/**
   * Interpolate {@link #frame()} at time {@code time} (expressed in seconds). {@link
   * #interpolationTime()} is set to {@code time} and {@link #frame()} is set accordingly.
   *
   * <p>If you simply want to change {@link #interpolationTime()} but not the {@link #frame()}
   * state, use {@link #setInterpolationTime(float)} instead.
   */
  public void interpolateAtTime(float time) {
    this.checkValidity();
    setInterpolationTime(time);

    if ((keyFrameList.isEmpty()) || (frame() == null)) return;

    if (!valuesAreValid) updateModifiedFrameValues();

    updateCurrentKeyFrameForTime(time);

    if (!splineCacheIsValid) updateSplineCache();

    float alpha;
    float dt =
        keyFrameList.get(currentFrame2.nextIndex()).time()
            - keyFrameList.get(currentFrame1.nextIndex()).time();
    if (Util.zero(dt)) alpha = 0.0f;
    else alpha = (time - keyFrameList.get(currentFrame1.nextIndex()).time()) / dt;

    Vec pos =
        Vec.add(
            keyFrameList.get(currentFrame1.nextIndex()).position(),
            Vec.multiply(
                Vec.add(
                    keyFrameList.get(currentFrame1.nextIndex()).tgP(),
                    Vec.multiply(Vec.add(pv1, Vec.multiply(pv2, alpha)), alpha)),
                alpha));

    float mag =
        Util.lerp(
            keyFrameList.get(currentFrame1.nextIndex()).magnitude(),
            keyFrameList.get(currentFrame2.nextIndex()).magnitude(),
            alpha);

    Rotation q;
    if (gScene.is3D()) {
      q =
          Quat.squad(
              (Quat) keyFrameList.get(currentFrame1.nextIndex()).orientation(),
              ((KeyFrame3D) keyFrameList.get(currentFrame1.nextIndex())).tgQ(),
              ((KeyFrame3D) keyFrameList.get(currentFrame2.nextIndex())).tgQ(),
              (Quat) keyFrameList.get(currentFrame2.nextIndex()).orientation(),
              alpha);
    } else {
      q =
          new Rot(
              Util.lerp(
                  keyFrameList.get(currentFrame1.nextIndex()).orientation().angle(),
                  keyFrameList.get(currentFrame2.nextIndex()).orientation().angle(),
                  (alpha)));
    }

    frame().setPositionWithConstraint(pos);
    frame().setRotationWithConstraint(q);
    frame().setMagnitude(mag);
  }
 protected void updateSplineCache() {
   Vec deltaP =
       Vec.subtract(
           keyFrameList.get(currentFrame2.nextIndex()).position(),
           keyFrameList.get(currentFrame1.nextIndex()).position());
   pv1 =
       Vec.add(
           Vec.multiply(deltaP, 3.0f),
           Vec.multiply(keyFrameList.get(currentFrame1.nextIndex()).tgP(), (-2.0f)));
   pv1 = Vec.subtract(pv1, keyFrameList.get(currentFrame2.nextIndex()).tgP());
   pv2 = Vec.add(Vec.multiply(deltaP, (-2.0f)), keyFrameList.get(currentFrame1.nextIndex()).tgP());
   pv2 = Vec.add(pv2, keyFrameList.get(currentFrame2.nextIndex()).tgP());
   splineCacheIsValid = true;
 }
  /** Intenal use. Call {@link #checkValidity()} and if path is not valid recomputes it. */
  protected void updatePath() {
    checkValidity();
    if (!pathIsValid) {
      path.clear();
      int nbSteps = 30;

      if (keyFrameList.isEmpty()) return;

      if (!valuesAreValid) updateModifiedFrameValues();

      if (keyFrameList.get(0) == keyFrameList.get(keyFrameList.size() - 1))
        // TODO experimenting really
        path.add(
            new Frame(
                keyFrameList.get(0).position(),
                keyFrameList.get(0).orientation(),
                keyFrameList.get(0).magnitude()));
      else {
        KeyFrame[] kf = new KeyFrame[4];
        kf[0] = keyFrameList.get(0);
        kf[1] = kf[0];

        int index = 1;
        kf[2] = (index < keyFrameList.size()) ? keyFrameList.get(index) : null;
        index++;
        kf[3] = (index < keyFrameList.size()) ? keyFrameList.get(index) : null;

        while (kf[2] != null) {
          Vec pdiff = Vec.subtract(kf[2].position(), kf[1].position());
          Vec pvec1 = Vec.add(Vec.multiply(pdiff, 3.0f), Vec.multiply(kf[1].tgP(), (-2.0f)));
          pvec1 = Vec.subtract(pvec1, kf[2].tgP());
          Vec pvec2 = Vec.add(Vec.multiply(pdiff, (-2.0f)), kf[1].tgP());
          pvec2 = Vec.add(pvec2, kf[2].tgP());

          for (int step = 0; step < nbSteps; ++step) {
            Frame frame = new Frame();
            float alpha = step / (float) nbSteps;
            frame.setPosition(
                Vec.add(
                    kf[1].position(),
                    Vec.multiply(
                        Vec.add(
                            kf[1].tgP(),
                            Vec.multiply(Vec.add(pvec1, Vec.multiply(pvec2, alpha)), alpha)),
                        alpha)));
            if (gScene.is3D()) {
              frame.setOrientation(
                  Quat.squad(
                      (Quat) kf[1].orientation(),
                      ((KeyFrame3D) kf[1]).tgQ(),
                      ((KeyFrame3D) kf[2]).tgQ(),
                      (Quat) kf[2].orientation(),
                      alpha));
            } else {
              // linear interpolation
              float start = kf[1].orientation().angle();
              float stop = kf[2].orientation().angle();
              frame.setOrientation(new Rot(start + (stop - start) * alpha));
            }
            frame.setMagnitude(Util.lerp(kf[1].magnitude(), kf[2].magnitude(), alpha));
            path.add(frame.get());
          }

          // Shift
          kf[0] = kf[1];
          kf[1] = kf[2];
          kf[2] = kf[3];

          index++;
          kf[3] = (index < keyFrameList.size()) ? keyFrameList.get(index) : null;
        }
        // Add last KeyFrame
        path.add(new Frame(kf[1].position(), kf[1].orientation(), kf[1].magnitude()));
      }
      pathIsValid = true;
    }
  }