#include "linear_alg.h"

#include <math.h>

vec3_t vec3_sub(vec3_t v, vec3_t u)
{
	return (vec3_t) { v.x - u.x, v.y - u.y, v.z - u.z };
}

float vec3_len(vec3_t v)
{
	return sqrtf(v.x * v.x + v.y * v.y + v.z * v.z);
}

vec3_t vec3_norm(vec3_t v)
{
	const float l = vec3_len(v);
	return (vec3_t) { v.x / l, v.y / l, v.z / l };
}

float vec3_dot(vec3_t v, vec3_t u)
{
	return v.x * u.x + v.y * u.y + v.z * u.z;
}

vec3_t vec3_cross(vec3_t v, vec3_t u)
{
	return (vec3_t) {
		v.y * u.z - v.z * u.y,
		v.z * u.x - v.x * u.z,
		v.x * u.y - v.y * u.x,
	};
}

mat4_t mat4_mul(mat4_t m, mat4_t n)
{
#define ELEM(i, j) m.x.i *n.j.x + m.y.i *n.j.y + m.z.i *n.j.z + m.w.i *n.j.w
	return (mat4_t) {
		{ ELEM(x, x), ELEM(y, x), ELEM(z, x), ELEM(w, x) },
		{ ELEM(x, y), ELEM(y, y), ELEM(z, y), ELEM(w, y) },
		{ ELEM(x, z), ELEM(y, z), ELEM(z, z), ELEM(w, z) },
		{ ELEM(x, w), ELEM(y, w), ELEM(z, w), ELEM(w, w) },
	};
#undef ELEM
}

mat4_t mat4_lookat(vec3_t camera, vec3_t target, vec3_t up)
{
	const vec3_t s = vec3_sub(target, camera);
	const vec3_t s_hat = vec3_norm(s);
	const vec3_t u_hat = vec3_norm(vec3_cross(up, s_hat));
	const vec3_t v_hat = vec3_cross(s_hat, u_hat);
	return (mat4_t) {
		{ u_hat.x, v_hat.x, s_hat.x, 0 },
		{ u_hat.y, v_hat.y, s_hat.y, 0 },
		{ u_hat.z, v_hat.z, s_hat.z, 0 },
		{
		    -vec3_dot(u_hat, camera),
		    -vec3_dot(v_hat, camera),
		    -vec3_dot(s_hat, camera),
		    1,
		},
	};
}

mat4_t mat4_perspective(float aspect, float fov, float near, float far)
{
	const float r = 2 * near * tanf(fov / 2);
	const float t = r * aspect;
	return (mat4_t) {
		{ near / t, 0, 0, 0 },
		{ 0, -near / r, 0, 0 },
		{ 0, 0, far / (far - near), 1 },
		{ 0, 0, -far * near / (far - near), 0 },
	};
}