/// <summary>
/// Constructs a new rotation transformation with Sin and Cos radians angle, rotation center and rotation axis.
/// </summary>
/// <param name="sinAngle">Sin radians angle.</param>
/// <param name="cosAngle">Cos radians angle.</param>
/// <param name="axis">Axis direction.</param>
/// <param name="origin">Rotation center.</param>
/// <returns>A transformation matrix which rotates geometry around an anchor.</returns>
private static Transform Rotation(double sinAngle, double cosAngle, Vector3 axis, Point3 origin)
{
double sAngle = sinAngle;
double cAngle = cosAngle;
GSharkMath.KillNoise(ref sAngle, ref cAngle);
Transform transform = Identity();
double oneMinusCosAngle = 1 - cosAngle;
transform[0][0] = axis[0] * axis[0] * oneMinusCosAngle + cAngle;
transform[0][1] = axis[0] * axis[1] * oneMinusCosAngle - axis[2] * sAngle;
transform[0][2] = axis[0] * axis[2] * oneMinusCosAngle + axis[1] * sAngle;
transform[1][0] = axis[1] * axis[0] * oneMinusCosAngle + axis[2] * sAngle;
transform[1][1] = axis[1] * axis[1] * oneMinusCosAngle + cAngle;
transform[1][2] = axis[1] * axis[2] * oneMinusCosAngle - axis[0] * sAngle;
transform[2][0] = axis[2] * axis[0] * oneMinusCosAngle - axis[1] * sAngle;
transform[2][1] = axis[2] * axis[1] * oneMinusCosAngle + axis[0] * sAngle;
transform[2][2] = axis[2] * axis[2] * oneMinusCosAngle + cAngle;
if (!origin.Equals(new Point3(0, 0, 0)))
{
transform[0][3] = -((transform[0][0] - 1) * origin[0] + transform[0][1] * origin[1] + transform[0][2] * origin[2]);
transform[1][3] = -(transform[1][0] * origin[0] + (transform[1][1] - 1) * origin[1] + transform[1][2] * origin[2]);
transform[2][3] = -(transform[2][0] * origin[0] + transform[2][1] * origin[1] + (transform[2][2] - 1) * origin[2]);
}
transform[3][0] = transform[3][1] = transform[3][0] = 0.0;
transform[3][3] = 1;
return(transform);
}
/// <summary>
/// Checks the validity of the input knot vector.<br/>
/// Confirm the relations between degree (p), number of control points(n+1), and the number of knots (m+1).<br/>
/// Refer to The NURBS Book (2nd Edition), p.50 for details.<br/>
/// <br/>
/// More specifically, this method checks if the knot vector is of the following structure:<br/>
/// The knot knots must be non-decreasing and of length (degree + 1) * 2 or greater<br/>
/// </summary>
/// <param name="degree">The degree of the curve.</param>
/// <param name="numberOfControlPts"></param>
/// <returns>Whether the knots are valid.</returns>
public bool IsValid(int degree, int numberOfControlPts)
{
if (Count == 0)
{
return(false);
}
if (Count < (degree + 1) * 2)
{
return(false);
}
// Check the formula: m = p + n + 1
if (numberOfControlPts + degree + 1 - Count != 0)
{
return(false);
}
for (int i = 0; i < Count; i++)
{
if (!GSharkMath.IsValidDouble(this[i]))
{
return(false);
}
}
bool hasMultiplicity = Multiplicity(0) > 1 || Multiplicity(this.Count - 1) > 1;
double rep = this[0];
for (int i = 0; i < Count; i++)
{
if (hasMultiplicity)
{
if (i < degree + 1)
{
if (Math.Abs(this[i] - rep) > GSharkMath.Epsilon)
{
return(false);
}
}
if (i > Count - degree - 1 && i < Count)
{
if (Math.Abs(this[i] - rep) > GSharkMath.Epsilon)
{
return(false);
}
}
}
if (this[i] < rep - GSharkMath.Epsilon)
{
return(false);
}
rep = this[i];
}
return(true);
}
/// <summary>
/// Converts normalized parameter to interval value, or pair of values.
/// </summary>
/// <param name="normalizedParameter">The normalized parameter between 0 and 1.</param>
/// <returns>Interval parameter t0*(1.0-normalizedParameter) + t1*normalizedParameter.</returns>
public double ParameterAt(double normalizedParameter)
{
return(!GSharkMath.IsValidDouble(normalizedParameter)
? GSharkMath.UnsetValue
: (1.0 - normalizedParameter) * T0 + normalizedParameter * T1);
}