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power_play/src/math.h

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#ifndef MATH_H
#define MATH_H
/* Math functions are default 32 bit (f32, i32, etc) unless specified */
#include "intrinsics.h"
INLINE f32 math_sqrt(f32 x);
/* ========================== *
* Float rounding
* ========================== */
/* TODO: Don't use intrinsics for these. */
/* Round */
INLINE f32 math_round(f32 f)
{
return ix_round_f32_to_f32(f);
}
INLINE f64 math_round64(f64 f)
{
return ix_round_f64_to_f64(f);
}
INLINE i32 math_round_to_int(f32 f)
{
return ix_round_f32_to_i32(f);
}
INLINE i64 math_round_to_int64(f64 f)
{
return ix_round_f64_to_i64(f);
}
/* Floor */
INLINE f32 math_floor(f32 f)
{
return ix_floor_f32_to_f32(f);
}
INLINE f64 math_floor64(f64 f)
{
return ix_floor_f64_to_f64(f);
}
INLINE i32 math_floor_to_int(f32 f)
{
return ix_floor_f32_to_i32(f);
}
INLINE i64 math_floor_to_int64(f64 f)
{
return ix_floor_f64_to_i64(f);
}
/* Ceil */
INLINE f32 math_ceil(f32 f)
{
return ix_ceil_f32_to_f32(f);
}
INLINE f64 math_ceil64(f64 f)
{
return ix_ceil_f64_to_f64(f);
}
INLINE i32 math_ceil_to_int(f32 f)
{
return ix_ceil_f32_to_i32(f);
}
INLINE i64 math_ceil_to_int64(f64 f)
{
return ix_ceil_f64_to_i64(f);
}
/* Truncate */
INLINE f32 math_trunc(f32 f)
{
return ix_trunc_f32_to_f32(f);
}
INLINE f64 math_trunc64(f64 f)
{
return ix_trunc_f64_to_f64(f);
}
/* ========================== *
* Float properties
* ========================== */
INLINE f32 math_fmod(f32 x, f32 m)
{
return x - m * math_trunc(x / m);
}
INLINE f64 math_fmod64(f64 x, f64 m)
{
return x - m * math_trunc64(x / m);
}
INLINE f32 math_fabs(f32 f)
{
u32 truncated = *(u32 *)&f & 0x7FFFFFFF;
return *(f32 *)&truncated;
}
INLINE f64 math_fabs64(f64 f)
{
u64 truncated = *(u64 *)&f & 0x7FFFFFFFFFFFFFFFULL;
return *(f64 *)&truncated;
}
INLINE i32 math_fsign(f32 f)
{
u32 sign_bit = (*(u32 *)&f >> 31) & 1;
return 1 + -((i32)(sign_bit << 1));
}
INLINE i64 math_fsign64(f64 f)
{
u64 sign_bit = (*(u64 *)&f >> 63) & 1;
return 1 + -((i64)(sign_bit << 1));
}
/* ========================== *
* 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;
}
}
/* Based on FreeBSD's implementation
* https://github.com/freebsd/freebsd-src/blob/main/lib/msun/src/e_logf.c */
INLINE f32 math_ln(f32 x)
{
LOCAL_PERSIST const f32 ln2_hi = 6.9313812256e-01f;
LOCAL_PERSIST const f32 ln2_lo = 9.0580006145e-06f;
i32 x_int = *(u32 *)&x;
i32 k = 0;
if (x_int < 0x00800000) {
f32 two_p25 = 3.3554432000e+07;
if ((x_int & 0x7fffffff) == 0) {
/* Return -inf if x is 0 */
return -two_p25 / 0;
} else if (x_int < 0) {
/* Return NaN if x is negative */
return (x - x) / 0;
}
k -= 25;
x *= two_p25;
x_int = *(u32 *)&x;
} else if (x_int >= 0x7f800000) {
return x + x;
}
k += (x_int >> 23) - 127;
x_int &= 0x007fffff;
i32 i = (x_int + (0x95f64 << 3)) & 0x800000;
i32 x_int_normalized = x_int | (i ^ 0x3f800000);
x = *(f32 *)&x_int_normalized - 1.0f;
k += (i >> 23);
if ((0x007fffff & (0x8000 + x_int)) < 0xc000) {
if (x == 0.0f) {
if (k == 0) {
return 0;
} else {
return (f32)k * ln2_hi + (f32)k * ln2_lo;
}
}
f32 r = x * x * (0.5f - 0.33333333333333333f * x);
if (k == 0) {
return x - r;
} else {
return (f32)k * ln2_hi - ((r - (f32)k * ln2_lo) - x);
}
}
f32 s = x / (2.0f + x);
f32 z = s * s;
f32 w = z * z;
f32 r = (z * (0.66666662693f + w * 0.28498786688f)) + (w * (0.40000972152f + w * 0.24279078841f));
if (((x_int - (0x6147a << 3)) | ((0x6b851 << 3) - x_int)) > 0) {
f32 hfsq = 0.5f * x * x;
if (k == 0) {
return x - (hfsq - s * (hfsq + r));
} else {
return (f32)k * ln2_hi - ((hfsq - (s * (hfsq + r) + (f32)k * ln2_lo)) - x);
}
} else {
if (k == 0) {
return x - s * (x - r);
} else {
return (f32)k * ln2_hi - ((s * (x - r) - (f32)k * ln2_lo) - x);
}
}
}
/* Based on FreeBSD's implementation
* https://github.com/freebsd/freebsd-src/blob/main/lib/msun/src/e_expf.c */
INLINE f32 math_exp(f32 x)
{
LOCAL_PERSIST const f32 half[2] = { 0.5, -0.5 };
LOCAL_PERSIST const f32 o_threshold = 8.8721679688e+01f;
LOCAL_PERSIST const f32 u_threshold = -1.0397208405e+02f;
LOCAL_PERSIST const f32 ln2_hi[2] = { 6.9314575195e-01f, -6.9314575195e-01f };
LOCAL_PERSIST const f32 ln2_lo[2] = { 1.4286067653e-06f, -1.4286067653e-06f };
LOCAL_PERSIST const f32 inv_ln2 = 1.4426950216e+00f;
LOCAL_PERSIST const f32 huge = 1.0e+30f;
LOCAL_PERSIST const f32 two_m100 = 7.8886090522e-31f;
u32 x_uint = *(u32 *)&x;
i32 x_sign_bit = (x_uint >> 31) & 1;
x_uint &= 0x7fffffff;
/* Filter out non-finite argument */
if (x_uint >= 0x42b17218) { /* if |x|>=88.721... */
if (x_uint > 0x7f800000) {
return x + x; /* NaN */
} else if (x_uint == 0x7f800000) {
return (x_sign_bit == 0) ? x : 0.0f;
}
if (x > o_threshold) {
/* Overflow */
return huge * huge;
} else if (x < u_threshold) {
/* Underflow */
return two_m100 * two_m100;
}
}
/* Argument reduction */
i32 k = 0;
f32 hi = 0;
f32 lo = 0;
if (x_uint > 0x3eb17218) {
if (x_uint < 0x3F851592) {
hi = x - ln2_hi[x_sign_bit];
lo = ln2_lo[x_sign_bit];
k = 1 - x_sign_bit - x_sign_bit;
} else {
k = (i32)(inv_ln2 * x + half[x_sign_bit]);
hi = x - (f32)k * ln2_hi[0];
lo = (f32)k * ln2_lo[0];
}
x = hi - lo;
} else if (x_uint < 0x39000000) {
if (huge + x > 1.0f) {
return 1.0f + x;
}
} else {
k = 0;
}
f32 two_pk;
if (k >= -125) {
u32 temp = ((u32)(0x7f + k)) << 23;
two_pk = *(f32 *)&temp;
} else {
u32 temp = ((u32)(0x7f + (k + 100))) << 23;
two_pk = *(f32 *)&temp;
}
f32 t = x * x;
f32 c = x - t * (1.6666625440e-1f + t * -2.7667332906e-3f);
if (k == 0) {
return 1.0f - ((x * c) / (c - 2.0f) - x);
} else {
f32 y = 1.0f - ((lo - (x * c)/(2.0f - c))-hi);
if (k >= -125) {
if (k==128) {
u32 temp = 0x7f800000;
return y * 2.0f * (*(f32 *)&temp);
}
return y * two_pk;
} else {
return y * two_pk * two_m100;
}
}
}
INLINE f32 math_pow(f32 a, f32 b)
{
if (a >= 0) {
/* a is positive */
return math_exp(math_ln(a) * b);
} else {
/* a is negative */
i32 res_sign = math_round_to_int(b) % 2 == 0 ? 1 : -1;
return math_exp(math_ln(-a) * b) * res_sign;
}
}
INLINE f32 math_sqrt(f32 x)
{
return ix_sqrt_f32(x);
}
INLINE f32 math_rsqrt(f32 x)
{
return ix_rsqrt_f32(x);
}
/* ========================== *
* Trig
* ========================== */
/* Functions based on Cephes implementation (https://www.netlib.org/cephes/):
* - math_sin_approx
* - math_cos_approx
* - math_reduce_positive_to_pio4
* - math_atan
*/
/* TODO: Vectorize */
/* Approximate sin in range [0, PI/4] */
INLINE f32 math_sin_approx(f32 x)
{
f32 x_sq = x * x;
return (((-1.9515295891E-4 * x_sq + 8.3321608736E-3) * x_sq - 1.6666654611E-1) * x_sq * x) + x;
}
/* Approximate cos in range [0, PI/4] */
INLINE f32 math_cos_approx(f32 x)
{
f32 x_sq = x * x;
return (((2.443315711809948E-005 * x_sq - 1.388731625493765E-003) * x_sq + 4.166664568298827E-002) * x_sq * x_sq) - (x_sq * 0.5) + 1;
}
/* Reduce postive x to range [0, PI/4] (Cody-Waite argument reduction).
* Returns 0 if x > (2^24 - 1);
* Sets octant_out=-1 on error. */
INLINE f32 math_reduce_positive_to_pio4(f32 x, i32 *octant_out)
{
i32 octant = -1;
if (x <= ((1 << 24) - 1)) {
octant = x * (4 / PI); /* Integer part of x/(PI/4) */
f32 y = octant;
if (octant & 1) {
octant += 1;
y += 1.0;
}
/* Modulo 360 degrees */
octant &= 7;
if (x > 8192) {
x = x - y * (PI / 4);
} else {
/* Extended precision modular arithmetic */
x = ((x - y * 0.78515625) - y * 2.4187564849853515625e-4) - y * 3.77489497744594108e-8;
}
}
*octant_out = octant;
return x;
}
INLINE f32 math_sin(f32 x)
{
i32 sign = 1;
if (F32_IS_NAN(x)) {
return 0;
} else if (x < 0) {
sign = -1;
x = -x;
}
i32 octant;
x = math_reduce_positive_to_pio4(x, &octant);
/* Reflect in x axis */
if (octant > 3) {
sign = -sign;
octant -= 4;
}
switch (octant) {
case -1: return 0;
case 1: case 2: return math_cos_approx(x) * sign;
default: return math_sin_approx(x) * sign;
}
}
INLINE f32 math_cos(f32 x)
{
i32 sign = 1;
if (F32_IS_NAN(x)) {
return 0;
} else if (x < 0) {
x = -x;
}
i32 octant;
x = math_reduce_positive_to_pio4(x, &octant);
/* Reflect in x axis */
if (octant > 3) {
sign = -sign;
octant -= 4;
}
if (octant > 1) {
sign = -sign;
}
switch (octant) {
case -1: return 0;
case 1: case 2: return math_sin_approx(x) * sign;
default: return math_cos_approx(x) * sign;
}
}
INLINE f32 math_atan(f32 x)
{
i32 sign = 1;
if (x < 0) {
sign = -1;
x = -x;
}
/* Reduce range */
f32 y;
if (x > 2.414213562373095) { /* tan((PI / 8) * 3) */
y = PI / 2;
x = -(1.f / x);
} else if (x > 0.4142135623730950) { /* tan(PI / 8) */
y = PI / 4;
x = (x - 1.f) / (x + 1.f);
} else {
y = 0;
}
f32 x_sq = x * x;
y += ((((8.05374449538e-2 * x_sq - 1.38776856032E-1) * x_sq + 1.99777106478E-1) * x_sq - 3.33329491539E-1) * x_sq * x + x);
return y * sign;
}
INLINE f32 math_atan2(f32 y, f32 x)
{
if (x == 0) {
if (y < 0) {
return -PI / 2;
} else if (y > 0) {
return PI / 2;
} else {
return 0;
}
} else if (y == 0) {
if (x < 0) {
return PI;
} else {
return 0;
}
} else {
f32 offset = (x < 0) * (PI - (2 * PI * (y < 0)));
return math_atan(y / x) + offset;
}
}
INLINE f32 math_asin(f32 x)
{
/* TODO: Dedicated arcsin approximation */
return math_atan2(x, math_sqrt(1.0f - (x * x)));
}
INLINE f32 math_acos(f32 x)
{
/* TODO: Dedicated arccos approximation */
return (PI / 2.0f) - math_atan2(x, math_sqrt(1.0f - (x * x)));
}
/* ========================== *
* Lerp
* ========================== */
INLINE f32 math_lerp(f32 val0, f32 val1, f32 t)
{
return val0 + ((val1 - val0) * t);
}
INLINE f64 math_lerp64(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_fmod(b - a, TAU);
diff = math_fmod(2.0f * diff, TAU) - diff;
return a + diff * t;
}
/* ========================== *
* 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_sq(struct v2 a)
{
return a.x * a.x + a.y * a.y;
}
INLINE f32 v2_dot(struct v2 a, struct v2 b)
{
return a.x * b.x + a.y * b.y;
}
/* Returns signed area between vectors (positive in clockwise direction)
* AKA perpendicular dot product
* AKA 2d cross-product */
INLINE f32 v2_wedge(struct v2 a, struct v2 b)
{
return a.x * b.y - a.y * b.x;
}
/* Clockwise perpendicular vector */
INLINE struct v2 v2_perp_right(struct v2 a)
{
return V2(-a.y, a.x);
}
/* Counter-clockwise perpendicular vector */
INLINE struct v2 v2_perp_left(struct v2 a)
{
return V2(a.y, -a.x);
}
/* Clockwise perpendicular vector scaled by s */
INLINE struct v2 v2_perp_right_mul(struct v2 a, f32 s)
{
return V2(s * -a.y, s * a.x);
}
/* Counter-clockwise perpendicular vector scaled by s */
INLINE struct v2 v2_perp_left_mul(struct v2 a, f32 s)
{
return V2(s * a.y, s * -a.x);
}
INLINE struct v2 v2_perp_towards_dir(struct v2 v, struct v2 dir)
{
f32 wedge = v2_wedge(v, dir);
return v2_perp_right_mul(v, (wedge >= 0) - (wedge < 0));
}
INLINE struct v2 v2_norm(struct v2 a)
{
f32 l = a.x * a.x + a.y * a.y;
if (l != 0) {
/* TODO: Benchmark with math_rqsrt(l) */
f32 denom = 1.f / math_sqrt(l);
a.x *= denom;
a.y *= denom;
}
return a;
}
INLINE struct v2 v2_round(struct v2 a)
{
return V2(math_round(a.x), math_round(a.y));
}
INLINE struct v2 v2_floor(struct v2 a)
{
return V2(math_floor(a.x), math_floor(a.y));
}
INLINE struct v2 v2_ceil(struct v2 a)
{
return V2(math_ceil(a.x), math_ceil(a.y));
}
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 b32 v2_is_zero(struct v2 a)
{
return a.x == 0 && a.y == 0;
}
INLINE struct v2 v2_lerp(struct v2 val0, struct v2 val1, f32 t)
{
return V2(math_lerp(val0.x, val1.x, t), math_lerp(val0.y, val1.y, t));
}
INLINE struct v2 v2_rotated(struct v2 v, f32 a)
{
f32 sin = math_sin(a);
f32 cos = math_cos(a);
return V2(v.x * cos - v.y * sin, v.x * sin + v.y * cos);
}
INLINE struct v2 v2_from_angle(f32 a)
{
return V2(math_cos(a), math_sin(a));
}
INLINE f32 v2_angle(struct v2 v)
{
return math_atan2(v.y, v.x);
}
INLINE f32 v2_angle_from_dirs(struct v2 dir1, struct v2 dir2)
{
return math_atan2(v2_wedge(dir1, dir2), v2_dot(dir1, dir2));
}
INLINE f32 v2_angle_from_points(struct v2 pt1, struct v2 pt2)
{
return v2_angle(v2_sub(pt2, pt1));
}
INLINE struct v2 v2_closest_point_ray(struct v2 ray_pos, struct v2 ray_dir_norm, struct v2 p)
{
struct v2 ray_p_dir = v2_sub(p, ray_pos);
f32 dot = v2_dot(ray_dir_norm, ray_p_dir);
struct v2 ray_dir_closest = v2_mul(ray_dir_norm, dot);
return v2_add(ray_pos, ray_dir_closest);
}
/* ========================== *
* Mat4x4
* ========================== */
INLINE struct mat4x4 mat4x4_from_xform(struct xform xf)
{
return (struct mat4x4) {
.e = {
{xf.bx.x, xf.bx.y, 0, 0},
{xf.by.x, xf.by.y, 0, 0},
{0, 0, 1, 0},
{xf.og.x, xf.og.y, 0, 1},
}
};
}
INLINE struct mat4x4 mat4x4_from_ortho(f32 left, f32 right, f32 bottom, f32 top, f32 near_z, f32 far_z)
{
struct mat4x4 m = {0};
f32 rl = 1.0f / (right - left);
f32 tb = 1.0f / (top - bottom);
f32 fn = -1.0f / (far_z - near_z);
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_z + near_z) * 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;
}
/* ========================== *
* Xform
* ========================== */
/* Construct identity xform */
#define XFORM_IDENT ((struct xform) { .bx.x = 1, .by.y = 1 })
#define XFORM_IDENT_NOCAST { .bx.x = 1, .by.y = 1 }
#define XFORM_POS(p) ((struct xform) { .bx.x = 1, .by.y = 1, .og = (p) })
/* Takes a translation, rotation, and scale as optional parameters for constructing an xform */
#define XFORM_TRS(...) xform_from_trs((struct trs) { .t = V2(0,0), .s = V2(1, 1), .r = 0, __VA_ARGS__ })
INLINE struct xform xform_rotated(struct xform xf, f32 angle);
INLINE struct xform xform_scaled(struct xform xf, struct v2 v);
INLINE struct v2 xform_basis_mul_v2(struct xform xf, struct v2 v);
INLINE struct v2 xform_mul_v2(struct xform xf, struct v2 v);
INLINE struct xform xform_scaled_to(struct xform xf, struct v2 s);
INLINE f32 xform_get_determinant(struct xform xf);
INLINE struct v2 xform_get_scale(struct xform xf);
INLINE f32 xform_get_skew(struct xform xf);
INLINE struct xform xform_skewed_to(struct xform xf, f32 s);
INLINE f32 xform_get_rotation(struct xform xf);
INLINE b32 xform_eq(struct xform xf1, struct xform xf2)
{
return v2_eq(xf1.og, xf2.og) && v2_eq(xf1.bx, xf2.bx) && v2_eq(xf1.by, xf2.by);
}
INLINE struct xform xform_from_pos(struct v2 v)
{
return (struct xform) {
.bx = {1, 0},
.by = {0, 1},
.og = {v.x, v.y}
};
}
INLINE struct xform xform_from_trs(struct trs trs)
{
struct xform xf = XFORM_POS(trs.t);
xf = xform_rotated(xf, trs.r);
xf = xform_scaled(xf, trs.s);
return xf;
}
INLINE struct xform xform_translated(struct xform xf, struct v2 v)
{
xf.og = V2(
xf.bx.x * v.x + xf.by.x * v.y + xf.og.x,
xf.bx.y * v.x + xf.by.y * v.y + xf.og.y
);
return xf;
}
INLINE struct xform xform_rotated(struct xform xf, f32 angle)
{
f32 c = math_cos(angle);
f32 s = math_sin(angle);
struct xform res = xf;
res.bx.x = xf.bx.x * c + xf.by.x * s;
res.bx.y = xf.bx.y * c + xf.by.y * s;
res.by.x = xf.bx.x * -s + xf.by.x * c;
res.by.y = xf.bx.y * -s + xf.by.y * c;
return res;
}
INLINE struct xform xform_scaled(struct xform xf, struct v2 v)
{
xf.bx = v2_mul(xf.bx, v.x);
xf.by = v2_mul(xf.by, v.y);
return xf;
}
INLINE struct xform xform_rotated_to(struct xform xf, f32 r)
{
struct v2 scale = xform_get_scale(xf);
f32 skew = xform_get_skew(xf);
f32 c = math_cos(r);
f32 s = math_sin(r);
xf.bx = V2(c, s);
xf.by = V2(-s, c);
xf = xform_scaled_to(xf, scale);
xf = xform_skewed_to(xf, skew);
return xf;
}
INLINE struct xform xform_scaled_to(struct xform xf, struct v2 s)
{
xf.bx = v2_mul(v2_norm(xf.bx), s.x);
xf.by = v2_mul(v2_norm(xf.by), s.y);
return xf;
}
INLINE struct xform xform_trs(struct xform xf, struct trs trs)
{
xf = xform_translated(xf, trs.t);
xf = xform_rotated(xf, trs.r);
xf = xform_scaled(xf, trs.s);
return xf;
}
INLINE struct xform xform_trs_pivot_r(struct xform xf, struct trs trs, struct v2 pivot)
{
xf = xform_translated(xf, trs.t);
xf = xform_rotated(xf, trs.r);
xf = xform_translated(xf, v2_neg(pivot));
xf = xform_scaled(xf, trs.s);
return xf;
}
INLINE struct xform xform_trs_pivot_rs(struct xform xf, struct trs trs, struct v2 pivot)
{
xf = xform_translated(xf, trs.t);
xf = xform_rotated(xf, trs.r);
xf = xform_scaled(xf, trs.s);
xf = xform_translated(xf, v2_neg(pivot));
return xf;
}
INLINE struct xform xform_lerp(struct xform a, struct xform b, f32 t)
{
struct v2 og = v2_lerp(a.og, b.og, t);
f32 rot = math_lerp_angle(xform_get_rotation(a), xform_get_rotation(b), t);
struct v2 scale = v2_lerp(xform_get_scale(a), xform_get_scale(b), t);
f32 skew = math_lerp_angle(xform_get_skew(a), xform_get_skew(b), t);
struct xform res = xform_from_pos(og);
res = xform_rotated(res, rot);
res = xform_scaled(res, scale);
res = xform_skewed_to(res, skew);
return res;
}
INLINE struct xform xform_invert(struct xform xf)
{
f32 det = xform_get_determinant(xf);
f32 inv_det = 1.0f / det;
f32 old_bx_x = xf.bx.x;
xf.bx.x = xf.by.y;
xf.by.y = old_bx_x;
xf.bx = v2_mul_v2(xf.bx, V2(inv_det, -inv_det));
xf.by = v2_mul_v2(xf.by, V2(-inv_det, inv_det));
xf.og = xform_basis_mul_v2(xf, v2_neg(xf.og));
return xf;
}
INLINE struct xform xform_mul(struct xform a, struct xform b)
{
struct xform res;
res.bx.x = a.bx.x * b.bx.x + a.by.x * b.bx.y;
res.bx.y = a.bx.y * b.bx.x + a.by.y * b.bx.y;
res.by.x = a.bx.x * b.by.x + a.by.x * b.by.y;
res.by.y = a.bx.y * b.by.x + a.by.y * b.by.y;
res.og = xform_mul_v2(a, b.og);
return res;
}
INLINE struct v2 xform_basis_mul_v2(struct xform xf, struct v2 v)
{
return V2(
xf.bx.x * v.x + xf.by.x * v.y,
xf.bx.y * v.x + xf.by.y * v.y
);
}
INLINE struct v2 xform_mul_v2(struct xform xf, struct v2 v)
{
struct v2 res = xform_basis_mul_v2(xf, v);
res = v2_add(res, xf.og);
return res;
}
INLINE struct v2 xform_basis_invert_mul_v2(struct xform xf, struct v2 v)
{
struct xform inv = xform_invert(xf);
struct v2 res = xform_basis_mul_v2(inv, v);
return res;
}
/* TODO: Get rid of this? Just force caller to use invert manually since it's expensive. */
INLINE struct v2 xform_invert_mul_v2(struct xform xf, struct v2 v)
{
struct xform inv = xform_invert(xf);
return xform_mul_v2(inv, v);
}
INLINE struct quad xform_mul_quad(struct xform xf, struct quad quad)
{
return (struct quad) {
xform_mul_v2(xf, quad.p1),
xform_mul_v2(xf, quad.p2),
xform_mul_v2(xf, quad.p3),
xform_mul_v2(xf, quad.p4)
};
}
INLINE f32 xform_get_determinant(struct xform xf)
{
return v2_wedge(xf.bx, xf.by);
}
INLINE f32 xform_get_skew(struct xform xf)
{
return v2_angle_from_dirs(v2_norm(xf.bx), v2_norm(xf.by)) - PI / 2;
}
INLINE struct xform xform_skewed_to(struct xform xf, f32 s)
{
f32 angle = v2_angle(xf.bx) + s + (PI / 2);
xf.by = v2_mul(v2_from_angle(angle), v2_len(xf.by));
return xf;
}
INLINE struct v2 xform_get_right(struct xform xf)
{
return xf.bx;
}
INLINE struct v2 xform_get_left(struct xform xf)
{
return v2_neg(xf.bx);
}
INLINE struct v2 xform_get_up(struct xform xf)
{
return v2_neg(xf.by);
}
INLINE struct v2 xform_get_down(struct xform xf)
{
return xf.by;
}
INLINE f32 xform_get_rotation(struct xform xf)
{
return v2_angle(xf.bx);
}
INLINE struct v2 xform_get_scale(struct xform xf)
{
f32 det_sign = math_fsign(xform_get_determinant(xf));
return V2(v2_len(xf.bx), det_sign * v2_len(xf.by));
}
/* ========================== *
* 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 dir = v2_norm(v2_sub(end, start));
struct v2 dir_perp = v2_perp_right(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_round(struct quad quad)
{
return (struct quad) {
v2_round(quad.p1),
v2_round(quad.p2),
v2_round(quad.p3),
v2_round(quad.p4)
};
}
INLINE struct quad quad_floor(struct quad quad)
{
return (struct quad) {
v2_floor(quad.p1),
v2_round(quad.p2),
v2_round(quad.p3),
v2_round(quad.p4)
};
}
/* ========================== *
* Convex polygon
* ========================== */
INLINE struct v2 math_poly_center(struct v2_array a)
{
struct v2 sum = V2(0, 0);
for (u64 i = 0; i < a.count; ++i) {
sum = v2_add(sum, a.points[i]);
}
return v2_div(sum, a.count);
}
#endif
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