diff options
Diffstat (limited to 'math.c')
| -rw-r--r-- | math.c | 718 |
1 files changed, 718 insertions, 0 deletions
@@ -0,0 +1,718 @@ +#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 float degrees(float r) { + return r * (180.0f / PIf); +} +static 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 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 float normf(float x, float a, float b) { + return (x-a) / (b-a); +} + +static float clampf(float x, float a, float b) { + if (x < a) return a; + if (x > b) return b; + return x; +} + +static int clampi(int x, int a, int b) { + if (x < a) return a; + if (x > b) return b; + return x; +} + +static i32 clampi32(i32 x, i32 a, i32 b) { + if (x < a) return a; + if (x > b) return b; + return x; +} + +// 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 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 float minf(float a, float b) { + return a < b ? a : b; +} + +static float maxf(float a, float b) { + return a > b ? a : b; +} + +static float sgnf(float x) { + if (x < 0) return -1; + if (x > 0) return +1; + return 0; +} + +static float smoothstepf(float x) { + if (x <= 0) return 0; + if (x >= 1) return 1; + return x * x * (3 - 2 * x); +} + +static 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 = randf(), V = randf(); + 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 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); +} + +#if MATH_GL +static void v2_gl_vertex(v2 v) { + glVertex2f(v.x, v.y); +} +#endif + +static v2 v2_rand_unit(void) { + float theta = rand_uniform(0, TAUf); + return V2(cosf(theta), sinf(theta)); +} + +#if MATH_GL +static void v2_rand_unit_test(void) { + int i; + glColor3f(1.0f, 0.0f, 0.0f); + glBegin(GL_POINTS); + for (i = 0; i < 100000; ++i) { + v2_gl_vertex(v2_rand_unit()); + } + glEnd(); +} +#endif + +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); +} + +#if MATH_GL +static void v3_gl_vertex(v3 v) { + glVertex3f(v.x, v.y, v.z); +} + +static void v3_gl_color(v3 v) { + glColor3f(v.x, v.y, v.z); +} + +static void v3_gl_color_alpha(v3 v, float alpha) { + glColor4f(v.x, v.y, v.z, alpha); +} +#endif + +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); +} + +#if MATH_GL +static void v3_rand_unit_test(void) { + int i; + glColor3f(1.0f, 0.0f, 0.0f); + glBegin(GL_POINTS); + for (i = 0; i < 100000; ++i) { + v3_gl_vertex(v3_rand_unit()); + } + glEnd(); +} +#endif + +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; +} + +#if MATH_GL +static void v4_gl_color(v4 v) { + glColor4f(v.x, v.y, v.z, v.w); +} +#endif + +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); +} + + +// 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 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 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_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 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 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); +} + +#if MATH_GL +// must be rendering GL_QUADS to use these functions! + +static void rect_render(Rect r) { + float x1 = r.pos.x, y1 = r.pos.y, x2 = x1 + r.size.x, y2 = y1 + r.size.y; + glVertex2f(x1, y1); + glVertex2f(x2, y1); + glVertex2f(x2, y2); + glVertex2f(x1, y2); +} + +static void rect_render_border(Rect r, float border_radius) { + float x1 = r.pos.x, y1 = r.pos.y, x2 = x1 + r.size.x, y2 = y1 + r.size.y; + //float a = 0.3f; // for debugging + + //glColor4f(1,0,0,a); + glVertex2f(x1+border_radius, y1-border_radius); + glVertex2f(x1+border_radius, y1+border_radius); + glVertex2f(x2+border_radius, y1+border_radius); + glVertex2f(x2+border_radius, y1-border_radius); + + //glColor4f(0,1,0,a); + glVertex2f(x1-border_radius, y2-border_radius); + glVertex2f(x1-border_radius, y2+border_radius); + glVertex2f(x2-border_radius, y2+border_radius); + glVertex2f(x2-border_radius, y2-border_radius); + + //glColor4f(0,0,1,a); + glVertex2f(x1-border_radius, y1-border_radius); + glVertex2f(x1+border_radius, y1-border_radius); + glVertex2f(x1+border_radius, y2-border_radius); + glVertex2f(x1-border_radius, y2-border_radius); + + //glColor4f(1,1,0,a); + glVertex2f(x2-border_radius, y1+border_radius); + glVertex2f(x2+border_radius, y1+border_radius); + glVertex2f(x2+border_radius, y2+border_radius); + glVertex2f(x2-border_radius, y2+border_radius); +} + + +/* + gl grayscale color + i am tired of not having this +*/ +static void gl_color1f(float v) { + glColor3f(v,v,v); +} + +/* + gl grayscale+alpha color +*/ +static void gl_color2f(float v, float a) { + glColor4f(v,v,v,a); +} + +// color is 0xRRGGBBAA +static void gl_color_rgba(u32 color) { + glColor4ub((u8)(color >> 24), (u8)(color >> 16), (u8)(color >> 8), (u8)color); +} + +// color is 0xRRGGBB +static void gl_color_rgb(u32 color) { + gl_color_rgba((color << 8) | 0xff); +} + +static void gl_quad(float x1, float y1, float x2, float y2) { + glVertex2f(x1, y1); + glVertex2f(x2, y1); + glVertex2f(x2, y2); + glVertex2f(x1, y2); +} + +// 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 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; +} +#endif + |