forked from M-Labs/nalgebra
728 lines
25 KiB
Rust
Executable File
728 lines
25 KiB
Rust
Executable File
use approx::{AbsDiffEq, RelativeEq, UlpsEq};
|
||
use std::fmt;
|
||
use std::hash;
|
||
#[cfg(feature = "abomonation-serialize")]
|
||
use std::io::{Result as IOResult, Write};
|
||
|
||
#[cfg(feature = "serde-serialize")]
|
||
use serde::{Deserialize, Serialize};
|
||
|
||
#[cfg(feature = "abomonation-serialize")]
|
||
use abomonation::Abomonation;
|
||
|
||
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::storage::Owned;
|
||
use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
|
||
use crate::geometry::{
|
||
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.
|
||
#[repr(C)]
|
||
#[derive(Debug)]
|
||
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
|
||
#[cfg_attr(
|
||
feature = "serde-serialize",
|
||
serde(bound(serialize = "R: Serialize,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
Owned<N, D>: Serialize"))
|
||
)]
|
||
#[cfg_attr(
|
||
feature = "serde-serialize",
|
||
serde(bound(deserialize = "R: Deserialize<'de>,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
Owned<N, D>: Deserialize<'de>"))
|
||
)]
|
||
pub struct Isometry<N: Scalar, D: DimName, R>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
/// The pure rotational part of this isometry.
|
||
pub rotation: R,
|
||
/// The pure translational part of this isometry.
|
||
pub translation: Translation<N, D>,
|
||
}
|
||
|
||
#[cfg(feature = "abomonation-serialize")]
|
||
impl<N, D, R> Abomonation for Isometry<N, D, R>
|
||
where
|
||
N: SimdRealField,
|
||
D: DimName,
|
||
R: Abomonation,
|
||
Translation<N, D>: Abomonation,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
|
||
self.rotation.entomb(writer)?;
|
||
self.translation.entomb(writer)
|
||
}
|
||
|
||
fn extent(&self) -> usize {
|
||
self.rotation.extent() + self.translation.extent()
|
||
}
|
||
|
||
unsafe fn exhume<'a, 'b>(&'a mut self, bytes: &'b mut [u8]) -> Option<&'b mut [u8]> {
|
||
self.rotation
|
||
.exhume(bytes)
|
||
.and_then(|bytes| self.translation.exhume(bytes))
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash
|
||
for Isometry<N, D, R>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
Owned<N, D>: hash::Hash,
|
||
{
|
||
fn hash<H: hash::Hasher>(&self, state: &mut H) {
|
||
self.translation.hash(state);
|
||
self.rotation.hash(state);
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar + Copy, D: DimName + Copy, R: Copy> Copy for Isometry<N, D, R>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
Owned<N, D>: Copy,
|
||
{
|
||
}
|
||
|
||
impl<N: Scalar, D: DimName, R: Clone> Clone for Isometry<N, D, R>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
#[inline]
|
||
fn clone(&self) -> Self {
|
||
Self {
|
||
rotation: self.rotation.clone(),
|
||
translation: self.translation.clone(),
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
/// Creates a new isometry from its rotational and translational parts.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
|
||
/// let tra = Translation3::new(0.0, 0.0, 3.0);
|
||
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::PI);
|
||
/// let iso = Isometry3::from_parts(tra, rot);
|
||
///
|
||
/// assert_relative_eq!(iso * Point3::new(1.0, 2.0, 3.0), Point3::new(-1.0, 2.0, 0.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn from_parts(translation: Translation<N, D>, rotation: R) -> Self {
|
||
Self {
|
||
rotation,
|
||
translation,
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
|
||
where
|
||
N::Element: SimdRealField,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
/// Inverts `self`.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry2, Point2, Vector2};
|
||
/// let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
|
||
/// let inv = iso.inverse();
|
||
/// let pt = Point2::new(1.0, 2.0);
|
||
///
|
||
/// assert_eq!(inv * (iso * pt), pt);
|
||
/// ```
|
||
#[inline]
|
||
#[must_use = "Did you mean to use inverse_mut()?"]
|
||
pub fn inverse(&self) -> Self {
|
||
let mut res = self.clone();
|
||
res.inverse_mut();
|
||
res
|
||
}
|
||
|
||
/// Inverts `self` in-place.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry2, Point2, Vector2};
|
||
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
|
||
/// let pt = Point2::new(1.0, 2.0);
|
||
/// let transformed_pt = iso * pt;
|
||
/// iso.inverse_mut();
|
||
///
|
||
/// assert_eq!(iso * transformed_pt, pt);
|
||
/// ```
|
||
#[inline]
|
||
pub fn inverse_mut(&mut self) {
|
||
self.rotation.inverse_mut();
|
||
self.translation.inverse_mut();
|
||
self.translation.vector = self.rotation.transform_vector(&self.translation.vector);
|
||
}
|
||
|
||
/// Appends to `self` the given translation in-place.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry2, Translation2, Vector2};
|
||
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
|
||
/// let tra = Translation2::new(3.0, 4.0);
|
||
/// // Same as `iso = tra * iso`.
|
||
/// iso.append_translation_mut(&tra);
|
||
///
|
||
/// assert_eq!(iso.translation, Translation2::new(4.0, 6.0));
|
||
/// ```
|
||
#[inline]
|
||
pub fn append_translation_mut(&mut self, t: &Translation<N, D>) {
|
||
self.translation.vector += &t.vector
|
||
}
|
||
|
||
/// Appends to `self` the given rotation in-place.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2};
|
||
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::PI / 6.0);
|
||
/// let rot = UnitComplex::new(f32::consts::PI / 2.0);
|
||
/// // Same as `iso = rot * iso`.
|
||
/// iso.append_rotation_mut(&rot);
|
||
///
|
||
/// assert_relative_eq!(iso, Isometry2::new(Vector2::new(-2.0, 1.0), f32::consts::PI * 2.0 / 3.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn append_rotation_mut(&mut self, r: &R) {
|
||
self.rotation = r.clone() * self.rotation.clone();
|
||
self.translation.vector = r.transform_vector(&self.translation.vector);
|
||
}
|
||
|
||
/// Appends in-place to `self` a rotation centered at the point `p`, i.e., the rotation that
|
||
/// lets `p` invariant.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2, Point2};
|
||
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
|
||
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
|
||
/// let pt = Point2::new(1.0, 0.0);
|
||
/// iso.append_rotation_wrt_point_mut(&rot, &pt);
|
||
///
|
||
/// assert_relative_eq!(iso * pt, Point2::new(-2.0, 0.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &Point<N, D>) {
|
||
self.translation.vector -= &p.coords;
|
||
self.append_rotation_mut(r);
|
||
self.translation.vector += &p.coords;
|
||
}
|
||
|
||
/// Appends in-place to `self` a rotation centered at the point with coordinates
|
||
/// `self.translation`.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2, Point2};
|
||
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
|
||
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
|
||
/// iso.append_rotation_wrt_center_mut(&rot);
|
||
///
|
||
/// // The translation part should not have changed.
|
||
/// assert_eq!(iso.translation.vector, Vector2::new(1.0, 2.0));
|
||
/// assert_eq!(iso.rotation, UnitComplex::new(f32::consts::PI));
|
||
/// ```
|
||
#[inline]
|
||
pub fn append_rotation_wrt_center_mut(&mut self, r: &R) {
|
||
self.rotation = r.clone() * self.rotation.clone();
|
||
}
|
||
|
||
/// Transform the given point by this isometry.
|
||
///
|
||
/// This is the same as the multiplication `self * pt`.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
|
||
/// let tra = Translation3::new(0.0, 0.0, 3.0);
|
||
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
|
||
/// let iso = Isometry3::from_parts(tra, rot);
|
||
///
|
||
/// let transformed_point = iso.transform_point(&Point3::new(1.0, 2.0, 3.0));
|
||
/// assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, 2.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
|
||
self * pt
|
||
}
|
||
|
||
/// Transform the given vector by this isometry, ignoring the translation
|
||
/// component of the isometry.
|
||
///
|
||
/// This is the same as the multiplication `self * v`.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
|
||
/// let tra = Translation3::new(0.0, 0.0, 3.0);
|
||
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
|
||
/// let iso = Isometry3::from_parts(tra, rot);
|
||
///
|
||
/// let transformed_point = iso.transform_vector(&Vector3::new(1.0, 2.0, 3.0));
|
||
/// assert_relative_eq!(transformed_point, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
|
||
self * v
|
||
}
|
||
|
||
/// Transform the given point by the inverse of this isometry. This may be
|
||
/// less expensive than computing the entire isometry inverse and then
|
||
/// transforming the point.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
|
||
/// let tra = Translation3::new(0.0, 0.0, 3.0);
|
||
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
|
||
/// let iso = Isometry3::from_parts(tra, rot);
|
||
///
|
||
/// let transformed_point = iso.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));
|
||
/// assert_relative_eq!(transformed_point, Point3::new(0.0, 2.0, 1.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
|
||
self.rotation
|
||
.inverse_transform_point(&(pt - &self.translation.vector))
|
||
}
|
||
|
||
/// Transform the given vector by the inverse of this isometry, ignoring the
|
||
/// translation component of the isometry. This may be
|
||
/// less expensive than computing the entire isometry inverse and then
|
||
/// transforming the point.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
|
||
/// let tra = Translation3::new(0.0, 0.0, 3.0);
|
||
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
|
||
/// let iso = Isometry3::from_parts(tra, rot);
|
||
///
|
||
/// let transformed_point = iso.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));
|
||
/// assert_relative_eq!(transformed_point, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
|
||
self.rotation.inverse_transform_vector(v)
|
||
}
|
||
|
||
/// Transform the given unit vector by the inverse of this isometry, ignoring the
|
||
/// translation component of the isometry. This may be
|
||
/// less expensive than computing the entire isometry inverse and then
|
||
/// transforming the point.
|
||
///
|
||
/// # Example
|
||
///
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
|
||
/// let tra = Translation3::new(0.0, 0.0, 3.0);
|
||
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::z() * f32::consts::FRAC_PI_2);
|
||
/// let iso = Isometry3::from_parts(tra, rot);
|
||
///
|
||
/// let transformed_point = iso.inverse_transform_unit_vector(&Vector3::x_axis());
|
||
/// assert_relative_eq!(transformed_point, -Vector3::y_axis(), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>> {
|
||
self.rotation.inverse_transform_unit_vector(v)
|
||
}
|
||
}
|
||
|
||
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).
|
||
impl<N: SimdRealField, D: DimName, R> Isometry<N, D, R>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
/// Converts this isometry into its equivalent homogeneous transformation 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
|
||
}
|
||
}
|
||
|
||
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, "}}")
|
||
}
|
||
}
|