     Quaternion, Rotation2, Rotation3, Similarity2, Similarity3, SimilarityMatrix2,
-    SimilarityMatrix3, Translation2, Translation3, Unit,
+    SimilarityMatrix3, Translation2, Translation3, Unit, Vector2,
 };
 use rand;
+use serde::{Deserialize, Serialize};
 use serde_json;
 
 macro_rules! test_serde(
@@ -54,3 +55,16 @@ fn serde_flat() {
     let serialized = serde_json::to_string(&v).unwrap();
     assert_eq!(serialized, "[0.0,0.0,1.0,0.0]");
 }
+
+#[derive(Serialize, Deserialize, Debug, PartialEq, Copy, Clone)]
+enum Stuff {
+    A(f64),
+    B(f64),
+}
+
+#[test]
+fn deserialize_enum() {
+    let json = r#"[{"letter":"A", "value":123.4}, {"letter":"B", "value":567.8}]"#;
+    let parsed: Result<Vector2<Stuff>, _> = serde_json::from_str(json);
+    println!("parsed: {:?}", parsed);
+}

tests/linalg/qr.rs

@@ -1,6 +1,5 @@
 #![cfg(feature = "arbitrary")]
 
-
 macro_rules! gen_tests(
     ($module: ident, $scalar: ty) => {
         mod $module {

tests/linalg/solve.rs

@@ -1,6 +1,5 @@
 #![cfg(feature = "arbitrary")]
 
-
 macro_rules! gen_tests(
     ($module: ident, $scalar: ty) => {
         mod $module {

tests/linalg/tridiagonal.rs

@@ -1,6 +1,5 @@
 #![cfg(feature = "arbitrary")]
 
-
 macro_rules! gen_tests(
     ($module: ident, $scalar: ty) => {
             mod $module {