[GLSL] Catmull-rom as expressed by ChatGPT

catmull-rom.glsl

// As expressed by ChatGPT -> https://openai.com/blog/chatgpt/

// Calculates a point along a Catmull-Rom spline
// given a set of control points, a tension parameter,
// and a step value in the range [0, 1].
vec2 catmullRom(vec2 p0, vec2 p1, vec2 p2, vec2 p3, float t, float tension) {
    vec2 a = 0.5 * (tension * (p2 - p0) + 2.0 * p1 + tension * (p3 - p1)) * t * t * t +
                (2.0 * tension * p0 - 3.0 * tension * p1 + (tension + 2.0) * p2 - tension * p3) * t * t +
                (tension * p1 + p3 - tension * p2) * t +
                2.0 * p1;
    return a;
}

// Calculate the tangent with tension taken under account
vec2 catmullRomTangent(vec2 p0, vec2 p1, vec2 p2, vec2 p3, float t, float tension) {
    vec2 a = 3.0 * tension * (p2 - p0) * t * t +
                2.0 * (2.0 * tension * p0 - 3.0 * tension * p1 + (tension + 2.0) * p2 - tension * p3) * t +
                tension * (p1 - p3) +
                2.0 * p1;
    return a;
}

// Calculate the normal using the tangent
vec2 catmullRomNormal(vec2 p0, vec2 p1, vec2 p2, vec2 p3, float t, float tension) {
    vec2 tangent = catmullRomTangent(p0, p1, p2, p3, t, tension);
    vec2 normal = vec2(-tangent.y, tangent.x);
    return normal;
}