export class CurveUtils {

   public static tangentQuadraticBezier(t, p0, p1, p2) {
      return 2 * (1 - t) * (p1 - p0) + 2 * t * (p2 - p1);
   }

   // Puay Bing, thanks for helping with this derivative!
   public static tangentCubicBezier(t, p0, p1, p2, p3) {
      return - 3 * p0 * (1 - t) * (1 - t) +
         3 * p1 * (1 - t) * (1 - t) - 6 * t * p1 * (1 - t) +
         6 * t * p2 * (1 - t) - 3 * t * t * p2 +
         3 * t * t * p3;
   }

   public static tangentSpline(t, p0, p1, p2, p3) {
      // To check if my formulas are correct
      var h00 = 6 * t * t - 6 * t; 	// derived from 2t^3 − 3t^2 + 1
      var h10 = 3 * t * t - 4 * t + 1; // t^3 − 2t^2 + t
      var h01 = - 6 * t * t + 6 * t; 	// − 2t3 + 3t2
      var h11 = 3 * t * t - 2 * t;	// t3 − t2
      return h00 + h10 + h01 + h11;
   }

   // Catmull-Rom
   public static interpolate(p0, p1, p2, p3, t) {
      var v0 = (p2 - p0) * 0.5;
      var v1 = (p3 - p1) * 0.5;
      var t2 = t * t;
      var t3 = t * t2;
      return (2 * p1 - 2 * p2 + v0 + v1) * t3 + (- 3 * p1 + 3 * p2 - 2 * v0 - v1) * t2 + v0 * t + p1;
   }
}