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// 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.
#![cfg_attr(feature = "cargo-clippy", allow(just_underscores_and_digits))]
use super::{UnknownUnit, Angle};
use approxeq::ApproxEq;
use homogen::HomogeneousVector;
#[cfg(feature = "mint")]
use mint;
use trig::Trig;
use point::{TypedPoint2D, TypedPoint3D};
use vector::{TypedVector2D, TypedVector3D, vec2, vec3};
use rect::TypedRect;
use transform2d::TypedTransform2D;
use scale::TypedScale;
use num::{One, Zero};
use core::ops::{Add, Mul, Sub, Div, Neg};
use core::marker::PhantomData;
use core::fmt;
use num_traits::NumCast;
define_matrix! {
/// A 3d transform stored as a 4 by 4 matrix in row-major order in memory.
///
/// Transforms can be parametrized over the source and destination units, to describe a
/// transformation from a space to another.
/// For example, `TypedTransform3D<f32, WorldSpace, ScreenSpace>::transform_point3d`
/// takes a `TypedPoint3D<f32, WorldSpace>` and returns a `TypedPoint3D<f32, ScreenSpace>`.
///
/// Transforms expose a set of convenience methods for pre- and post-transformations.
/// A pre-transformation corresponds to adding an operation that is applied before
/// the rest of the transformation, while a post-transformation adds an operation
/// that is applied after.
pub struct TypedTransform3D<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,
}
}
/// The default 3d transform type with no units.
pub type Transform3D<T> = TypedTransform3D<T, UnknownUnit, UnknownUnit>;
impl<T, Src, Dst> TypedTransform3D<T, Src, Dst> {
/// Create a transform specifying its components in row-major order.
///
/// For example, the translation terms m41, m42, m43 on the last row with the
/// row-major convention) are the 13rd, 14th and 15th parameters.
#[inline]
#[cfg_attr(feature = "cargo-clippy", allow(too_many_arguments))]
pub fn row_major(
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 {
TypedTransform3D {
m11, m12, m13, m14,
m21, m22, m23, m24,
m31, m32, m33, m34,
m41, m42, m43, m44,
_unit: PhantomData,
}
}
/// Create a transform specifying its components in column-major order.
///
/// For example, the translation terms m41, m42, m43 on the last column with the
/// column-major convention) are the 4th, 8th and 12nd parameters.
#[inline]
#[cfg_attr(feature = "cargo-clippy", allow(too_many_arguments))]
pub fn column_major(
m11: T, m21: T, m31: T, m41: T,
m12: T, m22: T, m32: T, m42: T,
m13: T, m23: T, m33: T, m43: T,
m14: T, m24: T, m34: T, m44: T)
-> Self {
TypedTransform3D {
m11, m12, m13, m14,
m21, m22, m23, m24,
m31, m32, m33, m34,
m41, m42, m43, m44,
_unit: PhantomData,
}
}
}
impl <T, Src, Dst> TypedTransform3D<T, Src, Dst>
where T: Copy + Clone +
PartialEq +
One + Zero {
#[inline]
pub fn identity() -> Self {
let (_0, _1): (T, T) = (Zero::zero(), One::one());
TypedTransform3D::row_major(
_1, _0, _0, _0,
_0, _1, _0, _0,
_0, _0, _1, _0,
_0, _0, _0, _1
)
}
// 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 {
*self == TypedTransform3D::identity()
}
}
impl <T, Src, Dst> TypedTransform3D<T, Src, Dst>
where T: Copy + Clone +
Add<T, Output=T> +
Sub<T, Output=T> +
Mul<T, Output=T> +
Div<T, Output=T> +
Neg<Output=T> +
PartialOrd +
Trig +
One + Zero {
/// Create a 4 by 4 transform representing a 2d transformation, specifying its components
/// in row-major order.
#[inline]
pub fn row_major_2d(m11: T, m12: T, m21: T, m22: T, m41: T, m42: T) -> Self {
let (_0, _1): (T, T) = (Zero::zero(), One::one());
TypedTransform3D::row_major(
m11, m12, _0, _0,
m21, m22, _0, _0,
_0, _0, _1, _0,
m41, m42, _0, _1
)
}
/// 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;
TypedTransform3D::row_major(
_2 / (right - left), _0 , _0 , _0,
_0 , _2 / (top - bottom), _0 , _0,
_0 , _0 , -_2 / (far - near), _0,
tx , ty , tz , _1
)
}
/// Returns true if this transform can be represented with a `TypedTransform2D`.
///
/// See <https://drafts.csswg.org/css-transforms/#2d-transform>
#[inline]
pub fn is_2d(&self) -> bool {
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
}
/// 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.
pub fn to_2d(&self) -> TypedTransform2D<T, Src, Dst> {
TypedTransform2D::row_major(
self.m11, self.m12,
self.m21, self.m22,
self.m41, self.m42
)
}
/// 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
}
pub fn approx_eq(&self, other: &Self) -> bool
where T : ApproxEq<T> {
self.m11.approx_eq(&other.m11) && self.m12.approx_eq(&other.m12) &&
self.m13.approx_eq(&other.m13) && self.m14.approx_eq(&other.m14) &&
self.m21.approx_eq(&other.m21) && self.m22.approx_eq(&other.m22) &&
self.m23.approx_eq(&other.m23) && self.m24.approx_eq(&other.m24) &&
self.m31.approx_eq(&other.m31) && self.m32.approx_eq(&other.m32) &&
self.m33.approx_eq(&other.m33) && self.m34.approx_eq(&other.m34) &&
self.m41.approx_eq(&other.m41) && self.m42.approx_eq(&other.m42) &&
self.m43.approx_eq(&other.m43) && self.m44.approx_eq(&other.m44)
}
/// Returns the same transform with a different destination unit.
#[inline]
pub fn with_destination<NewDst>(&self) -> TypedTransform3D<T, Src, NewDst> {
TypedTransform3D::row_major(
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<NewSrc>(&self) -> TypedTransform3D<T, NewSrc, Dst> {
TypedTransform3D::row_major(
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,
)
}
/// Drop the units, preserving only the numeric value.
#[inline]
pub fn to_untyped(&self) -> Transform3D<T> {
Transform3D::row_major(
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,
)
}
/// Tag a unitless value with units.
#[inline]
pub fn from_untyped(m: &Transform3D<T>) -> Self {
TypedTransform3D::row_major(
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,
)
}
/// Returns the multiplication of the two matrices such that mat's transformation
/// applies after self's transformation.
pub fn post_mul<NewDst>(&self, mat: &TypedTransform3D<T, Dst, NewDst>) -> TypedTransform3D<T, Src, NewDst> {
TypedTransform3D::row_major(
self.m11 * mat.m11 + self.m12 * mat.m21 + self.m13 * mat.m31 + self.m14 * mat.m41,
self.m11 * mat.m12 + self.m12 * mat.m22 + self.m13 * mat.m32 + self.m14 * mat.m42,
self.m11 * mat.m13 + self.m12 * mat.m23 + self.m13 * mat.m33 + self.m14 * mat.m43,
self.m11 * mat.m14 + self.m12 * mat.m24 + self.m13 * mat.m34 + self.m14 * mat.m44,
self.m21 * mat.m11 + self.m22 * mat.m21 + self.m23 * mat.m31 + self.m24 * mat.m41,
self.m21 * mat.m12 + self.m22 * mat.m22 + self.m23 * mat.m32 + self.m24 * mat.m42,
self.m21 * mat.m13 + self.m22 * mat.m23 + self.m23 * mat.m33 + self.m24 * mat.m43,
self.m21 * mat.m14 + self.m22 * mat.m24 + self.m23 * mat.m34 + self.m24 * mat.m44,
self.m31 * mat.m11 + self.m32 * mat.m21 + self.m33 * mat.m31 + self.m34 * mat.m41,
self.m31 * mat.m12 + self.m32 * mat.m22 + self.m33 * mat.m32 + self.m34 * mat.m42,
self.m31 * mat.m13 + self.m32 * mat.m23 + self.m33 * mat.m33 + self.m34 * mat.m43,
self.m31 * mat.m14 + self.m32 * mat.m24 + self.m33 * mat.m34 + self.m34 * mat.m44,
self.m41 * mat.m11 + self.m42 * mat.m21 + self.m43 * mat.m31 + self.m44 * mat.m41,
self.m41 * mat.m12 + self.m42 * mat.m22 + self.m43 * mat.m32 + self.m44 * mat.m42,
self.m41 * mat.m13 + self.m42 * mat.m23 + self.m43 * mat.m33 + self.m44 * mat.m43,
self.m41 * mat.m14 + self.m42 * mat.m24 + self.m43 * mat.m34 + self.m44 * mat.m44,
)
}
/// Returns the multiplication of the two matrices such that mat's transformation
/// applies before self's transformation.
pub fn pre_mul<NewSrc>(&self, mat: &TypedTransform3D<T, NewSrc, Src>) -> TypedTransform3D<T, NewSrc, Dst> {
mat.post_mul(self)
}
/// Returns the inverse transform if possible.
pub fn inverse(&self) -> Option<TypedTransform3D<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.
let m = TypedTransform3D::row_major(
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.
#[cfg_attr(feature = "unstable", must_use)]
pub fn mul_s(&self, x: T) -> Self {
TypedTransform3D::row_major(
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 `TypedScale`.
pub fn from_scale(scale: TypedScale<T, Src, Dst>) -> Self {
TypedTransform3D::create_scale(scale.get(), scale.get(), scale.get())
}
/// 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: &TypedPoint2D<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: &TypedPoint2D<T, Src>) -> Option<TypedPoint2D<T, Dst>> {
//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(TypedPoint2D::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: &TypedVector2D<T, Src>) -> TypedVector2D<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: &TypedPoint3D<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: &TypedPoint3D<T, Src>) -> Option<TypedPoint3D<T, Dst>> {
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: &TypedVector3D<T, Src>) -> TypedVector3D<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 transform_rect(&self, rect: &TypedRect<T, Src>) -> Option<TypedRect<T, Dst>> {
Some(TypedRect::from_points(&[
self.transform_point2d(&rect.origin)?,
self.transform_point2d(&rect.top_right())?,
self.transform_point2d(&rect.bottom_left())?,
self.transform_point2d(&rect.bottom_right())?,
]))
}
/// Create a 3d translation transform
pub fn create_translation(x: T, y: T, z: T) -> Self {
let (_0, _1): (T, T) = (Zero::zero(), One::one());
TypedTransform3D::row_major(
_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.
#[cfg_attr(feature = "unstable", must_use)]
pub fn pre_translate(&self, v: TypedVector3D<T, Src>) -> Self {
self.pre_mul(&TypedTransform3D::create_translation(v.x, v.y, v.z))
}
/// Returns a transform with a translation applied after self's transformation.
#[cfg_attr(feature = "unstable", must_use)]
pub fn post_translate(&self, v: TypedVector3D<T, Dst>) -> Self {
self.post_mul(&TypedTransform3D::create_translation(v.x, v.y, v.z))
}
/// Create a 3d scale transform
pub fn create_scale(x: T, y: T, z: T) -> Self {
let (_0, _1): (T, T) = (Zero::zero(), One::one());
TypedTransform3D::row_major(
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.
#[cfg_attr(feature = "unstable", must_use)]
pub fn pre_scale(&self, x: T, y: T, z: T) -> Self {
TypedTransform3D::row_major(
self.m11 * x, self.m12, self.m13, self.m14,
self.m21 , self.m22 * y, self.m23, self.m24,
self.m31 , self.m32, self.m33 * z, self.m34,
self.m41 , self.m42, self.m43, self.m44
)
}
/// Returns a transform with a scale applied after self's transformation.
#[cfg_attr(feature = "unstable", must_use)]
pub fn post_scale(&self, x: T, y: T, z: T) -> Self {
self.post_mul(&TypedTransform3D::create_scale(x, y, z))
}
/// Create a 3d rotation transform from an angle / axis.
/// The supplied axis must be normalized.
pub fn create_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();
TypedTransform3D::row_major(
_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.
#[cfg_attr(feature = "unstable", must_use)]
pub fn post_rotate(&self, x: T, y: T, z: T, theta: Angle<T>) -> Self {
self.post_mul(&TypedTransform3D::create_rotation(x, y, z, theta))
}
/// Returns a transform with a rotation applied before self's transformation.
#[cfg_attr(feature = "unstable", must_use)]
pub fn pre_rotate(&self, x: T, y: T, z: T, theta: Angle<T>) -> Self {
self.pre_mul(&TypedTransform3D::create_rotation(x, y, z, theta))
}
/// Create a 2d skew transform.
///
/// See <https://drafts.csswg.org/css-transforms/#funcdef-skew>
pub fn create_skew(alpha: Angle<T>, beta: Angle<T>) -> Self {
let (_0, _1): (T, T) = (Zero::zero(), One::one());
let (sx, sy) = (beta.get().tan(), alpha.get().tan());
TypedTransform3D::row_major(
_1, sx, _0, _0,
sy, _1, _0, _0,
_0, _0, _1, _0,
_0, _0, _0, _1
)
}
/// Create a simple perspective projection transform
pub fn create_perspective(d: T) -> Self {
let (_0, _1): (T, T) = (Zero::zero(), One::one());
TypedTransform3D::row_major(
_1, _0, _0, _0,
_0, _1, _0, _0,
_0, _0, _1, -_1 / d,
_0, _0, _0, _1
)
}
}
impl<T: Copy, Src, Dst> TypedTransform3D<T, Src, Dst> {
/// Returns an array containing this transform's terms in row-major order (the order
/// in which the transform is actually laid out in memory).
pub fn to_row_major_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 in column-major order.
pub fn to_column_major_array(&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
]
}
/// Returns an array containing this transform's 4 rows in (in row-major order)
/// as arrays.
///
/// This is a convenience method to interface with other libraries like glium.
pub fn to_row_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]
]
}
/// Returns an array containing this transform's 4 columns in (in row-major order,
/// or 4 rows in column-major order) as arrays.
///
/// This is a convenience method to interface with other libraries like glium.
pub fn to_column_arrays(&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]
]
}
/// Creates a transform from an array of 16 elements in row-major order.
pub fn from_array(array: [T; 16]) -> Self {
Self::row_major(
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],
)
}
/// Creates a transform from 4 rows of 4 elements (row-major order).
pub fn from_row_arrays(array: [[T; 4]; 4]) -> Self {
Self::row_major(
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],
)
}
}
impl<T0: NumCast + Copy, Src, Dst> TypedTransform3D<T0, Src, Dst> {
/// Cast from one numeric representation to another, preserving the units.
pub fn cast<T1: NumCast + Copy>(&self) -> TypedTransform3D<T1, Src, Dst> {
self.try_cast().unwrap()
}
/// Fallible cast from one numeric representation to another, preserving the units.
pub fn try_cast<T1: NumCast + Copy>(&self) -> Option<TypedTransform3D<T1, 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(TypedTransform3D::row_major(m11, m12, m13, m14,
m21, m22, m23, m24,
m31, m32, m33, m34,
m41, m42, m43, m44))
},
_ => None
}
}
}
impl <T, Src, Dst> Default for TypedTransform3D<T, Src, Dst>
where T: Copy + PartialEq + One + Zero
{
fn default() -> Self {
Self::identity()
}
}
impl<T, Src, Dst> fmt::Debug for TypedTransform3D<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_row_major_array().fmt(f)
}
}
}
#[cfg(feature = "mint")]
impl<T, Src, Dst> From<mint::RowMatrix4<T>> for TypedTransform3D<T, Src, Dst> {
fn from(m: mint::RowMatrix4<T>) -> Self {
TypedTransform3D {
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> Into<mint::RowMatrix4<T>> for TypedTransform3D<T, Src, Dst> {
fn into(self) -> mint::RowMatrix4<T> {
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 approxeq::ApproxEq;
use transform2d::Transform2D;
use point::{point2, point3};
use Angle;
use super::*;
use core::f32::consts::{FRAC_PI_2, PI};
type Mf32 = Transform3D<f32>;
// For convenience.
fn rad(v: f32) -> Angle<f32> { Angle::radians(v) }
#[test]
pub fn test_translation() {
let t1 = Mf32::create_translation(1.0, 2.0, 3.0);
let t2 = Mf32::identity().pre_translate(vec3(1.0, 2.0, 3.0));
let t3 = Mf32::identity().post_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.post_mul(&t1), Mf32::create_translation(2.0, 4.0, 6.0));
assert!(!t1.is_2d());
assert_eq!(Mf32::create_translation(1.0, 2.0, 3.0).to_2d(), Transform2D::create_translation(1.0, 2.0));
}
#[test]
pub fn test_rotation() {
let r1 = Mf32::create_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().post_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.post_mul(&r1).approx_eq(&Mf32::create_rotation(0.0, 0.0, 1.0, rad(FRAC_PI_2*2.0))));
assert!(r1.is_2d());
assert!(r1.to_2d().approx_eq(&Transform2D::create_rotation(rad(FRAC_PI_2))));
}
#[test]
pub fn test_scale() {
let s1 = Mf32::create_scale(2.0, 3.0, 4.0);
let s2 = Mf32::identity().pre_scale(2.0, 3.0, 4.0);
let s3 = Mf32::identity().post_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.post_mul(&s1), Mf32::create_scale(4.0, 9.0, 16.0));
assert!(!s1.is_2d());
assert_eq!(Mf32::create_scale(2.0, 3.0, 0.0).to_2d(), Transform2D::create_scale(2.0, 3.0));
}
#[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::row_major(
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::create_rotation(0.0, 0.0, 1.0, rad(0.7854)).is_2d());
assert!(!Mf32::create_rotation(0.0, 1.0, 0.0, rad(0.7854)).is_2d());
}
#[test]
pub fn test_row_major_2d() {
let m1 = Mf32::row_major_2d(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
let m2 = Mf32::row_major(
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]
fn test_column_major() {
assert_eq!(
Mf32::row_major(
1.0, 2.0, 3.0, 4.0,
5.0, 6.0, 7.0, 8.0,
9.0, 10.0, 11.0, 12.0,
13.0, 14.0, 15.0, 16.0,
),
Mf32::column_major(
1.0, 5.0, 9.0, 13.0,
2.0, 6.0, 10.0, 14.0,
3.0, 7.0, 11.0, 15.0,
4.0, 8.0, 12.0, 16.0,
)
);
}
#[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::create_scale(1.5, 0.3, 2.1);
let m2 = m1.inverse().unwrap();
assert!(m1.pre_mul(&m2).approx_eq(&Mf32::identity()));
}
#[test]
pub fn test_inverse_translate() {
let m1 = Mf32::create_translation(-132.0, 0.3, 493.0);
let m2 = m1.inverse().unwrap();
assert!(m1.pre_mul(&m2).approx_eq(&Mf32::identity()));
}
#[test]
pub fn test_inverse_rotate() {
let m1 = Mf32::create_rotation(0.0, 1.0, 0.0, rad(1.57));
let m2 = m1.inverse().unwrap();
assert!(m1.pre_mul(&m2).approx_eq(&Mf32::identity()));
}
#[test]
pub fn test_inverse_transform_point_2d() {
let m1 = Mf32::create_translation(100.0, 200.0, 0.0);
let m2 = m1.inverse().unwrap();
assert!(m1.pre_mul(&m2).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::create_scale(2.0, 0.0, 2.0).inverse().is_none());
assert!(Mf32::create_scale(2.0, 2.0, 2.0).inverse().is_some());
}
#[test]
pub fn test_pre_post() {
let m1 = Transform3D::identity().post_scale(1.0, 2.0, 3.0).post_translate(vec3(1.0, 2.0, 3.0));
let m2 = 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::create_rotation(0.0, 0.0, 1.0, rad(FRAC_PI_2));
let t = Mf32::create_translation(2.0, 3.0, 0.0);
let a = point3(1.0, 1.0, 1.0);
assert!(r.post_mul(&t).transform_point3d(&a).unwrap().approx_eq(&point3(3.0, 2.0, 1.0)));
assert!(t.post_mul(&r).transform_point3d(&a).unwrap().approx_eq(&point3(4.0, -3.0, 1.0)));
assert!(t.post_mul(&r).transform_point3d(&a).unwrap().approx_eq(&r.transform_point3d(&t.transform_point3d(&a).unwrap()).unwrap()));
assert!(r.pre_mul(&t).transform_point3d(&a).unwrap().approx_eq(&point3(4.0, -3.0, 1.0)));
assert!(t.pre_mul(&r).transform_point3d(&a).unwrap().approx_eq(&point3(3.0, 2.0, 1.0)));
assert!(t.pre_mul(&r).transform_point3d(&a).unwrap().approx_eq(&t.transform_point3d(&r.transform_point3d(&a).unwrap()).unwrap()));
}
#[test]
fn test_size_of() {
use core::mem::size_of;
assert_eq!(size_of::<Transform3D<f32>>(), 16*size_of::<f32>());
assert_eq!(size_of::<Transform3D<f64>>(), 16*size_of::<f64>());
}
#[test]
pub fn test_transform_associativity() {
let m1 = Mf32::row_major(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::row_major(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 = m2.pre_mul(&m1).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 = Transform3D::identity();
assert!(m1.is_identity());
let m2 = m1.post_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::create_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::create_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::create_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::create_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::create_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::create_scale(2.0, 0.0, 2.0);
assert!(!r1.is_backface_visible());
}
#[test]
pub fn test_homogeneous() {
let m = Mf32::row_major(
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::create_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);
}
}