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author | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-04-19 00:47:55 +0000 |
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committer | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-04-19 00:47:55 +0000 |
commit | 26a029d407be480d791972afb5975cf62c9360a6 (patch) | |
tree | f435a8308119effd964b339f76abb83a57c29483 /servo/components/style/values/animated/transform.rs | |
parent | Initial commit. (diff) | |
download | firefox-26a029d407be480d791972afb5975cf62c9360a6.tar.xz firefox-26a029d407be480d791972afb5975cf62c9360a6.zip |
Adding upstream version 124.0.1.upstream/124.0.1
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'servo/components/style/values/animated/transform.rs')
-rw-r--r-- | servo/components/style/values/animated/transform.rs | 1667 |
1 files changed, 1667 insertions, 0 deletions
diff --git a/servo/components/style/values/animated/transform.rs b/servo/components/style/values/animated/transform.rs new file mode 100644 index 0000000000..b91e3ed8bc --- /dev/null +++ b/servo/components/style/values/animated/transform.rs @@ -0,0 +1,1667 @@ +/* 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 ComputedTransformOperation; +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); + if v1.approx_eq(&v2) { + angle1.compute_squared_distance(&angle2) + } else { + let q1 = Quaternion::from_direction_and_angle(&v1, angle1.radians64()); + let q2 = Quaternion::from_direction_and_angle(&v2, angle2.radians64()); + q1.compute_squared_distance(&q2) + } + }, + (&Rotate::Rotate(_), _) | (_, &Rotate::Rotate(_)) => self + .resolve() + .3 + .compute_squared_distance(&other.resolve().3), + } + } +} + +/// <https://drafts.csswg.org/css-transforms-2/#propdef-translate> +impl ComputedTranslate { + fn resolve(&self) -> (LengthPercentage, LengthPercentage, Length) { + // According to the spec: + // https://drafts.csswg.org/css-transforms-2/#individual-transforms + // + // Unspecified translations default to 0px + match *self { + Translate::None => ( + LengthPercentage::zero(), + LengthPercentage::zero(), + Length::zero(), + ), + Translate::Translate(ref tx, ref ty, ref tz) => (tx.clone(), ty.clone(), tz.clone()), + } + } +} + +impl Animate for ComputedTranslate { + #[inline] + fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> { + match (self, other) { + (&Translate::None, &Translate::None) => Ok(Translate::None), + (&Translate::Translate(_, ..), _) | (_, &Translate::Translate(_, ..)) => { + let (from, to) = (self.resolve(), other.resolve()); + Ok(Translate::Translate( + from.0.animate(&to.0, procedure)?, + from.1.animate(&to.1, procedure)?, + from.2.animate(&to.2, procedure)?, + )) + }, + } + } +} + +impl ComputeSquaredDistance for ComputedTranslate { + #[inline] + fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> { + let (from, to) = (self.resolve(), other.resolve()); + Ok(from.0.compute_squared_distance(&to.0)? + + from.1.compute_squared_distance(&to.1)? + + from.2.compute_squared_distance(&to.2)?) + } +} + +/// <https://drafts.csswg.org/css-transforms-2/#propdef-scale> +impl ComputedScale { + fn resolve(&self) -> (Number, Number, Number) { + // According to the spec: + // https://drafts.csswg.org/css-transforms-2/#individual-transforms + // + // Unspecified scales default to 1 + match *self { + Scale::None => (1.0, 1.0, 1.0), + Scale::Scale(sx, sy, sz) => (sx, sy, sz), + } + } +} + +impl Animate for ComputedScale { + #[inline] + fn animate(&self, other: &Self, procedure: Procedure) -> Result<Self, ()> { + match (self, other) { + (&Scale::None, &Scale::None) => Ok(Scale::None), + (&Scale::Scale(_, ..), _) | (_, &Scale::Scale(_, ..)) => { + let (from, to) = (self.resolve(), other.resolve()); + // For transform lists, we add by appending to the list of + // transform functions. However, ComputedScale cannot be + // simply concatenated, so we have to calculate the additive + // result here. + if procedure == Procedure::Add { + // scale(x1,y1,z1)*scale(x2,y2,z2) = scale(x1*x2, y1*y2, z1*z2) + return Ok(Scale::Scale(from.0 * to.0, from.1 * to.1, from.2 * to.2)); + } + Ok(Scale::Scale( + animate_multiplicative_factor(from.0, to.0, procedure)?, + animate_multiplicative_factor(from.1, to.1, procedure)?, + animate_multiplicative_factor(from.2, to.2, procedure)?, + )) + }, + } + } +} + +impl ComputeSquaredDistance for ComputedScale { + #[inline] + fn compute_squared_distance(&self, other: &Self) -> Result<SquaredDistance, ()> { + let (from, to) = (self.resolve(), other.resolve()); + Ok(from.0.compute_squared_distance(&to.0)? + + from.1.compute_squared_distance(&to.1)? + + from.2.compute_squared_distance(&to.2)?) + } +} |