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