#include "math/constants.glsl"

uniform float polar_origin;


vec4 forward(float rho, float theta, float z, float w)
{
    return vec4(rho * cos(theta + polar_origin),
                rho * sin(theta + polar_origin),
                z, w);
}

vec4 forward(float x, float y) {return forward(x, y, 0.0, 1.0);}
vec4 forward(float x, float y, float z) {return forward(x, y, z, 1.0);}
vec4 forward(vec2 P) { return forward(P.x, P.y); }
vec4 forward(vec3 P) { return forward(P.x, P.y, P.z, 1.0); }
vec4 forward(vec4 P) { return forward(P.x, P.y, P.z, P.w); }

vec4 inverse(float x, float y, float z, float w)
{
    float rho = length(vec2(x,y));
    float theta = atan(y,x);
    if( theta < 0.0 )
        theta = 2.0*M_PI+theta;
    return vec4(rho, theta-polar_origin, z, w);
}


vec4 inverse(float x, float y) {return inverse(x,y,0.0,1.0); }
vec4 inverse(float x, float y, float z) {return inverse(x,y,z,1.0); }
vec4 inverse(vec2 P) { return inverse(P.x, P.y, 0.0, 1.0); }
vec4 inverse(vec3 P) { return inverse(P.x, P.y, P.z, 1.0); }
vec4 inverse(vec4 P) { return inverse(P.x, P.y, P.z, P.w); }