数学

Maths是一个旨在为游戏开发和图形设计提供高效且易用的线性代数库。如果您喜欢编写着色器，您会感到非常熟悉。除了向量和矩阵以及四元数的常规实现外，它还包括一个功能全面的实用函数集合、向量混叠、交点测试、点测试、距离函数、三角函数、图和信号处理函数。

该crate的大多数功能默认启用，如果您愿意，可以选择禁用。 serde 和 hash 的支持是可选的，默认禁用，可以通过以下方式启用：

features = ["serde", "hash"]

大部分代码都是从我的C++ maths库迁移过来的，有一个实时 WebGL演示，可以交互式地展示许多功能，并用于生成测试数据和验证函数是否正确工作。

向量

这是一个窄向量库，具有 Vec2、Vec3 和 Vec4 列向量的实现。

/// abbrivated types #[cfg(feature = "short_types")]
pub type Vec2f = Vec2<f32>;
pub type Vec3f = Vec3<f32>;
pub type Vec4f = Vec4<f32>;
pub type Vec4d = Vec4<f64>;
/// ... etc

// construct a vector
let v2 = Vec2f::new(2.0, 3.0);

// the short way #[cfg(feature = "short_hand_constructors")]
let v2_short = vec2f(5.0, 6.0);

// splat a scalar #[cfg(feature = "short_hand_constructors")]
let v3_splat = splat3f(9.0);

// quick common constructors
let y = Vec3f::unit_y();
let b = Vec3f::blue();
let z = Vec3f::zero();
let o = Vec3f::one();
let m = Vec3f::max_value();
// + more

// default
let vdefault = Vec3f::default(); // default is zero

// arithmetic / operators
let result = v2 * v2_short;
let result = v2 + v2_short;
let result = v2 / v2_short;
let result = v2 - v2_short;
let result = -v2;

// arithmetic with values and refs so no need for dereferencing
let v2ref = &v2;
let result = v2ref * v2; // ref * value
let result = v2 * v2ref; // value * ref
let result = v2ref * v2ref; // ref * ref

// construct from tuples and vectors of various sizes
let v4 = Vec4f::from((v2, v2)); // vec4 from 2x v2's
let v3 = Vec3f::from((v2, 1.0)); // vec3 from 1x v2 and 1x scalar
let v2 = Vec2f::from((5.0, 6.0)); // vec2 from 2x scalars
let v4 = Vec4f::from((v2, 0.0, 1.0)); // vec4 from 1x v2 and 2x scalars
let v4 = Vec4f::from(v2); // vec4 from vec2 (splat 0's)
let v2 = Vec2f::from(v4); // vec2 from vec4 (truncate)
// .. and so on

// swizzling
let wxyz = v4.wxyz(); // swizzle
let xyz = v4.xyz(); // truncate
let xxx = v4.xxx(); // and so on..
let xy = v3.yx(); // ..

// mutable swizzles
let mut v = Vec4f::zero();
x.set_xwyz(v); // set swizzle
x.set_xy(v.yx()); // assign truncated
x.set_yzx(v.zzz()); // etc..

// type casts #[cfg(feature = "casts")]
let veci = Vec3i::from(vec3f(1.0, 2.0, 3.0));

矩阵

具有 Mat2、Mat3、Mat34 和 Mat4 实现的行主序矩阵。

/// abbrivated types #[cfg(feature = "short_types")]
pub type Mat2f = Mat2<f32>;
pub type Mat3f = Mat3<f32>;
pub type Mat34f = Mat34<f32>;
pub type Mat4f = Mat4<f32>;

// identity
let mat_ident = Mat4f::identity();
let mat_default = Mat4f::default(); // default is identity

// construct from floats
let m4 = Mat4f::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
);

// construct from common matrices
let m34 = Mat34f::from_translation(vec3f(50.0, -10.0, 20.0));
let m4 = Mat4f::from_z_rotation(f32::deg_to_rad(90.0));
let m4 = Mat4f::from_scale(vec3f(10.0, 2.0, 30.0));
let m3 = Mat34f::from_scale(vec3f(10.0, 2.0, 30.0));

// arithmetic
// matrix multiplication
let result = x4 * m4;

// vector transformation
let v4 = vec4f(0.0, 1.0, 0.0, 1.0);
let result = m4 * v4;

// arithmetic with values and refs so no need for dereferencing
let v4ref = &v4;
let m4ref = &m4;
let result = m4ref * v4; // ref * value
let result = m4 * v4ref; // value * ref
let result = m4ref * v4ref; // ref * ref

// functions
let det = m4.determinant();
let inv = m4.inverse();

// construct rows from tuples
let m3v = Mat3f::from((
    vec3f(1.0, 2.0, 3.0),
    vec3f(4.0, 5.0, 6.0),
    vec3f(7.0, 8.0, 9.0)
));

let m4v = Mat4f::from((
    vec4f(1.0, 2.0, 3.0, 4.0),
    vec4f(5.0, 6.0, 7.0, 8.0),
    vec4f(9.0, 10.0, 11.0, 12.0),
    vec4f(13.0, 14.0, 15.0, 16.0),
));

let m4_rot = Mat4f::from(m3v); // mat4 from mat3
let m4r = Mat3f::from(quat); // from quaternion

// type casts #[cfg(feature = "casts")]
let matd = Mat4d::from(m4v);

四元数

通用浮点四元数。

// abbrivated types #[cfg(feature = "short_types")]
pub type Quatf = Quat<f32>;
pub type Quatd = Quat<f64>;

// construct from euler angles
let q = Quatf::from_euler_angles(x, y, z);

// construct from axis angle
let q2 = Quatf::from_axis_angle(axis, angle);

// identity
let qident = Quatf::identity();
let qdefault = Quat::default(); // default is identity

// arithmetic
let q3 = q * q2;
let q4 = q + q2;
let q5 = q - q2;
let q6 = -q;

// quat * vec
let v = vec3f(1.0, 0.0, 0.0);
let vv = q * v3;

// multiply with refs or values without need to deref
let qref = &q;
let vref = &v3;

let qr = qref * v3;
let qr = q * v3ref;
let qr = qref * vref;

// functions
let rev = q.reverse();
let inv = q.inverse();

// type casts #[cfg(feature = "casts")]
let quatd = Quatd::from(q2);

通用函数

您可以使用通用函数对不同尺寸的向量或标量进行操作： min, max, clamp, step, signum, copysign, abs, deg_to_rad, rad_to_deg, floor, ceil, round, approx, sqrt, powi, powf, sqrt, frac, trunc, modf, rsqrt, recip lerp, nlerp, slerp, smoothstep, dot, perp, cross, mag, mag2, length, distance, dist, dist2, normalize, chebyshev_normalize

// numeric ops
let int_abs = abs(-1);
let float_abs = abs(-1.0);
let int_max = max(5, 6);
let float_max = max(1.0, 2.0);
let vec_max = max(vec3f(1.0, 1.0, 1.0), vec3f(2.0, 2.0, 2.0));
let vec_min = min(vec4f(8.0, 7.0, 6.0, 5.0), vec4f(-8.0, -7.0, -6.0, -5.0));

// float ops
let fsat = saturate(22.0);
let vsat = saturate(vec3f(22.0, 22.0, 22.0));
let f = floor(5.5);
let vc = ceil(vec3f(5.0, 5.0, 5.0));

// vector ops
let dp = dot(vec2, vec2);
let dp = dot(vec3, vec3);
let cp = cross(vec3, Vec3::unit_y());
let n = normalize(vec3);
let qn = normalize(quat);
let m = mag(vec4);
let d = dist(vec31, vec32);

// interpolation
let fi : f32 = lerp(10.0, 2.0, 0.2);
let vi = lerp(vec2, vec2, 0.5);
let qi = lerp(quat1, quat2, 0.75);
let qs = slerp(quat1, quat2, 0.1);
let vn = nlerp(vec2, vec2, 0.3);
let f = smoothstep(5.0, 1.0, f);

三角函数和对数函数

这些函数对所有浮点标量或向量类型都可用：cos, sin, tan, acos, asin, atan, cosh, sinh, tanh, sin_cos, atan2, exp, exp2, log2, log10。

// trig functions
let s = sin(vec2);
let x = cos(vec3);
let f = acos(x);
let d = atan2(y, x);

// exp / log
let d = exp(y);
let l = log2(x);

函数

平面分类：point_vs_plane, aabb_vs_plane, sphere_vs_plane, capsule_vs_plane, cone_vs_plane。

重叠：sphere_vs_sphere, sphere_vs_aabb, sphere_vs_obb, aabb_vs_aabb, aabb_vs_frustum, sphere_vs_frustum, sphere_vs_capsule, capsule_vs_capsule, obb_vs_obb, aabb_vs_obb, convex_hull_vs_convex_hull, gjk_2d, gjk_3d。

点在内部：point_inside_aabb, point_inside_sphere, point_inside_obb, point_inside_triangle, point_inside_cone, point_inside_convex_hull, point_inside_poly, point_inside_frustum。

最近点：closest_point_on_aabb, closest_point_on_line, closest_point_on_plane, closest_point_on_obb, closest_point_on_sphere, closest_point_on_ray, closest_point_on_triangle, closest_point_on_polygon, closest_point_on_convex_hull, closest_point_on_cone。

点距离：point_aabb_distance, point_segment_distance, point_triangle_distance, distance_on_line, point_plane_distance, plane_distance, point_sphere_distance, point_polygon_distance, point_convex_hull_distance, point_cone_distance, point_obb_distance。

光线/直线：ray_vs_plane, ray_vs_triangle, ray_vs_sphere, ray_vs_line_segment, ray_vs_aabb, ray_vs_obb, ray_vs_capsule, ray_vs_cylinder, line_vs_line, line_vs_poly, shortest_line_segment_between_lines, shortest_line_segment_between_line_segments。

着色器样式函数：dot, cross, normalize, mag, mag2, dist, dist2, triple, vector_triple, lerp, nlerp, slerp, saturate, clamp, normalize, chebyshev_normalize, all, any, min, max, smoothstep, step, round, floor, ceil, abs, frac, trunc, exp, exp2, log, log2, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh。

图函数：smooth_start, smooth_stop, impulse, cubic_pulse, exp_step, parabola, pcurve, exp_sustained_impulse, sinc, gain, almost_identity, integral_smoothstep, quad_impulse, poly_impulse。

+ 更多包含在内！