diff options
Diffstat (limited to 'math.c')
| -rw-r--r-- | math.c | 640 |
1 files changed, 0 insertions, 640 deletions
@@ -1,640 +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 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 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 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)); -} - -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; -} - -#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); -} - -// 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; -} - -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_rgbacolor(u32 color) { - glColor4ub((color >> 24) & 0xff, (color >> 16) & 0xff, (color >> 8) & 0xff, color & 0xff); -} - -// color is 0xRRGGBB -static void gl_rgbcolor(u32 color) { - gl_rgbacolor((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); -} -#endif - |