forked from M-Labs/nalgebra
594 lines
21 KiB
Rust
Executable File
594 lines
21 KiB
Rust
Executable File
use approx::{AbsDiffEq, RelativeEq, UlpsEq};
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use std::fmt;
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use std::hash;
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#[cfg(feature = "abomonation-serialize")]
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use std::io::{Result as IOResult, Write};
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#[cfg(feature = "serde-serialize")]
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use serde::{Deserialize, Serialize};
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#[cfg(feature = "abomonation-serialize")]
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use abomonation::Abomonation;
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use simba::scalar::{RealField, SubsetOf};
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use simba::simd::SimdRealField;
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use crate::base::allocator::Allocator;
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use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
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use crate::base::storage::Owned;
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use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
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use crate::geometry::{AbstractRotation, Point, Translation};
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/// A direct isometry, i.e., a rotation followed by a translation (aka. a rigid-body motion).
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///
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/// This is also known as an element of a Special Euclidean (SE) group.
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/// The `Isometry` type can either represent a 2D or 3D isometry.
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/// A 2D isometry is composed of:
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/// - A translation part of type [`Translation2`](crate::Translation2)
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/// - A rotation part which can either be a [`UnitComplex`](crate::UnitComplex) or a [`Rotation2`](crate::Rotation2).
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/// A 3D isometry is composed of:
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/// - A translation part of type [`Translation3`](crate::Translation3)
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/// - A rotation part which can either be a [`UnitQuaternion`](crate::UnitQuaternion) or a [`Rotation3`](crate::Rotation3).
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///
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/// The [`Isometry2`](crate::Isometry2), [`Isometry3`](crate::Isometry3), [`IsometryMatrix2`](crate::IsometryMatrix2),
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/// and [`IsometryMatrix3`](crate::IsometryMatrix3) type aliases are provided for convenience. All
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/// their available methods are listed in this page and cant be grouped as follows.
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///
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/// Note that instead of using the [`Isometry`](crate::Isometry) type in your code directly, you should use one
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/// of its aliases: [`Isometry2`](crate::Isometry2), [`Isometry3`](crate::Isometry3),
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/// [`IsometryMatrix2`](crate::IsometryMatrix2), [`IsometryMatrix3`](crate::IsometryMatrix3). Though
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/// keep in mind that all the documentation of all the methods of these aliases will also appears on
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/// this page.
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///
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/// # Construction
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/// * [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)
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/// * [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)
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/// * [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)
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/// * [From the translation and rotation parts <span style="float:right;">`from_parts`…</span>](#from-the-translation-and-rotation-parts)
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///
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/// # Transformation and composition
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/// Note that transforming vectors and points can be done bu multiplication, e.g., `isometry * point`.
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/// Composing an isometry with another transformation can also be done by multiplication or division.
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///
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/// * [Transformation of a vector or a point <span style="float:right;">`transform_vector`, `inverse_transform_point`…</span>](#transformation-of-a-vector-or-a-point)
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/// * [Inversion and in-place composition <span style="float:right;">`inverse`, `append_rotation_wrt_point_mut`…</span>](#inversion-and-in-place-composition)
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/// * [2D interpolation <span style="float:right;">`lerp_slerp`…</span>](#2d-interpolation)
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/// * [3D interpolation <span style="float:right;">`lerp_slerp`…</span>](#3d-interpolation)
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///
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/// # Conversion to a matrix
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/// * [Conversion to a matrix <span style="float:right;">`to_matrix`…</span>](#conversion-to-a-matrix)
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///
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#[repr(C)]
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#[derive(Debug)]
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#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
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#[cfg_attr(
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feature = "serde-serialize",
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serde(bound(serialize = "R: Serialize,
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DefaultAllocator: Allocator<N, D>,
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Owned<N, D>: Serialize"))
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)]
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#[cfg_attr(
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feature = "serde-serialize",
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serde(bound(deserialize = "R: Deserialize<'de>,
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DefaultAllocator: Allocator<N, D>,
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Owned<N, D>: Deserialize<'de>"))
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)]
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pub struct Isometry<N: Scalar, D: DimName, R>
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where
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DefaultAllocator: Allocator<N, D>,
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{
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/// The pure rotational part of this isometry.
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pub rotation: R,
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/// The pure translational part of this isometry.
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pub translation: Translation<N, D>,
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}
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#[cfg(feature = "abomonation-serialize")]
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impl<N, D, R> Abomonation for Isometry<N, D, R>
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where
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N: SimdRealField,
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D: DimName,
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R: Abomonation,
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Translation<N, D>: Abomonation,
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DefaultAllocator: Allocator<N, D>,
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{
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unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
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self.rotation.entomb(writer)?;
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self.translation.entomb(writer)
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}
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fn extent(&self) -> usize {
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self.rotation.extent() + self.translation.extent()
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}
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unsafe fn exhume<'a, 'b>(&'a mut self, bytes: &'b mut [u8]) -> Option<&'b mut [u8]> {
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self.rotation
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.exhume(bytes)
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.and_then(|bytes| self.translation.exhume(bytes))
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}
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}
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impl<N: Scalar + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash
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for Isometry<N, D, R>
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where
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DefaultAllocator: Allocator<N, D>,
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Owned<N, D>: hash::Hash,
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{
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fn hash<H: hash::Hasher>(&self, state: &mut H) {
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self.translation.hash(state);
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self.rotation.hash(state);
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}
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}
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impl<N: Scalar + Copy, D: DimName + Copy, R: Copy> Copy for Isometry<N, D, R>
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where
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DefaultAllocator: Allocator<N, D>,
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Owned<N, D>: Copy,
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{
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}
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impl<N: Scalar, D: DimName, R: Clone> Clone for Isometry<N, D, R>
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where
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DefaultAllocator: Allocator<N, D>,
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{
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#[inline]
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fn clone(&self) -> Self {
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Self {
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rotation: self.rotation.clone(),
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translation: self.translation.clone(),
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}
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}
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}
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/// # From the translation and rotation parts
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impl<N: Scalar, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
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where
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DefaultAllocator: Allocator<N, D>,
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{
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/// Creates a new isometry from its rotational and translational parts.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
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/// let tra = Translation3::new(0.0, 0.0, 3.0);
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/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::PI);
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/// let iso = Isometry3::from_parts(tra, rot);
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///
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/// assert_relative_eq!(iso * Point3::new(1.0, 2.0, 3.0), Point3::new(-1.0, 2.0, 0.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn from_parts(translation: Translation<N, D>, rotation: R) -> Self {
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Self {
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rotation,
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translation,
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}
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}
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}
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/// # Inversion and in-place composition
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impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
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where
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N::Element: SimdRealField,
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DefaultAllocator: Allocator<N, D>,
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{
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/// Inverts `self`.
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///
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/// # Example
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///
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/// ```
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/// # use std::f32;
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/// # use nalgebra::{Isometry2, Point2, Vector2};
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/// let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
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/// let inv = iso.inverse();
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/// let pt = Point2::new(1.0, 2.0);
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///
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/// assert_eq!(inv * (iso * pt), pt);
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/// ```
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#[inline]
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#[must_use = "Did you mean to use inverse_mut()?"]
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pub fn inverse(&self) -> Self {
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let mut res = self.clone();
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res.inverse_mut();
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res
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}
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/// Inverts `self` in-place.
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///
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/// # Example
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///
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/// ```
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/// # use std::f32;
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/// # use nalgebra::{Isometry2, Point2, Vector2};
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/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
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/// let pt = Point2::new(1.0, 2.0);
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/// let transformed_pt = iso * pt;
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/// iso.inverse_mut();
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///
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/// assert_eq!(iso * transformed_pt, pt);
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/// ```
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#[inline]
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pub fn inverse_mut(&mut self) {
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self.rotation.inverse_mut();
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self.translation.inverse_mut();
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self.translation.vector = self.rotation.transform_vector(&self.translation.vector);
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}
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/// Appends to `self` the given translation in-place.
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///
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/// # Example
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///
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/// ```
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/// # use std::f32;
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/// # use nalgebra::{Isometry2, Translation2, Vector2};
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/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
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/// let tra = Translation2::new(3.0, 4.0);
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/// // Same as `iso = tra * iso`.
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/// iso.append_translation_mut(&tra);
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///
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/// assert_eq!(iso.translation, Translation2::new(4.0, 6.0));
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/// ```
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#[inline]
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pub fn append_translation_mut(&mut self, t: &Translation<N, D>) {
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self.translation.vector += &t.vector
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}
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/// Appends to `self` the given rotation in-place.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2};
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/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::PI / 6.0);
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/// let rot = UnitComplex::new(f32::consts::PI / 2.0);
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/// // Same as `iso = rot * iso`.
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/// iso.append_rotation_mut(&rot);
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///
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/// assert_relative_eq!(iso, Isometry2::new(Vector2::new(-2.0, 1.0), f32::consts::PI * 2.0 / 3.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn append_rotation_mut(&mut self, r: &R) {
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self.rotation = r.clone() * self.rotation.clone();
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self.translation.vector = r.transform_vector(&self.translation.vector);
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}
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/// Appends in-place to `self` a rotation centered at the point `p`, i.e., the rotation that
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/// lets `p` invariant.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2, Point2};
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/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
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/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
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/// let pt = Point2::new(1.0, 0.0);
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/// iso.append_rotation_wrt_point_mut(&rot, &pt);
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///
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/// assert_relative_eq!(iso * pt, Point2::new(-2.0, 0.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &Point<N, D>) {
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self.translation.vector -= &p.coords;
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self.append_rotation_mut(r);
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self.translation.vector += &p.coords;
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}
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/// Appends in-place to `self` a rotation centered at the point with coordinates
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/// `self.translation`.
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///
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/// # Example
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///
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/// ```
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/// # use std::f32;
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/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2, Point2};
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/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
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/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
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/// iso.append_rotation_wrt_center_mut(&rot);
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///
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/// // The translation part should not have changed.
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/// assert_eq!(iso.translation.vector, Vector2::new(1.0, 2.0));
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/// assert_eq!(iso.rotation, UnitComplex::new(f32::consts::PI));
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/// ```
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#[inline]
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pub fn append_rotation_wrt_center_mut(&mut self, r: &R) {
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self.rotation = r.clone() * self.rotation.clone();
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}
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}
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/// # Transformation of a vector or a point
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impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
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where
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N::Element: SimdRealField,
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DefaultAllocator: Allocator<N, D>,
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{
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/// Transform the given point by this isometry.
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///
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/// This is the same as the multiplication `self * pt`.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
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/// let tra = Translation3::new(0.0, 0.0, 3.0);
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/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
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/// let iso = Isometry3::from_parts(tra, rot);
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///
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/// let transformed_point = iso.transform_point(&Point3::new(1.0, 2.0, 3.0));
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/// assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, 2.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
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self * pt
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}
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/// Transform the given vector by this isometry, ignoring the translation
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/// component of the isometry.
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///
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/// This is the same as the multiplication `self * v`.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
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/// let tra = Translation3::new(0.0, 0.0, 3.0);
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/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
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/// let iso = Isometry3::from_parts(tra, rot);
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///
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/// let transformed_point = iso.transform_vector(&Vector3::new(1.0, 2.0, 3.0));
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/// assert_relative_eq!(transformed_point, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
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self * v
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}
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/// Transform the given point by the inverse of this isometry. This may be
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/// less expensive than computing the entire isometry inverse and then
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/// transforming the point.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
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/// let tra = Translation3::new(0.0, 0.0, 3.0);
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/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
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/// let iso = Isometry3::from_parts(tra, rot);
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///
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/// let transformed_point = iso.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));
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/// assert_relative_eq!(transformed_point, Point3::new(0.0, 2.0, 1.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
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self.rotation
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.inverse_transform_point(&(pt - &self.translation.vector))
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}
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/// Transform the given vector by the inverse of this isometry, ignoring the
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/// translation component of the isometry. This may be
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/// less expensive than computing the entire isometry inverse and then
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/// transforming the point.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
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/// let tra = Translation3::new(0.0, 0.0, 3.0);
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/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
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/// let iso = Isometry3::from_parts(tra, rot);
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///
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/// let transformed_point = iso.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));
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/// assert_relative_eq!(transformed_point, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
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self.rotation.inverse_transform_vector(v)
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}
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/// Transform the given unit vector by the inverse of this isometry, ignoring the
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/// translation component of the isometry. This may be
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/// less expensive than computing the entire isometry inverse and then
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/// transforming the point.
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///
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/// # Example
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///
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
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/// let tra = Translation3::new(0.0, 0.0, 3.0);
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/// let rot = UnitQuaternion::from_scaled_axis(Vector3::z() * f32::consts::FRAC_PI_2);
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/// let iso = Isometry3::from_parts(tra, rot);
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///
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/// let transformed_point = iso.inverse_transform_unit_vector(&Vector3::x_axis());
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/// assert_relative_eq!(transformed_point, -Vector3::y_axis(), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>> {
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self.rotation.inverse_transform_unit_vector(v)
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}
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||
}
|
||
|
||
// 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
|
||
///
|
||
/// ```
|
||
/// # #[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_homogeneous(), expected, epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn to_homogeneous(&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>>,
|
||
{
|
||
let mut res: MatrixN<N, _> = crate::convert_ref(&self.rotation);
|
||
res.fixed_slice_mut::<D, U1>(0, D::dim())
|
||
.copy_from(&self.translation.vector);
|
||
|
||
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>
|
||
where
|
||
R: AbstractRotation<N, D> + Eq,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
}
|
||
|
||
impl<N: SimdRealField, D: DimName, R> PartialEq for Isometry<N, D, R>
|
||
where
|
||
R: AbstractRotation<N, D> + PartialEq,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
#[inline]
|
||
fn eq(&self, right: &Self) -> bool {
|
||
self.translation == right.translation && self.rotation == right.rotation
|
||
}
|
||
}
|
||
|
||
impl<N: RealField, D: DimName, R> AbsDiffEq for Isometry<N, D, R>
|
||
where
|
||
R: AbstractRotation<N, D> + AbsDiffEq<Epsilon = N::Epsilon>,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
type Epsilon = N::Epsilon;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
N::default_epsilon()
|
||
}
|
||
|
||
#[inline]
|
||
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
|
||
self.translation.abs_diff_eq(&other.translation, epsilon)
|
||
&& self.rotation.abs_diff_eq(&other.rotation, epsilon)
|
||
}
|
||
}
|
||
|
||
impl<N: RealField, D: DimName, R> RelativeEq for Isometry<N, D, R>
|
||
where
|
||
R: AbstractRotation<N, D> + RelativeEq<Epsilon = N::Epsilon>,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
#[inline]
|
||
fn default_max_relative() -> Self::Epsilon {
|
||
N::default_max_relative()
|
||
}
|
||
|
||
#[inline]
|
||
fn relative_eq(
|
||
&self,
|
||
other: &Self,
|
||
epsilon: Self::Epsilon,
|
||
max_relative: Self::Epsilon,
|
||
) -> bool {
|
||
self.translation
|
||
.relative_eq(&other.translation, epsilon, max_relative)
|
||
&& self
|
||
.rotation
|
||
.relative_eq(&other.rotation, epsilon, max_relative)
|
||
}
|
||
}
|
||
|
||
impl<N: RealField, D: DimName, R> UlpsEq for Isometry<N, D, R>
|
||
where
|
||
R: AbstractRotation<N, D> + UlpsEq<Epsilon = N::Epsilon>,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
#[inline]
|
||
fn default_max_ulps() -> u32 {
|
||
N::default_max_ulps()
|
||
}
|
||
|
||
#[inline]
|
||
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
|
||
self.translation
|
||
.ulps_eq(&other.translation, epsilon, max_ulps)
|
||
&& self.rotation.ulps_eq(&other.rotation, epsilon, max_ulps)
|
||
}
|
||
}
|
||
|
||
/*
|
||
*
|
||
* Display
|
||
*
|
||
*/
|
||
impl<N: RealField + fmt::Display, D: DimName, R> fmt::Display for Isometry<N, D, R>
|
||
where
|
||
R: fmt::Display,
|
||
DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
|
||
{
|
||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||
let precision = f.precision().unwrap_or(3);
|
||
|
||
writeln!(f, "Isometry {{")?;
|
||
write!(f, "{:.*}", precision, self.translation)?;
|
||
write!(f, "{:.*}", precision, self.rotation)?;
|
||
writeln!(f, "}}")
|
||
}
|
||
}
|