tooll3--t3/Core/Utils/Splines/Bezier.cs

namespace T3.Core.Utils.Splines;

public static class Bezier
{
    public static Vector3 GetPoint(Vector3 p0, Vector3 p1, Vector3 p2, float t)
    {
        t = t.Clamp(0, 1);
        float oneMinusT = 1f - t;
        return
            oneMinusT * oneMinusT * p0 +
            2f * oneMinusT * t * p1 +
            t * t * p2;
    }

    public static Vector3 GetFirstDerivative(Vector3 p0, Vector3 p1, Vector3 p2, float t)
    {
        return
            2f * (1f - t) * (p1 - p0) +
            2f * t * (p2 - p1);
    }

    public static Vector3 GetPoint(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
    {
        t = t.Clamp(0, 1);
        float OneMinusT = 1f - t;
        return
            OneMinusT * OneMinusT * OneMinusT * p0 +
            3f * OneMinusT * OneMinusT * t * p1 +
            3f * OneMinusT * t * t * p2 +
            t * t * t * p3;
    }

    public static Vector3 GetFirstDerivative(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
    {
        t = t.Clamp(0, 1);
        float oneMinusT = 1f - t;
        return
            3f * oneMinusT * oneMinusT * (p1 - p0) +
            6f * oneMinusT * t * (p2 - p1) +
            3f * t * t * (p3 - p2);
    }
}