/// <summary>
/// Units the normal vector at.
/// </summary>
/// <param name="angleRadians">The angle radians.</param>
/// <returns>VectorParametric.</returns>
public VectorParametric UnitNormalVectorAt(double angleRadians)
{
VectorParametric unitTangentVector = UnitTangentVectorAt(angleRadians);
VectorParametric unitTangentVectorPrime = unitTangentVector.Differentiate();
return(unitTangentVectorPrime / unitTangentVectorPrime.Magnitude(angleRadians));
}
/// <summary>
/// Cross-product of two vectors.
/// </summary>
/// <param name="vector">The vector.</param>
/// <param name="angleRadians">The angle radians.</param>
/// <returns>System.Double.</returns>
public double CrossProductAt(VectorParametric vector, double angleRadians)
{
return(VectorLibrary.CrossProduct(
_curveParametric.Xcomponent.ValueAt(angleRadians),
_curveParametric.Ycomponent.ValueAt(angleRadians),
vector._curveParametric.Xcomponent.ValueAt(angleRadians),
vector._curveParametric.Ycomponent.ValueAt(angleRadians)));
}
/// <summary>
/// Curvatures the specified angle radians.
/// </summary>
/// <param name="angleRadians">The angle radians.</param>
/// <returns>System.Double.</returns>
public double Curvature(double angleRadians)
{
VectorParametric unitTangentVector = UnitTangentVectorAt(angleRadians);
VectorParametric unitTangentVectorPrime = unitTangentVector.Differentiate();
VectorParametric vectorPrime = Differentiate();
return(unitTangentVectorPrime.Magnitude(angleRadians) / vectorPrime.Magnitude(angleRadians));
}
/// <summary>
/// Units the tangent vector at.
/// </summary>
/// <param name="angleRadians">The angle radians.</param>
/// <returns>VectorParametric.</returns>
public VectorParametric UnitTangentVectorAt(double angleRadians)
{
VectorParametric vectorPrime = Differentiate();
return(vectorPrime / vectorPrime.Magnitude(angleRadians));
}
/// <summary>
/// Units the vector at.
/// </summary>
/// <param name="angleRadians">The angle radians.</param>
/// <returns>VectorParametric.</returns>
public VectorParametric UnitVectorAt(double angleRadians)
{
VectorParametric vector = new VectorParametric(_curveParametric, Tolerance);
return(vector / vector.Magnitude(angleRadians));
}
