power_play/src/math.h

#ifndef MATH_H
#define MATH_H

#include "intrinsics.h"

#define PI      ((f32)3.14159265358979323846)
#define TAU     ((f32)6.28318530717958647693)

INLINE struct trs trs_from_mat3x3(struct mat3x3 m);
INLINE struct trs trs_lerp(struct trs a, struct trs b, f32 t);

/* ========================== *
 * Rounding
 * ========================== */

/* TODO: Don't use intrinsics for these. */

INLINE i32 math_round_f32(f32 f)
{
    return ix_round_f32_to_i32(f);
}

INLINE i32 math_floor_f32(f32 f)
{
    return ix_floor_f32_to_i32(f);
}

INLINE i32 math_ceil_f32(f32 f)
{
    return ix_ceil_f32_to_i32(f);
}

INLINE i64 math_round_f64(f64 f)
{
    return ix_round_f64_to_i64(f);
}

INLINE i64 math_floor_f64(f64 f)
{
    return ix_floor_f64_to_i64(f);
}

INLINE i64 math_ceil_f64(f64 f)
{
    return ix_ceil_f64_to_i64(f);
}

INLINE f32 math_mod_f32(f32 x, f32 m)
{
    return x - m * (i32)(x / m);
}

INLINE f32 math_abs_f32(f32 f)
{
    u32 truncated = *(u32 *)&f & 0x7FFFFFFF;
    return *(f32 *)&truncated;
}

INLINE f64 math_abs_f64(f64 f)
{
    u64 truncated = *(u64 *)&f & 0x7FFFFFFFFFFFFFFF;
    return *(f64 *)&truncated;
}

INLINE i32 math_sign_f32(f32 f)
{
    u32 bits = *(u32 *)&f;
    i32 sign_bit = bits & ((u32)1 << 31);
    return 1 + (sign_bit * -2);
}

INLINE i32 math_sign_f64(f64 f)
{
    u64 bits = *(u64 *)&f;
    i32 sign_bit = bits & ((u64)1 << 31);
    return 1 + (sign_bit * -2);
}

/* ========================== *
 * Exponential
 * ========================== */

/* Taken from https://gist.github.com/orlp/3551590 */
INLINE u64 math_pow_u64(u64 base, u8 exp) {
    LOCAL_PERSIST const u8 highest_bit_set[] = {
        0, 1, 2, 2, 3, 3, 3, 3,
        4, 4, 4, 4, 4, 4, 4, 4,
        5, 5, 5, 5, 5, 5, 5, 5,
        5, 5, 5, 5, 5, 5, 5, 5,
        6, 6, 6, 6, 6, 6, 6, 6,
        6, 6, 6, 6, 6, 6, 6, 6,
        6, 6, 6, 6, 6, 6, 6, 6,
        6, 6, 6, 6, 6, 6, 6, 255, /* Anything past 63 is a guaranteed overflow with base > 1 */
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
        255, 255, 255, 255, 255, 255, 255, 255,
    };

    u64 result = 1;

    switch (highest_bit_set[exp]) {
        case 255: {
            /* 255 = overflow, return 0 */
            if (base == 1) {
                return 1;
            }
            // if (base == -1) {
            //     return 1 - 2 * (exp & 1);
            // }
            return 0;
        } break;
        case 6: {
            if (exp & 1) result *= base;
            exp >>= 1;
            base *= base;
        } FALLTHROUGH;
        case 5: {
            if (exp & 1) result *= base;
            exp >>= 1;
            base *= base;
        } FALLTHROUGH;
        case 4: {
            if (exp & 1) result *= base;
            exp >>= 1;
            base *= base;
        } FALLTHROUGH;
        case 3: {
            if (exp & 1) result *= base;
            exp >>= 1;
            base *= base;
        } FALLTHROUGH;
        case 2: {
            if (exp & 1) result *= base;
            exp >>= 1;
            base *= base;
        } FALLTHROUGH;
        case 1: {
            if (exp & 1) result *= base;
        } FALLTHROUGH;
        default: return result;
    }
}

/* From Quake III -
 * https://github.com/id-Software/Quake-III-Arena/blob/dbe4ddb10315479fc00086f08e25d968b4b43c49/code/game/q_math.c#L552
 */
INLINE f32 math_rsqrt(f32 x)
{
    const f32 three_halfs = 1.5f;
    f32 x2 = x * 0.5f;
    f32 y = x;
    i32 i = *(i32 *)&y;
    i = 0x5f3759df - (i >> 1);
    y = *(f32 *)&i;
    y *= three_halfs - (x2 * y * y);  /* 1st iteration */
    return y;
}

INLINE f32 math_sqrt(f32 x)
{
    return x * math_rsqrt(x);
}

/* ========================== *
 * Lerp
 * ========================== */

INLINE f32 math_lerp_f32(f32 val0, f32 val1, f32 t)
{
    return val0 + ((val1 - val0) * t);
}

INLINE f64 math_lerp_f64(f64 val0, f64 val1, f64 t)
{
    return val0 + ((val1 - val0) * t);
}

INLINE f32 math_lerp_angle(f32 a, f32 b, f32 t) {
    f32 diff = math_mod_f32(b - a, TAU);
    diff = math_mod_f32(2.0f * diff, TAU) - diff;
    return a + diff * t;
}

/* ========================== *
 * Trig
 * ========================== */

/* Sine approximation using a parabola adjusted to minimize error, as described in
 * https://web.archive.org/web/20080228213915/http://www.devmaster.net/forums/showthread.php?t=5784
 *
 * https://www.desmos.com/calculator/gbtjvt2we8
 * c: adjustment weight
 * f(x): original parabola
 * g(x): adjusted parabola
 * h(x): error
 */
INLINE f32 math_sin(f32 x)
{
    const f32 c = 0.225;
    x -= (TAU * (f32)math_floor_f32(x / TAU));  /* [0, TAU] */
    x += (TAU * (x < -PI)) - (TAU * (x > PI));  /* [-PI, PI] */
    f32 y = (4.0f/PI) * x + (-4.0f/(PI*PI)) * x * math_abs_f32(x);
    y = c * (y * math_abs_f32(y) - y) + y;
    return y;
}

INLINE f32 math_cos(f32 x)
{
    return math_sin(x + (PI / 2.0f));
}

/* https://mazzo.li/posts/vectorized-atan2.html */
INLINE f32 math_atan2(f32 x, f32 y) {
    const f32 a1  =  0.99997726f;
    const f32 a3  = -0.33262347f;
    const f32 a5  =  0.19354346f;
    const f32 a7  = -0.11643287f;
    const f32 a9  =  0.05265332f;
    const f32 a11 = -0.01172120f;

    /* Ensure input is in [-1, +1] */
    b32 swap = math_abs_f32(x) < math_abs_f32(y);
    f32 s = (swap ? x : y) / (swap ? y : x);

    /* Approximate atan */
    f32 s_sq = s*s;
    f32 res = s * (a1 + s_sq * (a3 + s_sq * (a5 + s_sq * (a7 + s_sq * (a9 + s_sq * a11)))));
    res = swap ? (s >= 0.0f ? (PI / 2.f) : -(PI / 2.f)) - res : res;

    /* Adjust quadrants */
    if      (x <  0.0f && y >= 0.0f)  { res =  PI + res; }  /* 2nd quadrant */
    else if (x <=  0.0f && y <  0.0f) { res = -PI + res; }  /* 3rd quadrant */

    return res;
}

INLINE f32 math_asin(f32 x)
{
    /* TODO: Dedicated arcsin approximation */
    return (PI / 2.0f) - math_atan2(x, math_sqrt(1.0f - (x*x)));
}

INLINE f32 math_acos(f32 x)
{
    /* TODO: Dedicated arccos approximation */
    return math_atan2(x, math_sqrt(1.0f - (x*x)));
}

/* ========================== *
 * V2
 * ========================== */

INLINE struct v2 v2_mul(struct v2 a, f32 s)
{
    return V2(a.x * s, a.y * s);
}

INLINE struct v2 v2_mul_v2(struct v2 a, struct v2 b)
{
    return V2(a.x * b.x, a.y * b.y);
}

INLINE struct v2 v2_div(struct v2 a, f32 s)
{
    f32 d = 1 / s;
    return V2(a.x * d, a.y * d);
}

INLINE struct v2 v2_div_v2(struct v2 a, struct v2 b)
{
    return V2(a.x * (1 / b.x), a.y * (1 / b.y));
}

INLINE struct v2 v2_neg(struct v2 a)
{
    return V2(-a.x, -a.y);
}

INLINE struct v2 v2_add(struct v2 a, struct v2 b)
{
    return V2(a.x + b.x, a.y + b.y);
}

INLINE struct v2 v2_sub(struct v2 a, struct v2 b)
{
    return V2(a.x - b.x, a.y - b.y);
}

INLINE f32 v2_len(struct v2 a)
{
    return math_sqrt(a.x * a.x + a.y * a.y);
}

INLINE f32 v2_len_squared(struct v2 a)
{
    return a.x * a.x + a.y * a.y;
}

INLINE struct v2 v2_perp(struct v2 a)
{
    return V2(-a.y, a.x);
}

INLINE struct v2 v2_norm(struct v2 a)
{
    f32 len_squared = v2_len_squared(a);
    f32 r_sqrt = math_rsqrt(len_squared);
    a.x *= r_sqrt;
    a.y *= r_sqrt;
    return a;
}


INLINE struct v2 v2_round(struct v2 a)
{
    return V2(
        (f32)math_round_f32(a.x),
        (f32)math_round_f32(a.y)
    );
}

INLINE f32 v2_dot(struct v2 a, struct v2 b)
{
    return a.x * b.x + a.y * b.y;
}

INLINE f32 v2_wedge(struct v2 a, struct v2 b)
{
    return a.x * b.y - a.y * b.x;
}

INLINE f32 v2_distance(struct v2 a, struct v2 b)
{
    f32 dx = b.x - a.x;
    f32 dy = b.y - a.y;
    return math_sqrt(dx * dx + dy * dy);
}

INLINE b32 v2_eq(struct v2 a, struct v2 b)
{
    return a.x == b.x && a.y == b.y;
}

INLINE struct v2 v2_lerp(struct v2 val0, struct v2 val1, f32 t)
{
    struct v2 res;
    res.x = math_lerp_f32(val0.x, val1.x, t);
    res.y = math_lerp_f32(val0.y, val1.y, t);
    return res;
}

/* ========================== *
 * Mat3x3
 * ========================== */

INLINE struct mat3x3 mat3x3_ident(void)
{
    return (struct mat3x3) {
        .e = {
            { 1, 0, 0 },
            { 0, 1, 0 },
            { 0, 0, 1 }
        }
    };
}

INLINE struct mat3x3 mat3x3_mul(struct mat3x3 a, struct mat3x3 b)
{
    f32 a00 =  a.e[0][0], a01 = a.e[0][1], a02 = a.e[0][2],
         a10 = a.e[1][0], a11 = a.e[1][1], a12 = a.e[1][2],
         a20 = a.e[2][0], a21 = a.e[2][1], a22 = a.e[2][2],
         b00 = b.e[0][0], b01 = b.e[0][1], b02 = b.e[0][2],
         b10 = b.e[1][0], b11 = b.e[1][1], b12 = b.e[1][2],
         b20 = b.e[2][0], b21 = b.e[2][1], b22 = b.e[2][2];

    struct mat3x3 res;

    res.e[0][0] = a00 * b00 + a10 * b01 + a20 * b02;
    res.e[0][1] = a01 * b00 + a11 * b01 + a21 * b02;
    res.e[0][2] = a02 * b00 + a12 * b01 + a22 * b02;
    res.e[1][0] = a00 * b10 + a10 * b11 + a20 * b12;
    res.e[1][1] = a01 * b10 + a11 * b11 + a21 * b12;
    res.e[1][2] = a02 * b10 + a12 * b11 + a22 * b12;
    res.e[2][0] = a00 * b20 + a10 * b21 + a20 * b22;
    res.e[2][1] = a01 * b20 + a11 * b21 + a21 * b22;
    res.e[2][2] = a02 * b20 + a12 * b21 + a22 * b22;

    return res;

}

INLINE struct mat3x3 mat3x3_from_translate(struct v2 v)
{
    return (struct mat3x3) {
        .e = {
            {1, 0, 0},
            {0, 1, 0},
            {v.x, v.y, 1}
        }
    };
}

INLINE struct mat3x3 mat3x3_translate(struct mat3x3 m, struct v2 v)
{
    m.e[2][0] = m.e[0][0] * v.x + m.e[1][0] * v.y + m.e[2][0];
    m.e[2][1] = m.e[0][1] * v.x + m.e[1][1] * v.y + m.e[2][1];
    m.e[2][2] = m.e[0][2] * v.x + m.e[1][2] * v.y + m.e[2][2];
    return m;
}

INLINE struct mat3x3 mat3x3_rotate(struct mat3x3 m, f32 angle)
{
    f32 c = math_cos(angle);
    f32 s = math_sin(angle);

    struct mat3x3 res = m;

    f32 m00 = m.e[0][0],  m10 = m.e[1][0],
        m01 = m.e[0][1],  m11 = m.e[1][1],
        m02 = m.e[0][2],  m12 = m.e[1][2];

    res.e[0][0] = m00 * c + m10 * s;
    res.e[0][1] = m01 * c + m11 * s;
    res.e[0][2] = m02 * c + m12 * s;

    res.e[1][0] = m00 * -s + m10 * c;
    res.e[1][1] = m01 * -s + m11 * c;
    res.e[1][2] = m02 * -s + m12 * c;

    return res;
}

INLINE struct mat3x3 mat3x3_scale(struct mat3x3 m, struct v3 v)
{
    m.e[0][0] *= v.x;
    m.e[0][1] *= v.x;
    m.e[0][2] *= v.x;
    m.e[1][0] *= v.y;
    m.e[1][1] *= v.y;
    m.e[1][2] *= v.y;
    m.e[2][0] *= v.z;
    m.e[2][1] *= v.z;
    m.e[2][2] *= v.z;
    return m;
}

INLINE struct mat3x3 mat3x3_from_trs(struct trs trs)
{
    struct mat3x3 m = mat3x3_from_translate(trs.t);
    m = mat3x3_rotate(m, trs.r);
    m = mat3x3_scale(m, V3(trs.s.x, trs.s.y, 1));
    return m;
}

INLINE struct mat3x3 mat3x3_trs(struct mat3x3 m, struct trs trs)
{
    m = mat3x3_translate(m, trs.t);
    m = mat3x3_rotate(m, trs.r);
    m = mat3x3_scale(m, V3(trs.s.x, trs.s.y, 1));
    return m;
}

INLINE struct mat3x3 mat3x3_trs_pivot_r(struct mat3x3 m, struct trs trs, struct v2 pivot)
{
    m = mat3x3_translate(m, trs.t);
    m = mat3x3_rotate(m, trs.r);
    m = mat3x3_translate(m, v2_neg(pivot));
    m = mat3x3_scale(m, V3(trs.s.x, trs.s.y, 1));
    return m;
}

INLINE struct mat3x3 mat3x3_trs_pivot_rs(struct mat3x3 m, struct trs trs, struct v2 pivot)
{
    m = mat3x3_translate(m, trs.t);
    m = mat3x3_rotate(m, trs.r);
    m = mat3x3_scale(m, V3(trs.s.x, trs.s.y, 1));
    m = mat3x3_translate(m, v2_neg(pivot));
    return m;
}

INLINE struct v3 mat3x3_mul_v3(struct mat3x3 m, struct v3 v)
{
    struct v3 res;
    res.x = m.e[0][0] * v.x + m.e[1][0] * v.y + m.e[2][0] * v.z;
    res.y = m.e[0][1] * v.x + m.e[1][1] * v.y + m.e[2][1] * v.z;
    res.z = m.e[0][2] * v.x + m.e[1][2] * v.y + m.e[2][2] * v.z;
    return res;
}

/* Equivalent to multiplying by V3(v.x, v.y, 1.0) */
INLINE struct v2 mat3x3_mul_v2(struct mat3x3 m, struct v2 v)
{
    struct v2 res;
    res.x = m.e[0][0] * v.x + m.e[1][0] * v.y + m.e[2][0];
    res.y = m.e[0][1] * v.x + m.e[1][1] * v.y + m.e[2][1];
    return res;
}

INLINE struct mat3x3 mat3x3_inverse(struct mat3x3 m)
{
    f32 a = m.e[0][0], b = m.e[0][1], c = m.e[0][2],
        d = m.e[1][0], e = m.e[1][1], f = m.e[1][2],
        g = m.e[2][0], h = m.e[2][1], i = m.e[2][2];

    struct mat3x3 res;
    res.e[0][0] =   e * i - f * h;
    res.e[0][1] = -(b * i - h * c);
    res.e[0][2] =   b * f - e * c;
    res.e[1][0] = -(d * i - g * f);
    res.e[1][1] =   a * i - c * g;
    res.e[1][2] = -(a * f - d * c);
    res.e[2][0] =   d * h - g * e;
    res.e[2][1] = -(a * h - g * b);
    res.e[2][2] =   a * e - b * d;

    f32 det = 1.0f / (a * res.e[0][0] + b * res.e[1][0] + c * res.e[2][0]);
    res = mat3x3_scale(res, V3(det, det, det));

    return res;
}

INLINE struct v2 mat3x3_get_right(struct mat3x3 m)
{
    return V2(m.e[0][0], m.e[0][1]);
}

INLINE struct v2 mat3x3_get_left(struct mat3x3 m)
{
    return V2(-m.e[0][0], -m.e[0][1]);
}

INLINE struct v2 mat3x3_get_up(struct mat3x3 m)
{
    return V2(-m.e[1][0], -m.e[1][1]);
}

INLINE struct v2 mat3x3_get_down(struct mat3x3 m)
{
    return V2(m.e[1][0], m.e[1][1]);
}

INLINE struct v2 mat3x3_get_pos(struct mat3x3 m)
{
    return V2(m.e[2][0], m.e[2][1]);
}

INLINE f32 mat3x3_get_determinant(struct mat3x3 m)
{
    return m.e[0][0] * m.e[1][1] - m.e[0][1] * m.e[1][0];
}

INLINE f32 mat3x3_get_rot(struct mat3x3 m)
{
    return math_atan2(m.e[0][0], m.e[0][1]);
}

INLINE struct v2 mat3x3_get_scale(struct mat3x3 m)
{
    f32 det_sign = math_sign_f32(mat3x3_get_determinant(m));
    struct v2 bx = V2(m.e[0][0], m.e[0][1]);
    struct v2 by = V2(m.e[1][0], m.e[1][1]);
	return V2(v2_len(bx), det_sign * v2_len(by));
}

INLINE f32 mat3x3_get_skew(struct mat3x3 m)
{
    f32 det = mat3x3_get_determinant(m);
    i32 det_sign = math_sign_f32(det);

    struct v2 bx_norm = v2_norm(V2(m.e[0][0], m.e[0][1]));

    struct v2 by_norm = v2_norm(V2(m.e[1][0], m.e[1][1]));
    by_norm = v2_mul(by_norm, det_sign);

    f32 dot = v2_dot(bx_norm, by_norm);

    return math_acos(dot) - (PI * 0.5f);
}

INLINE struct mat3x3 mat3x3_lerp(struct mat3x3 a, struct mat3x3 b, f32 t)
{
    struct trs trs_a = trs_from_mat3x3(a);
    struct trs trs_b = trs_from_mat3x3(b);

    struct trs trs = trs_lerp(trs_a, trs_b, t);

    return mat3x3_from_trs(trs);
}

/* ========================== *
 * Mat4x4
 * ========================== */

/* NOTE: Mat4x4 only used for projection matrix */

INLINE struct mat4x4 mat4x4_from_ortho(f32 left, f32 right, f32 bottom, f32 top, f32 near, f32 far)
{
    struct mat4x4 m = {0};

    f32 rl =  1.0f / (right - left);
    f32 tb =  1.0f / (top - bottom);
    f32 fn = -1.0f / (far - near);

    m.e[0][0] = 2.0f * rl;
    m.e[1][1] = 2.0f * tb;
    m.e[2][2] = 2.0f * fn;
    m.e[3][0] = -(right + left) * rl;
    m.e[3][1] = -(top + bottom) * tb;
    m.e[3][2] = (far + near) * fn;
    m.e[3][3] = 1.0f;

    return m;
}

INLINE struct mat4x4 mat4x4_mul(struct mat4x4 m1, struct mat4x4 m2)
{
    f32 a00 = m1.e[0][0], a01 = m1.e[0][1], a02 = m1.e[0][2], a03 = m1.e[0][3],
        a10 = m1.e[1][0], a11 = m1.e[1][1], a12 = m1.e[1][2], a13 = m1.e[1][3],
        a20 = m1.e[2][0], a21 = m1.e[2][1], a22 = m1.e[2][2], a23 = m1.e[2][3],
        a30 = m1.e[3][0], a31 = m1.e[3][1], a32 = m1.e[3][2], a33 = m1.e[3][3],

        b00 = m2.e[0][0], b01 = m2.e[0][1], b02 = m2.e[0][2], b03 = m2.e[0][3],
        b10 = m2.e[1][0], b11 = m2.e[1][1], b12 = m2.e[1][2], b13 = m2.e[1][3],
        b20 = m2.e[2][0], b21 = m2.e[2][1], b22 = m2.e[2][2], b23 = m2.e[2][3],
        b30 = m2.e[3][0], b31 = m2.e[3][1], b32 = m2.e[3][2], b33 = m2.e[3][3];

    struct mat4x4 res;
    res.e[0][0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;
    res.e[0][1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;
    res.e[0][2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;
    res.e[0][3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;
    res.e[1][0] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;
    res.e[1][1] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;
    res.e[1][2] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;
    res.e[1][3] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;
    res.e[2][0] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;
    res.e[2][1] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;
    res.e[2][2] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;
    res.e[2][3] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;
    res.e[3][0] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;
    res.e[3][1] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;
    res.e[3][2] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;
    res.e[3][3] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;

    return res;
}

/* ========================== *
 * Trs
 * ========================== */

INLINE struct trs trs_lerp(struct trs a, struct trs b, f32 t)
{
    struct trs res;
    res.t = v2_lerp(a.t, b.t, t);
    res.r = math_lerp_angle(a.r, b.r, t);
    res.s = v2_lerp(a.s, b.s, t);
    return res;
}

INLINE struct trs trs_from_mat3x3(struct mat3x3 m)
{
    struct trs trs = { 0 };
    trs.t = mat3x3_get_pos(m);
    trs.r = mat3x3_get_rot(m);
    trs.s = mat3x3_get_scale(m);
    return trs;
}

/* ========================== *
 * Quad
 * ========================== */

INLINE struct quad quad_from_rect(struct rect rect)
{
    return (struct quad) {
        (struct v2) { rect.x, rect.y },                             /* Top left */
        (struct v2) { rect.x + rect.width, rect.y },                /* Top right */
        (struct v2) { rect.x + rect.width, rect.y + rect.height },  /* Bottom right */
        (struct v2) { rect.x, rect.y + rect.height },               /* Bottom left */

    };
}

INLINE struct quad quad_from_line(struct v2 start, struct v2 end, f32 thickness)
{
    f32 width = thickness / 2.f;

    struct v2 rel = v2_sub(end, start);
    struct v2 dir = v2_norm(rel);
    struct v2 dir_perp = v2_perp(dir);

    struct v2 left = v2_mul(dir_perp, -width);
    struct v2 right = v2_mul(dir_perp, width);
    return (struct quad) {
        .p1 = v2_add(start, left),
        .p2 = v2_add(start, right),
        .p3 = v2_add(end, right),
        .p4 = v2_add(end, left)
    };
}

INLINE struct quad quad_from_ray(struct v2 pos, struct v2 rel, f32 thickness)
{
    struct v2 end = v2_add(pos, rel);
    return quad_from_line(pos, end, thickness);
}

INLINE struct quad quad_scale(struct quad q, f32 s)
{
    q.p1 = v2_mul(q.p1, s);
    q.p2 = v2_mul(q.p2, s);
    q.p3 = v2_mul(q.p3, s);
    q.p4 = v2_mul(q.p4, s);
    return q;
}

INLINE struct quad quad_mul_mat3x3(struct quad quad, struct mat3x3 m)
{
    return (struct quad) {
        mat3x3_mul_v2(m, quad.p1),
        mat3x3_mul_v2(m, quad.p2),
        mat3x3_mul_v2(m, quad.p3),
        mat3x3_mul_v2(m, quad.p4)
    };
}

#endif