Quelle transform.rs
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/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at https://mozilla.org/MPL/2.0/. */
//! Animated types for transform.
// There are still some implementation on Matrix3D in animated_properties.mako.rs
// because they still need mako to generate the code.
use super::animate_multiplicative_factor;
use super::{Animate, Procedure, ToAnimatedZero};
use crate::values::computed::transform::Rotate as ComputedRotate;
use crate::values::computed::transform::Scale as ComputedScale;
use crate::values::computed::transform::Transform as ComputedTransform;
use crate::values::computed::transform::TransformOperation as ComputedTransformOper ation;
use crate::values::computed::transform::Translate as ComputedTranslate;
use crate::values::computed::transform::{DirectionVector, Matrix, Matrix3D};
use crate::values::computed::Angle;
use crate::values::computed::{Length, LengthPercentage};
use crate::values::computed::{Number, Percentage};
use crate::values::distance::{ComputeSquaredDistance, SquaredDistance};
use crate::values::generics::transform::{self, Transform, TransformOperation};
use crate::values::generics::transform::{Rotate, Scale, Translate};
use crate::values::CSSFloat;
use crate::Zero;
use std::cmp;
use std::ops::Add;
// ------------------------------------
// Animations for Matrix/Matrix3D.
// ------------------------------------
/// A 2d matrix for interpolation.
#[derive(Clone, ComputeSquaredDistance, Copy, Debug)]
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
#[allow(missing_docs)]
// FIXME: We use custom derive for ComputeSquaredDistance. However, If possible, we should convert
// the InnerMatrix2D into types with physical meaning. This custom derive computes the squared
// distance from each matrix item, and this makes the result different from that in Gecko if we
// have skew factor in the Matrix3D.
pub struct InnerMatrix2D {
pub m11: CSSFloat,
pub m12: CSSFloat,
pub m21: CSSFloat,
pub m22: CSSFloat,
}
impl Animate for InnerMatrix2D {
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
Ok(InnerMatrix2D {
m11: animate_multiplicative_factor(self.m11, other.m11, procedure)?,
m12: self.m12.animate(&other.m12, procedure)?,
m21: self.m21.animate(&other.m21, procedure)?,
m22: animate_multiplicative_factor(self.m22, other.m22, procedure)?,
})
}
}
/// A 2d translation function.
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
#[derive(Animate, Clone, ComputeSquaredDistance, Copy, Debug)]
pub struct Translate2D(f32, f32);
/// A 2d scale function.
#[derive(Clone, ComputeSquaredDistance, Copy, Debug)]
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
pub struct Scale2D(f32, f32);
impl Animate for Scale2D {
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
Ok(Scale2D(
animate_multiplicative_factor(self.0, other.0, procedure)?,
animate_multiplicative_factor(self.1, other.1, procedure)?,
))
}
}
/// A decomposed 2d matrix.
#[derive(Clone, Copy, Debug)]
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
pub struct MatrixDecomposed2D {
/// The translation function.
pub translate: Translate2D,
/// The scale function.
pub scale: Scale2D,
/// The rotation angle.
pub angle: f32,
/// The inner matrix.
pub matrix: InnerMatrix2D,
}
impl Animate for MatrixDecomposed2D {
/// <https://drafts.csswg.org/css-transforms/#interpolation-of-decomposed-2d-matrix-values>
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
// If x-axis of one is flipped, and y-axis of the other,
// convert to an unflipped rotation.
let mut scale = self.scale;
let mut angle = self.angle;
let mut other_angle = other.angle;
if (scale.0 < 0.0 && other.scale.1 < 0.0) || (scale.1 < 0.0 && other.scale.0 < 0.0) {
scale.0 = -scale.0;
scale.1 = -scale.1;
angle += if angle < 0.0 { 180. } else { -180. };
}
// Don't rotate the long way around.
if angle == 0.0 {
angle = 360.
}
if other_angle == 0.0 {
other_angle = 360.
}
if (angle - other_angle).abs() > 180. {
if angle > other_angle {
angle -= 360.
} else {
other_angle -= 360.
}
}
// Interpolate all values.
let translate = self.translate.animate(&other.translate, procedure)?;
let scale = scale.animate(&other.scale, procedure)?;
let angle = angle.animate(&other_angle, procedure)?;
let matrix = self.matrix.animate(&other.matrix, procedure)?;
Ok(MatrixDecomposed2D {
translate,
scale,
angle,
matrix,
})
}
}
impl ComputeSquaredDistance for MatrixDecomposed2D {
#[inline]
fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> {
// Use Radian to compute the distance.
const RAD_PER_DEG: f64 = std::f64::consts::PI / 180.0;
let angle1 = self.angle as f64 * RAD_PER_DEG;
let angle2 = other.angle as f64 * RAD_PER_DEG;
Ok(self.translate.compute_squared_distance(&other.translate)? +
self.scale.compute_squared_distance(&other.scale)? +
angle1.compute_squared_distance(&angle2)? +
self.matrix.compute_squared_distance(&other.matrix)?)
}
}
impl From<Matrix3D> for MatrixDecomposed2D {
/// Decompose a 2D matrix.
/// <https://drafts.csswg.org/css-transforms/#decomposing-a-2d-matrix>
fn from(matrix: Matrix3D) -> MatrixDecomposed2D {
let mut row0x = matrix.m11;
let mut row0y = matrix.m12;
let mut row1x = matrix.m21;
let mut row1y = matrix.m22;
let translate = Translate2D(matrix.m41, matrix.m42);
let mut scale = Scale2D(
(row0x * row0x + row0y * row0y).sqrt(),
(row1x * row1x + row1y * row1y).sqrt(),
);
// If determinant is negative, one axis was flipped.
let determinant = row0x * row1y - row0y * row1x;
if determinant < 0. {
if row0x < row1y {
scale.0 = -scale.0;
} else {
scale.1 = -scale.1;
}
}
// Renormalize matrix to remove scale.
if scale.0 != 0.0 {
row0x *= 1. / scale.0;
row0y *= 1. / scale.0;
}
if scale.1 != 0.0 {
row1x *= 1. / scale.1;
row1y *= 1. / scale.1;
}
// Compute rotation and renormalize matrix.
let mut angle = row0y.atan2(row0x);
if angle != 0.0 {
let sn = -row0y;
let cs = row0x;
let m11 = row0x;
let m12 = row0y;
let m21 = row1x;
let m22 = row1y;
row0x = cs * m11 + sn * m21;
row0y = cs * m12 + sn * m22;
row1x = -sn * m11 + cs * m21;
row1y = -sn * m12 + cs * m22;
}
let m = InnerMatrix2D {
m11: row0x,
m12: row0y,
m21: row1x,
m22: row1y,
};
// Convert into degrees because our rotation functions expect it.
angle = angle.to_degrees();
MatrixDecomposed2D {
translate: translate,
scale: scale,
angle: angle,
matrix: m,
}
}
}
impl From<MatrixDecomposed2D> for Matrix3D {
/// Recompose a 2D matrix.
/// <https://drafts.csswg.org/css-transforms/#recomposing-to-a-2d-matrix>
fn from(decomposed: MatrixDecomposed2D) -> Matrix3D {
let mut computed_matrix = Matrix3D::identity();
computed_matrix.m11 = decomposed.matrix.m11;
computed_matrix.m12 = decomposed.matrix.m12;
computed_matrix.m21 = decomposed.matrix.m21;
computed_matrix.m22 = decomposed.matrix.m22;
// Translate matrix.
computed_matrix.m41 = decomposed.translate.0;
computed_matrix.m42 = decomposed.translate.1;
// Rotate matrix.
let angle = decomposed.angle.to_radians();
let cos_angle = angle.cos();
let sin_angle = angle.sin();
let mut rotate_matrix = Matrix3D::identity();
rotate_matrix.m11 = cos_angle;
rotate_matrix.m12 = sin_angle;
rotate_matrix.m21 = -sin_angle;
rotate_matrix.m22 = cos_angle;
// Multiplication of computed_matrix and rotate_matrix
computed_matrix = rotate_matrix.multiply(&computed_matrix);
// Scale matrix.
computed_matrix.m11 *= decomposed.scale.0;
computed_matrix.m12 *= decomposed.scale.0;
computed_matrix.m21 *= decomposed.scale.1;
computed_matrix.m22 *= decomposed.scale.1;
computed_matrix
}
}
impl Animate for Matrix {
#[cfg(feature = "servo")]
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
let this = Matrix3D::from(*self);
let other = Matrix3D::from(*other);
let this = MatrixDecomposed2D::from(this);
let other = MatrixDecomposed2D::from(other);
Matrix3D::from(this.animate(&other, procedure)?).into_2d()
}
#[cfg(feature = "gecko")]
// Gecko doesn't exactly follow the spec here; we use a different procedure
// to match it
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
let this = Matrix3D::from(*self);
let other = Matrix3D::from(*other);
let from = decompose_2d_matrix(&this)?;
let to = decompose_2d_matrix(&other)?;
Matrix3D::from(from.animate(&to, procedure)?).into_2d()
}
}
/// A 3d translation.
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
#[derive(Animate, Clone, ComputeSquaredDistance, Copy, Debug)]
pub struct Translate3D(pub f32, pub f32, pub f32);
/// A 3d scale function.
#[derive(Clone, ComputeSquaredDistance, Copy, Debug)]
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
pub struct Scale3D(pub f32, pub f32, pub f32);
impl Scale3D {
/// Negate self.
fn negate(&mut self) {
self.0 *= -1.0;
self.1 *= -1.0;
self.2 *= -1.0;
}
}
impl Animate for Scale3D {
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
Ok(Scale3D(
animate_multiplicative_factor(self.0, other.0, procedure)?,
animate_multiplicative_factor(self.1, other.1, procedure)?,
animate_multiplicative_factor(self.2, other.2, procedure)?,
))
}
}
/// A 3d skew function.
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
#[derive(Animate, Clone, Copy, Debug)]
pub struct Skew(f32, f32, f32);
impl ComputeSquaredDistance for Skew {
// We have to use atan() to convert the skew factors into skew angles, so implement
// ComputeSquaredDistance manually.
#[inline]
fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> {
Ok(self.0.atan().compute_squared_distance(&other.0.atan())? +
self.1.atan().compute_squared_distance(&other.1.atan())? +
self.2.atan().compute_squared_distance(&other.2.atan())?)
}
}
/// A 3d perspective transformation.
#[derive(Clone, ComputeSquaredDistance, Copy, Debug)]
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
pub struct Perspective(pub f32, pub f32, pub f32, pub f32);
impl Animate for Perspective {
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
Ok(Perspective(
self.0.animate(&other.0, procedure)?,
self.1.animate(&other.1, procedure)?,
self.2.animate(&other.2, procedure)?,
animate_multiplicative_factor(self.3, other.3, procedure)?,
))
}
}
/// A quaternion used to represent a rotation.
#[derive(Clone, Copy, Debug)]
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
pub struct Quaternion(f64, f64, f64, f64);
impl Quaternion {
/// Return a quaternion from a unit direction vector and angle (unit: radian).
#[inline]
fn from_direction_and_angle(vector: &DirectionVector, angle: f64) -> Self {
debug_assert!(
(vector.length() - 1.).abs() < 0.0001,
"Only accept an unit direction vector to create a quaternion"
);
// Quaternions between the range [360, 720] will treated as rotations at the other
// direction: [-360, 0]. And quaternions between the range [720*k, 720*(k+1)] will be
// treated as rotations [0, 720]. So it does not make sense to use quaternions to rotate
// the element more than ±360deg. Therefore, we have to make sure its range is (-360, 360).
let half_angle = angle
.abs()
.rem_euclid(std::f64::consts::TAU)
.copysign(angle) /
2.;
// Reference:
// https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
//
// if the direction axis is (x, y, z) = xi + yj + zk,
// and the angle is |theta|, this formula can be done using
// an extension of Euler's formula:
// q = cos(theta/2) + (xi + yj + zk)(sin(theta/2))
// = cos(theta/2) +
// x*sin(theta/2)i + y*sin(theta/2)j + z*sin(theta/2)k
Quaternion(
vector.x as f64 * half_angle.sin(),
vector.y as f64 * half_angle.sin(),
vector.z as f64 * half_angle.sin(),
half_angle.cos(),
)
}
/// Calculate the dot product.
#[inline]
fn dot(&self, other: &Self) -> f64 {
self.0 * other.0 + self.1 * other.1 + self.2 * other.2 + self.3 * other.3
}
/// Return the scaled quaternion by a factor.
#[inline]
fn scale(&self, factor: f64) -> Self {
Quaternion(
self.0 * factor,
self.1 * factor,
self.2 * factor,
self.3 * factor,
)
}
}
impl Add for Quaternion {
type Output = Self;
fn add(self, other: Self) -> Self {
Self(
self.0 + other.0,
self.1 + other.1,
self.2 + other.2,
self.3 + other.3,
)
}
}
impl Animate for Quaternion {
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
let (this_weight, other_weight) = procedure.weights();
debug_assert!(
// Doule EPSILON since both this_weight and other_weght have calculation errors
// which are approximately equal to EPSILON.
(this_weight + other_weight - 1.0f64).abs() <= f64::EPSILON * 2.0 ||
other_weight == 1.0f64 ||
other_weight == 0.0f64,
"animate should only be used for interpolating or accumulating transforms"
);
// We take a specialized code path for accumulation (where other_weight
// is 1).
if let Procedure::Accumulate { .. } = procedure {
debug_assert_eq!(other_weight, 1.0);
if this_weight == 0.0 {
return Ok(*other);
}
let clamped_w = self.3.min(1.0).max(-1.0);
// Determine the scale factor.
let mut theta = clamped_w.acos();
let mut scale = if theta == 0.0 { 0.0 } else { 1.0 / theta.sin() };
theta *= this_weight;
scale *= theta.sin();
// Scale the self matrix by this_weight.
let mut scaled_self = *self;
scaled_self.0 *= scale;
scaled_self.1 *= scale;
scaled_self.2 *= scale;
scaled_self.3 = theta.cos();
// Multiply scaled-self by other.
let a = &scaled_self;
let b = other;
return Ok(Quaternion(
a.3 * b.0 + a.0 * b.3 + a.1 * b.2 - a.2 * b.1,
a.3 * b.1 - a.0 * b.2 + a.1 * b.3 + a.2 * b.0,
a.3 * b.2 + a.0 * b.1 - a.1 * b.0 + a.2 * b.3,
a.3 * b.3 - a.0 * b.0 - a.1 * b.1 - a.2 * b.2,
));
}
// https://drafts.csswg.org/css-transforms-2/#interpolation-of-decomposed-3d-matrix-values
//
// Dot product, clamped between -1 and 1.
let cos_half_theta =
(self.0 * other.0 + self.1 * other.1 + self.2 * other.2 + self.3 * other.3)
.min(1.0)
.max(-1.0);
if cos_half_theta.abs() == 1.0 {
return Ok(*self);
}
let half_theta = cos_half_theta.acos();
let sin_half_theta = (1.0 - cos_half_theta * cos_half_theta).sqrt();
let right_weight = (other_weight * half_theta).sin() / sin_half_theta;
// The spec would like to use
// "(other_weight * half_theta).cos() - cos_half_theta * right_weight". However, this
// formula may produce some precision issues of floating-point number calculation, e.g.
// when the progress is 100% (i.e. |other_weight| is 1), the |left_weight| may not be
// perfectly equal to 0. It could be something like -2.22e-16, which is approximately equal
// to zero, in the test. And after we recompose the Matrix3D, these approximated zeros
// make us failed to treat this Matrix3D as a Matrix2D, when serializating it.
//
// Therefore, we use another formula to calculate |left_weight| here. Blink and WebKit also
// use this formula, which is defined in:
// https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/index.htm
// https://github.com/w3c/csswg-drafts/issues/9338
let left_weight = (this_weight * half_theta).sin() / sin_half_theta;
Ok(self.scale(left_weight) + other.scale(right_weight))
}
}
impl ComputeSquaredDistance for Quaternion {
#[inline]
fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> {
// Use quaternion vectors to get the angle difference. Both q1 and q2 are unit vectors,
// so we can get their angle difference by:
// cos(theta/2) = (q1 dot q2) / (|q1| * |q2|) = q1 dot q2.
let distance = self.dot(other).max(-1.0).min(1.0).acos() * 2.0;
Ok(SquaredDistance::from_sqrt(distance))
}
}
/// A decomposed 3d matrix.
#[derive(Animate, Clone, ComputeSquaredDistance, Copy, Debug)]
#[cfg_attr(feature = "servo", derive(MallocSizeOf))]
pub struct MatrixDecomposed3D {
/// A translation function.
pub translate: Translate3D,
/// A scale function.
pub scale: Scale3D,
/// The skew component of the transformation.
pub skew: Skew,
/// The perspective component of the transformation.
pub perspective: Perspective,
/// The quaternion used to represent the rotation.
pub quaternion: Quaternion,
}
impl From<MatrixDecomposed3D> for Matrix3D {
/// Recompose a 3D matrix.
/// <https://drafts.csswg.org/css-transforms/#recomposing-to-a-3d-matrix>
fn from(decomposed: MatrixDecomposed3D) -> Matrix3D {
let mut matrix = Matrix3D::identity();
// Apply perspective
matrix.set_perspective(&decomposed.perspective);
// Apply translation
matrix.apply_translate(&decomposed.translate);
// Apply rotation
{
let x = decomposed.quaternion.0;
let y = decomposed.quaternion.1;
let z = decomposed.quaternion.2;
let w = decomposed.quaternion.3;
// Construct a composite rotation matrix from the quaternion values
// rotationMatrix is a identity 4x4 matrix initially
let mut rotation_matrix = Matrix3D::identity();
rotation_matrix.m11 = 1.0 - 2.0 * (y * y + z * z) as f32;
rotation_matrix.m12 = 2.0 * (x * y + z * w) as f32;
rotation_matrix.m13 = 2.0 * (x * z - y * w) as f32;
rotation_matrix.m21 = 2.0 * (x * y - z * w) as f32;
rotation_matrix.m22 = 1.0 - 2.0 * (x * x + z * z) as f32;
rotation_matrix.m23 = 2.0 * (y * z + x * w) as f32;
rotation_matrix.m31 = 2.0 * (x * z + y * w) as f32;
rotation_matrix.m32 = 2.0 * (y * z - x * w) as f32;
rotation_matrix.m33 = 1.0 - 2.0 * (x * x + y * y) as f32;
matrix = rotation_matrix.multiply(&matrix);
}
// Apply skew
{
let mut temp = Matrix3D::identity();
if decomposed.skew.2 != 0.0 {
temp.m32 = decomposed.skew.2;
matrix = temp.multiply(&matrix);
temp.m32 = 0.0;
}
if decomposed.skew.1 != 0.0 {
temp.m31 = decomposed.skew.1;
matrix = temp.multiply(&matrix);
temp.m31 = 0.0;
}
if decomposed.skew.0 != 0.0 {
temp.m21 = decomposed.skew.0;
matrix = temp.multiply(&matrix);
}
}
// Apply scale
matrix.apply_scale(&decomposed.scale);
matrix
}
}
/// Decompose a 3D matrix.
/// https://drafts.csswg.org/css-transforms-2/#decomposing-a-3d-matrix
/// http://www.realtimerendering.com/resources/GraphicsGems/gemsii/unmatrix.c
fn decompose_3d_matrix(mut matrix: Matrix3D) -> Result<MatrixDecomposed3D, ()> {
// Combine 2 point.
let combine = |a: [f32; 3], b: [f32; 3], ascl: f32, bscl: f32| {
[
(ascl * a[0]) + (bscl * b[0]),
(ascl * a[1]) + (bscl * b[1]),
(ascl * a[2]) + (bscl * b[2]),
]
};
// Dot product.
let dot = |a: [f32; 3], b: [f32; 3]| a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
// Cross product.
let cross = |row1: [f32; 3], row2: [f32; 3]| {
[
row1[1] * row2[2] - row1[2] * row2[1],
row1[2] * row2[0] - row1[0] * row2[2],
row1[0] * row2[1] - row1[1] * row2[0],
]
};
if matrix.m44 == 0.0 {
return Err(());
}
let scaling_factor = matrix.m44;
// Normalize the matrix.
matrix.scale_by_factor(1.0 / scaling_factor);
// perspective_matrix is used to solve for perspective, but it also provides
// an easy way to test for singularity of the upper 3x3 component.
let mut perspective_matrix = matrix;
perspective_matrix.m14 = 0.0;
perspective_matrix.m24 = 0.0;
perspective_matrix.m34 = 0.0;
perspective_matrix.m44 = 1.0;
if perspective_matrix.determinant() == 0.0 {
return Err(());
}
// First, isolate perspective.
let perspective = if matrix.m14 != 0.0 || matrix.m24 != 0.0 || matrix.m34 != 0.0 {
let right_hand_side: [f32; 4] = [matrix.m14, matrix.m24, matrix.m34, matrix.m44];
perspective_matrix = perspective_matrix.inverse().unwrap().transpose();
let perspective = perspective_matrix.pre_mul_point4(&right_hand_side);
// NOTE(emilio): Even though the reference algorithm clears the
// fourth column here (matrix.m14..matrix.m44), they're not used below
// so it's not really needed.
Perspective(
perspective[0],
perspective[1],
perspective[2],
perspective[3],
)
} else {
Perspective(0.0, 0.0, 0.0, 1.0)
};
// Next take care of translation (easy).
let translate = Translate3D(matrix.m41, matrix.m42, matrix.m43);
// Now get scale and shear. 'row' is a 3 element array of 3 component vectors
let mut row = matrix.get_matrix_3x3_part();
// Compute X scale factor and normalize first row.
let row0len = (row[0][0] * row[0][0] + row[0][1] * row[0][1] + row[0][2] * row[0][2]).sqrt();
let mut scale = Scale3D(row0len, 0.0, 0.0);
row[0] = [
row[0][0] / row0len,
row[0][1] / row0len,
row[0][2] / row0len,
];
// Compute XY shear factor and make 2nd row orthogonal to 1st.
let mut skew = Skew(dot(row[0], row[1]), 0.0, 0.0);
row[1] = combine(row[1], row[0], 1.0, -skew.0);
// Now, compute Y scale and normalize 2nd row.
let row1len = (row[1][0] * row[1][0] + row[1][1] * row[1][1] + row[1][2] * row[1][2]).sqrt();
scale.1 = row1len;
row[1] = [
row[1][0] / row1len,
row[1][1] / row1len,
row[1][2] / row1len,
];
skew.0 /= scale.1;
// Compute XZ and YZ shears, orthogonalize 3rd row
skew.1 = dot(row[0], row[2]);
row[2] = combine(row[2], row[0], 1.0, -skew.1);
skew.2 = dot(row[1], row[2]);
row[2] = combine(row[2], row[1], 1.0, -skew.2);
// Next, get Z scale and normalize 3rd row.
let row2len = (row[2][0] * row[2][0] + row[2][1] * row[2][1] + row[2][2] * row[2][2]).sqrt();
scale.2 = row2len;
row[2] = [
row[2][0] / row2len,
row[2][1] / row2len,
row[2][2] / row2len,
];
skew.1 /= scale.2;
skew.2 /= scale.2;
// At this point, the matrix (in rows) is orthonormal.
// Check for a coordinate system flip. If the determinant
// is -1, then negate the matrix and the scaling factors.
if dot(row[0], cross(row[1], row[2])) < 0.0 {
scale.negate();
for i in 0..3 {
row[i][0] *= -1.0;
row[i][1] *= -1.0;
row[i][2] *= -1.0;
}
}
// Now, get the rotations out.
let mut quaternion = Quaternion(
0.5 * ((1.0 + row[0][0] - row[1][1] - row[2][2]).max(0.0) as f64).sqrt(),
0.5 * ((1.0 - row[0][0] + row[1][1] - row[2][2]).max(0.0) as f64).sqrt(),
0.5 * ((1.0 - row[0][0] - row[1][1] + row[2][2]).max(0.0) as f64).sqrt(),
0.5 * ((1.0 + row[0][0] + row[1][1] + row[2][2]).max(0.0) as f64).sqrt(),
);
if row[2][1] > row[1][2] {
quaternion.0 = -quaternion.0
}
if row[0][2] > row[2][0] {
quaternion.1 = -quaternion.1
}
if row[1][0] > row[0][1] {
quaternion.2 = -quaternion.2
}
Ok(MatrixDecomposed3D {
translate,
scale,
skew,
perspective,
quaternion,
})
}
/**
* The relevant section of the transitions specification:
* https://drafts.csswg.org/web-animations-1/#animation-types
* http://dev.w3.org/csswg/css3-transitions/#animation-of-property-types-
* defers all of the details to the 2-D and 3-D transforms specifications.
* For the 2-D transforms specification (all that's relevant for us, right
* now), the relevant section is:
* https://drafts.csswg.org/css-transforms-1/#interpolation-of-transforms
* This, in turn, refers to the unmatrix program in Graphics Gems,
* available from http://graphicsgems.org/ , and in
* particular as the file GraphicsGems/gemsii/unmatrix.c
* in http://graphicsgems.org/AllGems.tar.gz
*
* The unmatrix reference is for general 3-D transform matrices (any of the
* 16 components can have any value).
*
* For CSS 2-D transforms, we have a 2-D matrix with the bottom row constant:
*
* [ A C E ]
* [ B D F ]
* [ 0 0 1 ]
*
* For that case, I believe the algorithm in unmatrix reduces to:
*
* (1) If A * D - B * C == 0, the matrix is singular. Fail.
*
* (2) Set translation components (Tx and Ty) to the translation parts of
* the matrix (E and F) and then ignore them for the rest of the time.
* (For us, E and F each actually consist of three constants: a
* length, a multiplier for the width, and a multiplier for the
* height. This actually requires its own decomposition, but I'll
* keep that separate.)
*
* (3) Let the X scale (Sx) be sqrt(A^2 + B^2). Then divide both A and B
* by it.
*
* (4) Let the XY shear (K) be A * C + B * D. From C, subtract A times
* the XY shear. From D, subtract B times the XY shear.
*
* (5) Let the Y scale (Sy) be sqrt(C^2 + D^2). Divide C, D, and the XY
* shear (K) by it.
*
* (6) At this point, A * D - B * C is either 1 or -1. If it is -1,
* negate the XY shear (K), the X scale (Sx), and A, B, C, and D.
* (Alternatively, we could negate the XY shear (K) and the Y scale
* (Sy).)
*
* (7) Let the rotation be R = atan2(B, A).
*
* Then the resulting decomposed transformation is:
*
* translate(Tx, Ty) rotate(R) skewX(atan(K)) scale(Sx, Sy)
*
* An interesting result of this is that all of the simple transform
* functions (i.e., all functions other than matrix()), in isolation,
* decompose back to themselves except for:
* 'skewY(φ)', which is 'matrix(1, tan(φ), 0, 1, 0, 0)', which decomposes
* to 'rotate(φ) skewX(φ) scale(sec(φ), cos(φ))' since (ignoring the
* alternate sign possibilities that would get fixed in step 6):
* In step 3, the X scale factor is sqrt(1+tan²(φ)) = sqrt(sec²(φ)) =
* sec(φ). Thus, after step 3, A = 1/sec(φ) = cos(φ) and B = tan(φ) / sec(φ) =
* sin(φ). In step 4, the XY shear is sin(φ). Thus, after step 4, C =
* -cos(φ)sin(φ) and D = 1 - sin²(φ) = cos²(φ). Thus, in step 5, the Y scale is
* sqrt(cos²(φ)(sin²(φ) + cos²(φ)) = cos(φ). Thus, after step 5, C = -sin(φ), D
* = cos(φ), and the XY shear is tan(φ). Thus, in step 6, A * D - B * C =
* cos²(φ) + sin²(φ) = 1. In step 7, the rotation is thus φ.
*
* skew(θ, φ), which is matrix(1, tan(φ), tan(θ), 1, 0, 0), which decomposes
* to 'rotate(φ) skewX(θ + φ) scale(sec(φ), cos(φ))' since (ignoring
* the alternate sign possibilities that would get fixed in step 6):
* In step 3, the X scale factor is sqrt(1+tan²(φ)) = sqrt(sec²(φ)) =
* sec(φ). Thus, after step 3, A = 1/sec(φ) = cos(φ) and B = tan(φ) / sec(φ) =
* sin(φ). In step 4, the XY shear is cos(φ)tan(θ) + sin(φ). Thus, after step 4,
* C = tan(θ) - cos(φ)(cos(φ)tan(θ) + sin(φ)) = tan(θ)sin²(φ) - cos(φ)sin(φ)
* D = 1 - sin(φ)(cos(φ)tan(θ) + sin(φ)) = cos²(φ) - sin(φ)cos(φ)tan(θ)
* Thus, in step 5, the Y scale is sqrt(C² + D²) =
* sqrt(tan²(θ)(sin⁴(φ) + sin²(φ)cos²(φ)) -
* 2 tan(θ)(sin³(φ)cos(φ) + sin(φ)cos³(φ)) +
* (sin²(φ)cos²(φ) + cos⁴(φ))) =
* sqrt(tan²(θ)sin²(φ) - 2 tan(θ)sin(φ)cos(φ) + cos²(φ)) =
* cos(φ) - tan(θ)sin(φ) (taking the negative of the obvious solution so
* we avoid flipping in step 6).
* After step 5, C = -sin(φ) and D = cos(φ), and the XY shear is
* (cos(φ)tan(θ) + sin(φ)) / (cos(φ) - tan(θ)sin(φ)) =
* (dividing both numerator and denominator by cos(φ))
* (tan(θ) + tan(φ)) / (1 - tan(θ)tan(φ)) = tan(θ + φ).
* (See http://en.wikipedia.org/wiki/List_of_trigonometric_identities .)
* Thus, in step 6, A * D - B * C = cos²(φ) + sin²(φ) = 1.
* In step 7, the rotation is thus φ.
*
* To check this result, we can multiply things back together:
*
* [ cos(φ) -sin(φ) ] [ 1 tan(θ + φ) ] [ sec(φ) 0 ]
* [ sin(φ) cos(φ) ] [ 0 1 ] [ 0 cos(φ) ]
*
* [ cos(φ) cos(φ)tan(θ + φ) - sin(φ) ] [ sec(φ) 0 ]
* [ sin(φ) sin(φ)tan(θ + φ) + cos(φ) ] [ 0 cos(φ) ]
*
* but since tan(θ + φ) = (tan(θ) + tan(φ)) / (1 - tan(θ)tan(φ)),
* cos(φ)tan(θ + φ) - sin(φ)
* = cos(φ)(tan(θ) + tan(φ)) - sin(φ) + sin(φ)tan(θ)tan(φ)
* = cos(φ)tan(θ) + sin(φ) - sin(φ) + sin(φ)tan(θ)tan(φ)
* = cos(φ)tan(θ) + sin(φ)tan(θ)tan(φ)
* = tan(θ) (cos(φ) + sin(φ)tan(φ))
* = tan(θ) sec(φ) (cos²(φ) + sin²(φ))
* = tan(θ) sec(φ)
* and
* sin(φ)tan(θ + φ) + cos(φ)
* = sin(φ)(tan(θ) + tan(φ)) + cos(φ) - cos(φ)tan(θ)tan(φ)
* = tan(θ) (sin(φ) - sin(φ)) + sin(φ)tan(φ) + cos(φ)
* = sec(φ) (sin²(φ) + cos²(φ))
* = sec(φ)
* so the above is:
* [ cos(φ) tan(θ) sec(φ) ] [ sec(φ) 0 ]
* [ sin(φ) sec(φ) ] [ 0 cos(φ) ]
*
* [ 1 tan(θ) ]
* [ tan(φ) 1 ]
*/
/// Decompose a 2D matrix for Gecko. This implements the above decomposition algorithm.
#[cfg(feature = "gecko")]
fn decompose_2d_matrix(matrix: &Matrix3D) -> Result<MatrixDecomposed3D, ()> {
// The index is column-major, so the equivalent transform matrix is:
// | m11 m21 0 m41 | => | m11 m21 | and translate(m41, m42)
// | m12 m22 0 m42 | | m12 m22 |
// | 0 0 1 0 |
// | 0 0 0 1 |
let (mut m11, mut m12) = (matrix.m11, matrix.m12);
let (mut m21, mut m22) = (matrix.m21, matrix.m22);
// Check if this is a singular matrix.
if m11 * m22 == m12 * m21 {
return Err(());
}
let mut scale_x = (m11 * m11 + m12 * m12).sqrt();
m11 /= scale_x;
m12 /= scale_x;
let mut shear_xy = m11 * m21 + m12 * m22;
m21 -= m11 * shear_xy;
m22 -= m12 * shear_xy;
let scale_y = (m21 * m21 + m22 * m22).sqrt();
m21 /= scale_y;
m22 /= scale_y;
shear_xy /= scale_y;
let determinant = m11 * m22 - m12 * m21;
// Determinant should now be 1 or -1.
if 0.99 > determinant.abs() || determinant.abs() > 1.01 {
return Err(());
}
if determinant < 0. {
m11 = -m11;
m12 = -m12;
shear_xy = -shear_xy;
scale_x = -scale_x;
}
Ok(MatrixDecomposed3D {
translate: Translate3D(matrix.m41, matrix.m42, 0.),
scale: Scale3D(scale_x, scale_y, 1.),
skew: Skew(shear_xy, 0., 0.),
perspective: Perspective(0., 0., 0., 1.),
quaternion: Quaternion::from_direction_and_angle(
&DirectionVector::new(0., 0., 1.),
m12.atan2(m11) as f64,
),
})
}
impl Animate for Matrix3D {
#[cfg(feature = "servo")]
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
if self.is_3d() || other.is_3d() {
let decomposed_from = decompose_3d_matrix(*self);
let decomposed_to = decompose_3d_matrix(*other);
match (decomposed_from, decomposed_to) {
(Ok(this), Ok(other)) => Ok(Matrix3D::from(this.animate(&other, procedure)?)),
// Matrices can be undecomposable due to couple reasons, e.g.,
// non-invertible matrices. In this case, we should report Err
// here, and let the caller do the fallback procedure.
_ => Err(()),
}
} else {
let this = MatrixDecomposed2D::from(*self);
let other = MatrixDecomposed2D::from(*other);
Ok(Matrix3D::from(this.animate(&other, procedure)?))
}
}
#[cfg(feature = "gecko")]
// Gecko doesn't exactly follow the spec here; we use a different procedure
// to match it
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
let (from, to) = if self.is_3d() || other.is_3d() {
(decompose_3d_matrix(*self)?, decompose_3d_matrix(*other)?)
} else {
(decompose_2d_matrix(self)?, decompose_2d_matrix(other)?)
};
// Matrices can be undecomposable due to couple reasons, e.g.,
// non-invertible matrices. In this case, we should report Err here,
// and let the caller do the fallback procedure.
Ok(Matrix3D::from(from.animate(&to, procedure)?))
}
}
impl ComputeSquaredDistance for Matrix3D {
#[inline]
#[cfg(feature = "servo")]
fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> {
if self.is_3d() || other.is_3d() {
let from = decompose_3d_matrix(*self)?;
let to = decompose_3d_matrix(*other)?;
from.compute_squared_distance(&to)
} else {
let from = MatrixDecomposed2D::from(*self);
let to = MatrixDecomposed2D::from(*other);
from.compute_squared_distance(&to)
}
}
#[inline]
#[cfg(feature = "gecko")]
fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> {
let (from, to) = if self.is_3d() || other.is_3d() {
(decompose_3d_matrix(*self)?, decompose_3d_matrix(*other)?)
} else {
(decompose_2d_matrix(self)?, decompose_2d_matrix(other)?)
};
from.compute_squared_distance(&to)
}
}
// ------------------------------------
// Animation for Transform list.
// ------------------------------------
fn is_matched_operation(
first: &ComputedTransformOperation,
second: &ComputedTransformOperation,
) -> bool {
match (first, second) {
(&TransformOperation::Matrix(..), &TransformOperation::Matrix(..)) |
(&TransformOperation::Matrix3D(..), &TransformOperation::Matrix3D(..)) |
(&TransformOperation::Skew(..), &TransformOperation::Skew(..)) |
(&TransformOperation::SkewX(..), &TransformOperation::SkewX(..)) |
(&TransformOperation::SkewY(..), &TransformOperation::SkewY(..)) |
(&TransformOperation::Rotate(..), &TransformOperation::Rotate(..)) |
(&TransformOperation::Rotate3D(..), &TransformOperation::Rotate3D(..)) |
(&TransformOperation::RotateX(..), &TransformOperation::RotateX(..)) |
(&TransformOperation::RotateY(..), &TransformOperation::RotateY(..)) |
(&TransformOperation::RotateZ(..), &TransformOperation::RotateZ(..)) |
(&TransformOperation::Perspective(..), &TransformOperation::Perspective(..)) => true,
// Match functions that have the same primitive transform function
(a, b) if a.is_translate() && b.is_translate() => true,
(a, b) if a.is_scale() && b.is_scale() => true,
(a, b) if a.is_rotate() && b.is_rotate() => true,
// InterpolateMatrix and AccumulateMatrix are for mismatched transforms
_ => false,
}
}
/// <https://drafts.csswg.org/css-transforms/#interpolation-of-transforms>
impl Animate for ComputedTransform {
#[inline]
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
use std::borrow::Cow;
// Addition for transforms simply means appending to the list of
// transform functions. This is different to how we handle the other
// animation procedures so we treat it separately here rather than
// handling it in TransformOperation.
if procedure == Procedure::Add {
let result = self.0.iter().chain(&*other.0).cloned().collect();
return Ok(Transform(result));
}
let this = Cow::Borrowed(&self.0);
let other = Cow::Borrowed(&other.0);
// Interpolate the common prefix
let mut result = this
.iter()
.zip(other.iter())
.take_while(|(this, other)| is_matched_operation(this, other))
.map(|(this, other)| this.animate(other, procedure))
.collect::<Result<Vec<_>, _>>()?;
// Deal with the remainders
let this_remainder = if this.len() > result.len() {
Some(&this[result.len()..])
} else {
None
};
let other_remainder = if other.len() > result.len() {
Some(&other[result.len()..])
} else {
None
};
match (this_remainder, other_remainder) {
// If there is a remainder from *both* lists we must have had mismatched functions.
// => Add the remainders to a suitable ___Matrix function.
(Some(this_remainder), Some(other_remainder)) => {
result.push(TransformOperation::animate_mismatched_transforms(
this_remainder,
other_remainder,
procedure,
)?);
},
// If there is a remainder from just one list, then one list must be shorter but
// completely match the type of the corresponding functions in the longer list.
// => Interpolate the remainder with identity transforms.
(Some(remainder), None) | (None, Some(remainder)) => {
let fill_right = this_remainder.is_some();
result.append(
&mut remainder
.iter()
.map(|transform| {
let identity = transform.to_animated_zero().unwrap();
match transform {
TransformOperation::AccumulateMatrix { .. } |
TransformOperation::InterpolateMatrix { .. } => {
let (from, to) = if fill_right {
(transform, &identity)
} else {
(&identity, transform)
};
TransformOperation::animate_mismatched_transforms(
&[from.clone()],
&[to.clone()],
procedure,
)
},
_ => {
let (lhs, rhs) = if fill_right {
(transform, &identity)
} else {
(&identity, transform)
};
lhs.animate(rhs, procedure)
},
}
})
.collect::<Result<Vec<_>, _>>()?,
);
},
(None, None) => {},
}
Ok(Transform(result.into()))
}
}
impl ComputeSquaredDistance for ComputedTransform {
#[inline]
fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> {
let squared_dist = super::lists::with_zero::squared_distance(&self.0, &other.0);
// Roll back to matrix interpolation if there is any Err(()) in the
// transform lists, such as mismatched transform functions.
//
// FIXME: Using a zero size here seems a bit sketchy but matches the
// previous behavior.
if squared_dist.is_err() {
let rect = euclid::Rect::zero();
let matrix1: Matrix3D = self.to_transform_3d_matrix(Some(&rect))?.0.into();
let matrix2: Matrix3D = other.to_transform_3d_matrix(Some(&rect))?.0.into();
return matrix1.compute_squared_distance(&matrix2);
}
squared_dist
}
}
/// <http://dev.w3.org/csswg/css-transforms/#interpolation-of-transforms>
impl Animate for ComputedTransformOperation {
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
match (self, other) {
(&TransformOperation::Matrix3D(ref this), &TransformOperation::Matrix3D(ref other)) => {
Ok(TransformOperation::Matrix3D(
this.animate(other, procedure)?,
))
},
(&TransformOperation::Matrix(ref this), &TransformOperation::Matrix(ref other)) => {
Ok(TransformOperation::Matrix(this.animate(other, procedure)?))
},
(
&TransformOperation::Skew(ref fx, ref fy),
&TransformOperation::Skew(ref tx, ref ty),
) => Ok(TransformOperation::Skew(
fx.animate(tx, procedure)?,
fy.animate(ty, procedure)?,
)),
(&TransformOperation::SkewX(ref f), &TransformOperation::SkewX(ref t)) => {
Ok(TransformOperation::SkewX(f.animate(t, procedure)?))
},
(&TransformOperation::SkewY(ref f), &TransformOperation::SkewY(ref t)) => {
Ok(TransformOperation::SkewY(f.animate(t, procedure)?))
},
(
&TransformOperation::Translate3D(ref fx, ref fy, ref fz),
&TransformOperation::Translate3D(ref tx, ref ty, ref tz),
) => Ok(TransformOperation::Translate3D(
fx.animate(tx, procedure)?,
fy.animate(ty, procedure)?,
fz.animate(tz, procedure)?,
)),
(
&TransformOperation::Translate(ref fx, ref fy),
&TransformOperation::Translate(ref tx, ref ty),
) => Ok(TransformOperation::Translate(
fx.animate(tx, procedure)?,
fy.animate(ty, procedure)?,
)),
(&TransformOperation::TranslateX(ref f), &TransformOperation::TranslateX(ref t)) => {
Ok(TransformOperation::TranslateX(f.animate(t, procedure)?))
},
(&TransformOperation::TranslateY(ref f), &TransformOperation::TranslateY(ref t)) => {
Ok(TransformOperation::TranslateY(f.animate(t, procedure)?))
},
(&TransformOperation::TranslateZ(ref f), &TransformOperation::TranslateZ(ref t)) => {
Ok(TransformOperation::TranslateZ(f.animate(t, procedure)?))
},
(
&TransformOperation::Scale3D(ref fx, ref fy, ref fz),
&TransformOperation::Scale3D(ref tx, ref ty, ref tz),
) => Ok(TransformOperation::Scale3D(
animate_multiplicative_factor(*fx, *tx, procedure)?,
animate_multiplicative_factor(*fy, *ty, procedure)?,
animate_multiplicative_factor(*fz, *tz, procedure)?,
)),
(&TransformOperation::ScaleX(ref f), &TransformOperation::ScaleX(ref t)) => Ok(
TransformOperation::ScaleX(animate_multiplicative_factor(*f, *t, procedure)?),
),
(&TransformOperation::ScaleY(ref f), &TransformOperation::ScaleY(ref t)) => Ok(
TransformOperation::ScaleY(animate_multiplicative_factor(*f, *t, procedure)?),
),
(&TransformOperation::ScaleZ(ref f), &TransformOperation::ScaleZ(ref t)) => Ok(
TransformOperation::ScaleZ(animate_multiplicative_factor(*f, *t, procedure)?),
),
(
&TransformOperation::Scale(ref fx, ref fy),
&TransformOperation::Scale(ref tx, ref ty),
) => Ok(TransformOperation::Scale(
animate_multiplicative_factor(*fx, *tx, procedure)?,
animate_multiplicative_factor(*fy, *ty, procedure)?,
)),
(
&TransformOperation::Rotate3D(fx, fy, fz, fa),
&TransformOperation::Rotate3D(tx, ty, tz, ta),
) => {
let animated = Rotate::Rotate3D(fx, fy, fz, fa)
.animate(&Rotate::Rotate3D(tx, ty, tz, ta), procedure)?;
let (fx, fy, fz, fa) = ComputedRotate::resolve(&animated);
Ok(TransformOperation::Rotate3D(fx, fy, fz, fa))
},
(&TransformOperation::RotateX(fa), &TransformOperation::RotateX(ta)) => {
Ok(TransformOperation::RotateX(fa.animate(&ta, procedure)?))
},
(&TransformOperation::RotateY(fa), &TransformOperation::RotateY(ta)) => {
Ok(TransformOperation::RotateY(fa.animate(&ta, procedure)?))
},
(&TransformOperation::RotateZ(fa), &TransformOperation::RotateZ(ta)) => {
Ok(TransformOperation::RotateZ(fa.animate(&ta, procedure)?))
},
(&TransformOperation::Rotate(fa), &TransformOperation::Rotate(ta)) => {
Ok(TransformOperation::Rotate(fa.animate(&ta, procedure)?))
},
(&TransformOperation::Rotate(fa), &TransformOperation::RotateZ(ta)) => {
Ok(TransformOperation::Rotate(fa.animate(&ta, procedure)?))
},
(&TransformOperation::RotateZ(fa), &TransformOperation::Rotate(ta)) => {
Ok(TransformOperation::Rotate(fa.animate(&ta, procedure)?))
},
(
&TransformOperation::Perspective(ref fd),
&TransformOperation::Perspective(ref td),
) => {
use crate::values::computed::CSSPixelLength;
use crate::values::generics::transform::create_perspective_matrix;
// From https://drafts.csswg.org/css-transforms-2/#interpolation-of-transform-functions:
//
// The transform functions matrix(), matrix3d() and
// perspective() get converted into 4x4 matrices first and
// interpolated as defined in section Interpolation of
// Matrices afterwards.
//
let from = create_perspective_matrix(fd.infinity_or(|l| l.px()));
let to = create_perspective_matrix(td.infinity_or(|l| l.px()));
let interpolated = Matrix3D::from(from).animate(&Matrix3D::from(to), procedure)?;
let decomposed = decompose_3d_matrix(interpolated)?;
let perspective_z = decomposed.perspective.2;
// Clamp results outside of the -1 to 0 range so that we get perspective
// function values between 1 and infinity.
let used_value = if perspective_z >= 0. {
transform::PerspectiveFunction::None
} else {
transform::PerspectiveFunction::Length(CSSPixelLength::new(
if perspective_z <= -1. {
1.
} else {
-1. / perspective_z
},
))
};
Ok(TransformOperation::Perspective(used_value))
},
_ if self.is_translate() && other.is_translate() => self
.to_translate_3d()
.animate(&other.to_translate_3d(), procedure),
_ if self.is_scale() && other.is_scale() => {
self.to_scale_3d().animate(&other.to_scale_3d(), procedure)
},
_ if self.is_rotate() && other.is_rotate() => self
.to_rotate_3d()
.animate(&other.to_rotate_3d(), procedure),
_ => Err(()),
}
}
}
impl ComputedTransformOperation {
/// If there are no size dependencies, we try to animate in-place, to avoid
/// creating deeply nested Interpolate* operations.
fn try_animate_mismatched_transforms_in_place(
left: &[Self],
right: &[Self],
procedure: Procedure,
) -> Result<Self, ()> {
let (left, _left_3d) = Transform::components_to_transform_3d_matrix(left, None)?;
let (right, _right_3d) = Transform::components_to_transform_3d_matrix(right, None)?;
Ok(Self::Matrix3D(
Matrix3D::from(left).animate(&Matrix3D::from(right), procedure)?,
))
}
fn animate_mismatched_transforms(
left: &[Self],
right: &[Self],
procedure: Procedure,
) -> Result<Self, ()> {
if let Ok(op) = Self::try_animate_mismatched_transforms_in_place(left, right, procedure) {
return Ok(op);
}
let from_list = Transform(left.to_vec().into());
let to_list = Transform(right.to_vec().into());
Ok(match procedure {
Procedure::Add => {
debug_assert!(false, "Addition should've been handled earlier");
return Err(());
},
Procedure::Interpolate { progress } => Self::InterpolateMatrix {
from_list,
to_list,
progress: Percentage(progress as f32),
},
Procedure::Accumulate { count } => Self::AccumulateMatrix {
from_list,
to_list,
count: cmp::min(count, i32::max_value() as u64) as i32,
},
})
}
}
// This might not be the most useful definition of distance. It might be better, for example,
// to trace the distance travelled by a point as its transform is interpolated between the two
// lists. That, however, proves to be quite complicated so we take a simple approach for now.
// See https://bugzilla.mozilla.org/show_bug.cgi?id=1318591#c0.
impl ComputeSquaredDistance for ComputedTransformOperation {
fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> {
match (self, other) {
(&TransformOperation::Matrix3D(ref this), &TransformOperation::Matrix3D(ref other)) => {
this.compute_squared_distance(other)
},
(&TransformOperation::Matrix(ref this), &TransformOperation::Matrix(ref other)) => {
let this: Matrix3D = (*this).into();
let other: Matrix3D = (*other).into();
this.compute_squared_distance(&other)
},
(
&TransformOperation::Skew(ref fx, ref fy),
&TransformOperation::Skew(ref tx, ref ty),
) => Ok(fx.compute_squared_distance(&tx)? + fy.compute_squared_distance(&ty)?),
(&TransformOperation::SkewX(ref f), &TransformOperation::SkewX(ref t)) |
(&TransformOperation::SkewY(ref f), &TransformOperation::SkewY(ref t)) => {
f.compute_squared_distance(&t)
},
(
&TransformOperation::Translate3D(ref fx, ref fy, ref fz),
&TransformOperation::Translate3D(ref tx, ref ty, ref tz),
) => {
// For translate, We don't want to require doing layout in order
// to calculate the result, so drop the percentage part.
//
// However, dropping percentage makes us impossible to compute
// the distance for the percentage-percentage case, but Gecko
// uses the same formula, so it's fine for now.
let basis = Length::new(0.);
let fx = fx.resolve(basis).px();
let fy = fy.resolve(basis).px();
let tx = tx.resolve(basis).px();
let ty = ty.resolve(basis).px();
Ok(fx.compute_squared_distance(&tx)? +
fy.compute_squared_distance(&ty)? +
fz.compute_squared_distance(&tz)?)
},
(
&TransformOperation::Scale3D(ref fx, ref fy, ref fz),
&TransformOperation::Scale3D(ref tx, ref ty, ref tz),
) => Ok(fx.compute_squared_distance(&tx)? +
fy.compute_squared_distance(&ty)? +
fz.compute_squared_distance(&tz)?),
(
&TransformOperation::Rotate3D(fx, fy, fz, fa),
&TransformOperation::Rotate3D(tx, ty, tz, ta),
) => Rotate::Rotate3D(fx, fy, fz, fa)
.compute_squared_distance(&Rotate::Rotate3D(tx, ty, tz, ta)),
(&TransformOperation::RotateX(fa), &TransformOperation::RotateX(ta)) |
(&TransformOperation::RotateY(fa), &TransformOperation::RotateY(ta)) |
(&TransformOperation::RotateZ(fa), &TransformOperation::RotateZ(ta)) |
(&TransformOperation::Rotate(fa), &TransformOperation::Rotate(ta)) => {
fa.compute_squared_distance(&ta)
},
(
&TransformOperation::Perspective(ref fd),
&TransformOperation::Perspective(ref td),
) => fd
.infinity_or(|l| l.px())
.compute_squared_distance(&td.infinity_or(|l| l.px())),
(&TransformOperation::Perspective(ref p), &TransformOperation::Matrix3D(ref m)) |
(&TransformOperation::Matrix3D(ref m), &TransformOperation::Perspective(ref p)) => {
// FIXME(emilio): Is this right? Why interpolating this with
// Perspective but not with anything else?
let mut p_matrix = Matrix3D::identity();
let p = p.infinity_or(|p| p.px());
if p >= 0. {
p_matrix.m34 = -1. / p.max(1.);
}
p_matrix.compute_squared_distance(&m)
},
// Gecko cross-interpolates amongst all translate and all scale
// functions (See ToPrimitive in layout/style/StyleAnimationValue.cpp)
// without falling back to InterpolateMatrix
_ if self.is_translate() && other.is_translate() => self
.to_translate_3d()
.compute_squared_distance(&other.to_translate_3d()),
_ if self.is_scale() && other.is_scale() => self
.to_scale_3d()
.compute_squared_distance(&other.to_scale_3d()),
_ if self.is_rotate() && other.is_rotate() => self
.to_rotate_3d()
.compute_squared_distance(&other.to_rotate_3d()),
_ => Err(()),
}
}
}
// ------------------------------------
// Individual transforms.
// ------------------------------------
/// <https://drafts.csswg.org/css-transforms-2/#propdef-rotate>
impl ComputedRotate {
fn resolve(&self) -> (Number, Number, Number, Angle) {
// According to the spec:
// https://drafts.csswg.org/css-transforms-2/#individual-transforms
//
// If the axis is unspecified, it defaults to "0 0 1"
match *self {
Rotate::None => (0., 0., 1., Angle::zero()),
Rotate::Rotate3D(rx, ry, rz, angle) => (rx, ry, rz, angle),
Rotate::Rotate(angle) => (0., 0., 1., angle),
}
}
}
impl Animate for ComputedRotate {
#[inline]
fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> {
use euclid::approxeq::ApproxEq;
match (self, other) {
(&Rotate::None, &Rotate::None) => Ok(Rotate::None),
(&Rotate::Rotate3D(fx, fy, fz, fa), &Rotate::None) => {
// We always normalize direction vector for rotate3d() first, so we should also
// apply the same rule for rotate property. In other words, we promote none into
// a 3d rotate, and normalize both direction vector first, and then do
// interpolation.
let (fx, fy, fz, fa) = transform::get_normalized_vector_and_angle(fx, fy, fz, fa);
Ok(Rotate::Rotate3D(
fx,
fy,
fz,
fa.animate(&Angle::zero(), procedure)?,
))
},
(&Rotate::None, &Rotate::Rotate3D(tx, ty, tz, ta)) => {
// Normalize direction vector first.
let (tx, ty, tz, ta) = transform::get_normalized_vector_and_angle(tx, ty, tz, ta);
Ok(Rotate::Rotate3D(
tx,
ty,
tz,
Angle::zero().animate(&ta, procedure)?,
))
},
(&Rotate::Rotate3D(_, ..), _) | (_, &Rotate::Rotate3D(_, ..)) => {
// https://drafts.csswg.org/css-transforms-2/#interpolation-of-transform-functions
let (from, to) = (self.resolve(), other.resolve());
// For interpolations with the primitive rotate3d(), the direction vectors of the
// transform functions get normalized first.
let (fx, fy, fz, fa) =
transform::get_normalized_vector_and_angle(from.0, from.1, from.2, from.3);
let (tx, ty, tz, ta) =
transform::get_normalized_vector_and_angle(to.0, to.1, to.2, to.3);
// The rotation angle gets interpolated numerically and the rotation vector of the
// non-zero angle is used or (0, 0, 1) if both angles are zero.
//
// Note: the normalization may get two different vectors because of the
// floating-point precision, so we have to use approx_eq to compare two
// vectors.
let fv = DirectionVector::new(fx, fy, fz);
let tv = DirectionVector::new(tx, ty, tz);
if fa.is_zero() || ta.is_zero() || fv.approx_eq(&tv) {
let (x, y, z) = if fa.is_zero() && ta.is_zero() {
(0., 0., 1.)
} else if fa.is_zero() {
(tx, ty, tz)
} else {
// ta.is_zero() or both vectors are equal.
(fx, fy, fz)
};
return Ok(Rotate::Rotate3D(x, y, z, fa.animate(&ta, procedure)?));
}
// Slerp algorithm doesn't work well for Procedure::Add, which makes both
// |this_weight| and |other_weight| be 1.0, and this may make the cosine value of
// the angle be out of the range (i.e. the 4th component of the quaternion vector).
// (See Quaternion::animate() for more details about the Slerp formula.)
// Therefore, if the cosine value is out of range, we get an NaN after applying
// acos() on it, and so the result is invalid.
// Note: This is specialized for `rotate` property. The addition of `transform`
// property has been handled in `ComputedTransform::animate()` by merging two list
// directly.
let rq = if procedure == Procedure::Add {
// In Transform::animate(), it converts two rotations into transform matrices,
// and do matrix multiplication. This match the spec definition for the
// addition.
// https://drafts.csswg.org/css-transforms-2/#combining-transform-lists
let f = ComputedTransformOperation::Rotate3D(fx, fy, fz, fa);
let t = ComputedTransformOperation::Rotate3D(tx, ty, tz, ta);
let v =
Transform(vec![f].into()).animate(&Transform(vec![t].into()), procedure)?;
let (m, _) = v.to_transform_3d_matrix(None)?;
// Decompose the matrix and retrive the quaternion vector.
decompose_3d_matrix(Matrix3D::from(m))?.quaternion
} else {
// If the normalized vectors are not equal and both rotation angles are
// non-zero the transform functions get converted into 4x4 matrices first and
// interpolated as defined in section Interpolation of Matrices afterwards.
// However, per the spec issue [1], we prefer to converting the rotate3D into
// quaternion vectors directly, and then apply Slerp algorithm.
//
// Both ways should be identical, and converting rotate3D into quaternion
// vectors directly can avoid redundant math operations, e.g. the generation of
// the equivalent matrix3D and the unnecessary decomposition parts of
// translation, scale, skew, and persepctive in the matrix3D.
//
// [1] https://github.com/w3c/csswg-drafts/issues/9278
let fq = Quaternion::from_direction_and_angle(&fv, fa.radians64());
let tq = Quaternion::from_direction_and_angle(&tv, ta.radians64());
Quaternion::animate(&fq, &tq, procedure)?
};
debug_assert!(rq.3 <= 1.0 && rq.3 >= -1.0, "Invalid cosine value");
let (x, y, z, angle) = transform::get_normalized_vector_and_angle(
rq.0 as f32,
rq.1 as f32,
rq.2 as f32,
rq.3.acos() as f32 * 2.0,
);
Ok(Rotate::Rotate3D(x, y, z, Angle::from_radians(angle)))
},
(&Rotate::Rotate(_), _) | (_, &Rotate::Rotate(_)) => {
// If this is a 2D rotation, we just animate the <angle>
let (from, to) = (self.resolve().3, other.resolve().3);
Ok(Rotate::Rotate(from.animate(&to, procedure)?))
},
}
}
}
impl ComputeSquaredDistance for ComputedRotate {
#[inline]
fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> {
use euclid::approxeq::ApproxEq;
match (self, other) {
(&Rotate::None, &Rotate::None) => Ok(SquaredDistance::from_sqrt(0.)),
(&Rotate::Rotate3D(_, _, _, a), &Rotate::None) |
(&Rotate::None, &Rotate::Rotate3D(_, _, _, a)) => {
a.compute_squared_distance(&Angle::zero())
},
(&Rotate::Rotate3D(_, ..), _) | (_, &Rotate::Rotate3D(_, ..)) => {
let (from, to) = (self.resolve(), other.resolve());
let (mut fx, mut fy, mut fz, angle1) =
transform::get_normalized_vector_and_angle(from.0, from.1, from.2, from.3);
let (mut tx, mut ty, mut tz, angle2) =
transform::get_normalized_vector_and_angle(to.0, to.1, to.2, to.3);
if angle1.is_zero() && angle2.is_zero() {
(fx, fy, fz) = (0., 0., 1.);
(tx, ty, tz) = (0., 0., 1.);
} else if angle1.is_zero() {
(fx, fy, fz) = (tx, ty, tz);
} else if angle2.is_zero() {
(tx, ty, tz) = (fx, fy, fz);
}
let v1 = DirectionVector::new(fx, fy, fz);
let v2 = DirectionVector::new(tx, ty, tz);
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