forked from M-Labs/nalgebra
469 lines
16 KiB
Rust
469 lines
16 KiB
Rust
/*
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*
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* Computer-graphics specific implementations.
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* Currently, it is mostly implemented for homogeneous matrices in 2- and 3-space.
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*
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*/
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use num::{One, Zero};
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use crate::base::allocator::Allocator;
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use crate::base::dimension::{DimName, DimNameDiff, DimNameSub, U1};
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use crate::base::storage::{Storage, StorageMut};
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use crate::base::{
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Const, DefaultAllocator, Matrix3, Matrix4, OMatrix, OVector, Scalar, SquareMatrix, Unit,
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Vector, Vector2, Vector3,
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};
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use crate::geometry::{
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Isometry, IsometryMatrix3, Orthographic3, Perspective3, Point, Point2, Point3, Rotation2,
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Rotation3,
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};
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use simba::scalar::{ClosedAdd, ClosedMul, RealField};
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/// # Translation and scaling in any dimension
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impl<T, D: DimName> OMatrix<T, D, D>
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where
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T: Scalar + Zero + One,
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DefaultAllocator: Allocator<T, D, D>,
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{
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/// Creates a new homogeneous matrix that applies the same scaling factor on each dimension.
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#[inline]
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pub fn new_scaling(scaling: T) -> Self {
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let mut res = Self::from_diagonal_element(scaling);
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res[(D::dim() - 1, D::dim() - 1)] = T::one();
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res
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}
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/// Creates a new homogeneous matrix that applies a distinct scaling factor for each dimension.
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#[inline]
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pub fn new_nonuniform_scaling<SB>(scaling: &Vector<T, DimNameDiff<D, U1>, SB>) -> Self
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where
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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{
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let mut res = Self::identity();
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for i in 0..scaling.len() {
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res[(i, i)] = scaling[i].clone();
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}
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res
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}
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/// Creates a new homogeneous matrix that applies a pure translation.
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#[inline]
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pub fn new_translation<SB>(translation: &Vector<T, DimNameDiff<D, U1>, SB>) -> Self
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where
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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{
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let mut res = Self::identity();
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res.generic_view_mut(
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(0, D::dim() - 1),
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(DimNameDiff::<D, U1>::name(), Const::<1>),
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)
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.copy_from(translation);
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res
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}
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}
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/// # 2D transformations as a Matrix3
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impl<T: RealField> Matrix3<T> {
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/// Builds a 2 dimensional homogeneous rotation matrix from an angle in radian.
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#[inline]
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pub fn new_rotation(angle: T) -> Self {
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Rotation2::new(angle).to_homogeneous()
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}
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/// Creates a new homogeneous matrix that applies a scaling factor for each dimension with respect to point.
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///
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/// Can be used to implement `zoom_to` functionality.
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#[inline]
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pub fn new_nonuniform_scaling_wrt_point(scaling: &Vector2<T>, pt: &Point2<T>) -> Self {
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let zero = T::zero();
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let one = T::one();
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Matrix3::new(
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scaling.x.clone(),
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zero.clone(),
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pt.x.clone() - pt.x.clone() * scaling.x.clone(),
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zero.clone(),
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scaling.y.clone(),
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pt.y.clone() - pt.y.clone() * scaling.y.clone(),
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zero.clone(),
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zero,
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one,
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)
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}
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}
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/// # 3D transformations as a Matrix4
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impl<T: RealField> Matrix4<T> {
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/// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
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///
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/// Returns the identity matrix if the given argument is zero.
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#[inline]
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pub fn new_rotation(axisangle: Vector3<T>) -> Self {
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Rotation3::new(axisangle).to_homogeneous()
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}
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/// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
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///
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/// Returns the identity matrix if the given argument is zero.
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#[inline]
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pub fn new_rotation_wrt_point(axisangle: Vector3<T>, pt: Point3<T>) -> Self {
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let rot = Rotation3::from_scaled_axis(axisangle);
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Isometry::rotation_wrt_point(rot, pt).to_homogeneous()
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}
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/// Creates a new homogeneous matrix that applies a scaling factor for each dimension with respect to point.
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///
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/// Can be used to implement `zoom_to` functionality.
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#[inline]
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pub fn new_nonuniform_scaling_wrt_point(scaling: &Vector3<T>, pt: &Point3<T>) -> Self {
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let zero = T::zero();
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let one = T::one();
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Matrix4::new(
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scaling.x.clone(),
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zero.clone(),
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zero.clone(),
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pt.x.clone() - pt.x.clone() * scaling.x.clone(),
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zero.clone(),
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scaling.y.clone(),
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zero.clone(),
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pt.y.clone() - pt.y.clone() * scaling.y.clone(),
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zero.clone(),
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zero.clone(),
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scaling.z.clone(),
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pt.z.clone() - pt.z.clone() * scaling.z.clone(),
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zero.clone(),
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zero.clone(),
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zero,
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one,
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)
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}
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/// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
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///
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/// Returns the identity matrix if the given argument is zero.
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/// This is identical to `Self::new_rotation`.
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#[inline]
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pub fn from_scaled_axis(axisangle: Vector3<T>) -> Self {
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Rotation3::from_scaled_axis(axisangle).to_homogeneous()
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}
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/// Creates a new rotation from Euler angles.
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///
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/// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
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pub fn from_euler_angles(roll: T, pitch: T, yaw: T) -> Self {
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Rotation3::from_euler_angles(roll, pitch, yaw).to_homogeneous()
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}
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/// Builds a 3D homogeneous rotation matrix from an axis and a rotation angle.
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pub fn from_axis_angle(axis: &Unit<Vector3<T>>, angle: T) -> Self {
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Rotation3::from_axis_angle(axis, angle).to_homogeneous()
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}
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/// Creates a new homogeneous matrix for an orthographic projection.
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#[inline]
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pub fn new_orthographic(left: T, right: T, bottom: T, top: T, znear: T, zfar: T) -> Self {
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Orthographic3::new(left, right, bottom, top, znear, zfar).into_inner()
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}
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/// Creates a new homogeneous matrix for a perspective projection.
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#[inline]
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pub fn new_perspective(aspect: T, fovy: T, znear: T, zfar: T) -> Self {
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Perspective3::new(aspect, fovy, znear, zfar).into_inner()
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}
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/// Creates an isometry that corresponds to the local frame of an observer standing at the
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/// point `eye` and looking toward `target`.
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///
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/// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
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/// `eye`.
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#[inline]
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pub fn face_towards(eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>) -> Self {
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IsometryMatrix3::face_towards(eye, target, up).to_homogeneous()
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}
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/// Deprecated: Use [`Matrix4::face_towards`] instead.
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#[deprecated(note = "renamed to `face_towards`")]
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pub fn new_observer_frame(eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>) -> Self {
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Matrix4::face_towards(eye, target, up)
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}
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/// Builds a right-handed look-at view matrix.
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#[inline]
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pub fn look_at_rh(eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>) -> Self {
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IsometryMatrix3::look_at_rh(eye, target, up).to_homogeneous()
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}
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/// Builds a left-handed look-at view matrix.
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#[inline]
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pub fn look_at_lh(eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>) -> Self {
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IsometryMatrix3::look_at_lh(eye, target, up).to_homogeneous()
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}
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}
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/// # Append/prepend translation and scaling
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impl<T: Scalar + Zero + One + ClosedMul + ClosedAdd, D: DimName, S: Storage<T, D, D>>
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SquareMatrix<T, D, S>
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{
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/// Computes the transformation equal to `self` followed by an uniform scaling factor.
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#[inline]
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#[must_use = "Did you mean to use append_scaling_mut()?"]
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pub fn append_scaling(&self, scaling: T) -> OMatrix<T, D, D>
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where
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D: DimNameSub<U1>,
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DefaultAllocator: Allocator<T, D, D>,
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{
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let mut res = self.clone_owned();
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res.append_scaling_mut(scaling);
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res
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}
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/// Computes the transformation equal to an uniform scaling factor followed by `self`.
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#[inline]
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#[must_use = "Did you mean to use prepend_scaling_mut()?"]
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pub fn prepend_scaling(&self, scaling: T) -> OMatrix<T, D, D>
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where
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D: DimNameSub<U1>,
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DefaultAllocator: Allocator<T, D, D>,
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{
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let mut res = self.clone_owned();
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res.prepend_scaling_mut(scaling);
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res
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}
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/// Computes the transformation equal to `self` followed by a non-uniform scaling factor.
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#[inline]
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#[must_use = "Did you mean to use append_nonuniform_scaling_mut()?"]
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pub fn append_nonuniform_scaling<SB>(
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&self,
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scaling: &Vector<T, DimNameDiff<D, U1>, SB>,
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) -> OMatrix<T, D, D>
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where
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<T, D, D>,
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{
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let mut res = self.clone_owned();
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res.append_nonuniform_scaling_mut(scaling);
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res
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}
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/// Computes the transformation equal to a non-uniform scaling factor followed by `self`.
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#[inline]
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#[must_use = "Did you mean to use prepend_nonuniform_scaling_mut()?"]
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pub fn prepend_nonuniform_scaling<SB>(
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&self,
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scaling: &Vector<T, DimNameDiff<D, U1>, SB>,
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) -> OMatrix<T, D, D>
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where
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<T, D, D>,
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{
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let mut res = self.clone_owned();
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res.prepend_nonuniform_scaling_mut(scaling);
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res
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}
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/// Computes the transformation equal to `self` followed by a translation.
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#[inline]
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#[must_use = "Did you mean to use append_translation_mut()?"]
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pub fn append_translation<SB>(
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&self,
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shift: &Vector<T, DimNameDiff<D, U1>, SB>,
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) -> OMatrix<T, D, D>
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where
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<T, D, D>,
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{
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let mut res = self.clone_owned();
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res.append_translation_mut(shift);
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res
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}
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/// Computes the transformation equal to a translation followed by `self`.
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#[inline]
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#[must_use = "Did you mean to use prepend_translation_mut()?"]
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pub fn prepend_translation<SB>(
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&self,
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shift: &Vector<T, DimNameDiff<D, U1>, SB>,
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) -> OMatrix<T, D, D>
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where
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimNameDiff<D, U1>>,
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{
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let mut res = self.clone_owned();
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res.prepend_translation_mut(shift);
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res
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}
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/// Computes in-place the transformation equal to `self` followed by an uniform scaling factor.
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#[inline]
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pub fn append_scaling_mut(&mut self, scaling: T)
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where
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S: StorageMut<T, D, D>,
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D: DimNameSub<U1>,
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{
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let mut to_scale = self.rows_generic_mut(0, DimNameDiff::<D, U1>::name());
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to_scale *= scaling;
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}
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/// Computes in-place the transformation equal to an uniform scaling factor followed by `self`.
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#[inline]
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pub fn prepend_scaling_mut(&mut self, scaling: T)
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where
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S: StorageMut<T, D, D>,
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D: DimNameSub<U1>,
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{
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let mut to_scale = self.columns_generic_mut(0, DimNameDiff::<D, U1>::name());
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to_scale *= scaling;
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}
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/// Computes in-place the transformation equal to `self` followed by a non-uniform scaling factor.
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#[inline]
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pub fn append_nonuniform_scaling_mut<SB>(&mut self, scaling: &Vector<T, DimNameDiff<D, U1>, SB>)
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where
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S: StorageMut<T, D, D>,
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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{
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for i in 0..scaling.len() {
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let mut to_scale = self.fixed_rows_mut::<1>(i);
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to_scale *= scaling[i].clone();
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}
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}
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/// Computes in-place the transformation equal to a non-uniform scaling factor followed by `self`.
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#[inline]
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pub fn prepend_nonuniform_scaling_mut<SB>(
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&mut self,
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scaling: &Vector<T, DimNameDiff<D, U1>, SB>,
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) where
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S: StorageMut<T, D, D>,
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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{
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for i in 0..scaling.len() {
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let mut to_scale = self.fixed_columns_mut::<1>(i);
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to_scale *= scaling[i].clone();
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}
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}
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/// Computes the transformation equal to `self` followed by a translation.
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#[inline]
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pub fn append_translation_mut<SB>(&mut self, shift: &Vector<T, DimNameDiff<D, U1>, SB>)
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where
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S: StorageMut<T, D, D>,
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D: DimNameSub<U1>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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{
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for i in 0..D::dim() {
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for j in 0..D::dim() - 1 {
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let add = shift[j].clone() * self[(D::dim() - 1, i)].clone();
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self[(j, i)] += add;
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}
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}
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}
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/// Computes the transformation equal to a translation followed by `self`.
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#[inline]
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pub fn prepend_translation_mut<SB>(&mut self, shift: &Vector<T, DimNameDiff<D, U1>, SB>)
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where
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D: DimNameSub<U1>,
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S: StorageMut<T, D, D>,
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SB: Storage<T, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<T, DimNameDiff<D, U1>>,
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{
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let scale = self
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.generic_view(
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(D::dim() - 1, 0),
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(Const::<1>, DimNameDiff::<D, U1>::name()),
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)
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.tr_dot(shift);
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let post_translation = self.generic_view(
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(0, 0),
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(DimNameDiff::<D, U1>::name(), DimNameDiff::<D, U1>::name()),
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) * shift;
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self[(D::dim() - 1, D::dim() - 1)] += scale;
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let mut translation = self.generic_view_mut(
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(0, D::dim() - 1),
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(DimNameDiff::<D, U1>::name(), Const::<1>),
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);
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translation += post_translation;
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}
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}
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/// # Transformation of vectors and points
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impl<T: RealField, D: DimNameSub<U1>, S: Storage<T, D, D>> SquareMatrix<T, D, S>
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where
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DefaultAllocator: Allocator<T, D, D>
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+ Allocator<T, DimNameDiff<D, U1>>
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+ Allocator<T, DimNameDiff<D, U1>, DimNameDiff<D, U1>>,
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{
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/// Transforms the given vector, assuming the matrix `self` uses homogeneous coordinates.
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#[inline]
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pub fn transform_vector(
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&self,
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v: &OVector<T, DimNameDiff<D, U1>>,
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) -> OVector<T, DimNameDiff<D, U1>> {
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let transform = self.generic_view(
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(0, 0),
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(DimNameDiff::<D, U1>::name(), DimNameDiff::<D, U1>::name()),
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);
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let normalizer = self.generic_view(
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(D::dim() - 1, 0),
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(Const::<1>, DimNameDiff::<D, U1>::name()),
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);
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let n = normalizer.tr_dot(v);
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if !n.is_zero() {
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return transform * (v / n);
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}
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transform * v
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}
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}
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impl<T: RealField, S: Storage<T, Const<3>, Const<3>>> SquareMatrix<T, Const<3>, S> {
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/// Transforms the given point, assuming the matrix `self` uses homogeneous coordinates.
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#[inline]
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pub fn transform_point(&self, pt: &Point<T, 2>) -> Point<T, 2> {
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let transform = self.fixed_view::<2, 2>(0, 0);
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let translation = self.fixed_view::<2, 1>(0, 2);
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let normalizer = self.fixed_view::<1, 2>(2, 0);
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let n = normalizer.tr_dot(&pt.coords) + unsafe { self.get_unchecked((2, 2)).clone() };
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if !n.is_zero() {
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(transform * pt + translation) / n
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} else {
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transform * pt + translation
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}
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}
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}
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impl<T: RealField, S: Storage<T, Const<4>, Const<4>>> SquareMatrix<T, Const<4>, S> {
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/// Transforms the given point, assuming the matrix `self` uses homogeneous coordinates.
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#[inline]
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pub fn transform_point(&self, pt: &Point<T, 3>) -> Point<T, 3> {
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let transform = self.fixed_view::<3, 3>(0, 0);
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let translation = self.fixed_view::<3, 1>(0, 3);
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let normalizer = self.fixed_view::<1, 3>(3, 0);
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let n = normalizer.tr_dot(&pt.coords) + unsafe { self.get_unchecked((3, 3)).clone() };
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if !n.is_zero() {
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(transform * pt + translation) / n
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} else {
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transform * pt + translation
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}
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}
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}
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