// Copyright 2013 The Servo Project Developers. See the COPYRIGHT // file at the top-level directory of this distribution. // // Licensed under the Apache License, Version 2.0 or the MIT license // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. #![cfg_attr(feature = "cargo-clippy", allow(just_underscores_and_digits))] use super::{UnknownUnit, Angle}; use crate::approxeq::ApproxEq; use crate::homogen::HomogeneousVector; #[cfg(feature = "mint")] use mint; use crate::trig::Trig; use crate::point::{Point2D, point2, Point3D, point3}; use crate::vector::{Vector2D, Vector3D, vec2, vec3}; use crate::rect::Rect; use crate::box2d::Box2D; use crate::box3d::Box3D; use crate::transform2d::Transform2D; use crate::scale::Scale; use crate::num::{One, Zero}; use core::ops::{Add, Mul, Sub, Div, Neg}; use core::marker::PhantomData; use core::fmt; use core::cmp::{Eq, PartialEq}; use core::hash::{Hash}; use num_traits::NumCast; #[cfg(feature = "serde")] use serde::{Deserialize, Serialize}; #[cfg(feature = "bytemuck")] use bytemuck::{Zeroable, Pod}; /// A 3d transform stored as a column-major 4 by 4 matrix. /// /// Transforms can be parametrized over the source and destination units, to describe a /// transformation from a space to another. /// For example, `Transform3D::transform_point3d` /// takes a `Point3D` and returns a `Point3D`. /// /// Transforms expose a set of convenience methods for pre- and post-transformations. /// Pre-transformations (`pre_*` methods) correspond to adding an operation that is /// applied before the rest of the transformation, while post-transformations (`then_*` /// methods) add an operation that is applied after. /// /// When translating Transform3D into general matrix representations, consider that the /// representation follows the column major notation with column vectors. /// /// ```text /// |x'| | m11 m12 m13 m14 | |x| /// |y'| | m21 m22 m23 m24 | |y| /// |z'| = | m31 m32 m33 m34 | x |y| /// |w | | m41 m42 m43 m44 | |1| /// ``` /// /// The translation terms are m41, m42 and m43. #[repr(C)] #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))] #[cfg_attr( feature = "serde", serde(bound(serialize = "T: Serialize", deserialize = "T: Deserialize<'de>")) )] pub struct Transform3D { pub m11: T, pub m12: T, pub m13: T, pub m14: T, pub m21: T, pub m22: T, pub m23: T, pub m24: T, pub m31: T, pub m32: T, pub m33: T, pub m34: T, pub m41: T, pub m42: T, pub m43: T, pub m44: T, #[doc(hidden)] pub _unit: PhantomData<(Src, Dst)>, } #[cfg(feature = "arbitrary")] impl<'a, T, Src, Dst> arbitrary::Arbitrary<'a> for Transform3D where T: arbitrary::Arbitrary<'a>, { fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result { let (m11, m12, m13, m14) = arbitrary::Arbitrary::arbitrary(u)?; let (m21, m22, m23, m24) = arbitrary::Arbitrary::arbitrary(u)?; let (m31, m32, m33, m34) = arbitrary::Arbitrary::arbitrary(u)?; let (m41, m42, m43, m44) = arbitrary::Arbitrary::arbitrary(u)?; Ok(Transform3D { m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44, _unit: PhantomData, }) } } #[cfg(feature = "bytemuck")] unsafe impl Zeroable for Transform3D {} #[cfg(feature = "bytemuck")] unsafe impl Pod for Transform3D {} impl Copy for Transform3D {} impl Clone for Transform3D { fn clone(&self) -> Self { Transform3D { m11: self.m11.clone(), m12: self.m12.clone(), m13: self.m13.clone(), m14: self.m14.clone(), m21: self.m21.clone(), m22: self.m22.clone(), m23: self.m23.clone(), m24: self.m24.clone(), m31: self.m31.clone(), m32: self.m32.clone(), m33: self.m33.clone(), m34: self.m34.clone(), m41: self.m41.clone(), m42: self.m42.clone(), m43: self.m43.clone(), m44: self.m44.clone(), _unit: PhantomData, } } } impl Eq for Transform3D where T: Eq {} impl PartialEq for Transform3D where T: PartialEq { fn eq(&self, other: &Self) -> bool { self.m11 == other.m11 && self.m12 == other.m12 && self.m13 == other.m13 && self.m14 == other.m14 && self.m21 == other.m21 && self.m22 == other.m22 && self.m23 == other.m23 && self.m24 == other.m24 && self.m31 == other.m31 && self.m32 == other.m32 && self.m33 == other.m33 && self.m34 == other.m34 && self.m41 == other.m41 && self.m42 == other.m42 && self.m43 == other.m43 && self.m44 == other.m44 } } impl Hash for Transform3D where T: Hash { fn hash(&self, h: &mut H) { self.m11.hash(h); self.m12.hash(h); self.m13.hash(h); self.m14.hash(h); self.m21.hash(h); self.m22.hash(h); self.m23.hash(h); self.m24.hash(h); self.m31.hash(h); self.m32.hash(h); self.m33.hash(h); self.m34.hash(h); self.m41.hash(h); self.m42.hash(h); self.m43.hash(h); self.m44.hash(h); } } impl Transform3D { /// Create a transform specifying all of it's component as a 4 by 4 matrix. /// /// Components are specified following column-major-column-vector matrix notation. /// For example, the translation terms m41, m42, m43 are the 13rd, 14th and 15th parameters. /// /// ``` /// use euclid::default::Transform3D; /// let tx = 1.0; /// let ty = 2.0; /// let tz = 3.0; /// let translation = Transform3D::new( /// 1.0, 0.0, 0.0, 0.0, /// 0.0, 1.0, 0.0, 0.0, /// 0.0, 0.0, 1.0, 0.0, /// tx, ty, tz, 1.0, /// ); /// ``` #[inline] #[cfg_attr(feature = "cargo-clippy", allow(too_many_arguments))] pub const fn new( m11: T, m12: T, m13: T, m14: T, m21: T, m22: T, m23: T, m24: T, m31: T, m32: T, m33: T, m34: T, m41: T, m42: T, m43: T, m44: T, ) -> Self { Transform3D { m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44, _unit: PhantomData, } } /// Create a transform representing a 2d transformation from the components /// of a 2 by 3 matrix transformation. /// /// Components follow the column-major-column-vector notation (m41 and m42 /// representating the translation terms). /// /// ```text /// m11 m12 0 0 /// m21 m22 0 0 /// 0 0 1 0 /// m41 m42 0 1 /// ``` #[inline] pub fn new_2d(m11: T, m12: T, m21: T, m22: T, m41: T, m42: T) -> Self where T: Zero + One, { let _0 = || T::zero(); let _1 = || T::one(); Self::new( m11, m12, _0(), _0(), m21, m22, _0(), _0(), _0(), _0(), _1(), _0(), m41, m42, _0(), _1() ) } /// Returns `true` if this transform can be represented with a `Transform2D`. /// /// See #[inline] pub fn is_2d(&self) -> bool where T: Zero + One + PartialEq, { let (_0, _1): (T, T) = (Zero::zero(), One::one()); self.m31 == _0 && self.m32 == _0 && self.m13 == _0 && self.m23 == _0 && self.m43 == _0 && self.m14 == _0 && self.m24 == _0 && self.m34 == _0 && self.m33 == _1 && self.m44 == _1 } } impl Transform3D { /// Returns an array containing this transform's terms. /// /// The terms are laid out in the same order as they are /// specified in `Transform3D::new`, that is following the /// column-major-column-vector matrix notation. /// /// For example the translation terms are found on the /// 13th, 14th and 15th slots of the array. #[inline] pub fn to_array(&self) -> [T; 16] { [ self.m11, self.m12, self.m13, self.m14, self.m21, self.m22, self.m23, self.m24, self.m31, self.m32, self.m33, self.m34, self.m41, self.m42, self.m43, self.m44 ] } /// Returns an array containing this transform's terms transposed. /// /// The terms are laid out in transposed order from the same order of /// `Transform3D::new` and `Transform3D::to_array`, that is following /// the row-major-column-vector matrix notation. /// /// For example the translation terms are found at indices 3, 7 and 11 /// of the array. #[inline] pub fn to_array_transposed(&self) -> [T; 16] { [ self.m11, self.m21, self.m31, self.m41, self.m12, self.m22, self.m32, self.m42, self.m13, self.m23, self.m33, self.m43, self.m14, self.m24, self.m34, self.m44 ] } /// Equivalent to `to_array` with elements packed four at a time /// in an array of arrays. #[inline] pub fn to_arrays(&self) -> [[T; 4]; 4] { [ [self.m11, self.m12, self.m13, self.m14], [self.m21, self.m22, self.m23, self.m24], [self.m31, self.m32, self.m33, self.m34], [self.m41, self.m42, self.m43, self.m44] ] } /// Equivalent to `to_array_transposed` with elements packed /// four at a time in an array of arrays. #[inline] pub fn to_arrays_transposed(&self) -> [[T; 4]; 4] { [ [self.m11, self.m21, self.m31, self.m41], [self.m12, self.m22, self.m32, self.m42], [self.m13, self.m23, self.m33, self.m43], [self.m14, self.m24, self.m34, self.m44] ] } /// Create a transform providing its components via an array /// of 16 elements instead of as individual parameters. /// /// The order of the components corresponds to the /// column-major-column-vector matrix notation (the same order /// as `Transform3D::new`). #[inline] pub fn from_array(array: [T; 16]) -> Self { Self::new( array[0], array[1], array[2], array[3], array[4], array[5], array[6], array[7], array[8], array[9], array[10], array[11], array[12], array[13], array[14], array[15], ) } /// Equivalent to `from_array` with elements packed four at a time /// in an array of arrays. /// /// The order of the components corresponds to the /// column-major-column-vector matrix notation (the same order /// as `Transform3D::new`). #[inline] pub fn from_arrays(array: [[T; 4]; 4]) -> Self { Self::new( array[0][0], array[0][1], array[0][2], array[0][3], array[1][0], array[1][1], array[1][2], array[1][3], array[2][0], array[2][1], array[2][2], array[2][3], array[3][0], array[3][1], array[3][2], array[3][3], ) } /// Tag a unitless value with units. #[inline] pub fn from_untyped(m: &Transform3D) -> Self { Transform3D::new( m.m11, m.m12, m.m13, m.m14, m.m21, m.m22, m.m23, m.m24, m.m31, m.m32, m.m33, m.m34, m.m41, m.m42, m.m43, m.m44, ) } /// Drop the units, preserving only the numeric value. #[inline] pub fn to_untyped(&self) -> Transform3D { Transform3D::new( self.m11, self.m12, self.m13, self.m14, self.m21, self.m22, self.m23, self.m24, self.m31, self.m32, self.m33, self.m34, self.m41, self.m42, self.m43, self.m44, ) } /// Returns the same transform with a different source unit. #[inline] pub fn with_source(&self) -> Transform3D { Transform3D::new( self.m11, self.m12, self.m13, self.m14, self.m21, self.m22, self.m23, self.m24, self.m31, self.m32, self.m33, self.m34, self.m41, self.m42, self.m43, self.m44, ) } /// Returns the same transform with a different destination unit. #[inline] pub fn with_destination(&self) -> Transform3D { Transform3D::new( self.m11, self.m12, self.m13, self.m14, self.m21, self.m22, self.m23, self.m24, self.m31, self.m32, self.m33, self.m34, self.m41, self.m42, self.m43, self.m44, ) } /// Create a 2D transform picking the relevant terms from this transform. /// /// This method assumes that self represents a 2d transformation, callers /// should check that [`self.is_2d()`] returns `true` beforehand. /// /// [`self.is_2d()`]: #method.is_2d pub fn to_2d(&self) -> Transform2D { Transform2D::new( self.m11, self.m12, self.m21, self.m22, self.m41, self.m42 ) } } impl Transform3D where T: Zero + One, { /// Creates an identity matrix: /// /// ```text /// 1 0 0 0 /// 0 1 0 0 /// 0 0 1 0 /// 0 0 0 1 /// ``` #[inline] pub fn identity() -> Self { Self::translation(T::zero(), T::zero(), T::zero()) } /// Intentional not public, because it checks for exact equivalence /// while most consumers will probably want some sort of approximate /// equivalence to deal with floating-point errors. #[inline] fn is_identity(&self) -> bool where T: PartialEq, { *self == Self::identity() } /// Create a 2d skew transform. /// /// See pub fn skew(alpha: Angle, beta: Angle) -> Self where T: Trig, { let _0 = || T::zero(); let _1 = || T::one(); let (sx, sy) = (beta.radians.tan(), alpha.radians.tan()); Self::new( _1(), sx, _0(), _0(), sy, _1(), _0(), _0(), _0(), _0(), _1(), _0(), _0(), _0(), _0(), _1(), ) } /// Create a simple perspective transform, projecting to the plane `z = -d`. /// /// ```text /// 1 0 0 0 /// 0 1 0 0 /// 0 0 1 -1/d /// 0 0 0 1 /// ``` /// /// See . pub fn perspective(d: T) -> Self where T: Neg + Div, { let _0 = || T::zero(); let _1 = || T::one(); Self::new( _1(), _0(), _0(), _0(), _0(), _1(), _0(), _0(), _0(), _0(), _1(), -_1() / d, _0(), _0(), _0(), _1(), ) } } /// Methods for combining generic transformations impl Transform3D where T: Copy + Add + Mul, { /// Returns the multiplication of the two matrices such that mat's transformation /// applies after self's transformation. /// /// Assuming row vectors, this is equivalent to self * mat #[must_use] pub fn then(&self, other: &Transform3D) -> Transform3D { Transform3D::new( self.m11 * other.m11 + self.m12 * other.m21 + self.m13 * other.m31 + self.m14 * other.m41, self.m11 * other.m12 + self.m12 * other.m22 + self.m13 * other.m32 + self.m14 * other.m42, self.m11 * other.m13 + self.m12 * other.m23 + self.m13 * other.m33 + self.m14 * other.m43, self.m11 * other.m14 + self.m12 * other.m24 + self.m13 * other.m34 + self.m14 * other.m44, self.m21 * other.m11 + self.m22 * other.m21 + self.m23 * other.m31 + self.m24 * other.m41, self.m21 * other.m12 + self.m22 * other.m22 + self.m23 * other.m32 + self.m24 * other.m42, self.m21 * other.m13 + self.m22 * other.m23 + self.m23 * other.m33 + self.m24 * other.m43, self.m21 * other.m14 + self.m22 * other.m24 + self.m23 * other.m34 + self.m24 * other.m44, self.m31 * other.m11 + self.m32 * other.m21 + self.m33 * other.m31 + self.m34 * other.m41, self.m31 * other.m12 + self.m32 * other.m22 + self.m33 * other.m32 + self.m34 * other.m42, self.m31 * other.m13 + self.m32 * other.m23 + self.m33 * other.m33 + self.m34 * other.m43, self.m31 * other.m14 + self.m32 * other.m24 + self.m33 * other.m34 + self.m34 * other.m44, self.m41 * other.m11 + self.m42 * other.m21 + self.m43 * other.m31 + self.m44 * other.m41, self.m41 * other.m12 + self.m42 * other.m22 + self.m43 * other.m32 + self.m44 * other.m42, self.m41 * other.m13 + self.m42 * other.m23 + self.m43 * other.m33 + self.m44 * other.m43, self.m41 * other.m14 + self.m42 * other.m24 + self.m43 * other.m34 + self.m44 * other.m44, ) } } /// Methods for creating and combining translation transformations impl Transform3D where T: Zero + One, { /// Create a 3d translation transform: /// /// ```text /// 1 0 0 0 /// 0 1 0 0 /// 0 0 1 0 /// x y z 1 /// ``` #[inline] pub fn translation(x: T, y: T, z: T) -> Self { let _0 = || T::zero(); let _1 = || T::one(); Self::new( _1(), _0(), _0(), _0(), _0(), _1(), _0(), _0(), _0(), _0(), _1(), _0(), x, y, z, _1(), ) } /// Returns a transform with a translation applied before self's transformation. #[must_use] pub fn pre_translate(&self, v: Vector3D) -> Self where T: Copy + Add + Mul, { Transform3D::translation(v.x, v.y, v.z).then(self) } /// Returns a transform with a translation applied after self's transformation. #[must_use] pub fn then_translate(&self, v: Vector3D) -> Self where T: Copy + Add + Mul, { self.then(&Transform3D::translation(v.x, v.y, v.z)) } } /// Methods for creating and combining rotation transformations impl Transform3D where T: Copy + Add + Sub + Mul + Div + Zero + One + Trig, { /// Create a 3d rotation transform from an angle / axis. /// The supplied axis must be normalized. pub fn rotation(x: T, y: T, z: T, theta: Angle) -> Self { let (_0, _1): (T, T) = (Zero::zero(), One::one()); let _2 = _1 + _1; let xx = x * x; let yy = y * y; let zz = z * z; let half_theta = theta.get() / _2; let sc = half_theta.sin() * half_theta.cos(); let sq = half_theta.sin() * half_theta.sin(); Transform3D::new( _1 - _2 * (yy + zz) * sq, _2 * (x * y * sq + z * sc), _2 * (x * z * sq - y * sc), _0, _2 * (x * y * sq - z * sc), _1 - _2 * (xx + zz) * sq, _2 * (y * z * sq + x * sc), _0, _2 * (x * z * sq + y * sc), _2 * (y * z * sq - x * sc), _1 - _2 * (xx + yy) * sq, _0, _0, _0, _0, _1 ) } /// Returns a transform with a rotation applied after self's transformation. #[must_use] pub fn then_rotate(&self, x: T, y: T, z: T, theta: Angle) -> Self { self.then(&Transform3D::rotation(x, y, z, theta)) } /// Returns a transform with a rotation applied before self's transformation. #[must_use] pub fn pre_rotate(&self, x: T, y: T, z: T, theta: Angle) -> Self { Transform3D::rotation(x, y, z, theta).then(self) } } /// Methods for creating and combining scale transformations impl Transform3D where T: Zero + One, { /// Create a 3d scale transform: /// /// ```text /// x 0 0 0 /// 0 y 0 0 /// 0 0 z 0 /// 0 0 0 1 /// ``` #[inline] pub fn scale(x: T, y: T, z: T) -> Self { let _0 = || T::zero(); let _1 = || T::one(); Self::new( x, _0(), _0(), _0(), _0(), y, _0(), _0(), _0(), _0(), z, _0(), _0(), _0(), _0(), _1(), ) } /// Returns a transform with a scale applied before self's transformation. #[must_use] pub fn pre_scale(&self, x: T, y: T, z: T) -> Self where T: Copy + Add + Mul, { Transform3D::new( self.m11 * x, self.m12 * x, self.m13 * x, self.m14 * x, self.m21 * y, self.m22 * y, self.m23 * y, self.m24 * y, self.m31 * z, self.m32 * z, self.m33 * z, self.m34 * z, self.m41 , self.m42, self.m43, self.m44 ) } /// Returns a transform with a scale applied after self's transformation. #[must_use] pub fn then_scale(&self, x: T, y: T, z: T) -> Self where T: Copy + Add + Mul, { self.then(&Transform3D::scale(x, y, z)) } } /// Methods for apply transformations to objects impl Transform3D where T: Copy + Add + Mul, { /// Returns the homogeneous vector corresponding to the transformed 2d point. /// /// The input point must be use the unit Src, and the returned point has the unit Dst. #[inline] pub fn transform_point2d_homogeneous( &self, p: Point2D ) -> HomogeneousVector { let x = p.x * self.m11 + p.y * self.m21 + self.m41; let y = p.x * self.m12 + p.y * self.m22 + self.m42; let z = p.x * self.m13 + p.y * self.m23 + self.m43; let w = p.x * self.m14 + p.y * self.m24 + self.m44; HomogeneousVector::new(x, y, z, w) } /// Returns the given 2d point transformed by this transform, if the transform makes sense, /// or `None` otherwise. /// /// The input point must be use the unit Src, and the returned point has the unit Dst. #[inline] pub fn transform_point2d(&self, p: Point2D) -> Option> where T: Div + Zero + PartialOrd, { //Note: could use `transform_point2d_homogeneous()` but it would waste the calculus of `z` let w = p.x * self.m14 + p.y * self.m24 + self.m44; if w > T::zero() { let x = p.x * self.m11 + p.y * self.m21 + self.m41; let y = p.x * self.m12 + p.y * self.m22 + self.m42; Some(Point2D::new(x / w, y / w)) } else { None } } /// Returns the given 2d vector transformed by this matrix. /// /// The input point must be use the unit Src, and the returned point has the unit Dst. #[inline] pub fn transform_vector2d(&self, v: Vector2D) -> Vector2D { vec2( v.x * self.m11 + v.y * self.m21, v.x * self.m12 + v.y * self.m22, ) } /// Returns the homogeneous vector corresponding to the transformed 3d point. /// /// The input point must be use the unit Src, and the returned point has the unit Dst. #[inline] pub fn transform_point3d_homogeneous( &self, p: Point3D ) -> HomogeneousVector { let x = p.x * self.m11 + p.y * self.m21 + p.z * self.m31 + self.m41; let y = p.x * self.m12 + p.y * self.m22 + p.z * self.m32 + self.m42; let z = p.x * self.m13 + p.y * self.m23 + p.z * self.m33 + self.m43; let w = p.x * self.m14 + p.y * self.m24 + p.z * self.m34 + self.m44; HomogeneousVector::new(x, y, z, w) } /// Returns the given 3d point transformed by this transform, if the transform makes sense, /// or `None` otherwise. /// /// The input point must be use the unit Src, and the returned point has the unit Dst. #[inline] pub fn transform_point3d(&self, p: Point3D) -> Option> where T: Div + Zero + PartialOrd, { self.transform_point3d_homogeneous(p).to_point3d() } /// Returns the given 3d vector transformed by this matrix. /// /// The input point must be use the unit Src, and the returned point has the unit Dst. #[inline] pub fn transform_vector3d(&self, v: Vector3D) -> Vector3D { vec3( v.x * self.m11 + v.y * self.m21 + v.z * self.m31, v.x * self.m12 + v.y * self.m22 + v.z * self.m32, v.x * self.m13 + v.y * self.m23 + v.z * self.m33, ) } /// Returns a rectangle that encompasses the result of transforming the given rectangle by this /// transform, if the transform makes sense for it, or `None` otherwise. pub fn outer_transformed_rect(&self, rect: &Rect) -> Option> where T: Sub + Div + Zero + PartialOrd, { let min = rect.min(); let max = rect.max(); Some(Rect::from_points(&[ self.transform_point2d(min)?, self.transform_point2d(max)?, self.transform_point2d(point2(max.x, min.y))?, self.transform_point2d(point2(min.x, max.y))?, ])) } /// Returns a 2d box that encompasses the result of transforming the given box by this /// transform, if the transform makes sense for it, or `None` otherwise. pub fn outer_transformed_box2d(&self, b: &Box2D) -> Option> where T: Sub + Div + Zero + PartialOrd, { Some(Box2D::from_points(&[ self.transform_point2d(b.min)?, self.transform_point2d(b.max)?, self.transform_point2d(point2(b.max.x, b.min.y))?, self.transform_point2d(point2(b.min.x, b.max.y))?, ])) } /// Returns a 3d box that encompasses the result of transforming the given box by this /// transform, if the transform makes sense for it, or `None` otherwise. pub fn outer_transformed_box3d(&self, b: &Box3D) -> Option> where T: Sub + Div + Zero + PartialOrd, { Some(Box3D::from_points(&[ self.transform_point3d(point3(b.min.x, b.min.y, b.min.z))?, self.transform_point3d(point3(b.min.x, b.min.y, b.max.z))?, self.transform_point3d(point3(b.min.x, b.max.y, b.min.z))?, self.transform_point3d(point3(b.min.x, b.max.y, b.max.z))?, self.transform_point3d(point3(b.max.x, b.min.y, b.min.z))?, self.transform_point3d(point3(b.max.x, b.min.y, b.max.z))?, self.transform_point3d(point3(b.max.x, b.max.y, b.min.z))?, self.transform_point3d(point3(b.max.x, b.max.y, b.max.z))?, ])) } } impl Transform3D where T: Copy + Add + Sub + Mul + Div + Neg + PartialOrd + One + Zero { /// Create an orthogonal projection transform. pub fn ortho(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Self { let tx = -((right + left) / (right - left)); let ty = -((top + bottom) / (top - bottom)); let tz = -((far + near) / (far - near)); let (_0, _1): (T, T) = (Zero::zero(), One::one()); let _2 = _1 + _1; Transform3D::new( _2 / (right - left), _0 , _0 , _0, _0 , _2 / (top - bottom), _0 , _0, _0 , _0 , -_2 / (far - near), _0, tx , ty , tz , _1 ) } /// Check whether shapes on the XY plane with Z pointing towards the /// screen transformed by this matrix would be facing back. pub fn is_backface_visible(&self) -> bool { // inverse().m33 < 0; let det = self.determinant(); let m33 = self.m12 * self.m24 * self.m41 - self.m14 * self.m22 * self.m41 + self.m14 * self.m21 * self.m42 - self.m11 * self.m24 * self.m42 - self.m12 * self.m21 * self.m44 + self.m11 * self.m22 * self.m44; let _0: T = Zero::zero(); (m33 * det) < _0 } /// Returns whether it is possible to compute the inverse transform. #[inline] pub fn is_invertible(&self) -> bool { self.determinant() != Zero::zero() } /// Returns the inverse transform if possible. pub fn inverse(&self) -> Option> { let det = self.determinant(); if det == Zero::zero() { return None; } // todo(gw): this could be made faster by special casing // for simpler transform types. let m = Transform3D::new( self.m23*self.m34*self.m42 - self.m24*self.m33*self.m42 + self.m24*self.m32*self.m43 - self.m22*self.m34*self.m43 - self.m23*self.m32*self.m44 + self.m22*self.m33*self.m44, self.m14*self.m33*self.m42 - self.m13*self.m34*self.m42 - self.m14*self.m32*self.m43 + self.m12*self.m34*self.m43 + self.m13*self.m32*self.m44 - self.m12*self.m33*self.m44, self.m13*self.m24*self.m42 - self.m14*self.m23*self.m42 + self.m14*self.m22*self.m43 - self.m12*self.m24*self.m43 - self.m13*self.m22*self.m44 + self.m12*self.m23*self.m44, self.m14*self.m23*self.m32 - self.m13*self.m24*self.m32 - self.m14*self.m22*self.m33 + self.m12*self.m24*self.m33 + self.m13*self.m22*self.m34 - self.m12*self.m23*self.m34, self.m24*self.m33*self.m41 - self.m23*self.m34*self.m41 - self.m24*self.m31*self.m43 + self.m21*self.m34*self.m43 + self.m23*self.m31*self.m44 - self.m21*self.m33*self.m44, self.m13*self.m34*self.m41 - self.m14*self.m33*self.m41 + self.m14*self.m31*self.m43 - self.m11*self.m34*self.m43 - self.m13*self.m31*self.m44 + self.m11*self.m33*self.m44, self.m14*self.m23*self.m41 - self.m13*self.m24*self.m41 - self.m14*self.m21*self.m43 + self.m11*self.m24*self.m43 + self.m13*self.m21*self.m44 - self.m11*self.m23*self.m44, self.m13*self.m24*self.m31 - self.m14*self.m23*self.m31 + self.m14*self.m21*self.m33 - self.m11*self.m24*self.m33 - self.m13*self.m21*self.m34 + self.m11*self.m23*self.m34, self.m22*self.m34*self.m41 - self.m24*self.m32*self.m41 + self.m24*self.m31*self.m42 - self.m21*self.m34*self.m42 - self.m22*self.m31*self.m44 + self.m21*self.m32*self.m44, self.m14*self.m32*self.m41 - self.m12*self.m34*self.m41 - self.m14*self.m31*self.m42 + self.m11*self.m34*self.m42 + self.m12*self.m31*self.m44 - self.m11*self.m32*self.m44, self.m12*self.m24*self.m41 - self.m14*self.m22*self.m41 + self.m14*self.m21*self.m42 - self.m11*self.m24*self.m42 - self.m12*self.m21*self.m44 + self.m11*self.m22*self.m44, self.m14*self.m22*self.m31 - self.m12*self.m24*self.m31 - self.m14*self.m21*self.m32 + self.m11*self.m24*self.m32 + self.m12*self.m21*self.m34 - self.m11*self.m22*self.m34, self.m23*self.m32*self.m41 - self.m22*self.m33*self.m41 - self.m23*self.m31*self.m42 + self.m21*self.m33*self.m42 + self.m22*self.m31*self.m43 - self.m21*self.m32*self.m43, self.m12*self.m33*self.m41 - self.m13*self.m32*self.m41 + self.m13*self.m31*self.m42 - self.m11*self.m33*self.m42 - self.m12*self.m31*self.m43 + self.m11*self.m32*self.m43, self.m13*self.m22*self.m41 - self.m12*self.m23*self.m41 - self.m13*self.m21*self.m42 + self.m11*self.m23*self.m42 + self.m12*self.m21*self.m43 - self.m11*self.m22*self.m43, self.m12*self.m23*self.m31 - self.m13*self.m22*self.m31 + self.m13*self.m21*self.m32 - self.m11*self.m23*self.m32 - self.m12*self.m21*self.m33 + self.m11*self.m22*self.m33 ); let _1: T = One::one(); Some(m.mul_s(_1 / det)) } /// Compute the determinant of the transform. pub fn determinant(&self) -> T { self.m14 * self.m23 * self.m32 * self.m41 - self.m13 * self.m24 * self.m32 * self.m41 - self.m14 * self.m22 * self.m33 * self.m41 + self.m12 * self.m24 * self.m33 * self.m41 + self.m13 * self.m22 * self.m34 * self.m41 - self.m12 * self.m23 * self.m34 * self.m41 - self.m14 * self.m23 * self.m31 * self.m42 + self.m13 * self.m24 * self.m31 * self.m42 + self.m14 * self.m21 * self.m33 * self.m42 - self.m11 * self.m24 * self.m33 * self.m42 - self.m13 * self.m21 * self.m34 * self.m42 + self.m11 * self.m23 * self.m34 * self.m42 + self.m14 * self.m22 * self.m31 * self.m43 - self.m12 * self.m24 * self.m31 * self.m43 - self.m14 * self.m21 * self.m32 * self.m43 + self.m11 * self.m24 * self.m32 * self.m43 + self.m12 * self.m21 * self.m34 * self.m43 - self.m11 * self.m22 * self.m34 * self.m43 - self.m13 * self.m22 * self.m31 * self.m44 + self.m12 * self.m23 * self.m31 * self.m44 + self.m13 * self.m21 * self.m32 * self.m44 - self.m11 * self.m23 * self.m32 * self.m44 - self.m12 * self.m21 * self.m33 * self.m44 + self.m11 * self.m22 * self.m33 * self.m44 } /// Multiplies all of the transform's component by a scalar and returns the result. #[must_use] pub fn mul_s(&self, x: T) -> Self { Transform3D::new( self.m11 * x, self.m12 * x, self.m13 * x, self.m14 * x, self.m21 * x, self.m22 * x, self.m23 * x, self.m24 * x, self.m31 * x, self.m32 * x, self.m33 * x, self.m34 * x, self.m41 * x, self.m42 * x, self.m43 * x, self.m44 * x ) } /// Convenience function to create a scale transform from a `Scale`. pub fn from_scale(scale: Scale) -> Self { Transform3D::scale(scale.get(), scale.get(), scale.get()) } } impl Transform3D where T: Copy + Mul + Div + Zero + One + PartialEq, { /// Returns a projection of this transform in 2d space. pub fn project_to_2d(&self) -> Self { let (_0, _1): (T, T) = (Zero::zero(), One::one()); let mut result = self.clone(); result.m31 = _0; result.m32 = _0; result.m13 = _0; result.m23 = _0; result.m33 = _1; result.m43 = _0; result.m34 = _0; // Try to normalize perspective when possible to convert to a 2d matrix. // Some matrices, such as those derived from perspective transforms, can // modify m44 from 1, while leaving the rest of the fourth column // (m14, m24) at 0. In this case, after resetting the third row and // third column above, the value of m44 functions only to scale the // coordinate transform divide by W. The matrix can be converted to // a true 2D matrix by normalizing out the scaling effect of m44 on // the remaining components ahead of time. if self.m14 == _0 && self.m24 == _0 && self.m44 != _0 && self.m44 != _1 { let scale = _1 / self.m44; result.m11 = result.m11 * scale; result.m12 = result.m12 * scale; result.m21 = result.m21 * scale; result.m22 = result.m22 * scale; result.m41 = result.m41 * scale; result.m42 = result.m42 * scale; result.m44 = _1; } result } } impl Transform3D { /// Cast from one numeric representation to another, preserving the units. #[inline] pub fn cast(&self) -> Transform3D { self.try_cast().unwrap() } /// Fallible cast from one numeric representation to another, preserving the units. pub fn try_cast(&self) -> Option> { match (NumCast::from(self.m11), NumCast::from(self.m12), NumCast::from(self.m13), NumCast::from(self.m14), NumCast::from(self.m21), NumCast::from(self.m22), NumCast::from(self.m23), NumCast::from(self.m24), NumCast::from(self.m31), NumCast::from(self.m32), NumCast::from(self.m33), NumCast::from(self.m34), NumCast::from(self.m41), NumCast::from(self.m42), NumCast::from(self.m43), NumCast::from(self.m44)) { (Some(m11), Some(m12), Some(m13), Some(m14), Some(m21), Some(m22), Some(m23), Some(m24), Some(m31), Some(m32), Some(m33), Some(m34), Some(m41), Some(m42), Some(m43), Some(m44)) => { Some(Transform3D::new(m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44)) }, _ => None } } } impl, Src, Dst> Transform3D { /// Returns true is this transform is approximately equal to the other one, using /// T's default epsilon value. /// /// The same as [`ApproxEq::approx_eq()`] but available without importing trait. /// /// [`ApproxEq::approx_eq()`]: ./approxeq/trait.ApproxEq.html#method.approx_eq #[inline] pub fn approx_eq(&self, other: &Self) -> bool { >::approx_eq(&self, &other) } /// Returns true is this transform is approximately equal to the other one, using /// a provided epsilon value. /// /// The same as [`ApproxEq::approx_eq_eps()`] but available without importing trait. /// /// [`ApproxEq::approx_eq_eps()`]: ./approxeq/trait.ApproxEq.html#method.approx_eq_eps #[inline] pub fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool { >::approx_eq_eps(&self, &other, &eps) } } impl, Src, Dst> ApproxEq for Transform3D { #[inline] fn approx_epsilon() -> T { T::approx_epsilon() } fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool { self.m11.approx_eq_eps(&other.m11, eps) && self.m12.approx_eq_eps(&other.m12, eps) && self.m13.approx_eq_eps(&other.m13, eps) && self.m14.approx_eq_eps(&other.m14, eps) && self.m21.approx_eq_eps(&other.m21, eps) && self.m22.approx_eq_eps(&other.m22, eps) && self.m23.approx_eq_eps(&other.m23, eps) && self.m24.approx_eq_eps(&other.m24, eps) && self.m31.approx_eq_eps(&other.m31, eps) && self.m32.approx_eq_eps(&other.m32, eps) && self.m33.approx_eq_eps(&other.m33, eps) && self.m34.approx_eq_eps(&other.m34, eps) && self.m41.approx_eq_eps(&other.m41, eps) && self.m42.approx_eq_eps(&other.m42, eps) && self.m43.approx_eq_eps(&other.m43, eps) && self.m44.approx_eq_eps(&other.m44, eps) } } impl Default for Transform3D where T: Zero + One { /// Returns the [identity transform](#method.identity). fn default() -> Self { Self::identity() } } impl fmt::Debug for Transform3D where T: Copy + fmt::Debug + PartialEq + One + Zero { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { if self.is_identity() { write!(f, "[I]") } else { self.to_array().fmt(f) } } } #[cfg(feature = "mint")] impl From> for Transform3D { fn from(m: mint::RowMatrix4) -> Self { Transform3D { m11: m.x.x, m12: m.x.y, m13: m.x.z, m14: m.x.w, m21: m.y.x, m22: m.y.y, m23: m.y.z, m24: m.y.w, m31: m.z.x, m32: m.z.y, m33: m.z.z, m34: m.z.w, m41: m.w.x, m42: m.w.y, m43: m.w.z, m44: m.w.w, _unit: PhantomData, } } } #[cfg(feature = "mint")] impl Into> for Transform3D { fn into(self) -> mint::RowMatrix4 { mint::RowMatrix4 { x: mint::Vector4 { x: self.m11, y: self.m12, z: self.m13, w: self.m14 }, y: mint::Vector4 { x: self.m21, y: self.m22, z: self.m23, w: self.m24 }, z: mint::Vector4 { x: self.m31, y: self.m32, z: self.m33, w: self.m34 }, w: mint::Vector4 { x: self.m41, y: self.m42, z: self.m43, w: self.m44 }, } } } #[cfg(test)] mod tests { use crate::approxeq::ApproxEq; use super::*; use crate::{point2, point3}; use crate::default; use core::f32::consts::{FRAC_PI_2, PI}; type Mf32 = default::Transform3D; // For convenience. fn rad(v: f32) -> Angle { Angle::radians(v) } #[test] pub fn test_translation() { let t1 = Mf32::translation(1.0, 2.0, 3.0); let t2 = Mf32::identity().pre_translate(vec3(1.0, 2.0, 3.0)); let t3 = Mf32::identity().then_translate(vec3(1.0, 2.0, 3.0)); assert_eq!(t1, t2); assert_eq!(t1, t3); assert_eq!(t1.transform_point3d(point3(1.0, 1.0, 1.0)), Some(point3(2.0, 3.0, 4.0))); assert_eq!(t1.transform_point2d(point2(1.0, 1.0)), Some(point2(2.0, 3.0))); assert_eq!(t1.then(&t1), Mf32::translation(2.0, 4.0, 6.0)); assert!(!t1.is_2d()); assert_eq!(Mf32::translation(1.0, 2.0, 3.0).to_2d(), Transform2D::translation(1.0, 2.0)); } #[test] pub fn test_rotation() { let r1 = Mf32::rotation(0.0, 0.0, 1.0, rad(FRAC_PI_2)); let r2 = Mf32::identity().pre_rotate(0.0, 0.0, 1.0, rad(FRAC_PI_2)); let r3 = Mf32::identity().then_rotate(0.0, 0.0, 1.0, rad(FRAC_PI_2)); assert_eq!(r1, r2); assert_eq!(r1, r3); assert!(r1.transform_point3d(point3(1.0, 2.0, 3.0)).unwrap().approx_eq(&point3(-2.0, 1.0, 3.0))); assert!(r1.transform_point2d(point2(1.0, 2.0)).unwrap().approx_eq(&point2(-2.0, 1.0))); assert!(r1.then(&r1).approx_eq(&Mf32::rotation(0.0, 0.0, 1.0, rad(FRAC_PI_2*2.0)))); assert!(r1.is_2d()); assert!(r1.to_2d().approx_eq(&Transform2D::rotation(rad(FRAC_PI_2)))); } #[test] pub fn test_scale() { let s1 = Mf32::scale(2.0, 3.0, 4.0); let s2 = Mf32::identity().pre_scale(2.0, 3.0, 4.0); let s3 = Mf32::identity().then_scale(2.0, 3.0, 4.0); assert_eq!(s1, s2); assert_eq!(s1, s3); assert!(s1.transform_point3d(point3(2.0, 2.0, 2.0)).unwrap().approx_eq(&point3(4.0, 6.0, 8.0))); assert!(s1.transform_point2d(point2(2.0, 2.0)).unwrap().approx_eq(&point2(4.0, 6.0))); assert_eq!(s1.then(&s1), Mf32::scale(4.0, 9.0, 16.0)); assert!(!s1.is_2d()); assert_eq!(Mf32::scale(2.0, 3.0, 0.0).to_2d(), Transform2D::scale(2.0, 3.0)); } #[test] pub fn test_pre_then_scale() { let m = Mf32::rotation(0.0, 0.0, 1.0, rad(FRAC_PI_2)).then_translate(vec3(6.0, 7.0, 8.0)); let s = Mf32::scale(2.0, 3.0, 4.0); assert_eq!(m.then(&s), m.then_scale(2.0, 3.0, 4.0)); } #[test] pub fn test_ortho() { let (left, right, bottom, top) = (0.0f32, 1.0f32, 0.1f32, 1.0f32); let (near, far) = (-1.0f32, 1.0f32); let result = Mf32::ortho(left, right, bottom, top, near, far); let expected = Mf32::new( 2.0, 0.0, 0.0, 0.0, 0.0, 2.22222222, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, -1.0, -1.22222222, -0.0, 1.0 ); assert!(result.approx_eq(&expected)); } #[test] pub fn test_is_2d() { assert!(Mf32::identity().is_2d()); assert!(Mf32::rotation(0.0, 0.0, 1.0, rad(0.7854)).is_2d()); assert!(!Mf32::rotation(0.0, 1.0, 0.0, rad(0.7854)).is_2d()); } #[test] pub fn test_new_2d() { let m1 = Mf32::new_2d(1.0, 2.0, 3.0, 4.0, 5.0, 6.0); let m2 = Mf32::new( 1.0, 2.0, 0.0, 0.0, 3.0, 4.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 5.0, 6.0, 0.0, 1.0 ); assert_eq!(m1, m2); } #[test] pub fn test_inverse_simple() { let m1 = Mf32::identity(); let m2 = m1.inverse().unwrap(); assert!(m1.approx_eq(&m2)); } #[test] pub fn test_inverse_scale() { let m1 = Mf32::scale(1.5, 0.3, 2.1); let m2 = m1.inverse().unwrap(); assert!(m1.then(&m2).approx_eq(&Mf32::identity())); assert!(m2.then(&m1).approx_eq(&Mf32::identity())); } #[test] pub fn test_inverse_translate() { let m1 = Mf32::translation(-132.0, 0.3, 493.0); let m2 = m1.inverse().unwrap(); assert!(m1.then(&m2).approx_eq(&Mf32::identity())); assert!(m2.then(&m1).approx_eq(&Mf32::identity())); } #[test] pub fn test_inverse_rotate() { let m1 = Mf32::rotation(0.0, 1.0, 0.0, rad(1.57)); let m2 = m1.inverse().unwrap(); assert!(m1.then(&m2).approx_eq(&Mf32::identity())); assert!(m2.then(&m1).approx_eq(&Mf32::identity())); } #[test] pub fn test_inverse_transform_point_2d() { let m1 = Mf32::translation(100.0, 200.0, 0.0); let m2 = m1.inverse().unwrap(); assert!(m1.then(&m2).approx_eq(&Mf32::identity())); assert!(m2.then(&m1).approx_eq(&Mf32::identity())); let p1 = point2(1000.0, 2000.0); let p2 = m1.transform_point2d(p1); assert_eq!(p2, Some(point2(1100.0, 2200.0))); let p3 = m2.transform_point2d(p2.unwrap()); assert_eq!(p3, Some(p1)); } #[test] fn test_inverse_none() { assert!(Mf32::scale(2.0, 0.0, 2.0).inverse().is_none()); assert!(Mf32::scale(2.0, 2.0, 2.0).inverse().is_some()); } #[test] pub fn test_pre_post() { let m1 = default::Transform3D::identity().then_scale(1.0, 2.0, 3.0).then_translate(vec3(1.0, 2.0, 3.0)); let m2 = default::Transform3D::identity().pre_translate(vec3(1.0, 2.0, 3.0)).pre_scale(1.0, 2.0, 3.0); assert!(m1.approx_eq(&m2)); let r = Mf32::rotation(0.0, 0.0, 1.0, rad(FRAC_PI_2)); let t = Mf32::translation(2.0, 3.0, 0.0); let a = point3(1.0, 1.0, 1.0); assert!(r.then(&t).transform_point3d(a).unwrap().approx_eq(&point3(1.0, 4.0, 1.0))); assert!(t.then(&r).transform_point3d(a).unwrap().approx_eq(&point3(-4.0, 3.0, 1.0))); assert!(t.then(&r).transform_point3d(a).unwrap().approx_eq(&r.transform_point3d(t.transform_point3d(a).unwrap()).unwrap())); } #[test] fn test_size_of() { use core::mem::size_of; assert_eq!(size_of::>(), 16*size_of::()); assert_eq!(size_of::>(), 16*size_of::()); } #[test] pub fn test_transform_associativity() { let m1 = Mf32::new(3.0, 2.0, 1.5, 1.0, 0.0, 4.5, -1.0, -4.0, 0.0, 3.5, 2.5, 40.0, 0.0, 3.0, 0.0, 1.0); let m2 = Mf32::new(1.0, -1.0, 3.0, 0.0, -1.0, 0.5, 0.0, 2.0, 1.5, -2.0, 6.0, 0.0, -2.5, 6.0, 1.0, 1.0); let p = point3(1.0, 3.0, 5.0); let p1 = m1.then(&m2).transform_point3d(p).unwrap(); let p2 = m2.transform_point3d(m1.transform_point3d(p).unwrap()).unwrap(); assert!(p1.approx_eq(&p2)); } #[test] pub fn test_is_identity() { let m1 = default::Transform3D::identity(); assert!(m1.is_identity()); let m2 = m1.then_translate(vec3(0.1, 0.0, 0.0)); assert!(!m2.is_identity()); } #[test] pub fn test_transform_vector() { // Translation does not apply to vectors. let m = Mf32::translation(1.0, 2.0, 3.0); let v1 = vec3(10.0, -10.0, 3.0); assert_eq!(v1, m.transform_vector3d(v1)); // While it does apply to points. assert_ne!(Some(v1.to_point()), m.transform_point3d(v1.to_point())); // same thing with 2d vectors/points let v2 = vec2(10.0, -5.0); assert_eq!(v2, m.transform_vector2d(v2)); assert_ne!(Some(v2.to_point()), m.transform_point2d(v2.to_point())); } #[test] pub fn test_is_backface_visible() { // backface is not visible for rotate-x 0 degree. let r1 = Mf32::rotation(1.0, 0.0, 0.0, rad(0.0)); assert!(!r1.is_backface_visible()); // backface is not visible for rotate-x 45 degree. let r1 = Mf32::rotation(1.0, 0.0, 0.0, rad(PI * 0.25)); assert!(!r1.is_backface_visible()); // backface is visible for rotate-x 180 degree. let r1 = Mf32::rotation(1.0, 0.0, 0.0, rad(PI)); assert!(r1.is_backface_visible()); // backface is visible for rotate-x 225 degree. let r1 = Mf32::rotation(1.0, 0.0, 0.0, rad(PI * 1.25)); assert!(r1.is_backface_visible()); // backface is not visible for non-inverseable matrix let r1 = Mf32::scale(2.0, 0.0, 2.0); assert!(!r1.is_backface_visible()); } #[test] pub fn test_homogeneous() { let m = Mf32::new( 1.0, 2.0, 0.5, 5.0, 3.0, 4.0, 0.25, 6.0, 0.5, -1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 2.0, ); assert_eq!( m.transform_point2d_homogeneous(point2(1.0, 2.0)), HomogeneousVector::new(6.0, 11.0, 0.0, 19.0), ); assert_eq!( m.transform_point3d_homogeneous(point3(1.0, 2.0, 4.0)), HomogeneousVector::new(8.0, 7.0, 4.0, 15.0), ); } #[test] pub fn test_perspective_division() { let p = point2(1.0, 2.0); let mut m = Mf32::identity(); assert!(m.transform_point2d(p).is_some()); m.m44 = 0.0; assert_eq!(None, m.transform_point2d(p)); m.m44 = 1.0; m.m24 = -1.0; assert_eq!(None, m.transform_point2d(p)); } #[cfg(feature = "mint")] #[test] pub fn test_mint() { let m1 = Mf32::rotation(0.0, 0.0, 1.0, rad(FRAC_PI_2)); let mm: mint::RowMatrix4<_> = m1.into(); let m2 = Mf32::from(mm); assert_eq!(m1, m2); } }