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Author SHA1 Message Date
Gered 5159b8ef91 add Matrix4x4 method for creating a rotation about an arbitrary axis 2024-09-08 22:56:42 -04:00
Gered fbba97f168 normalize the resulting re-calculated "up" vector 2024-09-08 20:18:51 -04:00
Gered c3c6f1338d add Vector4 and Matrix4x4 multiplication 2024-09-08 18:42:49 -04:00
Gered 4156486228 add Vector4 2024-09-08 18:27:02 -04:00
Gered 1d09340c83 add a bunch of rustfmt::skip's because rustfmt is a piece of shit 
apparently the trailing comment trick doesn't work that well anymore?
or maybe only in certain cases?

oh well. rustfmt can fuck right off.
 2024-09-08 16:23:58 -04:00
Gered 7111624a7e add Matrix4x4 methods for creating projection and modelview matrices 
these all mimic OpenGL functions
 2024-09-08 15:47:36 -04:00
Gered 1f564253e3 Merge branch 'master' into 3dmath 2024-09-07 23:11:15 -04:00
Gered 2c5af8d559 add Matrix4x4 
will be expanded upon later with more useful methods
 2024-08-11 16:47:28 -04:00
Gered dc29f29289 add vector3 2024-07-21 18:15:44 -04:00
4 changed files with 1717 additions and 0 deletions
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ggdt/src/math/matrix4x4.rs Normal file
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use std::ops::{Mul, MulAssign};
use crate::math::{nearly_equal, Vector3, Vector4};
/// Represents a 4x4 column-major matrix and provides common methods for matrix math.
#[derive(Debug, Copy, Clone, PartialEq)]
pub struct Matrix4x4 {
pub m: [f32; 16],
}
impl Matrix4x4 {
pub const M11: usize = 0;
pub const M12: usize = 4;
pub const M13: usize = 8;
pub const M14: usize = 12;
pub const M21: usize = 1;
pub const M22: usize = 5;
pub const M23: usize = 9;
pub const M24: usize = 13;
pub const M31: usize = 2;
pub const M32: usize = 6;
pub const M33: usize = 10;
pub const M34: usize = 14;
pub const M41: usize = 3;
pub const M42: usize = 7;
pub const M43: usize = 11;
pub const M44: usize = 15;
#[rustfmt::skip]
pub const IDENTITY: Matrix4x4 = Matrix4x4 {
m: [
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
],
};
/// Returns a new identity matrix.
#[inline]
pub fn identity() -> Matrix4x4 {
Matrix4x4::IDENTITY
}
/// Creates a new matrix with the specified elements.
#[allow(clippy::too_many_arguments)]
#[rustfmt::skip]
#[inline]
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,
) -> Matrix4x4 {
Matrix4x4 {
m: [
m11, m21, m31, m41,
m12, m22, m32, m42,
m13, m23, m33, m43,
m14, m24, m34, m44,
]
}
}
/// Creates a new rotation matrix from a set of euler angles.
///
/// # Arguments
///
/// * `x`: the x angle (in radians)
/// * `y`: the y angle (in radians)
/// * `z`: the z angle (in radians)
pub fn from_euler_angles(x: f32, y: f32, z: f32) -> Matrix4x4 {
let rotate_z = Matrix4x4::new_rotation_z(z);
let rotate_y = Matrix4x4::new_rotation_y(y);
let rotate_x = Matrix4x4::new_rotation_x(x);
// "right-to-left" column-major matrix concatenation
rotate_z * rotate_y * rotate_x
}
// Creates a new rotation matrix about the specified axis.
//
// # Arguments
//
// * `radians`: angle to rotate by (in radians)
// * `x`: the x component of the axis vector to rotate around
// * `y`: the y component of the axis vector to rotate around
// * `z`: the z component of the axis vector to rotate around
pub fn new_rotation(radians: f32, x: f32, y: f32, z: f32) -> Matrix4x4 {
let (s, c) = radians.sin_cos();
Matrix4x4::new(
(x * x) * (1.0 - c) + c,
(x * y) * (1.0 - c) - (z * s),
(x * z) * (1.0 - c) + (y * s),
0.0,
(y * x) * (1.0 - c) + (z * s),
(y * y) * (1.0 - c) + c,
(y * z) * (1.0 - c) - (x * s),
0.0,
(z * x) * (1.0 - c) - (y * s),
(z * y) * (1.0 - c) + (x * s),
(z * z) * (1.0 - c) + c,
0.0,
0.0,
0.0,
0.0,
1.0,
)
}
/// Creates a new rotation matrix for rotation around the x axis.
///
/// # Arguments
///
/// * `radians`: angle to rotate the x axis around (in radians)
#[rustfmt::skip]
#[inline]
pub fn new_rotation_x(radians: f32) -> Matrix4x4 {
let (s, c) = radians.sin_cos();
Matrix4x4::new(
1.0, 0.0, 0.0, 0.0,
0.0, c, -s, 0.0,
0.0, s, c, 0.0,
0.0, 0.0, 0.0, 1.0
)
}
/// Creates a new rotation matrix for rotation around the y axis.
///
/// # Arguments
///
/// * `radians`: angle to rotate the y axis around (in radians)
#[rustfmt::skip]
#[inline]
pub fn new_rotation_y(radians: f32) -> Matrix4x4 {
let (s, c) = radians.sin_cos();
Matrix4x4::new(
c, 0.0, s, 0.0,
0.0, 1.0, 0.0, 0.0,
-s, 0.0, c, 0.0,
0.0, 0.0, 0.0, 1.0
)
}
/// Creates a new rotation matrix for rotation around the z axis.
///
/// # Arguments
///
/// * `radians`: angle to rotate the z axis around (in radians)
#[rustfmt::skip]
#[inline]
pub fn new_rotation_z(radians: f32) -> Matrix4x4 {
let (s, c) = radians.sin_cos();
Matrix4x4::new(
c, -s, 0.0, 0.0,
s, c, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0,
)
}
/// Creates a translation matrix.
///
/// # Arguments
///
/// * `x`: the amount to translate on the x axis
/// * `y`: the amount to translate on the y axis
/// * `z`: the amount to translate on the z axis
#[rustfmt::skip]
#[inline]
pub fn new_translation(x: f32, y: f32, z: f32) -> Matrix4x4 {
Matrix4x4::new(
1.0, 0.0, 0.0, x,
0.0, 1.0, 0.0, y,
0.0, 0.0, 1.0, z,
0.0, 0.0, 0.0, 1.0,
)
}
/// Creates a scaling matrix from scaling factors for each axis.
///
/// # Arguments
///
/// * `x`: the scale factor for the x axis
/// * `y`: the scale factor for the y axis
/// * `z`: the scale factor for the z axis
#[rustfmt::skip]
#[inline]
pub fn new_scaling(x: f32, y: f32, z: f32) -> Matrix4x4 {
Matrix4x4::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,
)
}
/// Calculates the determinant of this matrix.
#[rustfmt::skip]
#[inline]
pub fn determinant(&self) -> f32 {
(self.m[Matrix4x4::M11] * self.m[Matrix4x4::M22] - self.m[Matrix4x4::M21] * self.m[Matrix4x4::M12]) *
(self.m[Matrix4x4::M33] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M43] * self.m[Matrix4x4::M34]) -
(self.m[Matrix4x4::M11] * self.m[Matrix4x4::M32] - self.m[Matrix4x4::M31] * self.m[Matrix4x4::M12]) *
(self.m[Matrix4x4::M23] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M43] * self.m[Matrix4x4::M24]) +
(self.m[Matrix4x4::M11] * self.m[Matrix4x4::M42] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M12]) *
(self.m[Matrix4x4::M23] * self.m[Matrix4x4::M34] - self.m[Matrix4x4::M33] * self.m[Matrix4x4::M24]) +
(self.m[Matrix4x4::M21] * self.m[Matrix4x4::M32] - self.m[Matrix4x4::M31] * self.m[Matrix4x4::M22]) *
(self.m[Matrix4x4::M13] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M43] * self.m[Matrix4x4::M14]) -
(self.m[Matrix4x4::M21] * self.m[Matrix4x4::M42] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M22]) *
(self.m[Matrix4x4::M13] * self.m[Matrix4x4::M34] - self.m[Matrix4x4::M33] * self.m[Matrix4x4::M14]) +
(self.m[Matrix4x4::M31] * self.m[Matrix4x4::M42] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M32]) *
(self.m[Matrix4x4::M13] * self.m[Matrix4x4::M24] - self.m[Matrix4x4::M23] * self.m[Matrix4x4::M14])
}
/// Calculates the inverse of this matrix.
#[rustfmt::skip]
pub fn invert(&self) -> Matrix4x4 {
let d = self.determinant();
if nearly_equal(d, 0.0, 0.000001) {
Matrix4x4::IDENTITY
} else {
let d = 1.0 / d;
Matrix4x4 {
m: [
d * (self.m[Matrix4x4::M22] * (self.m[Matrix4x4::M33] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M43] * self.m[Matrix4x4::M34]) + self.m[Matrix4x4::M32] * (self.m[Matrix4x4::M43] * self.m[Matrix4x4::M24] - self.m[Matrix4x4::M23] * self.m[Matrix4x4::M44]) + self.m[Matrix4x4::M42] * (self.m[Matrix4x4::M23] * self.m[Matrix4x4::M34] - self.m[Matrix4x4::M33] * self.m[Matrix4x4::M24])),
d * (self.m[Matrix4x4::M23] * (self.m[Matrix4x4::M31] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M34]) + self.m[Matrix4x4::M33] * (self.m[Matrix4x4::M41] * self.m[Matrix4x4::M24] - self.m[Matrix4x4::M21] * self.m[Matrix4x4::M44]) + self.m[Matrix4x4::M43] * (self.m[Matrix4x4::M21] * self.m[Matrix4x4::M34] - self.m[Matrix4x4::M31] * self.m[Matrix4x4::M24])),
d * (self.m[Matrix4x4::M24] * (self.m[Matrix4x4::M31] * self.m[Matrix4x4::M42] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M32]) + self.m[Matrix4x4::M34] * (self.m[Matrix4x4::M41] * self.m[Matrix4x4::M22] - self.m[Matrix4x4::M21] * self.m[Matrix4x4::M42]) + self.m[Matrix4x4::M44] * (self.m[Matrix4x4::M21] * self.m[Matrix4x4::M32] - self.m[Matrix4x4::M31] * self.m[Matrix4x4::M22])),
d * (self.m[Matrix4x4::M21] * (self.m[Matrix4x4::M42] * self.m[Matrix4x4::M33] - self.m[Matrix4x4::M32] * self.m[Matrix4x4::M43]) + self.m[Matrix4x4::M31] * (self.m[Matrix4x4::M22] * self.m[Matrix4x4::M43] - self.m[Matrix4x4::M42] * self.m[Matrix4x4::M23]) + self.m[Matrix4x4::M41] * (self.m[Matrix4x4::M32] * self.m[Matrix4x4::M23] - self.m[Matrix4x4::M22] * self.m[Matrix4x4::M33])),
d * (self.m[Matrix4x4::M32] * (self.m[Matrix4x4::M13] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M43] * self.m[Matrix4x4::M14]) + self.m[Matrix4x4::M42] * (self.m[Matrix4x4::M33] * self.m[Matrix4x4::M14] - self.m[Matrix4x4::M13] * self.m[Matrix4x4::M34]) + self.m[Matrix4x4::M12] * (self.m[Matrix4x4::M43] * self.m[Matrix4x4::M34] - self.m[Matrix4x4::M33] * self.m[Matrix4x4::M44])),
d * (self.m[Matrix4x4::M33] * (self.m[Matrix4x4::M11] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M14]) + self.m[Matrix4x4::M43] * (self.m[Matrix4x4::M31] * self.m[Matrix4x4::M14] - self.m[Matrix4x4::M11] * self.m[Matrix4x4::M34]) + self.m[Matrix4x4::M13] * (self.m[Matrix4x4::M41] * self.m[Matrix4x4::M34] - self.m[Matrix4x4::M31] * self.m[Matrix4x4::M44])),
d * (self.m[Matrix4x4::M34] * (self.m[Matrix4x4::M11] * self.m[Matrix4x4::M42] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M12]) + self.m[Matrix4x4::M44] * (self.m[Matrix4x4::M31] * self.m[Matrix4x4::M12] - self.m[Matrix4x4::M11] * self.m[Matrix4x4::M32]) + self.m[Matrix4x4::M14] * (self.m[Matrix4x4::M41] * self.m[Matrix4x4::M32] - self.m[Matrix4x4::M31] * self.m[Matrix4x4::M42])),
d * (self.m[Matrix4x4::M31] * (self.m[Matrix4x4::M42] * self.m[Matrix4x4::M13] - self.m[Matrix4x4::M12] * self.m[Matrix4x4::M43]) + self.m[Matrix4x4::M41] * (self.m[Matrix4x4::M12] * self.m[Matrix4x4::M33] - self.m[Matrix4x4::M32] * self.m[Matrix4x4::M13]) + self.m[Matrix4x4::M11] * (self.m[Matrix4x4::M32] * self.m[Matrix4x4::M43] - self.m[Matrix4x4::M42] * self.m[Matrix4x4::M33])),
d * (self.m[Matrix4x4::M42] * (self.m[Matrix4x4::M13] * self.m[Matrix4x4::M24] - self.m[Matrix4x4::M23] * self.m[Matrix4x4::M14]) + self.m[Matrix4x4::M12] * (self.m[Matrix4x4::M23] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M43] * self.m[Matrix4x4::M24]) + self.m[Matrix4x4::M22] * (self.m[Matrix4x4::M43] * self.m[Matrix4x4::M14] - self.m[Matrix4x4::M13] * self.m[Matrix4x4::M44])),
d * (self.m[Matrix4x4::M43] * (self.m[Matrix4x4::M11] * self.m[Matrix4x4::M24] - self.m[Matrix4x4::M21] * self.m[Matrix4x4::M14]) + self.m[Matrix4x4::M13] * (self.m[Matrix4x4::M21] * self.m[Matrix4x4::M44] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M24]) + self.m[Matrix4x4::M23] * (self.m[Matrix4x4::M41] * self.m[Matrix4x4::M14] - self.m[Matrix4x4::M11] * self.m[Matrix4x4::M44])),
d * (self.m[Matrix4x4::M44] * (self.m[Matrix4x4::M11] * self.m[Matrix4x4::M22] - self.m[Matrix4x4::M21] * self.m[Matrix4x4::M12]) + self.m[Matrix4x4::M14] * (self.m[Matrix4x4::M21] * self.m[Matrix4x4::M42] - self.m[Matrix4x4::M41] * self.m[Matrix4x4::M22]) + self.m[Matrix4x4::M24] * (self.m[Matrix4x4::M41] * self.m[Matrix4x4::M12] - self.m[Matrix4x4::M11] * self.m[Matrix4x4::M42])),
d * (self.m[Matrix4x4::M41] * (self.m[Matrix4x4::M22] * self.m[Matrix4x4::M13] - self.m[Matrix4x4::M12] * self.m[Matrix4x4::M23]) + self.m[Matrix4x4::M11] * (self.m[Matrix4x4::M42] * self.m[Matrix4x4::M23] - self.m[Matrix4x4::M22] * self.m[Matrix4x4::M43]) + self.m[Matrix4x4::M21] * (self.m[Matrix4x4::M12] * self.m[Matrix4x4::M43] - self.m[Matrix4x4::M42] * self.m[Matrix4x4::M13])),
d * (self.m[Matrix4x4::M12] * (self.m[Matrix4x4::M33] * self.m[Matrix4x4::M24] - self.m[Matrix4x4::M23] * self.m[Matrix4x4::M34]) + self.m[Matrix4x4::M22] * (self.m[Matrix4x4::M13] * self.m[Matrix4x4::M34] - self.m[Matrix4x4::M33] * self.m[Matrix4x4::M14]) + self.m[Matrix4x4::M32] * (self.m[Matrix4x4::M23] * self.m[Matrix4x4::M14] - self.m[Matrix4x4::M13] * self.m[Matrix4x4::M24])),
d * (self.m[Matrix4x4::M13] * (self.m[Matrix4x4::M31] * self.m[Matrix4x4::M24] - self.m[Matrix4x4::M21] * self.m[Matrix4x4::M34]) + self.m[Matrix4x4::M23] * (self.m[Matrix4x4::M11] * self.m[Matrix4x4::M34] - self.m[Matrix4x4::M31] * self.m[Matrix4x4::M14]) + self.m[Matrix4x4::M33] * (self.m[Matrix4x4::M21] * self.m[Matrix4x4::M14] - self.m[Matrix4x4::M11] * self.m[Matrix4x4::M24])),
d * (self.m[Matrix4x4::M14] * (self.m[Matrix4x4::M31] * self.m[Matrix4x4::M22] - self.m[Matrix4x4::M21] * self.m[Matrix4x4::M32]) + self.m[Matrix4x4::M24] * (self.m[Matrix4x4::M11] * self.m[Matrix4x4::M32] - self.m[Matrix4x4::M31] * self.m[Matrix4x4::M12]) + self.m[Matrix4x4::M34] * (self.m[Matrix4x4::M21] * self.m[Matrix4x4::M12] - self.m[Matrix4x4::M11] * self.m[Matrix4x4::M22])),
d * (self.m[Matrix4x4::M11] * (self.m[Matrix4x4::M22] * self.m[Matrix4x4::M33] - self.m[Matrix4x4::M32] * self.m[Matrix4x4::M23]) + self.m[Matrix4x4::M21] * (self.m[Matrix4x4::M32] * self.m[Matrix4x4::M13] - self.m[Matrix4x4::M12] * self.m[Matrix4x4::M33]) + self.m[Matrix4x4::M31] * (self.m[Matrix4x4::M12] * self.m[Matrix4x4::M23] - self.m[Matrix4x4::M22] * self.m[Matrix4x4::M13])),
]
}
}
}
/// Calculates the transpose of this matrix.
#[rustfmt::skip]
pub fn transpose(&self) -> Matrix4x4 {
Matrix4x4::new(
self.m[Matrix4x4::M11], self.m[Matrix4x4::M21], self.m[Matrix4x4::M31], self.m[Matrix4x4::M41],
self.m[Matrix4x4::M12], self.m[Matrix4x4::M22], self.m[Matrix4x4::M32], self.m[Matrix4x4::M42],
self.m[Matrix4x4::M13], self.m[Matrix4x4::M23], self.m[Matrix4x4::M33], self.m[Matrix4x4::M43],
self.m[Matrix4x4::M14], self.m[Matrix4x4::M24], self.m[Matrix4x4::M34], self.m[Matrix4x4::M44],
)
}
/// Sets all of the elements of this matrix.
#[allow(clippy::too_many_arguments)]
#[rustfmt::skip]
#[inline]
pub fn set(
&mut self,
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,
) {
self.m = [
m11, m21, m31, m41,
m12, m22, m32, m42,
m13, m23, m33, m43,
m14, m24, m34, m44
];
}
/// Constructs a camera modelview matrix. This is equivalent to the OpenGL function `gluLookAt`.
///
/// # Arguments
///
/// * `position`: The position of the camera (eye).
/// * `target`: The direction that the camera is pointing (center).
/// * `up`: The up direction, relative to the camera.
#[rustfmt::skip]
pub fn new_look_at(position: &Vector3, target: &Vector3, up: &Vector3) -> Matrix4x4 {
let forward = (*target - *position).normalize();
let left = forward.cross(up).normalize();
let up = left.cross(&forward).normalize();
let out = Matrix4x4::new(
left.x, left.y, left.z, 0.0,
up.x, up.y, up.z, 0.0,
-forward.x, -forward.y, -forward.z, 0.0,
0.0, 0.0, 0.0, 1.0,
);
out * Matrix4x4::new_translation(position.x, position.y, position.z)
}
/// Constructs an orthogonal projection matrix. This is equivalent to the OpenGL function
/// `glOrtho`.
///
/// # Arguments
///
/// * `left`: Coordinate of the left vertical clipping plane.
/// * `right`: Coordinate of the right vertical clipping plane.
/// * `bottom`: Coordinate of the bottom horizontal clipping plane.
/// * `top`: Coordinate of the top horizontal clipping plane.
/// * `near`: Near clipping plane distance.
/// * `far`: Far clipping plane distance.
#[rustfmt::skip]
pub fn new_orthographic(left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32) -> Matrix4x4 {
Matrix4x4::new(
2.0 / (right - left), 0.0, 0.0, -((right + left) / (right - left)),
0.0, 2.0 / (top - bottom), 0.0, -((top + bottom) / (top - bottom)),
0.0, 0.0, -2.0 / (far - near), -((far + near) / (far - near)),
0.0, 0.0, 0.0, 1.0,
)
}
/// Constructs a perspective projection matrix. This is equivalent to a matrix created by the
/// OpenGL function `glFrustum`.
///
/// # Arguments
///
/// * `left`: Coordinate of the left vertical clipping plane.
/// * `right`: Coordinate of the right vertical clipping plane.
/// * `bottom`: Coordinate of the bottom horizontal clipping plane.
/// * `top`: Coordinate of the top horizontal clipping plane.
/// * `near`: Near clipping plane distance.
/// * `far`: Far clipping plane distance.
#[rustfmt::skip]
pub fn new_perspective(left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32) -> Matrix4x4 {
Matrix4x4::new(
(2.0 * near) / (right - left), 0.0, (right + left) / (right - left), 0.0,
0.0, (2.0 * near) / (top - bottom), (top + bottom) / (top - bottom), 0.0,
0.0, 0.0, -((far + near) / (far - near)), -((2.0 * far * near) / (far - near)),
0.0, 0.0, -1.0, 0.0,
)
}
/// Constructs a perspective projection matrix. This is equivalent to a matrix created by the
/// OpenGL function `gluPerspective`.
///
/// # Arguments
///
/// * `fov`: Angle specifying the field of view (in radians).
/// * `aspect_ratio`: The aspect ratio of the viewport.
/// * `near`: Near clipping plane distance.
/// * `far`: Far clipping plane distance.
#[rustfmt::skip]
pub fn new_perspective_fov(fov: f32, aspect_ratio: f32, near: f32, far: f32) -> Matrix4x4 {
let f = 1.0 / (fov / 2.0).tan();
Matrix4x4::new(
f / aspect_ratio, 0.0, 0.0, 0.0,
0.0, f, 0.0, 0.0,
0.0, 0.0, (far + near) / (near - far), (2.0 * far * near) / (near - far),
0.0, 0.0, -1.0, 0.0,
)
}
}
#[rustfmt::skip]
#[inline]
fn matrix4x4_mul(left: Matrix4x4, right: Matrix4x4) -> [f32; 16] {
[
left.m[Matrix4x4::M11] * right.m[Matrix4x4::M11] + left.m[Matrix4x4::M12] * right.m[Matrix4x4::M21] + left.m[Matrix4x4::M13] * right.m[Matrix4x4::M31] + left.m[Matrix4x4::M14] * right.m[Matrix4x4::M41],
left.m[Matrix4x4::M21] * right.m[Matrix4x4::M11] + left.m[Matrix4x4::M22] * right.m[Matrix4x4::M21] + left.m[Matrix4x4::M23] * right.m[Matrix4x4::M31] + left.m[Matrix4x4::M24] * right.m[Matrix4x4::M41],
left.m[Matrix4x4::M31] * right.m[Matrix4x4::M11] + left.m[Matrix4x4::M32] * right.m[Matrix4x4::M21] + left.m[Matrix4x4::M33] * right.m[Matrix4x4::M31] + left.m[Matrix4x4::M34] * right.m[Matrix4x4::M41],
left.m[Matrix4x4::M41] * right.m[Matrix4x4::M11] + left.m[Matrix4x4::M42] * right.m[Matrix4x4::M21] + left.m[Matrix4x4::M43] * right.m[Matrix4x4::M31] + left.m[Matrix4x4::M44] * right.m[Matrix4x4::M41],
left.m[Matrix4x4::M11] * right.m[Matrix4x4::M12] + left.m[Matrix4x4::M12] * right.m[Matrix4x4::M22] + left.m[Matrix4x4::M13] * right.m[Matrix4x4::M32] + left.m[Matrix4x4::M14] * right.m[Matrix4x4::M42],
left.m[Matrix4x4::M21] * right.m[Matrix4x4::M12] + left.m[Matrix4x4::M22] * right.m[Matrix4x4::M22] + left.m[Matrix4x4::M23] * right.m[Matrix4x4::M32] + left.m[Matrix4x4::M24] * right.m[Matrix4x4::M42],
left.m[Matrix4x4::M31] * right.m[Matrix4x4::M12] + left.m[Matrix4x4::M32] * right.m[Matrix4x4::M22] + left.m[Matrix4x4::M33] * right.m[Matrix4x4::M32] + left.m[Matrix4x4::M34] * right.m[Matrix4x4::M42],
left.m[Matrix4x4::M41] * right.m[Matrix4x4::M12] + left.m[Matrix4x4::M42] * right.m[Matrix4x4::M22] + left.m[Matrix4x4::M43] * right.m[Matrix4x4::M32] + left.m[Matrix4x4::M44] * right.m[Matrix4x4::M42],
left.m[Matrix4x4::M11] * right.m[Matrix4x4::M13] + left.m[Matrix4x4::M12] * right.m[Matrix4x4::M23] + left.m[Matrix4x4::M13] * right.m[Matrix4x4::M33] + left.m[Matrix4x4::M14] * right.m[Matrix4x4::M43],
left.m[Matrix4x4::M21] * right.m[Matrix4x4::M13] + left.m[Matrix4x4::M22] * right.m[Matrix4x4::M23] + left.m[Matrix4x4::M23] * right.m[Matrix4x4::M33] + left.m[Matrix4x4::M24] * right.m[Matrix4x4::M43],
left.m[Matrix4x4::M31] * right.m[Matrix4x4::M13] + left.m[Matrix4x4::M32] * right.m[Matrix4x4::M23] + left.m[Matrix4x4::M33] * right.m[Matrix4x4::M33] + left.m[Matrix4x4::M34] * right.m[Matrix4x4::M43],
left.m[Matrix4x4::M41] * right.m[Matrix4x4::M13] + left.m[Matrix4x4::M42] * right.m[Matrix4x4::M23] + left.m[Matrix4x4::M43] * right.m[Matrix4x4::M33] + left.m[Matrix4x4::M44] * right.m[Matrix4x4::M43],
left.m[Matrix4x4::M11] * right.m[Matrix4x4::M14] + left.m[Matrix4x4::M12] * right.m[Matrix4x4::M24] + left.m[Matrix4x4::M13] * right.m[Matrix4x4::M34] + left.m[Matrix4x4::M14] * right.m[Matrix4x4::M44],
left.m[Matrix4x4::M21] * right.m[Matrix4x4::M14] + left.m[Matrix4x4::M22] * right.m[Matrix4x4::M24] + left.m[Matrix4x4::M23] * right.m[Matrix4x4::M34] + left.m[Matrix4x4::M24] * right.m[Matrix4x4::M44],
left.m[Matrix4x4::M31] * right.m[Matrix4x4::M14] + left.m[Matrix4x4::M32] * right.m[Matrix4x4::M24] + left.m[Matrix4x4::M33] * right.m[Matrix4x4::M34] + left.m[Matrix4x4::M34] * right.m[Matrix4x4::M44],
left.m[Matrix4x4::M41] * right.m[Matrix4x4::M14] + left.m[Matrix4x4::M42] * right.m[Matrix4x4::M24] + left.m[Matrix4x4::M43] * right.m[Matrix4x4::M34] + left.m[Matrix4x4::M44] * right.m[Matrix4x4::M44],
]
}
impl Mul for Matrix4x4 {
type Output = Self;
#[inline]
fn mul(self, rhs: Self) -> Self::Output {
Matrix4x4 { m: matrix4x4_mul(self, rhs) }
}
}
impl MulAssign for Matrix4x4 {
#[inline]
fn mul_assign(&mut self, rhs: Self) {
self.m = matrix4x4_mul(*self, rhs);
}
}
impl Mul<Vector3> for Matrix4x4 {
type Output = Vector3;
#[rustfmt::skip]
#[inline]
fn mul(self, rhs: Vector3) -> Self::Output {
Vector3 {
x: rhs.x * self.m[Matrix4x4::M11] + rhs.y * self.m[Matrix4x4::M12] + rhs.z * self.m[Matrix4x4::M13] + self.m[Matrix4x4::M14],
y: rhs.x * self.m[Matrix4x4::M21] + rhs.y * self.m[Matrix4x4::M22] + rhs.z * self.m[Matrix4x4::M23] + self.m[Matrix4x4::M24],
z: rhs.x * self.m[Matrix4x4::M31] + rhs.y * self.m[Matrix4x4::M32] + rhs.z * self.m[Matrix4x4::M33] + self.m[Matrix4x4::M34],
}
}
}
impl Mul<Vector4> for Matrix4x4 {
type Output = Vector4;
#[rustfmt::skip]
#[inline]
fn mul(self, rhs: Vector4) -> Self::Output {
Vector4 {
x: rhs.x * self.m[Matrix4x4::M11] + rhs.y * self.m[Matrix4x4::M12] + rhs.z * self.m[Matrix4x4::M13] + rhs.w * self.m[Matrix4x4::M14],
y: rhs.x * self.m[Matrix4x4::M21] + rhs.y * self.m[Matrix4x4::M22] + rhs.z * self.m[Matrix4x4::M23] + rhs.w * self.m[Matrix4x4::M24],
z: rhs.x * self.m[Matrix4x4::M31] + rhs.y * self.m[Matrix4x4::M32] + rhs.z * self.m[Matrix4x4::M33] + rhs.w * self.m[Matrix4x4::M34],
w: rhs.x * self.m[Matrix4x4::M41] + rhs.y * self.m[Matrix4x4::M42] + rhs.z * self.m[Matrix4x4::M43] + rhs.w * self.m[Matrix4x4::M44],
}
}
}
#[cfg(test)]
mod tests {
use crate::math::*;
use super::*;
#[test]
pub fn test_new() {
let m = Matrix4x4::new(
1.1, 1.2, 1.3, 1.4, //
2.1, 2.2, 2.3, 2.4, //
3.1, 3.2, 3.3, 3.4, //
4.1, 4.2, 4.3, 4.4,
);
assert_eq!(1.1, m.m[Matrix4x4::M11]);
assert_eq!(1.2, m.m[Matrix4x4::M12]);
assert_eq!(1.3, m.m[Matrix4x4::M13]);
assert_eq!(1.4, m.m[Matrix4x4::M14]);
assert_eq!(2.1, m.m[Matrix4x4::M21]);
assert_eq!(2.2, m.m[Matrix4x4::M22]);
assert_eq!(2.3, m.m[Matrix4x4::M23]);
assert_eq!(2.4, m.m[Matrix4x4::M24]);
assert_eq!(3.1, m.m[Matrix4x4::M31]);
assert_eq!(3.2, m.m[Matrix4x4::M32]);
assert_eq!(3.3, m.m[Matrix4x4::M33]);
assert_eq!(3.4, m.m[Matrix4x4::M34]);
assert_eq!(4.1, m.m[Matrix4x4::M41]);
assert_eq!(4.2, m.m[Matrix4x4::M42]);
assert_eq!(4.3, m.m[Matrix4x4::M43]);
assert_eq!(4.4, m.m[Matrix4x4::M44]);
}
#[test]
pub fn test_set() {
let mut m = Matrix4x4 { m: [0.0; 16] };
m.set(
1.1, 1.2, 1.3, 1.4, //
2.1, 2.2, 2.3, 2.4, //
3.1, 3.2, 3.3, 3.4, //
4.1, 4.2, 4.3, 4.4,
);
assert_eq!(1.1, m.m[Matrix4x4::M11]);
assert_eq!(1.2, m.m[Matrix4x4::M12]);
assert_eq!(1.3, m.m[Matrix4x4::M13]);
assert_eq!(1.4, m.m[Matrix4x4::M14]);
assert_eq!(2.1, m.m[Matrix4x4::M21]);
assert_eq!(2.2, m.m[Matrix4x4::M22]);
assert_eq!(2.3, m.m[Matrix4x4::M23]);
assert_eq!(2.4, m.m[Matrix4x4::M24]);
assert_eq!(3.1, m.m[Matrix4x4::M31]);
assert_eq!(3.2, m.m[Matrix4x4::M32]);
assert_eq!(3.3, m.m[Matrix4x4::M33]);
assert_eq!(3.4, m.m[Matrix4x4::M34]);
assert_eq!(4.1, m.m[Matrix4x4::M41]);
assert_eq!(4.2, m.m[Matrix4x4::M42]);
assert_eq!(4.3, m.m[Matrix4x4::M43]);
assert_eq!(4.4, m.m[Matrix4x4::M44]);
}
#[test]
pub fn test_identity() {
let m = Matrix4x4::identity();
assert_eq!(1.0, m.m[Matrix4x4::M11]);
assert_eq!(0.0, m.m[Matrix4x4::M12]);
assert_eq!(0.0, m.m[Matrix4x4::M13]);
assert_eq!(0.0, m.m[Matrix4x4::M14]);
assert_eq!(0.0, m.m[Matrix4x4::M21]);
assert_eq!(1.0, m.m[Matrix4x4::M22]);
assert_eq!(0.0, m.m[Matrix4x4::M23]);
assert_eq!(0.0, m.m[Matrix4x4::M24]);
assert_eq!(0.0, m.m[Matrix4x4::M31]);
assert_eq!(0.0, m.m[Matrix4x4::M32]);
assert_eq!(1.0, m.m[Matrix4x4::M33]);
assert_eq!(0.0, m.m[Matrix4x4::M34]);
assert_eq!(0.0, m.m[Matrix4x4::M41]);
assert_eq!(0.0, m.m[Matrix4x4::M42]);
assert_eq!(0.0, m.m[Matrix4x4::M43]);
assert_eq!(1.0, m.m[Matrix4x4::M44]);
}
#[rustfmt::skip]
#[test]
pub fn test_transpose() {
let m = Matrix4x4::new(
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,
);
let t = m.transpose();
assert_eq!(1.0, t.m[Matrix4x4::M11]);
assert_eq!(5.0, t.m[Matrix4x4::M12]);
assert_eq!(9.0, t.m[Matrix4x4::M13]);
assert_eq!(13.0, t.m[Matrix4x4::M14]);
assert_eq!(2.0, t.m[Matrix4x4::M21]);
assert_eq!(6.0, t.m[Matrix4x4::M22]);
assert_eq!(10.0, t.m[Matrix4x4::M23]);
assert_eq!(14.0, t.m[Matrix4x4::M24]);
assert_eq!(3.0, t.m[Matrix4x4::M31]);
assert_eq!(7.0, t.m[Matrix4x4::M32]);
assert_eq!(11.0, t.m[Matrix4x4::M33]);
assert_eq!(15.0, t.m[Matrix4x4::M34]);
assert_eq!(4.0, t.m[Matrix4x4::M41]);
assert_eq!(8.0, t.m[Matrix4x4::M42]);
assert_eq!(12.0, t.m[Matrix4x4::M43]);
assert_eq!(16.0, t.m[Matrix4x4::M44]);
}
#[rustfmt::skip]
#[test]
pub fn test_mul() {
let a = Matrix4x4::new(
5.0, 7.0, 9.0, 10.0,
2.0, 3.0, 3.0, 8.0,
8.0, 10.0, 2.0, 3.0,
3.0, 3.0, 4.0, 8.0
);
let b = Matrix4x4::new(
3.0, 10.0, 12.0, 18.0,
12.0, 1.0, 4.0, 9.0,
9.0, 10.0, 12.0, 2.0,
3.0, 12.0, 4.0, 10.0
);
let c = a * b;
assert!(nearly_equal(210.0, c.m[Matrix4x4::M11], 0.001));
assert!(nearly_equal(267.0, c.m[Matrix4x4::M12], 0.001));
assert!(nearly_equal(236.0, c.m[Matrix4x4::M13], 0.001));
assert!(nearly_equal(271.0, c.m[Matrix4x4::M14], 0.001));
assert!(nearly_equal(93.0, c.m[Matrix4x4::M21], 0.001));
assert!(nearly_equal(149.0, c.m[Matrix4x4::M22], 0.001));
assert!(nearly_equal(104.0, c.m[Matrix4x4::M23], 0.001));
assert!(nearly_equal(149.0, c.m[Matrix4x4::M24], 0.001));
assert!(nearly_equal(171.0, c.m[Matrix4x4::M31], 0.001));
assert!(nearly_equal(146.0, c.m[Matrix4x4::M32], 0.001));
assert!(nearly_equal(172.0, c.m[Matrix4x4::M33], 0.001));
assert!(nearly_equal(268.0, c.m[Matrix4x4::M34], 0.001));
assert!(nearly_equal(105.0, c.m[Matrix4x4::M41], 0.001));
assert!(nearly_equal(169.0, c.m[Matrix4x4::M42], 0.001));
assert!(nearly_equal(128.0, c.m[Matrix4x4::M43], 0.001));
assert!(nearly_equal(169.0, c.m[Matrix4x4::M44], 0.001));
let c = b * a;
assert!(nearly_equal(185.0, c.m[Matrix4x4::M11], 0.001));
assert!(nearly_equal(225.0, c.m[Matrix4x4::M12], 0.001));
assert!(nearly_equal(153.0, c.m[Matrix4x4::M13], 0.001));
assert!(nearly_equal(290.0, c.m[Matrix4x4::M14], 0.001));
assert!(nearly_equal(121.0, c.m[Matrix4x4::M21], 0.001));
assert!(nearly_equal(154.0, c.m[Matrix4x4::M22], 0.001));
assert!(nearly_equal(155.0, c.m[Matrix4x4::M23], 0.001));
assert!(nearly_equal(212.0, c.m[Matrix4x4::M24], 0.001));
assert!(nearly_equal(167.0, c.m[Matrix4x4::M31], 0.001));
assert!(nearly_equal(219.0, c.m[Matrix4x4::M32], 0.001));
assert!(nearly_equal(143.0, c.m[Matrix4x4::M33], 0.001));
assert!(nearly_equal(222.0, c.m[Matrix4x4::M34], 0.001));
assert!(nearly_equal(101.0, c.m[Matrix4x4::M41], 0.001));
assert!(nearly_equal(127.0, c.m[Matrix4x4::M42], 0.001));
assert!(nearly_equal(111.0, c.m[Matrix4x4::M43], 0.001));
assert!(nearly_equal(218.0, c.m[Matrix4x4::M44], 0.001));
}
#[rustfmt::skip]
#[test]
pub fn test_mul_assign() {
let mut a = Matrix4x4::new(
5.0, 7.0, 9.0, 10.0,
2.0, 3.0, 3.0, 8.0,
8.0, 10.0, 2.0, 3.0,
3.0, 3.0, 4.0, 8.0
);
let b = Matrix4x4::new(
3.0, 10.0, 12.0, 18.0,
12.0, 1.0, 4.0, 9.0,
9.0, 10.0, 12.0, 2.0,
3.0, 12.0, 4.0, 10.0
);
a *= b;
assert!(nearly_equal(210.0, a.m[Matrix4x4::M11], 0.001));
assert!(nearly_equal(267.0, a.m[Matrix4x4::M12], 0.001));
assert!(nearly_equal(236.0, a.m[Matrix4x4::M13], 0.001));
assert!(nearly_equal(271.0, a.m[Matrix4x4::M14], 0.001));
assert!(nearly_equal(93.0, a.m[Matrix4x4::M21], 0.001));
assert!(nearly_equal(149.0, a.m[Matrix4x4::M22], 0.001));
assert!(nearly_equal(104.0, a.m[Matrix4x4::M23], 0.001));
assert!(nearly_equal(149.0, a.m[Matrix4x4::M24], 0.001));
assert!(nearly_equal(171.0, a.m[Matrix4x4::M31], 0.001));
assert!(nearly_equal(146.0, a.m[Matrix4x4::M32], 0.001));
assert!(nearly_equal(172.0, a.m[Matrix4x4::M33], 0.001));
assert!(nearly_equal(268.0, a.m[Matrix4x4::M34], 0.001));
assert!(nearly_equal(105.0, a.m[Matrix4x4::M41], 0.001));
assert!(nearly_equal(169.0, a.m[Matrix4x4::M42], 0.001));
assert!(nearly_equal(128.0, a.m[Matrix4x4::M43], 0.001));
assert!(nearly_equal(169.0, a.m[Matrix4x4::M44], 0.001));
let a = Matrix4x4::new(
5.0, 7.0, 9.0, 10.0,
2.0, 3.0, 3.0, 8.0,
8.0, 10.0, 2.0, 3.0,
3.0, 3.0, 4.0, 8.0
);
let mut b = Matrix4x4::new(
3.0, 10.0, 12.0, 18.0,
12.0, 1.0, 4.0, 9.0,
9.0, 10.0, 12.0, 2.0,
3.0, 12.0, 4.0, 10.0
);
b *= a;
assert!(nearly_equal(185.0, b.m[Matrix4x4::M11], 0.001));
assert!(nearly_equal(225.0, b.m[Matrix4x4::M12], 0.001));
assert!(nearly_equal(153.0, b.m[Matrix4x4::M13], 0.001));
assert!(nearly_equal(290.0, b.m[Matrix4x4::M14], 0.001));
assert!(nearly_equal(121.0, b.m[Matrix4x4::M21], 0.001));
assert!(nearly_equal(154.0, b.m[Matrix4x4::M22], 0.001));
assert!(nearly_equal(155.0, b.m[Matrix4x4::M23], 0.001));
assert!(nearly_equal(212.0, b.m[Matrix4x4::M24], 0.001));
assert!(nearly_equal(167.0, b.m[Matrix4x4::M31], 0.001));
assert!(nearly_equal(219.0, b.m[Matrix4x4::M32], 0.001));
assert!(nearly_equal(143.0, b.m[Matrix4x4::M33], 0.001));
assert!(nearly_equal(222.0, b.m[Matrix4x4::M34], 0.001));
assert!(nearly_equal(101.0, b.m[Matrix4x4::M41], 0.001));
assert!(nearly_equal(127.0, b.m[Matrix4x4::M42], 0.001));
assert!(nearly_equal(111.0, b.m[Matrix4x4::M43], 0.001));
assert!(nearly_equal(218.0, b.m[Matrix4x4::M44], 0.001));
}
#[rustfmt::skip]
#[test]
pub fn test_vector4_mul() {
let v = Vector4::new(1.0, 2.0, 3.0, 4.0);
let m = Matrix4x4::new(
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,
);
let t = m * v;
assert!(nearly_equal(t.x, 30.0, 0.0001));
assert!(nearly_equal(t.y, 70.0, 0.0001));
assert!(nearly_equal(t.z, 110.0, 0.0001));
assert!(nearly_equal(t.w, 150.0, 0.0001));
}
#[test]
pub fn test_translation() {
let v = Vector3::new(10.2, 5.7, 1.8);
let m = Matrix4x4::new_translation(2.0, 3.0, -1.7);
let t = m * v;
assert!(nearly_equal(12.2, t.x, 0.001));
assert!(nearly_equal(8.7, t.y, 0.001));
assert!(nearly_equal(0.1, t.z, 0.001));
}
#[test]
pub fn test_scaling() {
let v = Vector3::new(10.2, 5.7, 1.8);
let m = Matrix4x4::new_scaling(3.0, 4.0, 0.5);
let t = m * v;
assert!(nearly_equal(30.6, t.x, 0.001));
assert!(nearly_equal(22.8, t.y, 0.001));
assert!(nearly_equal(0.9, t.z, 0.001));
}
#[test]
pub fn test_rotation_x() {
let v = Vector3::new(10.2, 5.7, 1.8);
let m = Matrix4x4::new_rotation_x(45.0f32.to_radians());
let t = m * v;
assert!(nearly_equal(10.2, t.x, 0.001));
assert!(nearly_equal(2.757, t.y, 0.001));
assert!(nearly_equal(5.303, t.z, 0.001));
}
#[test]
pub fn test_rotation_y() {
let v = Vector3::new(10.2, 5.7, 1.8);
let m = Matrix4x4::new_rotation_y(45.0f32.to_radians());
let t = m * v;
assert!(nearly_equal(8.485, t.x, 0.001));
assert!(nearly_equal(5.7, t.y, 0.001));
assert!(nearly_equal(-5.939, t.z, 0.001));
}
#[test]
pub fn test_rotation_z() {
let v = Vector3::new(10.2, 5.7, 1.8);
let m = Matrix4x4::new_rotation_z(45.0f32.to_radians());
let t = m * v;
assert!(nearly_equal(3.181, t.x, 0.001));
assert!(nearly_equal(11.243, t.y, 0.001));
assert!(nearly_equal(1.8, t.z, 0.001));
}
#[rustfmt::skip]
#[test]
pub fn test_determinant() {
let m = Matrix4x4::new(
1.0, 2.0, 6.0, 6.0,
4.0, 7.0, 3.0, 2.0,
0.0, 0.0, 0.0, 0.0,
1.0, 2.0, 2.0, 9.0
);
let d = m.determinant();
assert!(nearly_equal(0.0, d, 0.000001));
let m = Matrix4x4::new(
5.0, 7.0, 9.0, 10.0,
2.0, 3.0, 3.0, 8.0,
8.0, 10.0, 2.0, 3.0,
3.0, 3.0, 4.0, 8.0
);
let d = m.determinant();
assert!(nearly_equal(-361.0, d, 0.001));
}
#[rustfmt::skip]
#[test]
pub fn test_invert() {
let m = Matrix4x4::new(
1.0, 2.0, 6.0, 6.0,
4.0, 7.0, 3.0, 2.0,
0.0, 0.0, 0.0, 0.0,
1.0, 2.0, 2.0, 9.0
);
let inv = m.invert();
assert!(nearly_equal(1.0, inv.m[Matrix4x4::M11], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M12], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M13], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M14], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M21], 0.000001));
assert!(nearly_equal(1.0, inv.m[Matrix4x4::M22], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M23], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M24], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M31], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M32], 0.000001));
assert!(nearly_equal(1.0, inv.m[Matrix4x4::M33], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M34], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M41], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M42], 0.000001));
assert!(nearly_equal(0.0, inv.m[Matrix4x4::M43], 0.000001));
assert!(nearly_equal(1.0, inv.m[Matrix4x4::M44], 0.000001));
let m = Matrix4x4::new(
5.0, 7.0, 9.0, 10.0,
2.0, 3.0, 3.0, 8.0,
8.0, 10.0, 2.0, 3.0,
3.0, 3.0, 4.0, 8.0
);
let inv = m.invert();
assert!(nearly_equal(-0.196676, inv.m[Matrix4x4::M11], 0.000001));
assert!(nearly_equal(-0.750693, inv.m[Matrix4x4::M12], 0.000001));
assert!(nearly_equal( 0.072022, inv.m[Matrix4x4::M13], 0.000001));
assert!(nearly_equal( 0.969529, inv.m[Matrix4x4::M14], 0.000001));
assert!(nearly_equal( 0.141274, inv.m[Matrix4x4::M21], 0.000001));
assert!(nearly_equal( 0.595568, inv.m[Matrix4x4::M22], 0.000001));
assert!(nearly_equal( 0.060941, inv.m[Matrix4x4::M23], 0.000001));
assert!(nearly_equal(-0.795014, inv.m[Matrix4x4::M24], 0.000001));
assert!(nearly_equal( 0.196676, inv.m[Matrix4x4::M31], 0.000001));
assert!(nearly_equal(-0.249307, inv.m[Matrix4x4::M32], 0.000001));
assert!(nearly_equal(-0.072022, inv.m[Matrix4x4::M33], 0.000001));
assert!(nearly_equal( 0.030471, inv.m[Matrix4x4::M34], 0.000001));
assert!(nearly_equal(-0.077562, inv.m[Matrix4x4::M41], 0.000001));
assert!(nearly_equal( 0.182825, inv.m[Matrix4x4::M42], 0.000001));
assert!(nearly_equal(-0.013850, inv.m[Matrix4x4::M43], 0.000001));
assert!(nearly_equal( 0.044321, inv.m[Matrix4x4::M44], 0.000001));
}
}

6
ggdt/src/math/mod.rs
View file

@ -4,13 +4,19 @@ use std::simd::prelude::{SimdFloat, SimdPartialOrd};
mod circle; mod circle;
mod matrix3x3; mod matrix3x3;
mod matrix4x4;
mod rect; mod rect;
mod vector2; mod vector2;
mod vector3;
mod vector4;
pub use circle::*; pub use circle::*;
pub use matrix3x3::*; pub use matrix3x3::*;
pub use matrix4x4::*;
pub use rect::*; pub use rect::*;
pub use vector2::*; pub use vector2::*;
pub use vector3::*;
pub use vector4::*;
pub const PI: f32 = std::f32::consts::PI; pub const PI: f32 = std::f32::consts::PI;
// 180 degrees // 180 degrees

455
ggdt/src/math/vector3.rs Normal file
View file

@ -0,0 +1,455 @@
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
use crate::math::{nearly_equal, NearlyEqual};
/// Represents a 3D vector and provides common methods for vector math.
/// Uses a right-handed 3D coordinate system.
#[derive(Debug, Copy, Clone, PartialEq)]
pub struct Vector3 {
pub x: f32,
pub y: f32,
pub z: f32,
}
impl Vector3 {
pub const ZERO: Vector3 = Vector3 { x: 0.0, y: 0.0, z: 0.0 };
pub const UP: Vector3 = Vector3 { x: 0.0, y: 1.0, z: 0.0 };
pub const DOWN: Vector3 = Vector3 { x: 0.0, y: -1.0, z: 0.0 };
pub const FORWARD: Vector3 = Vector3 { x: 0.0, y: 0.0, z: -1.0 };
pub const BACKWARD: Vector3 = Vector3 { x: 0.0, y: 0.0, z: 1.0 };
pub const LEFT: Vector3 = Vector3 { x: -1.0, y: 0.0, z: 0.0 };
pub const RIGHT: Vector3 = Vector3 { x: 1.0, y: 0.0, z: 0.0 };
pub const X_AXIS: Vector3 = Vector3 { x: 1.0, y: 0.0, z: 0.0 };
pub const Y_AXIS: Vector3 = Vector3 { x: 0.0, y: 1.0, z: 0.0 };
pub const Z_AXIS: Vector3 = Vector3 { x: 0.0, y: 0.0, z: 1.0 };
/// Creates a new vector with the specified X, Y and Z components.
#[inline]
pub fn new(x: f32, y: f32, z: f32) -> Vector3 {
Vector3 { x, y, z }
}
/// Returns the cross product of this and another vector.
#[inline]
pub fn cross(&self, other: &Vector3) -> Vector3 {
Vector3 {
x: (self.y * other.z) - (self.z * other.y),
y: (self.z * other.x) - (self.x * other.z),
z: (self.x * other.y) - (self.y * other.x),
}
}
/// Calculates the distance between this and another vector.
#[inline]
pub fn distance(&self, other: &Vector3) -> f32 {
self.distance_squared(other).sqrt()
}
/// Calculates the squared distance between this and another vector.
#[inline]
pub fn distance_squared(&self, other: &Vector3) -> f32 {
((other.x - self.x) * (other.x - self.x))
+ ((other.y - self.y) * (other.y - self.y))
+ ((other.z - self.z) * (other.z - self.z))
}
/// Calculates the dot product of this and another vector.
#[inline]
pub fn dot(&self, other: &Vector3) -> f32 {
(self.x * other.x) + (self.y * other.y) + (self.z * other.z)
}
/// Calculate the length (a.k.a. magnitude) of this vector.
#[inline]
pub fn length(&self) -> f32 {
self.length_squared().sqrt()
}
/// Calculates the squared length of this vector.
#[inline]
pub fn length_squared(&self) -> f32 {
(self.x * self.x) + (self.y * self.y) + (self.z * self.z)
}
/// Returns a normalized vector from this vector.
#[inline]
pub fn normalize(&self) -> Vector3 {
let inverse_length = 1.0 / self.length();
Vector3 {
x: self.x * inverse_length, //
y: self.y * inverse_length,
z: self.z * inverse_length,
}
}
/// Returns an extended (or shrunk) vector from this vector, where the returned vector will
/// have a length exactly matching the specified length, but will return the same direction.
#[inline]
pub fn extend(&self, length: f32) -> Vector3 {
*self * (length / self.length())
}
}
impl Neg for Vector3 {
type Output = Self;
#[inline]
fn neg(self) -> Self::Output {
Vector3 {
x: -self.x, //
y: -self.y,
z: -self.z,
}
}
}
impl Add for Vector3 {
type Output = Self;
#[inline]
fn add(self, rhs: Self) -> Self::Output {
Vector3 {
x: self.x + rhs.x, //
y: self.y + rhs.y,
z: self.z + rhs.z,
}
}
}
impl AddAssign for Vector3 {
#[inline]
fn add_assign(&mut self, rhs: Self) {
self.x += rhs.x;
self.y += rhs.y;
self.z += rhs.z;
}
}
impl Sub for Vector3 {
type Output = Self;
#[inline]
fn sub(self, rhs: Self) -> Self::Output {
Vector3 {
x: self.x - rhs.x, //
y: self.y - rhs.y,
z: self.z - rhs.z,
}
}
}
impl SubAssign for Vector3 {
#[inline]
fn sub_assign(&mut self, rhs: Self) {
self.x -= rhs.x;
self.y -= rhs.y;
self.z -= rhs.z;
}
}
impl Mul for Vector3 {
type Output = Self;
#[inline]
fn mul(self, rhs: Self) -> Self::Output {
Vector3 {
x: self.x * rhs.x, //
y: self.y * rhs.y,
z: self.z * rhs.z,
}
}
}
impl MulAssign for Vector3 {
#[inline]
fn mul_assign(&mut self, rhs: Self) {
self.x *= rhs.x;
self.y *= rhs.y;
self.z *= rhs.z;
}
}
impl Div for Vector3 {
type Output = Self;
#[inline]
fn div(self, rhs: Self) -> Self::Output {
Vector3 {
x: self.x / rhs.x, //
y: self.y / rhs.y,
z: self.z / rhs.z,
}
}
}
impl DivAssign for Vector3 {
#[inline]
fn div_assign(&mut self, rhs: Self) {
self.x /= rhs.x;
self.y /= rhs.y;
self.z /= rhs.z;
}
}
impl Mul<f32> for Vector3 {
type Output = Self;
#[inline]
fn mul(self, rhs: f32) -> Self::Output {
Vector3 {
x: self.x * rhs, //
y: self.y * rhs,
z: self.z * rhs,
}
}
}
impl MulAssign<f32> for Vector3 {
#[inline]
fn mul_assign(&mut self, rhs: f32) {
self.x *= rhs;
self.y *= rhs;
self.z *= rhs;
}
}
impl Div<f32> for Vector3 {
type Output = Self;
#[inline]
fn div(self, rhs: f32) -> Self::Output {
Vector3 {
x: self.x / rhs, //
y: self.y / rhs,
z: self.z / rhs,
}
}
}
impl DivAssign<f32> for Vector3 {
#[inline]
fn div_assign(&mut self, rhs: f32) {
self.x /= rhs;
self.y /= rhs;
self.z /= rhs;
}
}
impl NearlyEqual for Vector3 {
type Output = Self;
#[inline]
fn nearly_equal(self, other: Self::Output, epsilon: f32) -> bool {
nearly_equal(self.x, other.x, epsilon)
&& nearly_equal(self.y, other.y, epsilon)
&& nearly_equal(self.z, other.z, epsilon)
}
}
#[cfg(test)]
mod tests {
use crate::math::*;
use super::*;
#[test]
pub fn test_new() {
let v = Vector3::new(3.0, 7.0, -1.4);
assert!(nearly_equal(v.x, 3.0, 0.0001));
assert!(nearly_equal(v.y, 7.0, 0.0001));
assert!(nearly_equal(v.z, -1.4, 0.0001));
}
#[test]
pub fn test_neg() {
let v = Vector3 { x: 1.0, y: 2.0, z: -3.0 };
let neg = -v;
assert!(nearly_equal(neg.x, -1.0, 0.0001));
assert!(nearly_equal(neg.y, -2.0, 0.0001));
assert!(nearly_equal(neg.z, 3.0, 0.0001));
}
#[test]
pub fn test_add() {
let a = Vector3 { x: 3.0, y: 4.0, z: 6.0 };
let b = Vector3 { x: 1.0, y: 2.0, z: 5.0 };
let c = a + b;
assert!(nearly_equal(c.x, 4.0, 0.0001));
assert!(nearly_equal(c.y, 6.0, 0.0001));
assert!(nearly_equal(c.z, 11.0, 0.0001));
let mut a = Vector3 { x: 3.0, y: 4.0, z: 6.0 };
let b = Vector3 { x: 1.0, y: 2.0, z: 5.0 };
a += b;
assert!(nearly_equal(a.x, 4.0, 0.0001));
assert!(nearly_equal(a.y, 6.0, 0.0001));
assert!(nearly_equal(a.z, 11.0, 0.0001));
}
#[test]
pub fn test_sub() {
let a = Vector3 { x: 3.0, y: 4.0, z: 6.0 };
let b = Vector3 { x: 1.0, y: 2.0, z: 5.0 };
let c = a - b;
assert!(nearly_equal(c.x, 2.0, 0.0001));
assert!(nearly_equal(c.y, 2.0, 0.0001));
assert!(nearly_equal(c.z, 1.0, 0.0001));
let mut a = Vector3 { x: 3.0, y: 4.0, z: 6.0 };
let b = Vector3 { x: 1.0, y: 2.0, z: 5.0 };
a -= b;
assert!(nearly_equal(a.x, 2.0, 0.0001));
assert!(nearly_equal(a.y, 2.0, 0.0001));
assert!(nearly_equal(a.z, 1.0, 0.0001));
}
#[test]
pub fn test_mul() {
let a = Vector3 { x: 2.5, y: 6.0, z: 3.0 };
let b = Vector3 { x: 1.25, y: 2.0, z: 2.5 };
let c = a * b;
assert!(nearly_equal(c.x, 3.125, 0.0001));
assert!(nearly_equal(c.y, 12.0, 0.0001));
assert!(nearly_equal(c.z, 7.5, 0.0001));
let mut a = Vector3 { x: 2.5, y: 6.0, z: 3.0 };
let b = Vector3 { x: 1.25, y: 2.0, z: 2.5 };
a *= b;
assert!(nearly_equal(a.x, 3.125, 0.0001));
assert!(nearly_equal(a.y, 12.0, 0.0001));
assert!(nearly_equal(a.z, 7.5, 0.0001));
}
#[test]
pub fn test_div() {
let a = Vector3 { x: 2.5, y: 6.0, z: 3.0 };
let b = Vector3 { x: 1.25, y: 2.0, z: 2.5 };
let c = a / b;
assert!(nearly_equal(c.x, 2.0, 0.0001));
assert!(nearly_equal(c.y, 3.0, 0.0001));
assert!(nearly_equal(c.z, 1.2, 0.0001));
let mut a = Vector3 { x: 2.5, y: 6.0, z: 3.0 };
let b = Vector3 { x: 1.25, y: 2.0, z: 2.5 };
a /= b;
assert!(nearly_equal(a.x, 2.0, 0.0001));
assert!(nearly_equal(a.y, 3.0, 0.0001));
assert!(nearly_equal(a.z, 1.2, 0.0001));
}
#[test]
pub fn test_scalar_mul() {
let a = Vector3 { x: 1.0, y: 2.0, z: -3.0 };
let b = a * 2.0;
assert!(nearly_equal(b.x, 2.0, 0.0001));
assert!(nearly_equal(b.y, 4.0, 0.0001));
assert!(nearly_equal(b.z, -6.0, 0.0001));
let mut a = Vector3 { x: 1.0, y: 2.0, z: -3.0 };
a *= 2.0;
assert!(nearly_equal(b.x, 2.0, 0.0001));
assert!(nearly_equal(b.y, 4.0, 0.0001));
assert!(nearly_equal(b.z, -6.0, 0.0001));
}
#[test]
pub fn test_scalar_div() {
let a = Vector3 { x: 1.0, y: 2.0, z: -3.0 };
let b = a / 2.0;
assert!(nearly_equal(b.x, 0.5, 0.0001));
assert!(nearly_equal(b.y, 1.0, 0.0001));
assert!(nearly_equal(b.z, -1.5, 0.0001));
let mut a = Vector3 { x: 1.0, y: 2.0, z: -3.0 };
a /= 2.0;
assert!(nearly_equal(b.x, 0.5, 0.0001));
assert!(nearly_equal(b.y, 1.0, 0.0001));
assert!(nearly_equal(b.z, -1.5, 0.0001));
}
#[test]
pub fn test_nearly_equal() {
let a = Vector3 { x: 3.4, y: -7.1, z: 1.8 };
let b = Vector3 { x: 3.5, y: -7.1, z: 1.8 };
assert!(!a.nearly_equal(b, 0.0001));
let a = Vector3 { x: 2.0, y: 4.0, z: 6.1 };
let b = Vector3 { x: 2.0, y: 4.0, z: 6.1 };
assert!(a.nearly_equal(b, 0.0001));
}
#[test]
pub fn test_length() {
let v = Vector3 { x: 3.0, y: -2.0, z: 1.0 };
let length_squared = v.length_squared();
let length = v.length();
assert!(nearly_equal(length_squared, 14.0, 0.0001));
assert!(nearly_equal(length, 3.7416, 0.0001));
let v = Vector3 { x: 11.6, y: 0.0, z: 4.0 };
let length_squared = v.length_squared();
let length = v.length();
assert!(nearly_equal(length_squared, 150.56, 0.0001));
assert!(nearly_equal(length, 12.2702, 0.0001));
}
#[test]
pub fn test_dot() {
let a = Vector3 { x: -1.0, y: 2.0, z: 3.0 };
let b = Vector3 { x: 0.0, y: 5.0, z: 1.0 };
let dot = a.dot(&b);
assert!(nearly_equal(dot, 13.0, 0.0001));
let a = Vector3 { x: 4.0, y: 0.0, z: -3.0 };
let b = Vector3 { x: 0.0, y: -2.0, z: 0.0 };
let dot = a.dot(&b);
assert!(nearly_equal(dot, 0.0, 0.0001));
}
#[test]
pub fn test_distance() {
let a = Vector3 { x: 6.0, y: 2.5, z: -3.0 };
let b = Vector3 { x: 1.1, y: -4.0, z: 5.0 };
let distance_squared = a.distance_squared(&b);
let distance = a.distance(&b);
assert!(nearly_equal(distance_squared, 130.26, 0.0001));
assert!(nearly_equal(distance, 11.4131, 0.0001));
let a = Vector3 { x: 7.1, y: 4.0, z: 3.0 };
let b = Vector3 { x: 17.0, y: -6.0, z: 2.5 };
let distance_squared = a.distance_squared(&b);
let distance = a.distance(&b);
assert!(nearly_equal(distance_squared, 198.26, 0.0001));
assert!(nearly_equal(distance, 14.0804, 0.0001));
}
#[test]
pub fn test_normalize() {
let v = Vector3 { x: 3.0, y: 1.0, z: 2.0 };
let normalized = v.normalize();
assert!(nearly_equal(normalized.x, 0.8017, 0.0001));
assert!(nearly_equal(normalized.y, 0.2672, 0.0001));
assert!(nearly_equal(normalized.z, 0.5345, 0.0001));
}
#[test]
pub fn test_extend() {
let v = Vector3 { x: 3.0, y: -2.0, z: 1.0 };
let extended = v.extend(7.4832);
assert!(nearly_equal(extended.x, 6.0, 0.0001));
assert!(nearly_equal(extended.y, -4.0, 0.0001));
assert!(nearly_equal(extended.z, 2.0, 0.0001));
}
#[test]
pub fn test_lerp() {
let a = Vector3 { x: 5.0, y: 1.0, z: 3.0 };
let b = Vector3 { x: 10.0, y: 2.0, z: 6.0 };
let c = lerp(a, b, 0.5);
assert!(nearly_equal(c.x, 7.5, 0.0001));
assert!(nearly_equal(c.y, 1.5, 0.0001));
assert!(nearly_equal(c.z, 4.5, 0.0001));
}
}

456
ggdt/src/math/vector4.rs Normal file
View file

@ -0,0 +1,456 @@
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
use super::{nearly_equal, NearlyEqual};
/// Represents a 4D vector and provides common methods for vector math.
/// Uses a right-handed 3D coordinate system.
#[derive(Debug, Copy, Clone, PartialEq)]
pub struct Vector4 {
pub x: f32,
pub y: f32,
pub z: f32,
pub w: f32,
}
impl Vector4 {
pub const ZERO: Vector4 = Vector4 { x: 0.0, y: 0.0, z: 0.0, w: 0.0 };
/// Creates a new vector with the specified X, Y, Z and W components.
#[inline]
pub fn new(x: f32, y: f32, z: f32, w: f32) -> Vector4 {
Vector4 { x, y, z, w }
}
/// Calculates the distance between this and another vector.
#[inline]
pub fn distance(&self, other: &Vector4) -> f32 {
self.distance_squared(other).sqrt()
}
/// Calculates the squared distance between this and another vector.
#[inline]
pub fn distance_squared(&self, other: &Vector4) -> f32 {
((other.x - self.x) * (other.x - self.x))
+ ((other.y - self.y) * (other.y - self.y))
+ ((other.z - self.z) * (other.z - self.z))
+ ((other.w - self.w) * (other.w - self.w))
}
/// Calculates the dot product of this and another vector.
#[inline]
pub fn dot(&self, other: &Vector4) -> f32 {
(self.x * other.x) + (self.y * other.y) + (self.z * other.z) + (self.w * other.w)
}
/// Calculates the length (a.k.a. magnitude) of this vector.
#[inline]
pub fn length(&self) -> f32 {
self.length_squared().sqrt()
}
/// Calculates the squared length of this vector.
#[inline]
pub fn length_squared(&self) -> f32 {
(self.x * self.x) + (self.y * self.y) + (self.z * self.z) + (self.w * self.w)
}
/// Returns a normalized vector from this vector.
#[inline]
pub fn normalize(&self) -> Vector4 {
let inverse_length = 1.0 / self.length();
Vector4 {
x: self.x * inverse_length, //
y: self.y * inverse_length,
z: self.z * inverse_length,
w: self.w * inverse_length,
}
}
/// Returns an extended (or shrunk) vector from this vector, where the returned vector will
/// have a length exactly matching the specified length, but will retain the same
/// direction.
#[inline]
pub fn extend(&self, length: f32) -> Vector4 {
*self * (length / self.length())
}
}
impl Neg for Vector4 {
type Output = Self;
#[inline]
fn neg(self) -> Self::Output {
Vector4 {
x: -self.x, //
y: -self.y,
z: -self.z,
w: -self.w,
}
}
}
impl Add for Vector4 {
type Output = Self;
fn add(self, rhs: Self) -> Self::Output {
Vector4 {
x: self.x + rhs.x, //
y: self.y + rhs.y,
z: self.z + rhs.z,
w: self.w + rhs.w,
}
}
}
impl AddAssign for Vector4 {
fn add_assign(&mut self, rhs: Self) {
self.x += rhs.x;
self.y += rhs.y;
self.z += rhs.z;
self.w += rhs.w;
}
}
impl Sub for Vector4 {
type Output = Self;
fn sub(self, rhs: Self) -> Self::Output {
Vector4 {
x: self.x - rhs.x, //
y: self.y - rhs.y,
z: self.z - rhs.z,
w: self.w - rhs.w,
}
}
}
impl SubAssign for Vector4 {
fn sub_assign(&mut self, rhs: Self) {
self.x -= rhs.x;
self.y -= rhs.y;
self.z -= rhs.z;
self.w -= rhs.w;
}
}
impl Mul for Vector4 {
type Output = Self;
fn mul(self, rhs: Self) -> Self::Output {
Vector4 {
x: self.x * rhs.x, //
y: self.y * rhs.y,
z: self.z * rhs.z,
w: self.w * rhs.w,
}
}
}
impl MulAssign for Vector4 {
fn mul_assign(&mut self, rhs: Self) {
self.x *= rhs.x;
self.y *= rhs.y;
self.z *= rhs.z;
self.w *= rhs.w;
}
}
impl Div for Vector4 {
type Output = Self;
fn div(self, rhs: Self) -> Self::Output {
Vector4 {
x: self.x / rhs.x, //
y: self.y / rhs.y,
z: self.z / rhs.z,
w: self.w / rhs.w,
}
}
}
impl DivAssign for Vector4 {
fn div_assign(&mut self, rhs: Self) {
self.x /= rhs.x;
self.y /= rhs.y;
self.z /= rhs.z;
self.w /= rhs.w;
}
}
impl Mul<f32> for Vector4 {
type Output = Self;
fn mul(self, rhs: f32) -> Self::Output {
Vector4 {
x: self.x * rhs, //
y: self.y * rhs,
z: self.z * rhs,
w: self.w * rhs,
}
}
}
impl MulAssign<f32> for Vector4 {
fn mul_assign(&mut self, rhs: f32) {
self.x *= rhs;
self.y *= rhs;
self.z *= rhs;
self.w *= rhs;
}
}
impl Div<f32> for Vector4 {
type Output = Self;
fn div(self, rhs: f32) -> Self::Output {
Vector4 {
x: self.x / rhs, //
y: self.y / rhs,
z: self.z / rhs,
w: self.w / rhs,
}
}
}
impl DivAssign<f32> for Vector4 {
fn div_assign(&mut self, rhs: f32) {
self.x /= rhs;
self.y /= rhs;
self.z /= rhs;
self.w /= rhs;
}
}
impl NearlyEqual for Vector4 {
type Output = Self;
fn nearly_equal(self, other: Self::Output, epsilon: f32) -> bool {
nearly_equal(self.x, other.x, epsilon)
&& nearly_equal(self.y, other.y, epsilon)
&& nearly_equal(self.z, other.z, epsilon)
&& nearly_equal(self.w, other.w, epsilon)
}
}
#[cfg(test)]
mod tests {
use crate::math::*;
use super::*;
#[test]
pub fn test_new() {
let v = Vector4::new(3.0, 7.0, -1.4, 2.1);
assert!(nearly_equal(v.x, 3.0, 0.0001));
assert!(nearly_equal(v.y, 7.0, 0.0001));
assert!(nearly_equal(v.z, -1.4, 0.0001));
assert!(nearly_equal(v.w, 2.1, 0.0001));
}
#[test]
pub fn test_neg() {
let v = Vector4 { x: 1.0, y: 2.0, z: -3.0, w: 4.0 };
let neg = -v;
assert!(nearly_equal(neg.x, -1.0, 0.0001));
assert!(nearly_equal(neg.y, -2.0, 0.0001));
assert!(nearly_equal(neg.z, 3.0, 0.0001));
assert!(nearly_equal(neg.w, -4.0, 0.0001));
}
#[test]
pub fn test_add() {
let a = Vector4 { x: 3.0, y: 4.0, z: 6.0, w: 7.0 };
let b = Vector4 { x: 1.0, y: 2.0, z: 5.0, w: 8.0 };
let c = a + b;
assert!(nearly_equal(c.x, 4.0, 0.0001));
assert!(nearly_equal(c.y, 6.0, 0.0001));
assert!(nearly_equal(c.z, 11.0, 0.0001));
assert!(nearly_equal(c.w, 15.0, 0.0001));
let mut a = Vector4 { x: 3.0, y: 4.0, z: 6.0, w: 7.0 };
let b = Vector4 { x: 1.0, y: 2.0, z: 5.0, w: 8.0 };
a += b;
assert!(nearly_equal(a.x, 4.0, 0.0001));
assert!(nearly_equal(a.y, 6.0, 0.0001));
assert!(nearly_equal(a.z, 11.0, 0.0001));
assert!(nearly_equal(a.w, 15.0, 0.0001));
}
#[test]
pub fn test_sub() {
let a = Vector4 { x: 3.0, y: 4.0, z: 6.0, w: 7.0 };
let b = Vector4 { x: 1.0, y: 2.0, z: 5.0, w: 8.0 };
let c = a - b;
assert!(nearly_equal(c.x, 2.0, 0.0001));
assert!(nearly_equal(c.y, 2.0, 0.0001));
assert!(nearly_equal(c.z, 1.0, 0.0001));
assert!(nearly_equal(c.w, -1.0, 0.0001));
let mut a = Vector4 { x: 3.0, y: 4.0, z: 6.0, w: 7.0 };
let b = Vector4 { x: 1.0, y: 2.0, z: 5.0, w: 8.0 };
a -= b;
assert!(nearly_equal(a.x, 2.0, 0.0001));
assert!(nearly_equal(a.y, 2.0, 0.0001));
assert!(nearly_equal(a.z, 1.0, 0.0001));
assert!(nearly_equal(a.w, -1.0, 0.0001));
}
#[test]
pub fn test_mul() {
let a = Vector4 { x: 2.5, y: 6.0, z: 3.0, w: -4.1 };
let b = Vector4 { x: 1.25, y: 2.0, z: 2.5, w: 2.0 };
let c = a * b;
assert!(nearly_equal(c.x, 3.125, 0.0001));
assert!(nearly_equal(c.y, 12.0, 0.0001));
assert!(nearly_equal(c.z, 7.5, 0.0001));
assert!(nearly_equal(c.w, -8.2, 0.0001));
let mut a = Vector4 { x: 2.5, y: 6.0, z: 3.0, w: -4.1 };
let b = Vector4 { x: 1.25, y: 2.0, z: 2.5, w: 2.0 };
a *= b;
assert!(nearly_equal(a.x, 3.125, 0.0001));
assert!(nearly_equal(a.y, 12.0, 0.0001));
assert!(nearly_equal(a.z, 7.5, 0.0001));
assert!(nearly_equal(a.w, -8.2, 0.0001));
}
#[test]
pub fn test_div() {
let a = Vector4 { x: 2.5, y: 6.0, z: 3.0, w: -4.1 };
let b = Vector4 { x: 1.25, y: 2.0, z: 2.5, w: 2.0 };
let c = a / b;
assert!(nearly_equal(c.x, 2.0, 0.0001));
assert!(nearly_equal(c.y, 3.0, 0.0001));
assert!(nearly_equal(c.z, 1.2, 0.0001));
assert!(nearly_equal(c.w, -2.05, 0.0001));
let mut a = Vector4 { x: 2.5, y: 6.0, z: 3.0, w: -4.1 };
let b = Vector4 { x: 1.25, y: 2.0, z: 2.5, w: 2.0 };
a /= b;
assert!(nearly_equal(a.x, 2.0, 0.0001));
assert!(nearly_equal(a.y, 3.0, 0.0001));
assert!(nearly_equal(a.z, 1.2, 0.0001));
assert!(nearly_equal(a.w, -2.05, 0.0001));
}
#[test]
pub fn test_scalar_mul() {
let a = Vector4 { x: 1.0, y: 2.0, z: -3.0, w: 4.0 };
let b = a * 2.0;
assert!(nearly_equal(b.x, 2.0, 0.0001));
assert!(nearly_equal(b.y, 4.0, 0.0001));
assert!(nearly_equal(b.z, -6.0, 0.0001));
assert!(nearly_equal(b.w, 8.0, 0.0001));
let mut a = Vector4 { x: 1.0, y: 2.0, z: -3.0, w: 4.0 };
a *= 2.0;
assert!(nearly_equal(b.x, 2.0, 0.0001));
assert!(nearly_equal(b.y, 4.0, 0.0001));
assert!(nearly_equal(b.z, -6.0, 0.0001));
assert!(nearly_equal(b.w, 8.0, 0.0001));
}
#[test]
pub fn test_scalar_div() {
let a = Vector4 { x: 1.0, y: 2.0, z: -3.0, w: 4.0 };
let b = a / 2.0;
assert!(nearly_equal(b.x, 0.5, 0.0001));
assert!(nearly_equal(b.y, 1.0, 0.0001));
assert!(nearly_equal(b.z, -1.5, 0.0001));
assert!(nearly_equal(b.w, 2.0, 0.0001));
let mut a = Vector4 { x: 1.0, y: 2.0, z: -3.0, w: 4.0 };
a /= 2.0;
assert!(nearly_equal(b.x, 0.5, 0.0001));
assert!(nearly_equal(b.y, 1.0, 0.0001));
assert!(nearly_equal(b.z, -1.5, 0.0001));
assert!(nearly_equal(b.w, 2.0, 0.0001));
}
#[test]
pub fn test_nearly_equal() {
let a = Vector4 { x: 3.5, y: -7.1, z: 1.8, w: 2.1 };
let b = Vector4 { x: 3.5, y: -7.1, z: 1.8, w: 2.2 };
assert!(!a.nearly_equal(b, 0.0001));
let a = Vector4 { x: 2.0, y: 4.0, z: 6.1, w: 3.5 };
let b = Vector4 { x: 2.0, y: 4.0, z: 6.1, w: 3.5 };
assert!(a.nearly_equal(b, 0.0001));
}
#[test]
pub fn test_length() {
let v = Vector4 { x: 3.0, y: -2.0, z: 1.0, w: 4.0 };
let length_squared = v.length_squared();
let length = v.length();
assert!(nearly_equal(length_squared, 30.0, 0.0001));
assert!(nearly_equal(length, 5.4772, 0.0001));
let v = Vector4 { x: 11.6, y: 0.0, z: 4.0, w: 1.2 };
let length_squared = v.length_squared();
let length = v.length();
assert!(nearly_equal(length_squared, 152.0001, 0.0001));
assert!(nearly_equal(length, 12.3288, 0.0001));
}
#[test]
pub fn test_dot() {
let a = Vector4 { x: -1.0, y: 2.0, z: 3.0, w: 4.0 };
let b = Vector4 { x: 0.0, y: 5.0, z: 1.0, w: 6.0 };
let dot = a.dot(&b);
assert!(nearly_equal(dot, 37.0, 0.0001));
let a = Vector4 { x: 4.0, y: 0.0, z: -3.0, w: 1.0 };
let b = Vector4 { x: 0.0, y: -2.0, z: 0.0, w: 0.0 };
let dot = a.dot(&b);
assert!(nearly_equal(dot, 0.0, 0.0001));
}
#[test]
pub fn test_distance() {
let a = Vector4 { x: 6.0, y: 2.5, z: -3.0, w: 1.0 };
let b = Vector4 { x: 1.1, y: -4.0, z: 5.0, w: 2.0 };
let distance_squared = a.distance_squared(&b);
let distance = a.distance(&b);
assert!(nearly_equal(distance_squared, 131.26, 0.0001));
assert!(nearly_equal(distance, 11.4569, 0.0001));
let a = Vector4 { x: 7.1, y: 4.0, z: 3.0, w: 2.0 };
let b = Vector4 { x: 17.0, y: -6.0, z: 2.5, w: 1.0 };
let distance_squared = a.distance_squared(&b);
let distance = a.distance(&b);
assert!(nearly_equal(distance_squared, 199.26, 0.0001));
assert!(nearly_equal(distance, 14.1159, 0.0001));
}
#[test]
pub fn test_normalize() {
let v = Vector4 { x: 3.0, y: 1.0, z: 2.0, w: 4.0 };
let normalized = v.normalize();
assert!(nearly_equal(normalized.x, 0.5477, 0.0001));
assert!(nearly_equal(normalized.y, 0.1826, 0.0001));
assert!(nearly_equal(normalized.z, 0.3651, 0.0001));
assert!(nearly_equal(normalized.w, 0.7303, 0.0001));
}
#[test]
pub fn test_extend() {
let v = Vector4 { x: 3.0, y: -2.0, z: 1.0, w: 4.0 };
let extended = v.extend(10.9545);
assert!(nearly_equal(extended.x, 6.0, 0.0001));
assert!(nearly_equal(extended.y, -4.0, 0.0001));
assert!(nearly_equal(extended.z, 2.0, 0.0001));
assert!(nearly_equal(extended.w, 8.0, 0.0001));
}
#[test]
pub fn test_lerp() {
let a = Vector4 { x: 5.0, y: 1.0, z: 3.0, w: 1.2 };
let b = Vector4 { x: 10.0, y: 2.0, z: 6.0, w: 2.4 };
let c = lerp(a, b, 0.5);
assert!(nearly_equal(c.x, 7.5, 0.0001));
assert!(nearly_equal(c.y, 1.5, 0.0001));
assert!(nearly_equal(c.z, 4.5, 0.0001));
assert!(nearly_equal(c.w, 1.8, 0.0001));
}
}