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Add sections to the documentations of Isometry and Point.

This commit is contained in:
Crozet Sébastien 2020-11-20 17:45:11 +01:00
parent c0f4ee6db9
commit cf769522f8
7 changed files with 617 additions and 476 deletions
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294
src/geometry/isometry.rs
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@ -14,14 +14,50 @@ 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::{
AbstractRotation, Point, Rotation2, Rotation3, Translation, UnitComplex, UnitQuaternion,
};
use crate::geometry::{AbstractRotation, Point, Translation};
/// 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).
///
/// The [`Isometry2`](crate::Isometry2), [`Isometry3`](crate::Isometry3), [`IsometryMatrix2`](crate::IsometryMatrix2),
/// and [`IsometryMatrix3`](crate::IsometryMatrix3) type aliases are provided for convenience. All
/// their available methods are listed in this page and cant be grouped as follows.
///
/// 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 bu 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)
/// * [2D interpolation <span style="float:right;">`lerp_slerp`…</span>](#2d-interpolation)
/// * [3D interpolation <span style="float:right;">`lerp_slerp`…</span>](#3d-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 +139,7 @@ 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 +167,7 @@ where
}
}
/// # Inversion and in-place composition
impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
where
N::Element: SimdRealField,
@ -261,7 +298,14 @@ 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 +421,19 @@ 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 +460,33 @@ 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>

55
src/geometry/isometry_construction.rs
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@ -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,
Translation2, Translation3, UnitComplex, UnitQuaternion,
AbstractRotation, Isometry, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, Point,
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.
impl<N: SimdRealField> Isometry<N, U2, Rotation2<N>>
/// # Construction from a 2D vector and/or a rotation angle
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(
($RotId: ident < $($RotParams: ident),*>, $RRDim: ty, $RCDim: ty) => {
impl<N: SimdRealField> Isometry<N, U3, $RotId<$($RotParams),*>>
where N::Element: SimdRealField {
macro_rules! basic_isometry_construction_impl(
($RotId: ident < $($RotParams: ident),*>) => {
/// 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);
isometry_construction_impl!(UnitQuaternion<N>, U4, U1);
/// # Construction from a 3D vector and/or an axis-angle
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>);
}

211
src/geometry/isometry_interpolation.rs Normal file
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@ -0,0 +1,211 @@
use crate::{Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, RealField, SimdRealField};
/// # 3D 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))
}
}
/// # 2D interpolation
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)
}
}

1
src/geometry/mod.rs
View File

@ -83,6 +83,7 @@ mod transform_simba;
mod reflection;
mod isometry_interpolation;
mod orthographic;
mod perspective;

20
src/geometry/point.rs
View File

@ -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>

57
src/geometry/point_construction.rs
View File

@ -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),*);* $(;)*) => {$(
impl<N: Scalar> Point<N, $D>
where DefaultAllocator: Allocator<N, $D> {
($($doc: expr; $Point: ident, $Vector: ident, $($args: ident:$irow: expr),*);* $(;)*) => {$(
impl<N: Scalar> $Point<N> {
#[doc = "Initializes this point from its components."]
#[doc = "# Example\n```"]
#[doc = $doc]
#[doc = "```"]
#[inline]
pub fn new($($args: N),*) -> Self {
unsafe {
let mut res = Self::new_uninitialized();
$( *res.get_unchecked_mut($irow) = $args; )*
res
}
$Vector::new($($args),*).into()
}
}
)*}
);
componentwise_constructors_impl!(
"# use nalgebra::Point1;\nlet p = Point1::new(1.0);\nassert!(p.x == 1.0);";
U1, x:0;
"# use nalgebra::Point2;\nlet p = Point2::new(1.0, 2.0);\nassert!(p.x == 1.0 && p.y == 2.0);";
U2, x:0, y:1;
Point2, Vector2, x:0, y:1;
"# use nalgebra::Point3;\nlet p = Point3::new(1.0, 2.0, 3.0);\nassert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0);";
U3, x:0, y:1, z:2;
Point3, Vector3, x:0, y:1, z:2;
"# use nalgebra::Point4;\nlet p = Point4::new(1.0, 2.0, 3.0, 4.0);\nassert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0);";
U4, x:0, y:1, z:2, w:3;
Point4, Vector4, x:0, y:1, z:2, w:3;
"# use nalgebra::Point5;\nlet p = Point5::new(1.0, 2.0, 3.0, 4.0, 5.0);\nassert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0 && p.a == 5.0);";
U5, x:0, y:1, z:2, w:3, a:4;
Point5, Vector5, x:0, y:1, z:2, w:3, a:4;
"# use nalgebra::Point6;\nlet p = Point6::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);\nassert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0 && p.a == 5.0 && p.b == 6.0);";
U6, x:0, y:1, z:2, w:3, a:4, b:5;
Point6, Vector6, x:0, y:1, z:2, w:3, a:4, b:5;
);
macro_rules! from_array_impl(
($($D: ty, $len: expr);*) => {$(
impl <N: Scalar> From<[N; $len]> for Point<N, $D> {
($($Point: ident, $len: expr);*) => {$(
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);

15
src/geometry/swizzle.rs
View File

@ -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];
);
}