/// <summary>
/// Evaluates Frenet frame on the spline using curve distance from the start. Valid length is [0..TotalLength].
/// Caller must ensure that spline is valid before calling this method!
/// </summary>
public void EvalFrameParametrized(float length, out CurveFrame frame)
{
int i;
float t;
GetSegmentIndexAndTime(_parametrization.GetApproximateTimeParameter(length), out i, out t);
ItemData segment = _data[i];
frame.Position = segment.EvalPosition(t);
Vector3 velocity = segment.EvalFirstDerivative(t);
Vector3 acceleration = segment.EvalSecondDerivative(t);
float VDotV = velocity.Dot(velocity);
float VDotA = velocity.Dot(acceleration);
frame.Normal = VDotV * acceleration - VDotA * velocity;
frame.Normal.Normalize();
frame.Tangent = velocity;
frame.Tangent.Normalize();
frame.Binormal = frame.Tangent.Cross(frame.Normal);
}
/// <summary>
/// Evaluates torsion on the spline using curve distance from the start. Valid length is [0..TotalLength].
/// Caller must ensure that spline is valid before calling this method!
/// </summary>
public float EvalTorsionParametrized(float length)
{
int i;
float t;
GetSegmentIndexAndTime(_parametrization.GetApproximateTimeParameter(length), out i, out t);
ItemData segment = _data[i];
Vector3 velocity = segment.EvalFirstDerivative(t);
Vector3 acceleration = segment.EvalSecondDerivative(t);
Vector3 cross = velocity.Cross(acceleration);
float denom = cross.sqrMagnitude;
if (denom >= Mathfex.ZeroTolerance)
{
Vector3 jerk = segment.EvalThirdDerivative(t);
float numer = cross.Dot(jerk);
return(numer / denom);
}
return(0f);
}
/// <summary>
/// Evaluates curvature on the spline using curve distance from the start. Valid length is [0..TotalLength].
/// Caller must ensure that spline is valid before calling this method!
/// </summary>
public float EvalCurvatureParametrized(float length)
{
int i;
float t;
GetSegmentIndexAndTime(_parametrization.GetApproximateTimeParameter(length), out i, out t);
ItemData segment = _data[i];
Vector3 velocity = segment.EvalFirstDerivative(t);
float speedSqr = velocity.sqrMagnitude;
if (speedSqr >= Mathfex.ZeroTolerance)
{
Vector3 acceleration = segment.EvalSecondDerivative(t);
Vector3 cross = velocity.Cross(acceleration);
float numer = cross.magnitude;
float denom = Mathf.Pow(speedSqr, 1.5f);
return(numer / denom);
}
return(0f);
}
