move math.c functions to util.c

5 files changed, 966 insertions, 858 deletions

diff --git a/main.c b/main.c
index 4dd52af..9ae5b68 100644
--- a/main.c
+++ b/main.c
@@ -1,5 +1,6 @@
 /*
 @TODO:
+- rename v[234] to vec[234]
 - handle multiple symbols with same name in go-to-definition menu
 - better non-error window/showMessage(Request)
 - document lsp.h and lsp.c.
@@ -95,7 +96,6 @@ no_warn_end
 #error "Unrecognized operating system."
 #endif
 
-#include "math.c"
 #if _WIN32
 #include "process-win.c"
 #elif __unix__
diff --git a/math.c b/math.c
deleted file mode 100644
index db8e4f2..0000000
--- a/math.c
+++ /dev/null
@@ -1,856 +0,0 @@
-#ifdef MATH_GL
-#undef MATH_GL
-#define MATH_GL 1
-#endif
-
-#include <stdlib.h>
-#include <stdio.h>
-#include <assert.h>
-
-#define PIf 3.14159265358979f
-#define HALF_PIf 1.5707963267948966f
-#define TAUf 6.283185307179586f
-#define SQRT2f 1.4142135623730951f
-#define HALF_SQRT2f 0.7071067811865476f
-#define SQRT3f 1.7320508075688772f
-#define HALF_SQRT3f 0.8660254037844386f
-
-#include <math.h>
-
-static inline float degrees(float r) {
-	return r * (180.0f / PIf);
-}
-static inline float radians(float r) {
-	return r * (PIf / 180.f);
-}
-
-// map x from the interval [0, 1] to the interval [a, b]. does NOT clamp.
-static inline float lerpf(float x, float a, float b) {
-	return x * (b-a) + a;
-}
-
-// opposite of lerp; map x from the interval [a, b] to the interval [0, 1]. does NOT clamp.
-static inline float normf(float x, float a, float b) {
-	return (x-a) / (b-a);
-}
-
-static inline float clampf(float x, float a, float b) {
-	if (x < a) return a;
-	if (x > b) return b;
-	return x;
-}
-
-static inline int clampi(int x, int a, int b) {
-	if (x < a) return a;
-	if (x > b) return b;
-	return x;
-}
-
-static inline i16 clamp_i16(i16 x, i16 a, i16 b) {
-	if (x < a) return a;
-	if (x > b) return b;
-	return x;
-}
-
-static inline u16 clamp_u16(u16 x, u16 a, u16 b) {
-	if (x < a) return a;
-	if (x > b) return b;
-	return x;
-}
-
-static inline i32 clamp_i32(i32 x, i32 a, i32 b) {
-	if (x < a) return a;
-	if (x > b) return b;
-	return x;
-}
-
-static inline u32 clamp_u32(u32 x, u32 a, u32 b) {
-	if (x < a) return a;
-	if (x > b) return b;
-	return x;
-}
-
-static inline u8 ndigits_u64(u64 x) {
-	u8 ndigits = 1;
-	while (x > 9) {
-		x /= 10;
-		++ndigits;
-	}
-	return ndigits;
-}
-
-// remap x from the interval [from_a, from_b] to the interval [to_a, to_b], NOT clamping if x is outside the "from" interval.
-static inline float remapf(float x, float from_a, float from_b, float to_a, float to_b) {
-	float pos = (x - from_a) / (from_b - from_a);
-	return lerpf(pos, to_a, to_b);
-}
-
-static inline float minf(float a, float b) {
-	return a < b ? a : b;
-}
-
-static inline float maxf(float a, float b) {
-	return a > b ? a : b;
-}
-
-static inline double maxd(double a, double b) {
-	return a > b ? a : b;
-}
-
-static inline double mind(double a, double b) {
-	return a < b ? a : b;
-}
-
-static inline u32 min_u32(u32 a, u32 b) {
-	return a < b ? a : b;
-}
-
-static inline u32 max_u32(u32 a, u32 b) {
-	return a > b ? a : b;
-}
-
-// set *a to the minimum of *a and *b, and *b to the maximum
-static inline void sort2_u32(u32 *a, u32 *b) {
-	u32 x = *a, y = *b;
-	if (x > y) {
-		*a = y;
-		*b = x;
-	}
-}
-
-static inline i32 min_i32(i32 a, i32 b) {
-	return a < b ? a : b;
-}
-
-static inline i32 max_i32(i32 a, i32 b) {
-	return a > b ? a : b;
-}
-
-static inline u64 min_u64(u64 a, u64 b) {
-	return a < b ? a : b;
-}
-
-static inline u64 max_u64(u64 a, u64 b) {
-	return a > b ? a : b;
-}
-
-static inline i64 min_i64(i64 a, i64 b) {
-	return a < b ? a : b;
-}
-
-static inline i64 max_i64(i64 a, i64 b) {
-	return a > b ? a : b;
-}
-
-static inline i64 mod_i64(i64 a, i64 b) {
-	i64 ret = a % b;
-	if (ret < 0) ret += b;
-	return ret;
-}
-static inline i32 mod_i32(i32 a, i32 b) {
-	i32 ret = a % b;
-	if (ret < 0) ret += b;
-	return ret;
-}
-
-static inline i64 abs_i64(i64 x) {
-	return x < 0 ? -x : +x;
-}
-
-static inline i64 sgn_i64(i64 x) {
-	if (x < 0) return -1;
-	if (x > 0) return +1;
-	return 0;
-}
-
-static inline float sgnf(float x) {
-	if (x < 0) return -1;
-	if (x > 0) return +1;
-	return 0;
-}
-
-static inline float smoothstepf(float x) {
-	if (x <= 0) return 0;
-	if (x >= 1) return 1;
-	return x * x * (3 - 2 * x);
-}
-
-static inline float randf(void) {
-	return (float)rand() / (float)((ulong)RAND_MAX + 1);
-}
-
-static float rand_gauss(void) {
-	// https://en.wikipedia.org/wiki/Normal_distribution#Generating_values_from_normal_distribution
-	float U, V;
-	do
-		U = randf(), V = randf();
-	while (U == 0 || V == 0);
-	return sqrtf(-2 * logf(U)) * cosf(TAUf * V);
-}
-
-static u32 rand_u32(void) {
-	return ((u32)rand() & 0xfff)
-		| ((u32)rand() & 0xfff) << 12
-		| ((u32)rand() & 0xff) << 24;
-}
-
-static float rand_uniform(float from, float to) {
-	return lerpf(randf(), from, to);
-}
-
-static float sigmoidf(float x) {
-	return 1.0f / (1.0f + expf(-x));
-}
-
-// returns ⌈x/y⌉ (x/y rounded up)
-static i32 ceildivi32(i32 x, i32 y) {
-	if (y < 0) {
-		// negating both operands doesn't change the answer
-		x = -x;
-		y = -y;
-	}
-	if (x < 0) {
-		// truncation is the same as ceiling for negative numbers
-		return x / y;
-	} else {
-		return (x + (y-1)) / y;
-	}
-}
-
-typedef struct {
-	float x, y;
-} v2;
-
-static v2 const v2_zero = {0, 0};
-static v2 V2(float x, float y) {
-	v2 v;
-	v.x = x;
-	v.y = y;
-	return v;
-}
-
-static v2 v2_add(v2 a, v2 b) {
-	return V2(a.x + b.x, a.y + b.y);
-}
-
-static v2 v2_add_const(v2 a, float c) {
-	return V2(a.x + c, a.y + c);
-}
-
-static v2 v2_sub(v2 a, v2 b) {
-	return V2(a.x - b.x, a.y - b.y);
-}
-
-static v2 v2_scale(v2 v, float s) {
-	return V2(v.x * s, v.y * s);
-}
-
-static v2 v2_mul(v2 a, v2 b) {
-	return V2(a.x * b.x, a.y * b.y);
-}
-
-static v2 v2_clamp(v2 x, v2 a, v2 b) {
-	return V2(clampf(x.x, a.x, b.x), clampf(x.y, a.y, b.y));
-}
-
-static float v2_dot(v2 a, v2 b) {
-	return a.x * b.x + a.y * b.y;
-}
-
-static float v2_len(v2 v) {
-	return sqrtf(v2_dot(v, v));
-}
-
-static v2 v2_lerp(float x, v2 a, v2 b) {
-	return V2(lerpf(x, a.x, b.x), lerpf(x, a.y, b.y));
-}
-
-// rotate v theta radians counterclockwise
-static v2 v2_rotate(v2 v, float theta) {
-	float c = cosf(theta), s = sinf(theta);
-	return V2(
-		c * v.x - s * v.y,
-		s * v.x + c * v.y
-	);
-}
-
-static v2 v2_normalize(v2 v) {
-	float len = v2_len(v);
-	float mul = len == 0.0f ? 1.0f : 1.0f/len;
-	return v2_scale(v, mul);
-}
-
-static float v2_dist(v2 a, v2 b) {
-	return v2_len(v2_sub(a, b));
-}
-
-static float v2_dist_squared(v2 a, v2 b) {
-	v2 diff = v2_sub(a, b);
-	return v2_dot(diff, diff);
-}
-
-static void v2_print(v2 v) {
-	printf("(%f, %f)\n", v.x, v.y);
-}
-
-static v2 v2_rand_unit(void) {
-	float theta = rand_uniform(0, TAUf);
-	return V2(cosf(theta), sinf(theta));
-}
-
-static v2 v2_polar(float r, float theta) {
-	return V2(r * cosf(theta), r * sinf(theta));
-}
-
-typedef struct {
-	float x, y, z;
-} v3;
-
-static v3 const v3_zero = {0, 0, 0};
-
-static v3 V3(float x, float y, float z) {
-	v3 v;
-	v.x = x;
-	v.y = y;
-	v.z = z;
-	return v;
-}
-
-static v3 v3_from_v2(v2 v) {
-	return V3(v.x, v.y, 0);
-}
-
-static v3 v3_add(v3 a, v3 b) {
-	return V3(a.x + b.x, a.y + b.y, a.z + b.z);
-}
-
-static v3 v3_sub(v3 a, v3 b) {
-	return V3(a.x - b.x, a.y - b.y, a.z - b.z);
-}
-
-static v3 v3_scale(v3 v, float s) {
-	return V3(v.x * s, v.y * s, v.z * s);
-}
-
-static v3 v3_lerp(float x, v3 a, v3 b) {
-	return V3(lerpf(x, a.x, b.x), lerpf(x, a.y, b.y), lerpf(x, a.z, b.z));
-}
-
-static float v3_dot(v3 u, v3 v) {
-	return u.x*v.x + u.y*v.y + u.z*v.z;
-}
-
-static v3 v3_cross(v3 u, v3 v) {
-	v3 prod = V3(u.y*v.z - u.z*v.y, u.z*v.x - u.x*v.z, u.x*v.y - u.y*v.x);
-	return prod;
-}
-
-static float v3_len(v3 v) {
-	return sqrtf(v3_dot(v, v));
-}
-
-static float v3_dist(v3 a, v3 b) {
-	return v3_len(v3_sub(a, b));
-}
-
-static float v3_dist_squared(v3 a, v3 b) {
-	v3 diff = v3_sub(a, b);
-	return v3_dot(diff, diff);
-}
-
-static v3 v3_normalize(v3 v) {
-	float len = v3_len(v);
-	float mul = len == 0.0f ? 1.0f : 1.0f/len;
-	return v3_scale(v, mul);
-}
-
-static v2 v3_xy(v3 v) {
-	return V2(v.x, v.y);
-}
-
-// a point on a unit sphere 
-static v3 v3_on_sphere(float yaw, float pitch) {
-	return V3(cosf(yaw) * cosf(pitch), sinf(pitch), sinf(yaw) * cosf(pitch));
-}
-
-static void v3_print(v3 v) {
-	printf("(%f, %f, %f)\n", v.x, v.y, v.z);
-}
-
-static v3 v3_rand(void) {
-	return V3(randf(), randf(), randf());
-}
-
-static v3 v3_rand_unit(void) {
-	/*
-		monte carlo method
-		keep generating random points in cube of radius 1 (width 2) centered at origin,
-		until you get a point in the unit sphere, then extend it to find the point lying
-		on the sphere.
-	*/
-	while (1) {
-		v3 v = V3(rand_uniform(-1.0f, +1.0f), rand_uniform(-1.0f, +1.0f), rand_uniform(-1.0f, +1.0f));
-		float dist_squared_to_origin = v3_dot(v, v);
-		if (dist_squared_to_origin <= 1 && dist_squared_to_origin != 0.0f) {
-			return v3_scale(v, 1.0f / sqrtf(dist_squared_to_origin));
-		}
-	}
-	return V3(0, 0, 0);
-}
-
-typedef struct {
-	float x, y, z, w;
-} v4;
-
-static v4 const v4_zero = {0, 0, 0, 0};
-
-static v4 V4(float x, float y, float z, float w) {
-	v4 v;
-	v.x = x;
-	v.y = y;
-	v.z = z;
-	v.w = w;
-	return v;
-}
-
-static v4 v4_add(v4 a, v4 b) {
-	return V4(a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w);
-}
-
-static v4 v4_sub(v4 a, v4 b) {
-	return V4(a.x - b.x, a.y - b.y, a.z - b.z, a.w - b.w);
-}
-
-static v4 v4_scale(v4 v, float s) {
-	return V4(v.x * s, v.y * s, v.z * s, v.w * s);
-}
-
-static v4 v4_scale_xyz(v4 v, float s) {
-	return V4(v.x * s, v.y * s, v.z * s, v.w);
-}
-
-static v4 v4_lerp(float x, v4 a, v4 b) {
-	return V4(lerpf(x, a.x, b.x), lerpf(x, a.y, b.y), lerpf(x, a.z, b.z), lerpf(x, a.w, b.w));
-}
-
-static float v4_dot(v4 u, v4 v) {
-	return u.x*v.x + u.y*v.y + u.z*v.z + u.w*v.w;
-}
-
-// create a new vector by multiplying the respective components of u and v 
-static v4 v4_mul(v4 u, v4 v) {
-	return V4(u.x * v.x, u.y * v.y, u.z * v.z, u.w * v.w);
-}
-
-static float v4_len(v4 v) {
-	return sqrtf(v4_dot(v, v));
-}
-
-static v4 v4_normalize(v4 v) {
-	float len = v4_len(v);
-	float mul = len == 0.0f ? 1.0f : 1.0f/len;
-	return v4_scale(v, mul);
-}
-
-static v3 v4_xyz(v4 v) {
-	return V3(v.x, v.y, v.z);
-}
-
-static v4 v4_rand(void) {
-	return V4(randf(), randf(), randf(), randf());
-}
-
-static void v4_print(v4 v) {
-	printf("(%f, %f, %f, %f)\n", v.x, v.y, v.z, v.w);
-}
-
-typedef struct {
-	double x, y;
-} v2d;
-
-static v2d V2D(double x, double y) {
-	v2d v;
-	v.x = x;
-	v.y = y;
-	return v;
-}
-
-// matrices are column-major, because that's what they are in OpenGL 
-typedef struct {
-	float e[16];
-} m4;
-
-static m4 const m4_identity = {{
-	1, 0, 0, 0,
-	0, 1, 0, 0,
-	0, 0, 1, 0,
-	0, 0, 0, 1
-}};
-
-static void m4_print(m4 m) {
-	int i;
-	for (i = 0; i < 4; ++i)
-		printf("[ %f %f %f %f ]\n", m.e[i], m.e[i+4], m.e[i+8], m.e[i+12]);
-	printf("\n");
-}
-
-static m4 M4(
-	float a, float b, float c, float d,
-	float e, float f, float g, float h,
-	float i, float j, float k, float l,
-	float m, float n, float o, float p) {
-	m4 ret;
-	float *x = ret.e;
-	x[0] = a; x[4] = b; x[ 8] = c; x[12] = d;
-	x[1] = e; x[5] = f; x[ 9] = g; x[13] = h;
-	x[2] = i; x[6] = j; x[10] = k; x[14] = l;
-	x[3] = m; x[7] = n; x[11] = o; x[15] = p;
-	return ret;
-}
-
-// see https://en.wikipedia.org/wiki/Rotation_matrix#General_rotations 
-static m4 m4_yaw(float yaw) {
-	float c = cosf(yaw), s = sinf(yaw);
-	return M4(
-		c, 0, -s, 0,
-		0, 1,  0, 0,
-		s, 0,  c, 0,
-		0, 0,  0, 1
-	);
-}
-
-static m4 m4_pitch(float pitch) {
-	float c = cosf(pitch), s = sinf(pitch);
-	return M4(
-		1, 0,  0, 0,
-		0, c, -s, 0,
-		0, s,  c, 0,
-		0, 0,  0, 1
-	);
-}
-
-// https://en.wikipedia.org/wiki/Translation_(geometry) 
-static m4 m4_translate(v3 t) {
-	return M4(
-		1, 0, 0, t.x,
-		0, 1, 0, t.y,
-		0, 0, 1, t.z,
-		0, 0, 0, 1
-	);
-}
-
-// multiply m by [v.x, v.y, v.z, 1] 
-static v3 m4_mul_v3(m4 m, v3 v) {
-	return v3_add(v3_scale(V3(m.e[0], m.e[1], m.e[2]), v.x), v3_add(v3_scale(V3(m.e[4], m.e[5], m.e[6]), v.y),
-		v3_add(v3_scale(V3(m.e[8], m.e[9], m.e[10]), v.z), V3(m.e[12], m.e[13], m.e[14]))));
-}
-
-/*
-4x4 perspective matrix.
-fov - field of view in radians, aspect - width:height aspect ratio, z_near/z_far - clipping planes
-math stolen from gluPerspective (https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml)
-*/
-static m4 m4_perspective(float fov, float aspect, float z_near, float z_far) {
-	float f = 1.0f / tanf(fov / 2.0f);
-	return M4(
-		f/aspect, 0, 0, 0,
-		0, f, 0, 0,
-		0, 0, (z_far+z_near) / (z_near-z_far), (2.0f*z_far*z_near) / (z_near-z_far),
-		0, 0, -1, 0
-	);
-}
-
-// windows.h defines near and far, so let's not use those 
-static m4 m4_ortho(float left, float right, float bottom, float top, float near_, float far_) {
-	float tx = -(right + left)/(right - left);
-	float ty = -(top + bottom)/(top - bottom);
-	float tz = -(far_ + near_)/(far_ - near_);
-	return M4(
-		2.0f / (right - left), 0, 0, tx,
-		0, 2.0f / (top - bottom), 0, ty,
-		0, 0, -2.0f / (far_ - near_), tz,
-		0, 0, 0, 1
-	);
-}
-
-
-static m4 m4_mul(m4 a, m4 b) {
-	m4 prod = {0};
-	int i, j;
-	float *x = prod.e;
-	for (i = 0; i < 4; ++i) {
-		for (j = 0; j < 4; ++j, ++x) {
-			float *as = &a.e[j];
-			float *bs = &b.e[4*i];
-			*x = as[0]*bs[0] + as[4]*bs[1] + as[8]*bs[2] + as[12]*bs[3];
-		}
-	}
-	return prod;
-}
-
-static m4 m4_inv(m4 mat) {
-	m4 ret;
-	float *inv = ret.e;
-	float *m = mat.e;
-
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-	inv[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];
-
-	float det = m[0] * inv[0] + m[1] * inv[4] + m[2] * inv[8] + m[3] * inv[12];
-
-	if (det == 0) {
-		memset(inv, 0, sizeof *inv);
-	} else {
-		det = 1 / det;
-
-		for (int i = 0; i < 16; i++)
-			inv[i] *= det;
-	}
-
-	return ret;
-}
-typedef struct {
-	int x, y;
-} v2i;
-
-static v2i V2I(int x, int y) {
-	v2i v;
-	v.x = x;
-	v.y = y;
-	return v;
-}
-
-static void rgba_u32_to_floats(u32 rgba, float floats[4]) {
-	floats[0] = (float)((rgba >> 24) & 0xFF) / 255.f;
-	floats[1] = (float)((rgba >> 16) & 0xFF) / 255.f;
-	floats[2] = (float)((rgba >>  8) & 0xFF) / 255.f;
-	floats[3] = (float)((rgba >>  0) & 0xFF) / 255.f;
-}
-
-static v4 rgba_u32_to_v4(u32 rgba) {
-	float c[4];
-	rgba_u32_to_floats(rgba, c);
-	return V4(c[0], c[1], c[2], c[3]);
-}
-
-static u32 rgba_v4_to_u32(v4 color) {
-	return (u32)(color.x * 255) << 24
-		| (u32)(color.y * 255) << 16
-		| (u32)(color.z * 255) << 8
-		| (u32)(color.w * 255);
-}
-
-// returns average of red green and blue components of color
-static float rgba_brightness(u32 color) {
-	u8 r = (u8)(color >> 24), g = (u8)(color >> 16), b = (u8)(color >> 8);
-	return ((float)r+(float)g+(float)b) * (1.0f / 3);
-}
-
-static bool rect_contains_point_v2(v2 pos, v2 size, v2 point) {
-	float x1 = pos.x, y1 = pos.y, x2 = pos.x + size.x, y2 = pos.y + size.y,
-		x = point.x, y = point.y;
-	return x >= x1 && x < x2 && y >= y1 && y < y2;
-}
-
-static bool centered_rect_contains_point(v2 center, v2 size, v2 point) {
-	return rect_contains_point_v2(v2_sub(center, v2_scale(size, 0.5f)), size, point);
-}
-
-typedef struct {
-	v2 pos, size;
-} Rect;
-
-static Rect rect(v2 pos, v2 size) {
-	Rect r;
-	r.pos = pos;
-	r.size = size;
-	return r;
-}
-
-static Rect rect_endpoints(v2 e1, v2 e2) {
-	Rect r;
-	r.pos = e1;
-	r.size = v2_sub(e2, e1);
-	return r;
-}
-
-static Rect rect4(float x1, float y1, float x2, float y2) {
-	assert(x2 >= x1);
-	assert(y2 >= y1);
-	return rect(V2(x1,y1), V2(x2-x1, y2-y1));
-}
-
-static Rect rect_xywh(float x, float y, float w, float h) {
-	assert(w >= 0);
-	assert(h >= 0);
-	return rect(V2(x, y), V2(w, h));
-}
-
-static Rect rect_centered(v2 center, v2 size) {
-	Rect r;
-	r.pos = v2_sub(center, v2_scale(size, 0.5f));
-	r.size = size;
-	return r;
-}
-
-static v2 rect_center(Rect r) {
-	return v2_add(r.pos, v2_scale(r.size, 0.5f));
-}
-
-static bool rect_contains_point(Rect r, v2 point) {
-	return rect_contains_point_v2(r.pos, r.size, point);
-}
-
-static Rect rect_translate(Rect r, v2 by) {
-	return rect(v2_add(r.pos, by), r.size);
-}
-
-static float rect_x1(Rect r) { return r.pos.x; }
-static float rect_y1(Rect r) { return r.pos.y; }
-static float rect_x2(Rect r) { return r.pos.x + r.size.x; }
-static float rect_y2(Rect r) { return r.pos.y + r.size.y; }
-static float rect_xmid(Rect r) { return r.pos.x + r.size.x * 0.5f; }
-static float rect_ymid(Rect r) { return r.pos.y + r.size.y * 0.5f; }
-
-static void rect_coords(Rect r, float *x1, float *y1, float *x2, float *y2) {
-	*x1 = r.pos.x;
-	*y1 = r.pos.y;
-	*x2 = r.pos.x + r.size.x;
-	*y2 = r.pos.y + r.size.y;
-}
-
-static void rect_print(Rect r) {
-	printf("Position: (%f, %f), Size: (%f, %f)\n", r.pos.x, r.pos.y, r.size.x, r.size.y);
-}
-
-
-static float rects_intersect(Rect r1, Rect r2) {
-	if (r1.pos.x >= r2.pos.x + r2.size.x) return false; // r1 is to the right of r2
-	if (r2.pos.x >= r1.pos.x + r1.size.x) return false; // r2 is to the right of r1
-	if (r1.pos.y >= r2.pos.y + r2.size.y) return false; // r1 is above r2
-	if (r2.pos.y >= r1.pos.y + r1.size.y) return false; // r2 is above r1
-	return true;
-}
-
-// returns whether or not there is any of the clipped rectangle left
-static bool rect_clip_to_rect(Rect *clipped, Rect clipper) {
-	v2 start_pos = clipped->pos;
-	clipped->pos.x = maxf(clipped->pos.x, clipper.pos.x);
-	clipped->pos.y = maxf(clipped->pos.y, clipper.pos.y);
-	clipped->size = v2_add(clipped->size, v2_sub(start_pos, clipped->pos));
-
-	clipped->size.x = clampf(clipped->size.x, 0, clipper.pos.x + clipper.size.x - clipped->pos.x);
-	clipped->size.y = clampf(clipped->size.y, 0, clipper.pos.y + clipper.size.y - clipped->pos.y);
-	return clipped->size.x > 0 && clipped->size.y > 0;
-}
-
-// removes `amount` from all sides of r
-static Rect rect_shrink(Rect r, float amount) {
-	r.pos.x += amount;
-	r.pos.y += amount;
-	r.size.x -= 2 * amount;
-	r.size.y -= 2 * amount;
-	r.size.x = maxf(r.size.x, 0);
-	r.size.y = maxf(r.size.y, 0);
-	return r;
-}
-
-// adds `amount` to all sides of r
-static Rect rect_grow(Rect r, float amount) {
-	r.pos.x -= amount;
-	r.pos.y -= amount;
-	r.size.x += 2 * amount;
-	r.size.y += 2 * amount;
-	return r;
-}
-
-static v4 color_rgba_to_hsva(v4 rgba) {
-	float R = rgba.x, G = rgba.y, B = rgba.z, A = rgba.w;
-	float M = maxf(R, maxf(G, B));
-	float m = minf(R, minf(G, B));
-	float C = M - m;
-	float H = 0;
-	if (C == 0)
-		H = 0;
-	else if (M == R)
-		H = fmodf((G - B) / C, 6);
-	else if (M == G)
-		H = (B - R) / C + 2;
-	else if (M == B)
-		H = (R - G) / C + 4;
-	H *= 60;
-	float V = M;
-	float S = V == 0 ? 0 : C / V;
-	return V4(H, S, V, A);
-}
-
-static v4 color_hsva_to_rgba(v4 hsva) {
-	float H = hsva.x, S = hsva.y, V = hsva.z, A = hsva.w;
-	H /= 60;
-	float C = S * V;
-	float X = C * (1 - fabsf(fmodf(H, 2) - 1));
-	float R, G, B;
-	if (H <= 1)
-		R=C, G=X, B=0;
-	else if (H <= 2)
-		R=X, G=C, B=0;
-	else if (H <= 3)
-		R=0, G=C, B=X;
-	else if (H <= 4)
-		R=0, G=X, B=C;
-	else if (H <= 5)
-		R=X, G=0, B=C;
-	else
-		R=C, G=0, B=X;
-	
-	float m = V-C;
-	R += m;
-	G += m;
-	B += m;
-	return V4(R, G, B, A);
-}
-
-static u32 color_interpolate(float x, u32 color1, u32 color2) {
-	x = x * x * (3 - 2*x); // hermite interpolation
-
-	v4 c1 = rgba_u32_to_v4(color1), c2 = rgba_u32_to_v4(color2);
-	// to make it interpolate more nicely, convert to hsv, interpolate in that space, then convert back
-	c1 = color_rgba_to_hsva(c1);
-	c2 = color_rgba_to_hsva(c2);
-	// v_1/2 named differently to avoid shadowing
-	float h1 = c1.x, s1 = c1.y, v_1 = c1.z, a1 = c1.w;
-	float h2 = c2.x, s2 = c2.y, v_2 = c2.z, a2 = c2.w;
-	
-	float s_out = lerpf(x, s1, s2);
-	float v_out = lerpf(x, v_1, v_2);
-	float a_out = lerpf(x, a1, a2);
-	
-	float h_out;
-	// because hue is on a circle, we need to make sure we take the shorter route around the circle
-	if (fabsf(h1 - h2) < 180) {
-		h_out = lerpf(x, h1, h2);
-	} else if (h1 > h2) {
-		h_out = lerpf(x, h1, h2 + 360);
-	} else {
-		h_out = lerpf(x, h1 + 360, h2);
-	}
-	h_out = fmodf(h_out, 360);
-	
-	v4 c_out = V4(h_out, s_out, v_out, a_out);
-	c_out = color_hsva_to_rgba(c_out);
-	return rgba_v4_to_u32(c_out);
-}
diff --git a/ui.c b/ui.c
index a187d26..01e8b47 100644
--- a/ui.c
+++ b/ui.c
@@ -587,7 +587,7 @@ static void popup_get_rects(Ted const *ted, u32 options, Rect *popup, Rect *butt
 	float button_height = 30;
 	u16 nbuttons = util_popcount(options);
 	float button_width = popup->size.x / nbuttons;
-	popup->size = v2_clamp(popup->size, v2_zero, V2(window_width, window_height));
+	popup->size = v2_clamp(popup->size, V2(0, 0), V2(window_width, window_height));
 	Rect r = rect(V2(popup->pos.x, rect_y2(*popup) - button_height), V2(button_width, button_height));
 	if (options & POPUP_YES) {
 		*button_yes = r;
diff --git a/util.c b/util.c
index 3da5f30..39d1e39 100644
--- a/util.c
+++ b/util.c
@@ -425,3 +425,806 @@ bool copy_file(const char *src, const char *dst) {
 }
 
 
+#ifdef MATH_GL
+#undef MATH_GL
+#define MATH_GL 1
+#endif
+
+float degrees(float r) {
+	return r * (180.0f / PIf);
+}
+float radians(float r) {
+	return r * (PIf / 180.f);
+}
+
+// map x from the interval [0, 1] to the interval [a, b]. does NOT clamp.
+float lerpf(float x, float a, float b) {
+	return x * (b-a) + a;
+}
+
+// opposite of lerp; map x from the interval [a, b] to the interval [0, 1]. does NOT clamp.
+float normf(float x, float a, float b) {
+	return (x-a) / (b-a);
+}
+
+float clampf(float x, float a, float b) {
+	if (x < a) return a;
+	if (x > b) return b;
+	return x;
+}
+
+int clampi(int x, int a, int b) {
+	if (x < a) return a;
+	if (x > b) return b;
+	return x;
+}
+
+i16 clamp_i16(i16 x, i16 a, i16 b) {
+	if (x < a) return a;
+	if (x > b) return b;
+	return x;
+}
+
+u16 clamp_u16(u16 x, u16 a, u16 b) {
+	if (x < a) return a;
+	if (x > b) return b;
+	return x;
+}
+
+i32 clamp_i32(i32 x, i32 a, i32 b) {
+	if (x < a) return a;
+	if (x > b) return b;
+	return x;
+}
+
+u32 clamp_u32(u32 x, u32 a, u32 b) {
+	if (x < a) return a;
+	if (x > b) return b;
+	return x;
+}
+
+u8 ndigits_u64(u64 x) {
+	u8 ndigits = 1;
+	while (x > 9) {
+		x /= 10;
+		++ndigits;
+	}
+	return ndigits;
+}
+
+// remap x from the interval [from_a, from_b] to the interval [to_a, to_b], NOT clamping if x is outside the "from" interval.
+float remapf(float x, float from_a, float from_b, float to_a, float to_b) {
+	float pos = (x - from_a) / (from_b - from_a);
+	return lerpf(pos, to_a, to_b);
+}
+
+float minf(float a, float b) {
+	return a < b ? a : b;
+}
+
+float maxf(float a, float b) {
+	return a > b ? a : b;
+}
+
+double maxd(double a, double b) {
+	return a > b ? a : b;
+}
+
+double mind(double a, double b) {
+	return a < b ? a : b;
+}
+
+u32 min_u32(u32 a, u32 b) {
+	return a < b ? a : b;
+}
+
+u32 max_u32(u32 a, u32 b) {
+	return a > b ? a : b;
+}
+
+// set *a to the minimum of *a and *b, and *b to the maximum
+void sort2_u32(u32 *a, u32 *b) {
+	u32 x = *a, y = *b;
+	if (x > y) {
+		*a = y;
+		*b = x;
+	}
+}
+
+i32 min_i32(i32 a, i32 b) {
+	return a < b ? a : b;
+}
+
+i32 max_i32(i32 a, i32 b) {
+	return a > b ? a : b;
+}
+
+u64 min_u64(u64 a, u64 b) {
+	return a < b ? a : b;
+}
+
+u64 max_u64(u64 a, u64 b) {
+	return a > b ? a : b;
+}
+
+i64 min_i64(i64 a, i64 b) {
+	return a < b ? a : b;
+}
+
+i64 max_i64(i64 a, i64 b) {
+	return a > b ? a : b;
+}
+
+i64 mod_i64(i64 a, i64 b) {
+	i64 ret = a % b;
+	if (ret < 0) ret += b;
+	return ret;
+}
+i32 mod_i32(i32 a, i32 b) {
+	i32 ret = a % b;
+	if (ret < 0) ret += b;
+	return ret;
+}
+
+i64 abs_i64(i64 x) {
+	return x < 0 ? -x : +x;
+}
+
+i64 sgn_i64(i64 x) {
+	if (x < 0) return -1;
+	if (x > 0) return +1;
+	return 0;
+}
+
+float sgnf(float x) {
+	if (x < 0) return -1;
+	if (x > 0) return +1;
+	return 0;
+}
+
+float smoothstepf(float x) {
+	if (x <= 0) return 0;
+	if (x >= 1) return 1;
+	return x * x * (3 - 2 * x);
+}
+
+float randf(void) {
+	return (float)rand() / (float)((ulong)RAND_MAX + 1);
+}
+
+float rand_gauss(void) {
+	// https://en.wikipedia.org/wiki/Normal_distribution#Generating_values_from_normal_distribution
+	float U, V;
+	do
+		U = randf(), V = randf();
+	while (U == 0 || V == 0);
+	return sqrtf(-2 * logf(U)) * cosf(TAUf * V);
+}
+
+u32 rand_u32(void) {
+	return ((u32)rand() & 0xfff)
+		| ((u32)rand() & 0xfff) << 12
+		| ((u32)rand() & 0xff) << 24;
+}
+
+float rand_uniform(float from, float to) {
+	return lerpf(randf(), from, to);
+}
+
+float sigmoidf(float x) {
+	return 1.0f / (1.0f + expf(-x));
+}
+
+// returns ⌈x/y⌉ (x/y rounded up)
+i32 ceildivi32(i32 x, i32 y) {
+	if (y < 0) {
+		// negating both operands doesn't change the answer
+		x = -x;
+		y = -y;
+	}
+	if (x < 0) {
+		// truncation is the same as ceiling for negative numbers
+		return x / y;
+	} else {
+		return (x + (y-1)) / y;
+	}
+}
+
+v2 V2(float x, float y) {
+	v2 v;
+	v.x = x;
+	v.y = y;
+	return v;
+}
+
+v2 v2_add(v2 a, v2 b) {
+	return V2(a.x + b.x, a.y + b.y);
+}
+
+v2 v2_add_const(v2 a, float c) {
+	return V2(a.x + c, a.y + c);
+}
+
+v2 v2_sub(v2 a, v2 b) {
+	return V2(a.x - b.x, a.y - b.y);
+}
+
+v2 v2_scale(v2 v, float s) {
+	return V2(v.x * s, v.y * s);
+}
+
+v2 v2_mul(v2 a, v2 b) {
+	return V2(a.x * b.x, a.y * b.y);
+}
+
+v2 v2_clamp(v2 x, v2 a, v2 b) {
+	return V2(clampf(x.x, a.x, b.x), clampf(x.y, a.y, b.y));
+}
+
+float v2_dot(v2 a, v2 b) {
+	return a.x * b.x + a.y * b.y;
+}
+
+float v2_len(v2 v) {
+	return sqrtf(v2_dot(v, v));
+}
+
+v2 v2_lerp(float x, v2 a, v2 b) {
+	return V2(lerpf(x, a.x, b.x), lerpf(x, a.y, b.y));
+}
+
+// rotate v theta radians counterclockwise
+v2 v2_rotate(v2 v, float theta) {
+	float c = cosf(theta), s = sinf(theta);
+	return V2(
+		c * v.x - s * v.y,
+		s * v.x + c * v.y
+	);
+}
+
+v2 v2_normalize(v2 v) {
+	float len = v2_len(v);
+	float mul = len == 0.0f ? 1.0f : 1.0f/len;
+	return v2_scale(v, mul);
+}
+
+float v2_dist(v2 a, v2 b) {
+	return v2_len(v2_sub(a, b));
+}
+
+float v2_dist_squared(v2 a, v2 b) {
+	v2 diff = v2_sub(a, b);
+	return v2_dot(diff, diff);
+}
+
+void v2_print(v2 v) {
+	printf("(%f, %f)\n", v.x, v.y);
+}
+
+v2 v2_rand_unit(void) {
+	float theta = rand_uniform(0, TAUf);
+	return V2(cosf(theta), sinf(theta));
+}
+
+v2 v2_polar(float r, float theta) {
+	return V2(r * cosf(theta), r * sinf(theta));
+}
+
+v3 V3(float x, float y, float z) {
+	v3 v;
+	v.x = x;
+	v.y = y;
+	v.z = z;
+	return v;
+}
+
+v3 v3_from_v2(v2 v) {
+	return V3(v.x, v.y, 0);
+}
+
+v3 v3_add(v3 a, v3 b) {
+	return V3(a.x + b.x, a.y + b.y, a.z + b.z);
+}
+
+v3 v3_sub(v3 a, v3 b) {
+	return V3(a.x - b.x, a.y - b.y, a.z - b.z);
+}
+
+v3 v3_scale(v3 v, float s) {
+	return V3(v.x * s, v.y * s, v.z * s);
+}
+
+v3 v3_lerp(float x, v3 a, v3 b) {
+	return V3(lerpf(x, a.x, b.x), lerpf(x, a.y, b.y), lerpf(x, a.z, b.z));
+}
+
+float v3_dot(v3 u, v3 v) {
+	return u.x*v.x + u.y*v.y + u.z*v.z;
+}
+
+v3 v3_cross(v3 u, v3 v) {
+	v3 prod = V3(u.y*v.z - u.z*v.y, u.z*v.x - u.x*v.z, u.x*v.y - u.y*v.x);
+	return prod;
+}
+
+float v3_len(v3 v) {
+	return sqrtf(v3_dot(v, v));
+}
+
+float v3_dist(v3 a, v3 b) {
+	return v3_len(v3_sub(a, b));
+}
+
+float v3_dist_squared(v3 a, v3 b) {
+	v3 diff = v3_sub(a, b);
+	return v3_dot(diff, diff);
+}
+
+v3 v3_normalize(v3 v) {
+	float len = v3_len(v);
+	float mul = len == 0.0f ? 1.0f : 1.0f/len;
+	return v3_scale(v, mul);
+}
+
+v2 v3_xy(v3 v) {
+	return V2(v.x, v.y);
+}
+
+// a point on a unit sphere 
+v3 v3_on_sphere(float yaw, float pitch) {
+	return V3(cosf(yaw) * cosf(pitch), sinf(pitch), sinf(yaw) * cosf(pitch));
+}
+
+void v3_print(v3 v) {
+	printf("(%f, %f, %f)\n", v.x, v.y, v.z);
+}
+
+v3 v3_rand(void) {
+	return V3(randf(), randf(), randf());
+}
+
+v3 v3_rand_unit(void) {
+	/*
+		monte carlo method
+		keep generating random points in cube of radius 1 (width 2) centered at origin,
+		until you get a point in the unit sphere, then extend it to find the point lying
+		on the sphere.
+	*/
+	while (1) {
+		v3 v = V3(rand_uniform(-1.0f, +1.0f), rand_uniform(-1.0f, +1.0f), rand_uniform(-1.0f, +1.0f));
+		float dist_squared_to_origin = v3_dot(v, v);
+		if (dist_squared_to_origin <= 1 && dist_squared_to_origin != 0.0f) {
+			return v3_scale(v, 1.0f / sqrtf(dist_squared_to_origin));
+		}
+	}
+	return V3(0, 0, 0);
+}
+
+v4 V4(float x, float y, float z, float w) {
+	v4 v;
+	v.x = x;
+	v.y = y;
+	v.z = z;
+	v.w = w;
+	return v;
+}
+
+v4 v4_add(v4 a, v4 b) {
+	return V4(a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w);
+}
+
+v4 v4_sub(v4 a, v4 b) {
+	return V4(a.x - b.x, a.y - b.y, a.z - b.z, a.w - b.w);
+}
+
+v4 v4_scale(v4 v, float s) {
+	return V4(v.x * s, v.y * s, v.z * s, v.w * s);
+}
+
+v4 v4_scale_xyz(v4 v, float s) {
+	return V4(v.x * s, v.y * s, v.z * s, v.w);
+}
+
+v4 v4_lerp(float x, v4 a, v4 b) {
+	return V4(lerpf(x, a.x, b.x), lerpf(x, a.y, b.y), lerpf(x, a.z, b.z), lerpf(x, a.w, b.w));
+}
+
+float v4_dot(v4 u, v4 v) {
+	return u.x*v.x + u.y*v.y + u.z*v.z + u.w*v.w;
+}
+
+// create a new vector by multiplying the respective components of u and v 
+v4 v4_mul(v4 u, v4 v) {
+	return V4(u.x * v.x, u.y * v.y, u.z * v.z, u.w * v.w);
+}
+
+float v4_len(v4 v) {
+	return sqrtf(v4_dot(v, v));
+}
+
+v4 v4_normalize(v4 v) {
+	float len = v4_len(v);
+	float mul = len == 0.0f ? 1.0f : 1.0f/len;
+	return v4_scale(v, mul);
+}
+
+v3 v4_xyz(v4 v) {
+	return V3(v.x, v.y, v.z);
+}
+
+v4 v4_rand(void) {
+	return V4(randf(), randf(), randf(), randf());
+}
+
+void v4_print(v4 v) {
+	printf("(%f, %f, %f, %f)\n", v.x, v.y, v.z, v.w);
+}
+
+
+v2d V2D(double x, double y) {
+	v2d v;
+	v.x = x;
+	v.y = y;
+	return v;
+}
+
+void m4_print(m4 m) {
+	int i;
+	for (i = 0; i < 4; ++i)
+		printf("[ %f %f %f %f ]\n", m.e[i], m.e[i+4], m.e[i+8], m.e[i+12]);
+	printf("\n");
+}
+
+m4 M4(
+	float a, float b, float c, float d,
+	float e, float f, float g, float h,
+	float i, float j, float k, float l,
+	float m, float n, float o, float p) {
+	m4 ret;
+	float *x = ret.e;
+	x[0] = a; x[4] = b; x[ 8] = c; x[12] = d;
+	x[1] = e; x[5] = f; x[ 9] = g; x[13] = h;
+	x[2] = i; x[6] = j; x[10] = k; x[14] = l;
+	x[3] = m; x[7] = n; x[11] = o; x[15] = p;
+	return ret;
+}
+
+// see https://en.wikipedia.org/wiki/Rotation_matrix#General_rotations 
+m4 m4_yaw(float yaw) {
+	float c = cosf(yaw), s = sinf(yaw);
+	return M4(
+		c, 0, -s, 0,
+		0, 1,  0, 0,
+		s, 0,  c, 0,
+		0, 0,  0, 1
+	);
+}
+
+m4 m4_pitch(float pitch) {
+	float c = cosf(pitch), s = sinf(pitch);
+	return M4(
+		1, 0,  0, 0,
+		0, c, -s, 0,
+		0, s,  c, 0,
+		0, 0,  0, 1
+	);
+}
+
+// https://en.wikipedia.org/wiki/Translation_(geometry) 
+m4 m4_translate(v3 t) {
+	return M4(
+		1, 0, 0, t.x,
+		0, 1, 0, t.y,
+		0, 0, 1, t.z,
+		0, 0, 0, 1
+	);
+}
+
+// multiply m by [v.x, v.y, v.z, 1] 
+v3 m4_mul_v3(m4 m, v3 v) {
+	return v3_add(v3_scale(V3(m.e[0], m.e[1], m.e[2]), v.x), v3_add(v3_scale(V3(m.e[4], m.e[5], m.e[6]), v.y),
+		v3_add(v3_scale(V3(m.e[8], m.e[9], m.e[10]), v.z), V3(m.e[12], m.e[13], m.e[14]))));
+}
+
+/*
+4x4 perspective matrix.
+fov - field of view in radians, aspect - width:height aspect ratio, z_near/z_far - clipping planes
+math stolen from gluPerspective (https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml)
+*/
+m4 m4_perspective(float fov, float aspect, float z_near, float z_far) {
+	float f = 1.0f / tanf(fov / 2.0f);
+	return M4(
+		f/aspect, 0, 0, 0,
+		0, f, 0, 0,
+		0, 0, (z_far+z_near) / (z_near-z_far), (2.0f*z_far*z_near) / (z_near-z_far),
+		0, 0, -1, 0
+	);
+}
+
+// windows.h defines near and far, so let's not use those 
+m4 m4_ortho(float left, float right, float bottom, float top, float near_, float far_) {
+	float tx = -(right + left)/(right - left);
+	float ty = -(top + bottom)/(top - bottom);
+	float tz = -(far_ + near_)/(far_ - near_);
+	return M4(
+		2.0f / (right - left), 0, 0, tx,
+		0, 2.0f / (top - bottom), 0, ty,
+		0, 0, -2.0f / (far_ - near_), tz,
+		0, 0, 0, 1
+	);
+}
+
+
+m4 m4_mul(m4 a, m4 b) {
+	m4 prod = {0};
+	int i, j;
+	float *x = prod.e;
+	for (i = 0; i < 4; ++i) {
+		for (j = 0; j < 4; ++j, ++x) {
+			float *as = &a.e[j];
+			float *bs = &b.e[4*i];
+			*x = as[0]*bs[0] + as[4]*bs[1] + as[8]*bs[2] + as[12]*bs[3];
+		}
+	}
+	return prod;
+}
+
+m4 m4_inv(m4 mat) {
+	m4 ret;
+	float *inv = ret.e;
+	float *m = mat.e;
+
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+	inv[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];
+
+	float det = m[0] * inv[0] + m[1] * inv[4] + m[2] * inv[8] + m[3] * inv[12];
+
+	if (det == 0) {
+		memset(inv, 0, sizeof *inv);
+	} else {
+		det = 1 / det;
+
+		for (int i = 0; i < 16; i++)
+			inv[i] *= det;
+	}
+
+	return ret;
+}
+
+v2i V2I(int x, int y) {
+	v2i v;
+	v.x = x;
+	v.y = y;
+	return v;
+}
+
+void rgba_u32_to_floats(u32 rgba, float floats[4]) {
+	floats[0] = (float)((rgba >> 24) & 0xFF) / 255.f;
+	floats[1] = (float)((rgba >> 16) & 0xFF) / 255.f;
+	floats[2] = (float)((rgba >>  8) & 0xFF) / 255.f;
+	floats[3] = (float)((rgba >>  0) & 0xFF) / 255.f;
+}
+
+v4 rgba_u32_to_v4(u32 rgba) {
+	float c[4];
+	rgba_u32_to_floats(rgba, c);
+	return V4(c[0], c[1], c[2], c[3]);
+}
+
+u32 rgba_v4_to_u32(v4 color) {
+	return (u32)(color.x * 255) << 24
+		| (u32)(color.y * 255) << 16
+		| (u32)(color.z * 255) << 8
+		| (u32)(color.w * 255);
+}
+
+// returns average of red green and blue components of color
+float rgba_brightness(u32 color) {
+	u8 r = (u8)(color >> 24), g = (u8)(color >> 16), b = (u8)(color >> 8);
+	return ((float)r+(float)g+(float)b) * (1.0f / 3);
+}
+
+bool rect_contains_point_v2(v2 pos, v2 size, v2 point) {
+	float x1 = pos.x, y1 = pos.y, x2 = pos.x + size.x, y2 = pos.y + size.y,
+		x = point.x, y = point.y;
+	return x >= x1 && x < x2 && y >= y1 && y < y2;
+}
+
+bool centered_rect_contains_point(v2 center, v2 size, v2 point) {
+	return rect_contains_point_v2(v2_sub(center, v2_scale(size, 0.5f)), size, point);
+}
+
+Rect rect(v2 pos, v2 size) {
+	Rect r;
+	r.pos = pos;
+	r.size = size;
+	return r;
+}
+
+Rect rect_endpoints(v2 e1, v2 e2) {
+	Rect r;
+	r.pos = e1;
+	r.size = v2_sub(e2, e1);
+	return r;
+}
+
+Rect rect4(float x1, float y1, float x2, float y2) {
+	assert(x2 >= x1);
+	assert(y2 >= y1);
+	return rect(V2(x1,y1), V2(x2-x1, y2-y1));
+}
+
+Rect rect_xywh(float x, float y, float w, float h) {
+	assert(w >= 0);
+	assert(h >= 0);
+	return rect(V2(x, y), V2(w, h));
+}
+
+Rect rect_centered(v2 center, v2 size) {
+	Rect r;
+	r.pos = v2_sub(center, v2_scale(size, 0.5f));
+	r.size = size;
+	return r;
+}
+
+v2 rect_center(Rect r) {
+	return v2_add(r.pos, v2_scale(r.size, 0.5f));
+}
+
+bool rect_contains_point(Rect r, v2 point) {
+	return rect_contains_point_v2(r.pos, r.size, point);
+}
+
+Rect rect_translate(Rect r, v2 by) {
+	return rect(v2_add(r.pos, by), r.size);
+}
+
+float rect_x1(Rect r) { return r.pos.x; }
+float rect_y1(Rect r) { return r.pos.y; }
+float rect_x2(Rect r) { return r.pos.x + r.size.x; }
+float rect_y2(Rect r) { return r.pos.y + r.size.y; }
+float rect_xmid(Rect r) { return r.pos.x + r.size.x * 0.5f; }
+float rect_ymid(Rect r) { return r.pos.y + r.size.y * 0.5f; }
+
+void rect_coords(Rect r, float *x1, float *y1, float *x2, float *y2) {
+	*x1 = r.pos.x;
+	*y1 = r.pos.y;
+	*x2 = r.pos.x + r.size.x;
+	*y2 = r.pos.y + r.size.y;
+}
+
+void rect_print(Rect r) {
+	printf("Position: (%f, %f), Size: (%f, %f)\n", r.pos.x, r.pos.y, r.size.x, r.size.y);
+}
+
+
+float rects_intersect(Rect r1, Rect r2) {
+	if (r1.pos.x >= r2.pos.x + r2.size.x) return false; // r1 is to the right of r2
+	if (r2.pos.x >= r1.pos.x + r1.size.x) return false; // r2 is to the right of r1
+	if (r1.pos.y >= r2.pos.y + r2.size.y) return false; // r1 is above r2
+	if (r2.pos.y >= r1.pos.y + r1.size.y) return false; // r2 is above r1
+	return true;
+}
+
+// returns whether or not there is any of the clipped rectangle left
+bool rect_clip_to_rect(Rect *clipped, Rect clipper) {
+	v2 start_pos = clipped->pos;
+	clipped->pos.x = maxf(clipped->pos.x, clipper.pos.x);
+	clipped->pos.y = maxf(clipped->pos.y, clipper.pos.y);
+	clipped->size = v2_add(clipped->size, v2_sub(start_pos, clipped->pos));
+
+	clipped->size.x = clampf(clipped->size.x, 0, clipper.pos.x + clipper.size.x - clipped->pos.x);
+	clipped->size.y = clampf(clipped->size.y, 0, clipper.pos.y + clipper.size.y - clipped->pos.y);
+	return clipped->size.x > 0 && clipped->size.y > 0;
+}
+
+// removes `amount` from all sides of r
+Rect rect_shrink(Rect r, float amount) {
+	r.pos.x += amount;
+	r.pos.y += amount;
+	r.size.x -= 2 * amount;
+	r.size.y -= 2 * amount;
+	r.size.x = maxf(r.size.x, 0);
+	r.size.y = maxf(r.size.y, 0);
+	return r;
+}
+
+// adds `amount` to all sides of r
+Rect rect_grow(Rect r, float amount) {
+	r.pos.x -= amount;
+	r.pos.y -= amount;
+	r.size.x += 2 * amount;
+	r.size.y += 2 * amount;
+	return r;
+}
+
+v4 color_rgba_to_hsva(v4 rgba) {
+	float R = rgba.x, G = rgba.y, B = rgba.z, A = rgba.w;
+	float M = maxf(R, maxf(G, B));
+	float m = minf(R, minf(G, B));
+	float C = M - m;
+	float H = 0;
+	if (C == 0)
+		H = 0;
+	else if (M == R)
+		H = fmodf((G - B) / C, 6);
+	else if (M == G)
+		H = (B - R) / C + 2;
+	else if (M == B)
+		H = (R - G) / C + 4;
+	H *= 60;
+	float V = M;
+	float S = V == 0 ? 0 : C / V;
+	return V4(H, S, V, A);
+}
+
+v4 color_hsva_to_rgba(v4 hsva) {
+	float H = hsva.x, S = hsva.y, V = hsva.z, A = hsva.w;
+	H /= 60;
+	float C = S * V;
+	float X = C * (1 - fabsf(fmodf(H, 2) - 1));
+	float R, G, B;
+	if (H <= 1)
+		R=C, G=X, B=0;
+	else if (H <= 2)
+		R=X, G=C, B=0;
+	else if (H <= 3)
+		R=0, G=C, B=X;
+	else if (H <= 4)
+		R=0, G=X, B=C;
+	else if (H <= 5)
+		R=X, G=0, B=C;
+	else
+		R=C, G=0, B=X;
+	
+	float m = V-C;
+	R += m;
+	G += m;
+	B += m;
+	return V4(R, G, B, A);
+}
+
+u32 color_interpolate(float x, u32 color1, u32 color2) {
+	x = x * x * (3 - 2*x); // hermite interpolation
+
+	v4 c1 = rgba_u32_to_v4(color1), c2 = rgba_u32_to_v4(color2);
+	// to make it interpolate more nicely, convert to hsv, interpolate in that space, then convert back
+	c1 = color_rgba_to_hsva(c1);
+	c2 = color_rgba_to_hsva(c2);
+	// v_1/2 named differently to avoid shadowing
+	float h1 = c1.x, s1 = c1.y, v_1 = c1.z, a1 = c1.w;
+	float h2 = c2.x, s2 = c2.y, v_2 = c2.z, a2 = c2.w;
+	
+	float s_out = lerpf(x, s1, s2);
+	float v_out = lerpf(x, v_1, v_2);
+	float a_out = lerpf(x, a1, a2);
+	
+	float h_out;
+	// because hue is on a circle, we need to make sure we take the shorter route around the circle
+	if (fabsf(h1 - h2) < 180) {
+		h_out = lerpf(x, h1, h2);
+	} else if (h1 > h2) {
+		h_out = lerpf(x, h1, h2 + 360);
+	} else {
+		h_out = lerpf(x, h1 + 360, h2);
+	}
+	h_out = fmodf(h_out, 360);
+	
+	v4 c_out = V4(h_out, s_out, v_out, a_out);
+	c_out = color_hsva_to_rgba(c_out);
+	return rgba_v4_to_u32(c_out);
+}
diff --git a/util.h b/util.h
index 8d5aeef..cbde09c 100644
--- a/util.h
+++ b/util.h
@@ -14,6 +14,49 @@
 #define strbuf_cpy(dst, src) str_cpy(dst, sizeof dst, src)
 #define strbuf_cat(dst, src) str_cat(dst, sizeof dst, src)
 
+
+#define PIf 3.14159265358979f
+#define HALF_PIf 1.5707963267948966f
+#define TAUf 6.283185307179586f
+#define SQRT2f 1.4142135623730951f
+#define HALF_SQRT2f 0.7071067811865476f
+#define SQRT3f 1.7320508075688772f
+#define HALF_SQRT3f 0.8660254037844386f
+
+
+typedef struct {
+	float x, y;
+} v2;
+typedef struct {
+	float x, y, z;
+} v3;
+typedef struct {
+	float x, y, z, w;
+} v4;
+typedef struct {
+	double x, y;
+} v2d;
+typedef struct {
+	int x, y;
+} v2i;
+
+// matrices are column-major, because that's what they are in OpenGL 
+typedef struct {
+	float e[16];
+} m4;
+
+static const m4 m4_identity = {{
+	1, 0, 0, 0,
+	0, 1, 0, 0,
+	0, 0, 1, 0,
+	0, 0, 0, 1
+}};
+
+typedef struct {
+	v2 pos, size;
+} Rect;
+
+
 // ctype functions for 32-bit chars.
 bool is_word(char32_t c);
 bool is_digit(char32_t c);
@@ -88,5 +131,123 @@ bool copy_file(const char *src, const char *dst);
 void qsort_with_context(void *base, size_t nmemb, size_t size,
 	int (*compar)(void *, const void *, const void *),
 	void *arg);
+float degrees(float r);
+float radians(float r);
+float lerpf(float x, float a, float b);
+float normf(float x, float a, float b);
+float clampf(float x, float a, float b);
+int clampi(int x, int a, int b);
+i16 clamp_i16(i16 x, i16 a, i16 b);
+u16 clamp_u16(u16 x, u16 a, u16 b);
+i32 clamp_i32(i32 x, i32 a, i32 b);
+u32 clamp_u32(u32 x, u32 a, u32 b);
+u8 ndigits_u64(u64 x);
+float remapf(float x, float from_a, float from_b, float to_a, float to_b);
+float minf(float a, float b);
+float maxf(float a, float b);
+double maxd(double a, double b);
+double mind(double a, double b);
+u32 min_u32(u32 a, u32 b);
+u32 max_u32(u32 a, u32 b);
+void sort2_u32(u32 *a, u32 *b);
+i32 min_i32(i32 a, i32 b);
+i32 max_i32(i32 a, i32 b);
+u64 min_u64(u64 a, u64 b);
+u64 max_u64(u64 a, u64 b);
+i64 min_i64(i64 a, i64 b);
+i64 max_i64(i64 a, i64 b);
+i64 mod_i64(i64 a, i64 b);
+i32 mod_i32(i32 a, i32 b);
+i64 abs_i64(i64 x);
+i64 sgn_i64(i64 x);
+float sgnf(float x);
+float smoothstepf(float x);
+float randf(void);
+float rand_gauss(void);
+u32 rand_u32(void);
+float rand_uniform(float from, float to);
+float sigmoidf(float x);
+i32 ceildivi32(i32 x, i32 y);
+v2 V2(float x, float y);
+v2 v2_add(v2 a, v2 b);
+v2 v2_add_const(v2 a, float c);
+v2 v2_sub(v2 a, v2 b);
+v2 v2_scale(v2 v, float s);
+v2 v2_mul(v2 a, v2 b);
+v2 v2_clamp(v2 x, v2 a, v2 b);
+float v2_dot(v2 a, v2 b);
+float v2_len(v2 v);
+v2 v2_lerp(float x, v2 a, v2 b);
+v2 v2_rotate(v2 v, float theta);
+v2 v2_normalize(v2 v);
+float v2_dist(v2 a, v2 b);
+float v2_dist_squared(v2 a, v2 b);
+void v2_print(v2 v);
+v2 v2_rand_unit(void);
+v2 v2_polar(float r, float theta);
+v3 V3(float x, float y, float z);
+v3 v3_from_v2(v2 v);
+v3 v3_add(v3 a, v3 b);
+v3 v3_sub(v3 a, v3 b);
+v3 v3_scale(v3 v, float s);
+v3 v3_lerp(float x, v3 a, v3 b);
+float v3_dot(v3 u, v3 v);
+v3 v3_cross(v3 u, v3 v);
+float v3_len(v3 v);
+float v3_dist(v3 a, v3 b);
+float v3_dist_squared(v3 a, v3 b);
+v3 v3_normalize(v3 v);
+v2 v3_xy(v3 v);
+v3 v3_on_sphere(float yaw, float pitch);
+void v3_print(v3 v);
+v3 v3_rand(void);
+v3 v3_rand_unit(void);
+v4 V4(float x, float y, float z, float w);
+v4 v4_add(v4 a, v4 b);
+v4 v4_sub(v4 a, v4 b);
+v4 v4_scale(v4 v, float s);
+v4 v4_scale_xyz(v4 v, float s);
+v4 v4_lerp(float x, v4 a, v4 b);
+float v4_dot(v4 u, v4 v);
+v4 v4_mul(v4 u, v4 v);
+float v4_len(v4 v);
+v4 v4_normalize(v4 v);
+v3 v4_xyz(v4 v);
+v4 v4_rand(void);
+void v4_print(v4 v);
+v2d V2D(double x, double y);
+void m4_print(m4 m);
+m4 m4_yaw(float yaw);
+m4 m4_pitch(float pitch);
+m4 m4_translate(v3 t);
+v3 m4_mul_v3(m4 m, v3 v);
+m4 m4_perspective(float fov, float aspect, float z_near, float z_far);
+m4 m4_ortho(float left, float right, float bottom, float top, float near_, float far_);
+m4 m4_mul(m4 a, m4 b);
+m4 m4_inv(m4 mat);
+v2i V2I(int x, int y);
+void rgba_u32_to_floats(u32 rgba, float floats[4]);
+v4 rgba_u32_to_v4(u32 rgba);
+u32 rgba_v4_to_u32(v4 color);
+float rgba_brightness(u32 color);
+bool rect_contains_point_v2(v2 pos, v2 size, v2 point);
+bool centered_rect_contains_point(v2 center, v2 size, v2 point);
+Rect rect(v2 pos, v2 size);
+Rect rect_endpoints(v2 e1, v2 e2);
+Rect rect4(float x1, float y1, float x2, float y2);
+Rect rect_xywh(float x, float y, float w, float h);
+Rect rect_centered(v2 center, v2 size);
+v2 rect_center(Rect r);
+bool rect_contains_point(Rect r, v2 point);
+Rect rect_translate(Rect r, v2 by);
+void rect_coords(Rect r, float *x1, float *y1, float *x2, float *y2);
+void rect_print(Rect r);
+float rects_intersect(Rect r1, Rect r2);
+bool rect_clip_to_rect(Rect *clipped, Rect clipper);
+Rect rect_shrink(Rect r, float amount);
+Rect rect_grow(Rect r, float amount);
+v4 color_rgba_to_hsva(v4 rgba);
+v4 color_hsva_to_rgba(v4 hsva);
+u32 color_interpolate(float x, u32 color1, u32 color2);
 
 #endif // UTIL_H_