math.rin

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// Vectors and 4x4 matrices: what glm is to LearnOpenGL.
//
// Conventions, chosen to match the maths in LearnOpenGL so its formulas carry
// over unchanged:
//
//   * right-handed world: +x right, +y up, the camera looks down -z
//   * column vectors: a point is transformed as `M * p`, so `T * R * S`
//     scales first and translates last
//   * clip-space depth runs 0..1, which is D3D's range (GL's is -1..1)
//
// A mat4 is stored row by row, `m[row * 4 + col]`. Every shader starts with
// `#pragma pack_matrix(row_major)`, which makes HLSL read the constant buffer
// the same way, so `mul(M, v)` in a shader is exactly `M * v` here.

cinclude "math.h"

sqrtf: proc[external](x: f32) -> f32 = {}
sinf: proc[external](x: f32) -> f32 = {}
cosf: proc[external](x: f32) -> f32 = {}
tanf: proc[external](x: f32) -> f32 = {}
powf: proc[external](x: f32, y: f32) -> f32 = {}
fabsf: proc[external](x: f32) -> f32 = {}
floorf: proc[external](x: f32) -> f32 = {}
fminf: proc[external](a: f32, b: f32) -> f32 = {}
fmaxf: proc[external](a: f32, b: f32) -> f32 = {}

pi: f32 = 3.14159265358979;

radians: proc(degrees: f32) -> f32 = {
    return degrees * pi / 180.0;
}

clampf: proc(x: f32, lo: f32, hi: f32) -> f32 = {
    return fminf(fmaxf(x, lo), hi);
}

lerpf: proc(a: f32, b: f32, t: f32) -> f32 = {
    return a + (b - a) * t;
}

vec2: struct = {
    x: f32;
    y: f32;
}

vec3: struct = {
    x: f32;
    y: f32;
    z: f32;
}

vec4: struct = {
    x: f32;
    y: f32;
    z: f32;
    w: f32;
}

mat4: struct = {
    m: [16]f32;
}

v2: proc(x: f32, y: f32) -> vec2 = {
    return { .x = x, .y = y };
}

v3: proc(x: f32, y: f32, z: f32) -> vec3 = {
    return { .x = x, .y = y, .z = z };
}

v4: proc(x: f32, y: f32, z: f32, w: f32) -> vec4 = {
    return { .x = x, .y = y, .z = z, .w = w };
}

v3_add: proc(a: vec3, b: vec3) -> vec3 = {
    return v3(a.x + b.x, a.y + b.y, a.z + b.z);
}

v3_sub: proc(a: vec3, b: vec3) -> vec3 = {
    return v3(a.x - b.x, a.y - b.y, a.z - b.z);
}

v3_mul: proc(a: vec3, b: vec3) -> vec3 = {
    return v3(a.x * b.x, a.y * b.y, a.z * b.z);
}

v3_scale: proc(a: vec3, s: f32) -> vec3 = {
    return v3(a.x * s, a.y * s, a.z * s);
}

v3_dot: proc(a: vec3, b: vec3) -> f32 = {
    return a.x * b.x + a.y * b.y + a.z * b.z;
}

v3_cross: proc(a: vec3, b: vec3) -> vec3 = {
    return v3(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
}

v3_length: proc(a: vec3) -> f32 = {
    return sqrtf(v3_dot(a, a));
}

v3_normalize: proc(a: vec3) -> vec3 = {
    len: f32 = v3_length(a);
    if (len == 0.0) { return a; }
    return v3_scale(a, 1.0 / len);
}

v3_lerp: proc(a: vec3, b: vec3, t: f32) -> vec3 = {
    return v3(lerpf(a.x, b.x, t), lerpf(a.y, b.y, t), lerpf(a.z, b.z, t));
}

m4_identity: proc() -> mat4 = {
    r: mat4 = {
        .m = {
            [0] = 1.0,
            [5] = 1.0,
            [10] = 1.0,
            [15] = 1.0,
        },
    };
    return r;
}

m4_mul: proc(a: mat4, b: mat4) -> mat4 = {
    r: mat4 = {};
    for (row: i32 = 0; row < 4; row += 1) {
        for (col: i32 = 0; col < 4; col += 1) {
            sum: f32 = 0.0;
            for (k: i32 = 0; k < 4; k += 1) {
                sum += a.m[row * 4 + k] * b.m[k * 4 + col];
            }
            r.m[row * 4 + col] = sum;
        }
    }
    return r;
}

m4_mul_v4: proc(a: mat4, v: vec4) -> vec4 = {
    return v4(a.m[0] * v.x + a.m[1] * v.y + a.m[2] * v.z + a.m[3] * v.w,
              a.m[4] * v.x + a.m[5] * v.y + a.m[6] * v.z + a.m[7] * v.w,
              a.m[8] * v.x + a.m[9] * v.y + a.m[10] * v.z + a.m[11] * v.w,
              a.m[12] * v.x + a.m[13] * v.y + a.m[14] * v.z + a.m[15] * v.w);
}

m4_transpose: proc(a: mat4) -> mat4 = {
    r: mat4 = {};
    for (row: i32 = 0; row < 4; row += 1) {
        for (col: i32 = 0; col < 4; col += 1) {
            r.m[col * 4 + row] = a.m[row * 4 + col];
        }
    }
    return r;
}

m4_translate: proc(t: vec3) -> mat4 = {
    r: mat4 = m4_identity();
    r.m[3] = t.x;
    r.m[7] = t.y;
    r.m[11] = t.z;
    return r;
}

m4_scale: proc(s: vec3) -> mat4 = {
    r: mat4 = m4_identity();
    r.m[0] = s.x;
    r.m[5] = s.y;
    r.m[10] = s.z;
    return r;
}

// A rotation of `angle` radians about `axis`, counter-clockwise when looking
// down the axis towards the origin.
m4_rotate: proc(angle: f32, axis: vec3) -> mat4 = {
    a: vec3 = v3_normalize(axis);
    c: f32 = cosf(angle);
    s: f32 = sinf(angle);
    t: f32 = 1.0 - c;
    r: mat4 = m4_identity();
    r.m[0] = c + a.x * a.x * t;
    r.m[1] = a.x * a.y * t - a.z * s;
    r.m[2] = a.x * a.z * t + a.y * s;
    r.m[4] = a.y * a.x * t + a.z * s;
    r.m[5] = c + a.y * a.y * t;
    r.m[6] = a.y * a.z * t - a.x * s;
    r.m[8] = a.z * a.x * t - a.y * s;
    r.m[9] = a.z * a.y * t + a.x * s;
    r.m[10] = c + a.z * a.z * t;
    return r;
}

// Right-handed perspective onto D3D's 0..1 depth range.
// (`near` and `far` are empty macros in windows.h, so the planes are z_near/z_far.)
m4_perspective: proc(fovy: f32, aspect: f32, z_near: f32, z_far: f32) -> mat4 = {
    f: f32 = 1.0 / tanf(fovy * 0.5);
    r: mat4 = {
        .m = {
            [0] = f / aspect,
            [5] = f,
            [10] = z_far / (z_near - z_far),
            [11] = z_near * z_far / (z_near - z_far),
            [14] = -1.0,
        },
    };
    return r;
}

// Right-handed orthographic projection onto 0..1 depth.
m4_ortho: proc(left: f32, right: f32, bottom: f32, top: f32, z_near: f32, z_far: f32) -> mat4 = {
    r: mat4 = m4_identity();
    r.m[0] = 2.0 / (right - left);
    r.m[3] = -(right + left) / (right - left);
    r.m[5] = 2.0 / (top - bottom);
    r.m[7] = -(top + bottom) / (top - bottom);
    r.m[10] = 1.0 / (z_near - z_far);
    r.m[11] = z_near / (z_near - z_far);
    return r;
}

// The view matrix of a camera at `eye` looking at `target`.
m4_look_at: proc(eye: vec3, target: vec3, up: vec3) -> mat4 = {
    f: vec3 = v3_normalize(v3_sub(target, eye));
    s: vec3 = v3_normalize(v3_cross(f, up));
    u: vec3 = v3_cross(s, f);
    r: mat4 = m4_identity();
    r.m[0] = s.x;
    r.m[1] = s.y;
    r.m[2] = s.z;
    r.m[3] = -v3_dot(s, eye);
    r.m[4] = u.x;
    r.m[5] = u.y;
    r.m[6] = u.z;
    r.m[7] = -v3_dot(u, eye);
    r.m[8] = -f.x;
    r.m[9] = -f.y;
    r.m[10] = -f.z;
    r.m[11] = v3_dot(f, eye);
    return r;
}

// The view matrix with its translation removed: what a skybox is drawn with,
// so it turns with the camera but never gets closer.
m4_without_translation: proc(a: mat4) -> mat4 = {
    r: mat4 = a;
    r.m[3] = 0.0;
    r.m[7] = 0.0;
    r.m[11] = 0.0;
    r.m[12] = 0.0;
    r.m[13] = 0.0;
    r.m[14] = 0.0;
    r.m[15] = 1.0;
    return r;
}

// General inverse by cofactors. Used for normal matrices; a singular matrix
// comes back unchanged.
m4_inverse: proc(a: mat4) -> mat4 = {
    m: [*]const f32 = a.m[0]&;
    inv: mat4 = {
        .m = {
            [0] = m[5] * m[10] * m[15] - m[5] * m[11] * m[14] - m[9] * m[6] * m[15] + m[9] * m[7] * m[14] + m[13] * m[6] * m[11] - m[13] * m[7] * m[10],
            [4] = -m[4] * m[10] * m[15] + m[4] * m[11] * m[14] + m[8] * m[6] * m[15] - m[8] * m[7] * m[14] - m[12] * m[6] * m[11] + m[12] * m[7] * m[10],
            [8] = m[4] * m[9] * m[15] - m[4] * m[11] * m[13] - m[8] * m[5] * m[15] + m[8] * m[7] * m[13] + m[12] * m[5] * m[11] - m[12] * m[7] * m[9],
            [12] = -m[4] * m[9] * m[14] + m[4] * m[10] * m[13] + m[8] * m[5] * m[14] - m[8] * m[6] * m[13] - m[12] * m[5] * m[10] + m[12] * m[6] * m[9],
            [1] = -m[1] * m[10] * m[15] + m[1] * m[11] * m[14] + m[9] * m[2] * m[15] - m[9] * m[3] * m[14] - m[13] * m[2] * m[11] + m[13] * m[3] * m[10],
            [5] = m[0] * m[10] * m[15] - m[0] * m[11] * m[14] - m[8] * m[2] * m[15] + m[8] * m[3] * m[14] + m[12] * m[2] * m[11] - m[12] * m[3] * m[10],
            [9] = -m[0] * m[9] * m[15] + m[0] * m[11] * m[13] + m[8] * m[1] * m[15] - m[8] * m[3] * m[13] - m[12] * m[1] * m[11] + m[12] * m[3] * m[9],
            [13] = m[0] * m[9] * m[14] - m[0] * m[10] * m[13] - m[8] * m[1] * m[14] + m[8] * m[2] * m[13] + m[12] * m[1] * m[10] - m[12] * m[2] * m[9],
            [2] = m[1] * m[6] * m[15] - m[1] * m[7] * m[14] - m[5] * m[2] * m[15] + m[5] * m[3] * m[14] + m[13] * m[2] * m[7] - m[13] * m[3] * m[6],
            [6] = -m[0] * m[6] * m[15] + m[0] * m[7] * m[14] + m[4] * m[2] * m[15] - m[4] * m[3] * m[14] - m[12] * m[2] * m[7] + m[12] * m[3] * m[6],
            [10] = m[0] * m[5] * m[15] - m[0] * m[7] * m[13] - m[4] * m[1] * m[15] + m[4] * m[3] * m[13] + m[12] * m[1] * m[7] - m[12] * m[3] * m[5],
            [14] = -m[0] * m[5] * m[14] + m[0] * m[6] * m[13] + m[4] * m[1] * m[14] - m[4] * m[2] * m[13] - m[12] * m[1] * m[6] + m[12] * m[2] * m[5],
            [3] = -m[1] * m[6] * m[11] + m[1] * m[7] * m[10] + m[5] * m[2] * m[11] - m[5] * m[3] * m[10] - m[9] * m[2] * m[7] + m[9] * m[3] * m[6],
            [7] = m[0] * m[6] * m[11] - m[0] * m[7] * m[10] - m[4] * m[2] * m[11] + m[4] * m[3] * m[10] + m[8] * m[2] * m[7] - m[8] * m[3] * m[6],
            [11] = -m[0] * m[5] * m[11] + m[0] * m[7] * m[9] + m[4] * m[1] * m[11] - m[4] * m[3] * m[9] - m[8] * m[1] * m[7] + m[8] * m[3] * m[5],
            [15] = m[0] * m[5] * m[10] - m[0] * m[6] * m[9] - m[4] * m[1] * m[10] + m[4] * m[2] * m[9] + m[8] * m[1] * m[6] - m[8] * m[2] * m[5],
        },
    };
    det: f32 = m[0] * inv.m[0] + m[1] * inv.m[4] + m[2] * inv.m[8] + m[3] * inv.m[12];
    if (det == 0.0) { return a; }
    for (i: i32 = 0; i < 16; i += 1) {
        inv.m[i] = inv.m[i] / det;
    }
    return inv;
}

// What normals are transformed by: the inverse transpose of the model matrix,
// so a non-uniform scale does not tilt them.
m4_normal_matrix: proc(model: mat4) -> mat4 = {
    return m4_transpose(m4_inverse(model));
}