transform3d.rs代码定义了一个名为 Transform3D 的 Rust 结构体，它用于表示一个3D变换矩阵。这个结构体是泛型的，包含三个类型参数：T、Src 和 Dst。其中，T 用于矩阵元素的数据类型，Src 和 Dst 用于表示变换的源和目标类型（虽然在这段代码中，Src 和 Dst 类型通过 PhantomData 引入，但并未在结构体功能上直接使用）。
一、transform3d.rs源码
// 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 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
#![allow(clippy::just_underscores_and_digits)]
use super::{Angle, UnknownUnit};
use crate::approxeq::ApproxEq;
use crate::box2d::Box2D;
use crate::box3d::Box3D;
use crate::homogen::HomogeneousVector;
use crate::num::{One, Zero};
use crate::point::{point2, point3, Point2D, Point3D};
use crate::rect::Rect;
use crate::scale::Scale;
use crate::transform2d::Transform2D;
use crate::trig::Trig;
use crate::vector::{vec2, vec3, Vector2D, Vector3D};
use core::cmp::{Eq, PartialEq};
use core::fmt;
use core::hash::Hash;
use core::marker::PhantomData;
use core::ops::{Add, Div, Mul, Neg, Sub};
#[cfg(feature = "bytemuck")]
use bytemuck::{Pod, Zeroable};
#[cfg(feature = "mint")]
use mint;
use num_traits::NumCast;
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
/// 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<f32, WorldSpace, ScreenSpace>::transform_point3d`
/// takes a `Point3D<f32, WorldSpace>` and returns a `Point3D<f32, ScreenSpace>`.
///
/// 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>"))
)]
#[rustfmt::skip]
pub struct Transform3D<T, Src, Dst> {
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<T, Src, Dst>
where
T: arbitrary::Arbitrary<'a>,
{
fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
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<T: Zeroable, Src, Dst> Zeroable for Transform3D<T, Src, Dst> {}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Pod, Src: 'static, Dst: 'static> Pod for Transform3D<T, Src, Dst> {}
impl<T: Copy, Src, Dst> Copy for Transform3D<T, Src, Dst> {}
impl<T: Clone, Src, Dst> Clone for Transform3D<T, Src, Dst> {
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<T, Src, Dst> Eq for Transform3D<T, Src, Dst> where T: Eq {}
impl<T, Src, Dst> PartialEq for Transform3D<T, Src, Dst>
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<T, Src, Dst> Hash for Transform3D<T, Src, Dst>
where
T: Hash,
{
fn hash<H: core::hash::Hasher>(&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<T, Src, Dst> Transform3D<T, Src, Dst> {
/// 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]
#[allow(clippy::too_many_arguments)]
#[rustfmt::skip]
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
/// representing the translation terms).
///
/// ```text
/// m11 m12 0 0
/// m21 m22 0 0
/// 0 0 1 0
/// m41 m42 0 1
/// ```
#[inline]
#[rustfmt::skip]
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 <https://drafts.csswg.org/css-transforms/#2d-transform>
#[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<T: Copy, Src, Dst> Transform3D<T, Src, Dst> {
/// 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]
#[rustfmt::skip]
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]
#[rustfmt::skip]
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]
#[rustfmt::skip]
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]
#[rustfmt::skip]
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]
#[rustfmt::skip]
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]
#[rustfmt::skip]
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]
#[rustfmt::skip]
pub fn from_untyped(m: &Transform3D<T, UnknownUnit, UnknownUnit>) -> 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]
#[rustfmt::skip]
pub fn to_untyped(&self) -> Transform3D<T, UnknownUnit, UnknownUnit> {
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]
#[rustfmt::skip]
pub fn with_source<NewSrc>(&self) -> Transform3D<T, NewSrc, Dst> {
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]
#[rustfmt::skip]
pub fn with_destination<NewDst>(&self) -> Transform3D<T, Src, NewDst> {
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 [`is_2d`] returns `true` beforehand.
///
/// [`is_2d`]: Self::is_2d
pub fn to_2d(&self) -> Transform2D<T, Src, Dst> {
Transform2D::new(self.m11, self.m12, self.m21, self.m22, self.m41, self.m42)
}
}
impl<T, Src, Dst> Transform3D<T, Src, Dst>
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 <https://drafts.csswg.org/css-transforms/#funcdef-skew>
#[rustfmt::skip]
pub fn skew(alpha: Angle<T>, beta: Angle<T>) -> 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 <https://drafts.csswg.org/css-transforms-2/#PerspectiveDefined>.
pub fn perspective(d: T) -> Self
where
T: Neg<Output = T> + Div<Output = T>,
{
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<T, Src, Dst> Transform3D<T, Src, Dst>
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
/// 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]
#[rustfmt::skip]
pub fn then<NewDst>(&self, other: &Transform3D<T, Dst, NewDst>) -> Transform3D<T, Src, NewDst> {
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<T, Src, Dst> Transform3D<T, Src, Dst>
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]
#[rustfmt::skip]
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<T, Src>) -> Self
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
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<T, Dst>) -> Self
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
self.then(&Transform3D::translation(v.x, v.y, v.z))
}
}
/// Methods for creating and combining rotation transformations
impl<T, Src, Dst> Transform3D<T, Src, Dst>
where
T: Copy
+ Add<Output = T>
+ Sub<Output = T>
+ Mul<Output = T>
+ Div<Output = T>
+ Zero
+ One
+ Trig,
{
/// Create a 3d rotation transform from an angle / axis.
/// The supplied axis must be normalized.
#[rustfmt::skip]
pub fn rotation(x: T, y: T, z: T, theta: Angle<T>) -> 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<T>) -> 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<T>) -> Self {
Transform3D::rotation(x, y, z, theta).then(self)
}
}
/// Methods for creating and combining scale transformations
impl<T, Src, Dst> Transform3D<T, Src, Dst>
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]
#[rustfmt::skip]
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]
#[rustfmt::skip]
pub fn pre_scale(&self, x: T, y: T, z: T) -> Self
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
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<Output = T> + Mul<Output = T>,
{
self.then(&Transform3D::scale(x, y, z))
}
}
/// Methods for apply transformations to objects
impl<T, Src, Dst> Transform3D<T, Src, Dst>
where
T: Copy + Add<Output = T> + Mul<Output = T>,
{
/// 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]
#[rustfmt::skip]
pub fn transform_point2d_homogeneous(
&self, p: Point2D<T, Src>
) -> HomogeneousVector<T, Dst> {
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<T, Src>) -> Option<Point2D<T, Dst>>
where
T: Div<Output = T> + 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<T, Src>) -> Vector2D<T, Dst> {
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<T, Src>) -> HomogeneousVector<T, Dst> {
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<T, Src>) -> Option<Point3D<T, Dst>>
where
T: Div<Output = T> + 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<T, Src>) -> Vector3D<T, Dst> {
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<T, Src>) -> Option<Rect<T, Dst>>
where
T: Sub<Output = T> + Div<Output = T> + 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<T, Src>) -> Option<Box2D<T, Dst>>
where
T: Sub<Output = T> + Div<Output = T> + 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<T, Src>) -> Option<Box3D<T, Dst>>
where
T: Sub<Output = T> + Div<Output = T> + 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<T, Src, Dst> Transform3D<T, Src, Dst>
where
T: Copy
+ Add<T, Output = T>
+ Sub<T, Output = T>
+ Mul<T, Output = T>
+ Div<T, Output = T>
+ Neg<Output = T>
+ PartialOrd
+ One
+ Zero,
{
/// Create an orthogonal projection transform.
#[rustfmt::skip]
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.
#[rustfmt::skip]
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<Transform3D<T, Dst, Src>> {
let det = self.determinant();
if det == Zero::zero() {
return None;
}
// todo(gw): this could be made faster by special casing
// for simpler transform types.
#[rustfmt::skip]
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.
#[rustfmt::skip]
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]
#[rustfmt::skip]
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<T, Src, Dst>) -> Self {
Transform3D::scale(scale.get(), scale.get(), scale.get())
}
}
impl<T, Src, Dst> Transform3D<T, Src, Dst>
where
T: Copy + Mul<Output = T> + Div<Output = T> + 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<T: NumCast + Copy, Src, Dst> Transform3D<T, Src, Dst> {
/// Cast from one numeric representation to another, preserving the units.
#[inline]
pub fn cast<NewT: NumCast>(&self) -> Transform3D<NewT, Src, Dst> {
self.try_cast().unwrap()
}
/// Fallible cast from one numeric representation to another, preserving the units.
#[rustfmt::skip]
pub fn try_cast<NewT: NumCast>(&self) -> Option<Transform3D<NewT, Src, Dst>> {
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<T: ApproxEq<T>, Src, Dst> Transform3D<T, Src, Dst> {
/// Returns `true` if 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.
#[inline]
pub fn approx_eq(&self, other: &Self) -> bool {
<Self as ApproxEq<T>>::approx_eq(self, other)
}
/// Returns `true` if 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.
#[inline]
pub fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool {
<Self as ApproxEq<T>>::approx_eq_eps(self, other, eps)
}
}
impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform3D<T, Src, Dst> {
#[inline]
fn approx_epsilon() -> T {
T::approx_epsilon()
}
#[rustfmt::skip]
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<T, Src, Dst> Default for Transform3D<T, Src, Dst>
where
T: Zero + One,
{
/// Returns the [identity transform](Self::identity).
fn default() -> Self {
Self::identity()
}
}
impl<T, Src, Dst> fmt::Debug for Transform3D<T, Src, Dst>
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<T, Src, Dst> From<mint::RowMatrix4<T>> for Transform3D<T, Src, Dst> {
#[rustfmt::skip]
fn from(m: mint::RowMatrix4<T>) -> 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<T, Src, Dst> From<Transform3D<T, Src, Dst>> for mint::RowMatrix4<T> {
#[rustfmt::skip]
fn from(t: Transform3D<T, Src, Dst>) -> Self {
mint::RowMatrix4 {
x: mint::Vector4 { x: t.m11, y: t.m12, z: t.m13, w: t.m14 },
y: mint::Vector4 { x: t.m21, y: t.m22, z: t.m23, w: t.m24 },
z: mint::Vector4 { x: t.m31, y: t.m32, z: t.m33, w: t.m34 },
w: mint::Vector4 { x: t.m41, y: t.m42, z: t.m43, w: t.m44 },
}
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::approxeq::ApproxEq;
use crate::default;
use crate::{point2, point3};
use core::f32::consts::{FRAC_PI_2, PI};
type Mf32 = default::Transform3D<f32>;
// For convenience.
fn rad(v: f32) -> Angle<f32> {
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]
#[rustfmt::skip]
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]
#[rustfmt::skip]
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::<default::Transform3D<f32>>(),
16 * size_of::<f32>()
);
assert_eq!(
size_of::<default::Transform3D<f64>>(),
16 * size_of::<f64>()
);
}
#[test]
#[rustfmt::skip]
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() {
#[rustfmt::skip]
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);
}
}
二、结构体定义
- #[repr©]: 这个属性确保结构体在内存中的布局与C语言中的结构体兼容。这对于与C语言库进行互操作时非常有用，可以确保数据的二进制表示一致。
- 条件编译属性 #[cfg_attr(feature = “serde”, derive(Serialize, Deserialize))]:
- 这个属性是条件编译的一部分，它检查是否启用了名为 serde 的特性（feature）。
- 如果启用了 serde 特性，那么 Transform3D 结构体将派生（derive）Serialize 和 Deserialize 这两个 trait，使得结构体可以被序列化和反序列化。这对于将数据保存到文件、通过网络传输数据等场景非常有用。
- #[cfg_attr(feature = “serde”, serde(bound(serialize = “T: Serialize”, deserialize = “T: Deserialize<'de>”)) )]:
- 这个属性进一步指定了当 serde 特性启用时，对于 T 类型有额外的约束。
- 在序列化时，T 必须实现 Serialize trait；在反序列化时，T 必须实现 Deserialize trait（注意这里 'de 是一个生命周期参数，用于泛型反序列化）。
- #[rustfmt::skip]: 这个属性告诉 Rust 的代码格式化工具 rustfmt 忽略此结构体的格式化。这可能是因为结构体布局有特殊需求，或者为了保持某些手动调整的格式。
- 结构体定义:
- Transform3D 结构体有16个公开字段，分别表示4x4矩阵的行和列（m11 到 m44）。
- 最后一个字段 _unit 是一个 PhantomData<(Src, Dst)> 类型的实例。PhantomData 用于在类型系统中表示某种类型的存在，而不占用实际的内存空间。这里它用于保留 Src 和 Dst 类型信息，可能是为了泛型代码的类型安全性或约束，尽管在这段代码中它们并没有直接的功能作用。
- 总结
这个结构体可以用于图形编程、物理模拟等领域，其中3D变换矩阵非常常见，用于表示旋转、缩放、平移等变换。
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