math2d 0.2.0-alpha3

2D Mathematics library designed for use with 2D drawing applications. Primarily designed for the needs of Direct2D, but this library should be perfectly capable of filling in the needs of other libraries such as Cairo. If you would like interoperability defitions added please feel free to open a pull request on the repository. Currently compatible with: - `Direct2D` (winapi types) - `Mint` (crate)
Documentation 
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extern crate math2d;
extern crate rand;

use std::f32::consts::PI;

use math2d::matrix3x2f::IDENTITY;
use math2d::point2f::ORIGIN;
use math2d::vector2f::{ONE, ZERO};
use math2d::Matrix3x2f;

const EPSILON: f32 = 1e-5;
const SEED: [u8; 16] = [
    0x68, 0x16, 0x78, 0x24, 0x6a, 0xc0, 0x74, 0x5f, 0xf0, 0x60, 0xf8, 0xe9, 0x8f, 0x66, 0xcc, 0x12,
];

#[test]
fn identity() {
    let decomp = IDENTITY.decompose();

    assert!(decomp.translation.is_approx_eq(ZERO, EPSILON));
    assert!(decomp.scaling.is_approx_eq(ONE, EPSILON));
    assert!(decomp.rotation.abs() <= EPSILON);
}

#[test]
fn scaling_only_2() {
    let scale = Matrix3x2f::scaling(2.0, ORIGIN);
    let decomp = scale.decompose();

    assert!(decomp.translation.is_approx_eq(ZERO, EPSILON));
    assert!(decomp.scaling.is_approx_eq(2.0, EPSILON));
    assert_angle_approx(decomp.rotation, 0.0);

    let composed: Matrix3x2f = decomp.into();
    assert!(composed.is_approx_eq(&scale, EPSILON));
}

#[test]
fn scaling_only_various() {
    for i in 0..=20 {
        let s = i as f32 / 10.0;
        let scale = Matrix3x2f::scaling(s, ORIGIN);
        let decomp = scale.decompose();

        assert!(decomp.translation.is_approx_eq(ZERO, EPSILON));
        assert!(decomp.scaling.is_approx_eq(s, EPSILON));
        assert_angle_approx(decomp.rotation, 0.0);

        let composed: Matrix3x2f = decomp.into();
        assert!(composed.is_approx_eq(&scale, EPSILON));
    }
}

#[test]
fn rotation_only_180() {
    let rot = Matrix3x2f::rotation(PI, ORIGIN);
    let decomp = rot.decompose();

    assert!(decomp.translation.is_approx_eq(ZERO, EPSILON));
    assert!(decomp.scaling.is_approx_eq(ONE, EPSILON));
    assert_angle_approx(decomp.rotation, PI);

    let composed: Matrix3x2f = decomp.into();
    assert!(composed.is_approx_eq(&rot, EPSILON));
}

#[test]
fn rotation_only_various() {
    for i in 1..=360 {
        let angle = 2.0 * PI * i as f32 / 360.0;
        let rot = Matrix3x2f::rotation(angle, ORIGIN);
        let decomp = rot.decompose();

        assert!(decomp.translation.is_approx_eq(ZERO, EPSILON));
        assert!(decomp.scaling.is_approx_eq(ONE, EPSILON));
        assert_angle_approx(decomp.rotation, angle);

        let composed: Matrix3x2f = decomp.into();
        assert!(composed.is_approx_eq(&rot, EPSILON));
    }
}

#[test]
fn scaling_2_rotation_180() {
    let mat = Matrix3x2f::scaling(2.0, ORIGIN) * Matrix3x2f::rotation(PI, ORIGIN);
    let decomp = mat.decompose();

    assert!(decomp.translation.is_approx_eq(ZERO, EPSILON));
    assert!(decomp.scaling.is_approx_eq(2.0, EPSILON));
    assert_angle_approx(decomp.rotation, PI);

    let composed: Matrix3x2f = decomp.into();
    assert!(composed.is_approx_eq(&mat, EPSILON));
}

#[test]
fn scaling_rotation_various() {
    for i in 1..=20 {
        for j in 0..=36 {
            let s = i as f32 / 10.0;
            let angle = 2.0 * PI * j as f32 / 36.0;
            let mat = Matrix3x2f::scaling(s, ORIGIN) * Matrix3x2f::rotation(angle, ORIGIN);
            let decomp = mat.decompose();

            assert!(decomp.translation.is_approx_eq(ZERO, EPSILON));
            assert!(decomp.scaling.is_approx_eq(s, EPSILON));
            assert_angle_approx(decomp.rotation, angle);

            let composed: Matrix3x2f = decomp.into();
            assert!(composed.is_approx_eq(&mat, EPSILON));
        }
    }
}

#[test]
fn random_compositions() {
    use rand::{Rng, SeedableRng, XorShiftRng};
    let mut rng = XorShiftRng::from_seed(SEED);

    for _ in 0..1_000_000 {
        let angle = rng.gen::<f32>() * 2.0 * PI - PI;
        let sx = rng.gen::<f32>() * 5.0 + EPSILON;
        let sy = rng.gen::<f32>() * 5.0 + EPSILON;
        let tx = rng.gen::<f32>() * 50.0 - 25.0;
        let ty = rng.gen::<f32>() * 50.0 - 25.0;
        println!("s({}, {}) * r({}) * t({}, {})", sx, sy, angle, tx, ty);

        let mat = Matrix3x2f::compose([sx, sy], angle, [tx, ty]);
        let decomp = mat.decompose();

        assert!(decomp.translation.is_approx_eq([tx, ty], EPSILON));
        assert!(decomp.scaling.is_approx_eq([sx, sy], EPSILON));
        assert_angle_approx(decomp.rotation, angle);

        let composed: Matrix3x2f = decomp.into();
        assert!(composed.is_approx_eq(&mat, EPSILON));
    }
}

fn assert_angle_approx(a1: f32, a2: f32) {
    let diff = (a1 - a2).abs();
    assert!(
        diff <= EPSILON || (diff - 2.0 * PI).abs() <= EPSILON,
        "Angles which should have been equivalent were different: {} and {}",
        a1,
        a2
    );
}