public Point3D Evaluate(double u, double v)
{
var subpoints = new List <Point3D>();
for (var i = 0; i < 4; ++i)
{
var subpoint = BernsteinPolynomial.Evaluate3DPolynomial(
ArrayHelpers.GetRow(ControlPoints, i), u
);
subpoints.Add(subpoint);
}
return(BernsteinPolynomial.Evaluate3DPolynomial(subpoints, v));
}
public Vector3D Derivative(
double u, double v,
DerivativeParameter parameter
)
{
double firstParameter, secondParameter;
Func <int, Point3D[]> generator;
switch (parameter)
{
case DerivativeParameter.U:
generator = (i) => ArrayHelpers.GetColumn(ControlPoints, i);
firstParameter = v;
secondParameter = u;
break;
case DerivativeParameter.V:
generator = (i) => ArrayHelpers.GetRow(ControlPoints, i);
firstParameter = u;
secondParameter = v;
break;
default:
throw new ArgumentOutOfRangeException(
nameof(parameter),
parameter,
null
);
}
var subpoints = new List <Point3D>();
for (var i = 0; i < 4; ++i)
{
subpoints.Add(BernsteinPolynomial.Evaluate3DPolynomial(
generator(i),
firstParameter
));
}
var derivative = BernsteinPolynomial.CalculateDerivative(subpoints);
return((Vector3D)BernsteinPolynomial.Evaluate3DPolynomial(
derivative,
secondParameter
));
}
public void ReshapeEdge(
int edgeId,
Func <double, Point3D> boundaryCurve,
Func <double, Vector3D> boundaryDerivative,
Vector3D a0,
Vector3D b0,
Vector3D a3,
Vector3D b3
)
{
var c0 = boundaryDerivative(0);
var c2 = boundaryDerivative(1);
var g0 = (a0 + b0) / 2.0;
var g2 = (a3 + b3) / 2.0;
var g1 = (g0 + g2) / 2.0;
var gPolynomial = new List <Point3D>()
{
(Point3D)g0,
(Point3D)g1,
(Point3D)g2
};
double k0, k1, h0, h1;
CalculateTangentVectorFieldCoefficients(b0, g0, c0, out k0, out h0);
CalculateTangentVectorFieldCoefficients(b3, g2, c2, out k1, out h1);
Func <double, double> k = v => k0 * (1 - v) + k1 * v;
Func <double, double> h = v => h0 * (1 - v) + h1 * v;
Func <double, Vector3D> g = v =>
(Vector3D)BernsteinPolynomial.Evaluate3DPolynomial(
gPolynomial, v
);
Func <double, Vector3D> d =
v => k(v) * g(v) + h(v) * boundaryDerivative(v);
int v0 = 3, v1 = 1, derivativeIndex = 0;
if (edgeId == 0)
{
v0 = 0;
v1 = 2;
derivativeIndex = 0;
}
else if (edgeId == 1)
{
v0 = 1;
v1 = 0;
derivativeIndex = 1;
}
else if (edgeId == 2)
{
v0 = 2;
v1 = 3;
derivativeIndex = 1;
}
else if (edgeId == 3)
{
v0 = 1;
v1 = 3;
derivativeIndex = 0;
}
_cornerPoints[v0] = boundaryCurve(0);
_cornerPoints[v1] = boundaryCurve(1);
_cornerDerivatives[v0, derivativeIndex] = c0;
_cornerDerivatives[v1, derivativeIndex] = c2;
_cornerTwistVectors[v0, derivativeIndex] = d(1.0 / 3.0);
_cornerTwistVectors[v1, derivativeIndex] = d(2.0 / 3.0);
}
