euclid 0.3.1

Geometry primitives
Documentation 
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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.

use approxeq::ApproxEq;
use point::{Point2D, Point4D};


#[derive(Debug, Copy, Clone, PartialEq)]
#[cfg_attr(feature = "plugins", derive(HeapSizeOf, Deserialize, Serialize))]
pub struct Matrix4 {
    pub m11: f32, pub m12: f32, pub m13: f32, pub m14: f32,
    pub m21: f32, pub m22: f32, pub m23: f32, pub m24: f32,
    pub m31: f32, pub m32: f32, pub m33: f32, pub m34: f32,
    pub m41: f32, pub m42: f32, pub m43: f32, pub m44: f32,
}

impl Matrix4 {
    pub fn new(
            m11: f32, m12: f32, m13: f32, m14: f32,
            m21: f32, m22: f32, m23: f32, m24: f32,
            m31: f32, m32: f32, m33: f32, m34: f32,
            m41: f32, m42: f32, m43: f32, m44: f32)
         -> Matrix4 {
        Matrix4 {
            m11: m11, m12: m12, m13: m13, m14: m14,
            m21: m21, m22: m22, m23: m23, m24: m24,
            m31: m31, m32: m32, m33: m33, m34: m34,
            m41: m41, m42: m42, m43: m43, m44: m44
        }
    }

    pub fn ortho(left: f32, right: f32,
                 bottom: f32, top: f32,
                 near: f32, far: f32) -> Matrix4 {
        let tx = -((right + left) / (right - left));
        let ty = -((top + bottom) / (top - bottom));
        let tz = -((far + near) / (far - near));

        Matrix4::new(2.0 / (right - left),
                     0.0,
                     0.0,
                     0.0,

                     0.0,
                     2.0 / (top - bottom),
                     0.0,
                     0.0,

                     0.0,
                     0.0,
                     -2.0 / (far - near),
                     0.0,

                     tx,
                     ty,
                     tz,
                     1.0)
    }

    pub fn identity() -> Matrix4 {
        Matrix4::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,
                     0.0, 0.0, 0.0, 1.0)
    }

    pub fn approx_eq(&self, other: &Matrix4) -> bool {
        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)
    }

    pub fn mul(&self, m: &Matrix4) -> Matrix4 {
        Matrix4::new(m.m11*self.m11 + m.m12*self.m21 + m.m13*self.m31 + m.m14*self.m41,
                     m.m11*self.m12 + m.m12*self.m22 + m.m13*self.m32 + m.m14*self.m42,
                     m.m11*self.m13 + m.m12*self.m23 + m.m13*self.m33 + m.m14*self.m43,
                     m.m11*self.m14 + m.m12*self.m24 + m.m13*self.m34 + m.m14*self.m44,
                     m.m21*self.m11 + m.m22*self.m21 + m.m23*self.m31 + m.m24*self.m41,
                     m.m21*self.m12 + m.m22*self.m22 + m.m23*self.m32 + m.m24*self.m42,
                     m.m21*self.m13 + m.m22*self.m23 + m.m23*self.m33 + m.m24*self.m43,
                     m.m21*self.m14 + m.m22*self.m24 + m.m23*self.m34 + m.m24*self.m44,
                     m.m31*self.m11 + m.m32*self.m21 + m.m33*self.m31 + m.m34*self.m41,
                     m.m31*self.m12 + m.m32*self.m22 + m.m33*self.m32 + m.m34*self.m42,
                     m.m31*self.m13 + m.m32*self.m23 + m.m33*self.m33 + m.m34*self.m43,
                     m.m31*self.m14 + m.m32*self.m24 + m.m33*self.m34 + m.m34*self.m44,
                     m.m41*self.m11 + m.m42*self.m21 + m.m43*self.m31 + m.m44*self.m41,
                     m.m41*self.m12 + m.m42*self.m22 + m.m43*self.m32 + m.m44*self.m42,
                     m.m41*self.m13 + m.m42*self.m23 + m.m43*self.m33 + m.m44*self.m43,
                     m.m41*self.m14 + m.m42*self.m24 + m.m43*self.m34 + m.m44*self.m44)
    }

    pub fn invert(&self) -> Matrix4 {
        let det = self.determinant();

        if det == 0.0 {
            return Matrix4::identity();
        }

        // todo(gw): this could be made faster by special casing
        // for simpler matrix types.
        let m = Matrix4::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
        );

        m.mul_s(1.0 / det)
    }

    pub fn determinant(&self) -> f32 {
        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
    }

    pub fn mul_s(&self, x: f32) -> Matrix4 {
        Matrix4::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)
    }

    pub fn scale(&self, x: f32, y: f32, z: f32) -> Matrix4 {
        Matrix4::new(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 the given point transformed by this matrix.
    #[inline]
    pub fn transform_point(&self, p: &Point2D<f32>) -> Point2D<f32> {
        Point2D::new(p.x * self.m11 + p.y * self.m21 + self.m41,
                     p.x * self.m12 + p.y * self.m22 + self.m42)
    }

    #[inline]
    pub fn transform_point4d(&self, p: &Point4D<f32>) -> Point4D<f32> {
        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;
        Point4D::new(x, y, z, w)
    }

    pub fn to_array(&self) -> [f32; 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
        ]
    }

    pub fn translate(&self, x: f32, y: f32, z: f32) -> Matrix4 {
        let matrix = Matrix4::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,
                                    x,   y,   z, 1.0);

        return self.mul(&matrix);
    }

    /// Create a 3d translation matrix
    pub fn create_translation(x: f32, y: f32, z: f32) -> Matrix4 {
        Matrix4::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,
                       x,   y,   z, 1.0)
    }

    /// Create a 3d scale matrix
    pub fn create_scale(x: f32, y: f32, z: f32) -> Matrix4 {
        Matrix4::new(  x, 0.0, 0.0, 0.0,
                     0.0,   y, 0.0, 0.0,
                     0.0, 0.0,   z, 0.0,
                     0.0, 0.0, 0.0, 1.0)
    }

    /// Create a 3d rotation matrix from an angle / axis.
    /// The supplied axis must be normalized.
    pub fn create_rotation(x: f32, y: f32, z: f32, theta: f32) -> Matrix4 {
        let xx = x * x;
        let yy = y * y;
        let zz = z * z;

        let half_theta = theta * 0.5;
        let sc = half_theta.sin() * half_theta.cos();
        let sq = half_theta.sin() * half_theta.sin();

        Matrix4::new(
            1.0 - 2.0 * (yy + zz) * sq,
            2.0 * (x * y * sq - z * sc),
            2.0 * (x * z * sq + y * sc),
            0.0,

            2.0 * (x * y * sq + z * sc),
            1.0 - 2.0 * (xx + zz) * sq,
            2.0 * (y * z * sq - x * sc),
            0.0,

            2.0 * (x * z * sq - y * sc),
            2.0 * (y * z * sq + x * sc),
            1.0 - 2.0 * (xx + yy) * sq,
            0.0,

            0.0,
            0.0,
            0.0,
            1.0
        )
    }

    /// Create a 2d skew matrix.
    /// https://drafts.csswg.org/css-transforms/#funcdef-skew
    pub fn create_skew(alpha: f32, beta: f32) -> Matrix4 {
        let (sx, sy) = (beta.tan(), alpha.tan());
        Matrix4::new(1.0,  sx, 0.0, 0.0,
                      sy, 1.0, 0.0, 0.0,
                     0.0, 0.0, 1.0, 0.0,
                     0.0, 0.0, 0.0, 1.0)
    }

    /// Create a simple perspective projection matrix
    pub fn create_perspective(d: f32) -> Matrix4 {
        Matrix4::new(1.0, 0.0, 0.0, 0.0,
                     0.0, 1.0, 0.0, 0.0,
                     0.0, 0.0, 1.0, -1.0 / d,
                     0.0, 0.0, 0.0, 1.0)
    }
}

#[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 = Matrix4::ortho(left, right, bottom, top, near, far);
    let expected = Matrix4::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);
    debug!("result={:?} expected={:?}", result, expected);
    assert!(result.approx_eq(&expected));
}

#[test]
pub fn test_invert_simple() {
    let m1 = Matrix4::identity();
    let m2 = m1.invert();
    assert!(m1.approx_eq(&m2));
}

#[test]
pub fn test_invert_scale() {
    let m1 = Matrix4::create_scale(1.5, 0.3, 2.1);
    let m2 = m1.invert();
    assert!(m1.mul(&m2).approx_eq(&Matrix4::identity()));
}

#[test]
pub fn test_invert_translate() {
    let m1 = Matrix4::create_translation(-132.0, 0.3, 493.0);
    let m2 = m1.invert();
    assert!(m1.mul(&m2).approx_eq(&Matrix4::identity()));
}

#[test]
pub fn test_invert_rotate() {
    let m1 = Matrix4::create_rotation(0.0, 1.0, 0.0, 1.57);
    let m2 = m1.invert();
    assert!(m1.mul(&m2).approx_eq(&Matrix4::identity()));
}

#[test]
pub fn test_invert_transform_point_2d() {
    let m1 = Matrix4::create_translation(100.0, 200.0, 0.0);
    let m2 = m1.invert();
    assert!(m1.mul(&m2).approx_eq(&Matrix4::identity()));

    let p1 = Point2D::new(1000.0, 2000.0);
    let p2 = m1.transform_point(&p1);
    assert!(p2.eq(&Point2D::new(1100.0, 2200.0)));

    let p3 = m2.transform_point(&p2);
    assert!(p3.eq(&p1));
}