346 lines
9.0 KiB
Rust
346 lines
9.0 KiB
Rust
// pathfinder/geometry/src/basic/transform2d.rs
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//
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// Copyright © 2019 The Pathfinder Project Developers.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! 2D affine transforms.
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use crate::line_segment::LineSegment2F;
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use crate::rect::RectF;
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use crate::transform3d::Transform4F;
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use crate::unit_vector::UnitVector;
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use crate::vector::{IntoVector2F, Vector2F, vec2f};
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use pathfinder_simd::default::F32x4;
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use std::ops::{Mul, MulAssign, Sub};
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/// A 2x2 matrix, optimized with SIMD, in column-major order.
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#[derive(Clone, Copy, Debug, PartialEq)]
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pub struct Matrix2x2F(pub F32x4);
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impl Default for Matrix2x2F {
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#[inline]
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fn default() -> Matrix2x2F {
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Self::from_scale(1.0)
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}
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}
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impl Matrix2x2F {
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#[inline]
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pub fn from_scale<S>(scale: S) -> Matrix2x2F where S: IntoVector2F {
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let scale = scale.into_vector_2f();
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Matrix2x2F(F32x4::new(scale.x(), 0.0, 0.0, scale.y()))
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}
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#[inline]
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pub fn from_rotation(theta: f32) -> Matrix2x2F {
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Matrix2x2F::from_rotation_vector(UnitVector::from_angle(theta))
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}
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#[inline]
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pub fn from_rotation_vector(vector: UnitVector) -> Matrix2x2F {
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Matrix2x2F((vector.0).0.to_f32x4().xyyx() * F32x4::new(1.0, 1.0, -1.0, 1.0))
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}
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#[inline]
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pub fn row_major(m00: f32, m01: f32, m10: f32, m11: f32) -> Matrix2x2F {
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Matrix2x2F(F32x4::new(m00, m10, m01, m11))
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}
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#[inline]
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pub fn entrywise_mul(&self, other: &Matrix2x2F) -> Matrix2x2F {
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Matrix2x2F(self.0 * other.0)
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}
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#[inline]
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pub fn adjugate(&self) -> Matrix2x2F {
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Matrix2x2F(self.0.wyzx() * F32x4::new(1.0, -1.0, -1.0, 1.0))
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}
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#[inline]
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pub fn det(&self) -> f32 {
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self.0[0] * self.0[3] - self.0[2] * self.0[1]
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}
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#[inline]
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pub fn inverse(&self) -> Matrix2x2F {
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Matrix2x2F(F32x4::splat(1.0 / self.det()) * self.adjugate().0)
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}
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#[inline]
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pub fn scale(&self, factor: f32) -> Matrix2x2F {
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Matrix2x2F(self.0 * F32x4::splat(factor))
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}
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/// Extracts the scale from this matrix.
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#[inline]
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pub fn extract_scale(&self) -> Vector2F {
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let squared = self.0 * self.0;
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Vector2F((squared.xy() + squared.zw()).sqrt())
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}
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#[inline]
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pub fn m11(&self) -> f32 {
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self.0[0]
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}
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#[inline]
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pub fn m21(&self) -> f32 {
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self.0[1]
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}
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#[inline]
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pub fn m12(&self) -> f32 {
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self.0[2]
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}
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#[inline]
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pub fn m22(&self) -> f32 {
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self.0[3]
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}
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}
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impl Sub<Matrix2x2F> for Matrix2x2F {
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type Output = Matrix2x2F;
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#[inline]
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fn sub(self, other: Matrix2x2F) -> Matrix2x2F {
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Matrix2x2F(self.0 - other.0)
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}
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}
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impl Mul<Matrix2x2F> for Matrix2x2F {
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type Output = Matrix2x2F;
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#[inline]
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fn mul(self, other: Matrix2x2F) -> Matrix2x2F {
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Matrix2x2F(self.0.xyxy() * other.0.xxzz() + self.0.zwzw() * other.0.yyww())
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}
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}
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impl Mul<Vector2F> for Matrix2x2F {
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type Output = Vector2F;
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#[inline]
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fn mul(self, vector: Vector2F) -> Vector2F {
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let halves = self.0 * vector.0.to_f32x4().xxyy();
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Vector2F(halves.xy() + halves.zw())
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}
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}
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/// An affine transform, optimized with SIMD.
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#[derive(Clone, Copy, Debug, PartialEq)]
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pub struct Transform2F {
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pub matrix: Matrix2x2F,
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pub vector: Vector2F,
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}
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impl Default for Transform2F {
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#[inline]
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fn default() -> Transform2F {
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Self::from_scale(vec2f(1.0, 1.0))
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}
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}
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impl Transform2F {
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#[inline]
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pub fn from_scale<S>(scale: S) -> Transform2F where S: IntoVector2F {
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let scale = scale.into_vector_2f();
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Transform2F {
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matrix: Matrix2x2F::from_scale(scale),
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vector: Vector2F::zero(),
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}
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}
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#[inline]
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pub fn from_rotation(theta: f32) -> Transform2F {
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Transform2F {
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matrix: Matrix2x2F::from_rotation(theta),
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vector: Vector2F::zero(),
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}
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}
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#[inline]
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pub fn from_rotation_vector(vector: UnitVector) -> Transform2F {
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Transform2F {
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matrix: Matrix2x2F::from_rotation_vector(vector),
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vector: Vector2F::zero(),
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}
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}
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#[inline]
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pub fn from_translation(vector: Vector2F) -> Transform2F {
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Transform2F { matrix: Matrix2x2F::default(), vector }
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}
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#[inline]
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pub fn from_scale_rotation_translation<S>(scale: S, theta: f32, translation: Vector2F)
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-> Transform2F where S: IntoVector2F {
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let scale = scale.into_vector_2f();
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let rotation = Transform2F::from_rotation(theta);
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let translation = Transform2F::from_translation(translation);
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Transform2F::from_scale(scale) * rotation * translation
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}
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#[inline]
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pub fn row_major(m11: f32, m12: f32, m13: f32, m21: f32, m22: f32, m23: f32) -> Transform2F {
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Transform2F {
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matrix: Matrix2x2F::row_major(m11, m12, m21, m22),
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vector: Vector2F::new(m13, m23),
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}
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}
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// TODO(pcwalton): Optimize better with SIMD.
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#[inline]
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pub fn to_3d(&self) -> Transform4F {
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Transform4F::row_major(
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self.matrix.0[0],
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self.matrix.0[1],
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0.0,
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self.vector.x(),
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self.matrix.0[2],
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self.matrix.0[3],
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0.0,
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self.vector.y(),
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0.0,
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0.0,
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0.0,
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0.0,
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0.0,
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0.0,
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0.0,
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1.0,
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)
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}
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#[inline]
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pub fn is_identity(&self) -> bool {
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*self == Transform2F::default()
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}
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/// Extracts the scale from this matrix.
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#[inline]
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pub fn extract_scale(&self) -> Vector2F {
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self.matrix.extract_scale()
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}
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#[inline]
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pub fn m11(&self) -> f32 {
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self.matrix.m11()
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}
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#[inline]
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pub fn m21(&self) -> f32 {
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self.matrix.m21()
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}
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#[inline]
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pub fn m12(&self) -> f32 {
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self.matrix.m12()
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}
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#[inline]
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pub fn m22(&self) -> f32 {
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self.matrix.m22()
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}
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#[inline]
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pub fn m13(&self) -> f32 {
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self.vector.x()
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}
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#[inline]
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pub fn m23(&self) -> f32 {
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self.vector.y()
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}
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#[inline]
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pub fn translate(&self, vector: Vector2F) -> Transform2F {
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Transform2F::from_translation(vector) * *self
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}
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#[inline]
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pub fn rotate(&self, theta: f32) -> Transform2F {
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Transform2F::from_rotation(theta) * *self
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}
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#[inline]
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pub fn scale<S>(&self, scale: S) -> Transform2F where S: IntoVector2F {
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let scale = scale.into_vector_2f();
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Transform2F::from_scale(scale) * *self
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}
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/// Returns the translation part of this matrix.
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///
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/// This decomposition assumes that scale, rotation, and translation are applied in that order.
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#[inline]
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pub fn translation(&self) -> Vector2F {
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self.vector
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}
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/// Returns the rotation angle of this matrix.
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///
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/// This decomposition assumes that scale, rotation, and translation are applied in that order.
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#[inline]
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pub fn rotation(&self) -> f32 {
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f32::atan2(self.m21(), self.m11())
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}
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/// Returns the scale factor of this matrix.
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///
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/// This decomposition assumes that scale, rotation, and translation are applied in that order.
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#[inline]
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pub fn scale_factor(&self) -> f32 {
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Vector2F(self.matrix.0.zw()).length()
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}
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#[inline]
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pub fn inverse(&self) -> Transform2F {
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let matrix_inv = self.matrix.inverse();
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let vector_inv = -(matrix_inv * self.vector);
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Transform2F { matrix: matrix_inv, vector: vector_inv }
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}
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}
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impl Mul<Transform2F> for Transform2F {
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type Output = Transform2F;
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#[inline]
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fn mul(self, other: Transform2F) -> Transform2F {
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Transform2F {
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matrix: self.matrix * other.matrix,
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vector: self * other.vector,
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}
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}
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}
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impl Mul<Vector2F> for Transform2F {
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type Output = Vector2F;
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#[inline]
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fn mul(self, vector: Vector2F) -> Vector2F {
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self.matrix * vector + self.vector
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}
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}
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impl Mul<LineSegment2F> for Transform2F {
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type Output = LineSegment2F;
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#[inline]
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fn mul(self, line_segment: LineSegment2F) -> LineSegment2F {
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LineSegment2F::new(self * line_segment.from(), self * line_segment.to())
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}
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}
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impl Mul<RectF> for Transform2F {
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type Output = RectF;
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#[inline]
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fn mul(self, rect: RectF) -> RectF {
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let (upper_left, upper_right) = (self * rect.origin(), self * rect.upper_right());
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let (lower_left, lower_right) = (self * rect.lower_left(), self * rect.lower_right());
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let min_point = upper_left.min(upper_right).min(lower_left).min(lower_right);
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let max_point = upper_left.max(upper_right).max(lower_left).max(lower_right);
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RectF::from_points(min_point, max_point)
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}
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}
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impl MulAssign for Transform2F {
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#[inline]
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fn mul_assign(&mut self, other: Transform2F) {
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*self = *self * other
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}
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}
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