RT

#version 430 core

    uniform ivec2 viewportDimensions;
    uniform mat4 gl_ProjectionMatrix;
    uniform ivec4 viewport;
    uniform float imageAspectRatio;
    uniform float angle;

    out vec3 color;

    struct Ray {
        vec3 origin;
        vec3 direction;
    };

    struct Sphere {
        vec3 origin;
        float radius;
    };

    bool intersect(Ray r, Sphere s);


    void main() {

        focal = 60;
        angle = tan(focal * 0.5 * 3.1415926535897932384626433832795 / 180); // convert from degree to radian
        float xx = (2 * (gl_FragCoord.x + 0.5) / viewportDimensions.x - 1) * angle * imageAspectRatio;
        float yy = (1 - 2 * (gl_FragCoord.y + 0.5) / viewportDimensions.y) * angle;

        vec3 rayOrigin = vec3(0,0,0);
        vec3 rayDirection = vec3(xx, yy, -1) - rayOrigin;
        normalize(rayDirection);

        Ray r;
        r.origin = rayOrigin;
        r.direction = rayDirection;

        Sphere s;
        s.origin = vec3(0.0f,0.0f,-1.1f);
        s.radius =0.55f;


        if (intersect(r,s))
            color = vec3(1,0,1);
        else
            color = vec3(0,0,0);
        }


    bool intersect(Ray r, Sphere s) {
        float a = dot(r.direction,r.direction);
        float b = dot(r.direction, 2.0 * (r.origin-s.origin));
        float c = dot(s.origin, s.origin) + dot(r.origin,r.origin) +-2.0*dot(r.origin,s.origin) - (s.radius*s.radius);

        float disc = b*b + (-4.0)*a*c;

        if (disc < 0)
            return false;

        return true;

    }