248 lines
6.3 KiB
C
248 lines
6.3 KiB
C
|
#include <math.h>
|
||
|
|
|
||
|
|
#include "matrix.h"
|
||
|
|
#include "stdio.h"
|
||
|
|
|
||
|
|
mat4_t mat4_identity(void) {
|
||
|
|
// | 1 0 0 0 |
|
||
|
|
// | 0 1 0 0 |
|
||
|
|
// | 0 0 1 0 |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
|
||
|
|
mat4_t eye = { // eye for identity
|
||
|
|
.m = { // can skip the .m = part - it's just for clarity
|
||
|
|
{1, 0, 0, 0},
|
||
|
|
{0, 1, 0, 0},
|
||
|
|
{0, 0, 1, 0},
|
||
|
|
{0, 0, 0, 1}
|
||
|
|
}
|
||
|
|
};
|
||
|
|
return eye;
|
||
|
|
}
|
||
|
|
|
||
|
|
vec4_t mat4_mul_vec4(mat4_t m, vec4_t v){
|
||
|
|
// Example of this multiplication (values can be all different):
|
||
|
|
// | sx 0 0 0 | | x | | x'|
|
||
|
|
// | 0 sy 0 0 | X | y | = | y'|
|
||
|
|
// | 0 0 sz 0 | | z | | z'|
|
||
|
|
// | 0 0 0 1 | | 1 | | 1 |
|
||
|
|
|
||
|
|
vec4_t result;
|
||
|
|
|
||
|
|
result.x = m.m[0][0] * v.x + m.m[0][1] * v.y + m.m[0][2] * v.z + m.m[0][3] * v.w;
|
||
|
|
result.y = m.m[1][0] * v.x + m.m[1][1] * v.y + m.m[1][2] * v.z + m.m[1][3] * v.w;
|
||
|
|
result.z = m.m[2][0] * v.x + m.m[2][1] * v.y + m.m[2][2] * v.z + m.m[2][3] * v.w;
|
||
|
|
result.w = m.m[3][0] * v.x + m.m[3][1] * v.y + m.m[3][2] * v.z + m.m[3][3] * v.w;
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_mul_mat4(mat4_t a, mat4_t b) {
|
||
|
|
mat4_t m;
|
||
|
|
for (int i = 0; i < 4; i++) {
|
||
|
|
for (int j = 0; j < 4; j++) {
|
||
|
|
m.m[i][j] = a.m[i][0] * b.m[0][j] + a.m[i][1] * b.m[1][j] + a.m[i][2] * b.m[2][j] + a.m[i][3] * b.m[3][j];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_make_scale(float sx, float sy, float sz){
|
||
|
|
// | sx 0 0 0 |
|
||
|
|
// | 0 sy 0 0 |
|
||
|
|
// | 0 0 sz 0 |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
|
||
|
|
mat4_t m = mat4_identity();
|
||
|
|
|
||
|
|
m.m[0][0] = sx;
|
||
|
|
m.m[1][1] = sy;
|
||
|
|
m.m[2][2] = sz;
|
||
|
|
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_make_translation(float tx, float ty, float tz){
|
||
|
|
// | 1 0 0 tx |
|
||
|
|
// | 0 1 0 ty |
|
||
|
|
// | 0 0 1 tz |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
|
||
|
|
mat4_t m = mat4_identity();
|
||
|
|
|
||
|
|
m.m[0][3] = tx;
|
||
|
|
m.m[1][3] = ty;
|
||
|
|
m.m[2][3] = tz;
|
||
|
|
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_make_rotation_x(float angle) {
|
||
|
|
float c = cos(angle);
|
||
|
|
float s = sin(angle);
|
||
|
|
// | 1 0 0 0 |
|
||
|
|
// | 0 c -s 0 |
|
||
|
|
// | 0 s c 0 |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
mat4_t m = mat4_identity();
|
||
|
|
m.m[1][1] = c;
|
||
|
|
m.m[1][2] = -s;
|
||
|
|
m.m[2][1] = s;
|
||
|
|
m.m[2][2] = c;
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_make_rotation_y(float angle) {
|
||
|
|
float c = cos(angle);
|
||
|
|
float s = sin(angle);
|
||
|
|
// | c 0 s 0 |
|
||
|
|
// | 0 1 0 0 |
|
||
|
|
// | -s 0 c 0 |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
mat4_t m = mat4_identity();
|
||
|
|
m.m[0][0] = c;
|
||
|
|
m.m[0][2] = s;
|
||
|
|
m.m[2][0] = -s;
|
||
|
|
m.m[2][2] = c;
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_make_rotation_z(float angle) {
|
||
|
|
float c = cos(angle);
|
||
|
|
float s = sin(angle);
|
||
|
|
// | c -s 0 0 |
|
||
|
|
// | s c 0 0 |
|
||
|
|
// | 0 0 1 0 |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
mat4_t m = mat4_identity();
|
||
|
|
m.m[0][0] = c;
|
||
|
|
m.m[0][1] = -s;
|
||
|
|
m.m[1][0] = s;
|
||
|
|
m.m[1][1] = c;
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
//https://www.youtube.com/watch?v=U0_ONQQ5ZNM - more explanation of this those matrices
|
||
|
|
//https://www.youtube.com/watch?v=vu1VNKHfzqQ here too - start with this one
|
||
|
|
|
||
|
|
vec4_t mat4_mul_vec4_project(mat4_t mat_proj, vec4_t v) {
|
||
|
|
// multiply the projection matrix by our original vector
|
||
|
|
vec4_t result = mat4_mul_vec4(mat_proj, v);
|
||
|
|
|
||
|
|
// perform perspective divide with original z-value that is now stored in w
|
||
|
|
if (result.w != 0.0) {
|
||
|
|
result.x /= result.w;
|
||
|
|
result.y /= result.w;
|
||
|
|
result.z /= result.w;
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
// translate and scale projected vector to -1 to 1 range
|
||
|
|
mat4_t mat4_make_ortho(float l, float b, float n, float r, float t, float f) {
|
||
|
|
// translate to origin and scale to -1 to 1 range -> width, height, depth should be 2
|
||
|
|
|
||
|
|
// Coordinates of center of the provided cube are:
|
||
|
|
float c_x = (l + r) / 2;
|
||
|
|
float c_y = (b + t) / 2;
|
||
|
|
float c_z = (n + f) / 2;
|
||
|
|
|
||
|
|
// To translate the cube to the origin, we need to subtract the center coordinates from each vertex
|
||
|
|
// | 1 0 0 -c_x |
|
||
|
|
// | 0 1 0 -c_y |
|
||
|
|
// | 0 0 1 -c_z |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
mat4_t trans = mat4_identity();
|
||
|
|
trans.m[0][3] = -c_x;
|
||
|
|
trans.m[1][3] = -c_y;
|
||
|
|
trans.m[2][3] = -c_z;
|
||
|
|
|
||
|
|
// Current width, height, depth of the cube:
|
||
|
|
float width = r - l;
|
||
|
|
float height = t - b;
|
||
|
|
float depth = f - n;
|
||
|
|
|
||
|
|
// To scale the cube to have width, height, depth of 2 (be from -1 to 1)
|
||
|
|
// we need to multiply each vertex by 2/width, 2/height, 2/depth
|
||
|
|
// | 2/width 0 0 0 |
|
||
|
|
// | 0 2/height 0 0 |
|
||
|
|
// | 0 0 2/depth 0 |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
|
||
|
|
mat4_t scale = mat4_identity();
|
||
|
|
scale.m[0][0] = 2.0 / width;
|
||
|
|
scale.m[1][1] = 2.0 / height;
|
||
|
|
scale.m[2][2] = 2.0 / depth;
|
||
|
|
|
||
|
|
// Now we need to combine the two matrices into one
|
||
|
|
return mat4_mul_mat4(trans, scale);
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_make_perspective(float n, float f) {
|
||
|
|
// | n 0 0 0 |
|
||
|
|
// | 0 n 0 0 |
|
||
|
|
// | 0 0 (f+n) (-fn) |
|
||
|
|
// | 0 0 1 0 |
|
||
|
|
|
||
|
|
mat4_t m = {{{ 0 }}};
|
||
|
|
m.m[0][0] = n;
|
||
|
|
m.m[1][1] = n;
|
||
|
|
m.m[2][2] = f + n;
|
||
|
|
m.m[2][3] = -f * n;
|
||
|
|
m.m[3][2] = 1.0;
|
||
|
|
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_make_projection(float fov, float aspect_ratio, float near, float far) {
|
||
|
|
// Orthographic matrix X Perspective matrix
|
||
|
|
|
||
|
|
float r = near * tan(fov / 2.0) * aspect_ratio; // aspect_ratio = width / height
|
||
|
|
float t = near * tan(fov / 2.0);
|
||
|
|
float f = far;
|
||
|
|
|
||
|
|
float l = -r;
|
||
|
|
float b = -t;
|
||
|
|
float n = near;
|
||
|
|
|
||
|
|
mat4_t t_ortho = mat4_make_ortho(l, b, n, r, t, f);
|
||
|
|
mat4_t t_perspective = mat4_make_perspective(near, far);
|
||
|
|
|
||
|
|
mat4_t m = mat4_mul_mat4(t_ortho, t_perspective);
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_make_perspective_old(float fov, float aspect, float znear, float zfar){
|
||
|
|
// | (w/h)*1/tan(fov/2) 0 0 0 |
|
||
|
|
// | 0 1/tan(fov/2) 0 0 |
|
||
|
|
// | 0 0 zf/(zf-zn) (-zf*zn)/(zf-zn) |
|
||
|
|
// | 0 0 1 0 |
|
||
|
|
mat4_t m = {{{ 0 }}};
|
||
|
|
m.m[0][0] = aspect * (1 / tan(fov / 2));
|
||
|
|
m.m[1][1] = 1 / tan(fov / 2);
|
||
|
|
m.m[2][2] = zfar / (zfar - znear);
|
||
|
|
m.m[2][3] = (-zfar * znear) / (zfar - znear);
|
||
|
|
m.m[3][2] = 1.0;
|
||
|
|
return m;
|
||
|
|
}
|
||
|
|
|
||
|
|
mat4_t mat4_look_at(vec3_t eye, vec3_t target, vec3_t up) {
|
||
|
|
// Compute the forward (z), right (x), and up (y) vectors
|
||
|
|
vec3_t z = vec3_sub(target, eye);
|
||
|
|
vec3_normalize(&z);
|
||
|
|
vec3_t x = vec3_cross(up, z);
|
||
|
|
vec3_normalize(&x);
|
||
|
|
vec3_t y = vec3_cross(z, x);
|
||
|
|
|
||
|
|
// | x.x x.y x.z -dot(x,eye) |
|
||
|
|
// | y.x y.y y.z -dot(y,eye) |
|
||
|
|
// | z.x z.y z.z -dot(z,eye) |
|
||
|
|
// | 0 0 0 1 |
|
||
|
|
mat4_t view_matrix = {{
|
||
|
|
{ x.x, x.y, x.z, -vec3_dot(x, eye) },
|
||
|
|
{ y.x, y.y, y.z, -vec3_dot(y, eye) },
|
||
|
|
{ z.x, z.y, z.z, -vec3_dot(z, eye) },
|
||
|
|
{ 0, 0, 0, 1 }
|
||
|
|
}};
|
||
|
|
return view_matrix;
|
||
|
|
}
|