308 lines
12 KiB
Rust
308 lines
12 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;
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use core::{DefaultAllocator, Scalar, SquareMatrix, Vector, Unit,
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VectorN, MatrixN, Vector3, Matrix3, Matrix4};
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use core::dimension::{DimName, DimNameSub, DimNameDiff, U1};
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use core::storage::{Storage, StorageMut};
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use core::allocator::Allocator;
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use geometry::{Point, Isometry, Point3, Rotation2, Rotation3, Orthographic3, Perspective3, IsometryMatrix3};
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use alga::general::{Real, Field};
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use alga::linear::Transformation;
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impl<N, D: DimName> MatrixN<N, D>
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where N: Scalar + Field,
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DefaultAllocator: Allocator<N, D, D> {
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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: N) -> Self {
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let mut res = Self::from_diagonal_element(scaling);
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res[(D::dim() - 1, D::dim() - 1)] = N::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<N, DimNameDiff<D, U1>, SB>) -> Self
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>> {
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let mut res = Self::one();
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for i in 0 .. scaling.len() {
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res[(i, i)] = scaling[i];
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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<N, DimNameDiff<D, U1>, SB>) -> Self
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>> {
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let mut res = Self::one();
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res.fixed_slice_mut::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1).copy_from(translation);
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res
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}
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}
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impl<N: Real> Matrix3<N> {
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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: N) -> Self {
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Rotation2::new(angle).to_homogeneous()
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}
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}
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impl<N: Real> Matrix4<N> {
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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<N>) -> 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<N>, pt: Point3<N>) -> 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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/// 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<N>) -> 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: N, pitch: N, yaw: N) -> 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<N>>, angle: N) -> 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: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Self {
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Orthographic3::new(left, right, bottom, top, znear, zfar).unwrap()
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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: N, fovy: N, znear: N, zfar: N) -> Self {
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Perspective3::new(aspect, fovy, znear, zfar).unwrap()
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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 new_observer_frame(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
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IsometryMatrix3::new_observer_frame(eye, target, up).to_homogeneous()
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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<N>, target: &Point3<N>, up: &Vector3<N>) -> 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<N>, target: &Point3<N>, up: &Vector3<N>) -> 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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impl<N: Scalar + Field, D: DimName, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
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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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pub fn append_scaling(&self, scaling: N) -> MatrixN<N, D>
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where D: DimNameSub<U1>,
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DefaultAllocator: Allocator<N, D, D> {
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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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pub fn prepend_scaling(&self, scaling: N) -> MatrixN<N, D>
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where D: DimNameSub<U1>,
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DefaultAllocator: Allocator<N, D, D> {
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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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pub fn append_nonuniform_scaling<SB>(&self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<N, D, D> {
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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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pub fn prepend_nonuniform_scaling<SB>(&self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<N, D, D> {
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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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pub fn append_translation<SB>(&self, shift: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<N, D, D> {
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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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pub fn prepend_translation<SB>(&self, shift: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<N, D, D> +
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Allocator<N, DimNameDiff<D, U1>> {
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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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}
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impl<N: Scalar + Field, D: DimName, S: StorageMut<N, D, D>> SquareMatrix<N, D, S> {
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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: N)
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where D: DimNameSub<U1> {
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let mut to_scale = self.fixed_rows_mut::<DimNameDiff<D, U1>>(0);
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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: N)
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where D: DimNameSub<U1> {
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let mut to_scale = self.fixed_columns_mut::<DimNameDiff<D, U1>>(0);
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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<N, DimNameDiff<D, U1>, SB>)
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>> {
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for i in 0 .. scaling.len() {
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let mut to_scale = self.fixed_rows_mut::<U1>(i);
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to_scale *= scaling[i];
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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>(&mut self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>)
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>> {
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for i in 0 .. scaling.len() {
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let mut to_scale = self.fixed_columns_mut::<U1>(i);
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to_scale *= scaling[i];
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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<N, DimNameDiff<D, U1>, SB>)
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>> {
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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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self[(j, i)] += shift[j] * self[(D::dim() - 1, i)];
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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<N, DimNameDiff<D, U1>, SB>)
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where D: DimNameSub<U1>,
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SB: Storage<N, DimNameDiff<D, U1>>,
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DefaultAllocator: Allocator<N, DimNameDiff<D, U1>> {
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let scale = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0).tr_dot(&shift);
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let post_translation = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0) * shift;
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self[(D::dim() - 1, D::dim() - 1)] += scale;
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let mut translation = self.fixed_slice_mut::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1);
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translation += post_translation;
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}
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}
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impl<N: Real, D: DimNameSub<U1>> Transformation<Point<N, DimNameDiff<D, U1>>> for MatrixN<N, D>
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where DefaultAllocator: Allocator<N, D, D> +
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Allocator<N, DimNameDiff<D, U1>> +
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Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> {
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#[inline]
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fn transform_vector(&self, v: &VectorN<N, DimNameDiff<D, U1>>) -> VectorN<N, DimNameDiff<D, U1>> {
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let transform = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
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let normalizer = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);
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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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#[inline]
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fn transform_point(&self, pt: &Point<N, DimNameDiff<D, U1>>) -> Point<N, DimNameDiff<D, U1>> {
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let transform = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
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let translation = self.fixed_slice::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1);
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let normalizer = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);
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let n = normalizer.tr_dot(&pt.coords) + unsafe { *self.get_unchecked(D::dim() - 1, D::dim() - 1) };
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if !n.is_zero() {
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return transform * (pt / n) + translation;
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}
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transform * pt + translation
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}
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}
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