#pragma once

mat3 translate(float Tx, float Ty)
{
	mat3* res = new mat3(1.f);
	(*res)[0][2] = Tx;
	(*res)[1][2] = Ty;
	return *res;
}

mat4 translate(float Tx, float Ty, float Tz)
{
	mat4* res = new mat4(1.f);
	(*res)[0][3] = Tx;
	(*res)[1][3] = Ty;
	(*res)[2][3] = Tz;
	return *res;
}

mat3 scale(float Sx, float Sy)
{
	mat3* res = new mat3(1.f);
	(*res)[0][0] = Sx;
	(*res)[1][1] = Sy;
	return *res;
}

mat4 scale(float Sx, float Sy, float Sz)
{
	mat4* res = new mat4(1.f);
	(*res)[0][0] = Sx;
	(*res)[1][1] = Sy;
	(*res)[2][2] = Sz;
	return *res;
}

mat3 scale(float S)
{
	return scale(S, S);
}

mat3 rotate(float theta)
{
	mat3* res = new mat3(1.f);
	(*res)[0][0] = (*res)[1][1] = (float)cos(theta);
	(*res)[0][1] = (float)sin(theta);
	(*res)[1][0] = -(*res)[0][1];
	return *res;
}

mat4 rotate(float theta, vec3 n)
{
	n = norm(n);
	mat3 nCross = crossM(n);
	mat3 id = mat3(1.f);
	mat3 m1 = id + nCross * sin(theta);
	mat3 m2 = nCross * (nCross * (1.f - cos(theta)));
	mat3 m = m1 + m2;
	
	return mat4(vec4(m[0], 0.f),
				vec4(m[1], 0.f),
				vec4(m[2], 0.f),
				vec4(0.f, 0.f, 0.f, 0.f));
}

mat4 rotateP(float theta, vec3 n, vec3 P) {
	return translate(P.x, P.y, P.z) * 
		   (rotate(theta, n) * translate(-P.x, -P.y, -P.z));
}

mat4 lookAt(vec3 S, vec3 P, vec3 u) {
	vec3 e3 = S - P;
	e3 *= 1.f / length(e3);

	vec3 e1 = cross(u, e3);
	e1 *= 1.f / length(e1);
	
	vec3 e2 = cross(e3, e1);
	e2 *= 1.f / length(e2);

	mat4 T = translate(-S.x, -S.y, -S.z);
	return mat4(vec4(e1, 0.f),
				vec4(e2, 0.f),
				vec4(e3, 0.f),
				vec4(0.f, 0.f, 0.f, 1.f)) * T;
}

mat4 ortho(float l, float r, float b, float t, float zn, float zf) {
	return mat4(
		vec4(2.f / (r - l), 0.f, 0.f, -(r + l) / (r - l)),
		vec4(0.f, 2.f / (t - b),  0.f, -(t + b) / (t - b)),
		vec4(0.f, 0.f, -2 / (zf - zn), -(zf + zn) / (zf - zn)),
		vec4(0.f, 0.f, 0.f, 1.f));
}
mat4 frustum(float l, float r, float b, float t, float n, float f) {
	return mat4(
		vec4(2.f * n / (r - l), 0.f, (r + l) / (r - l), 0.f),
		vec4(0.f, 2.f * n / (t - b),  (t + b) / (t - b), 0.f),
		vec4(0.f, 0.f, -(f + n) / (f - n), -(2.f * f * n) / (f - n)),
		vec4(0.f, 0.f, -1.f, 0.f));
}
mat4 perspective(float fovy, float aspect, float n, float f) {
	return mat4(
		vec4(1.f / aspect / tanf(fovy / 2.f), 0.f, 0.f, 0.f),
		vec4(0.f, 1.f / tanf(fovy / 2.f), 0.f, 0.f),
		vec4(0.f, 0.f, -(f + n) / (f - n), -2.f * f * n / (f - n)),
		vec4(0.f, 0.f, -1.f, 0.f));
}

mat3 cadrRL(vec2 Vc, vec2 V, vec2 Wc, vec2 W) {
	return translate(Wc.x, Wc.y) *
		   (scale(W.x / V.x, -W.y / V.y) * translate(-Vc.x, -Vc.y));
}

mat3 mirrorX()
{
	mat3* res = new mat3(1.f);
	(*res)[1][1] = -1;
	return *res;
}

mat3 mirrorY() 
{
	mat3* res = new mat3(1.f);
	(*res)[0][0] = -1;
	return *res;
}