private void AdjustDerivativeParameter(ref DerivativeParameter parameter)
{
if (FlipUV)
{
parameter = parameter == DerivativeParameter.U
? DerivativeParameter.V
: DerivativeParameter.U;
}
}
public static Vector3D Derivative(
this IParametricSurface surface,
Parametrisation parametrisation,
DerivativeParameter parameter
)
{
return(surface.Derivative(
parametrisation.U,
parametrisation.V,
parameter
));
}
public void DrawDerivative(
IParametricSurface surface,
double u,
double v,
DerivativeParameter parameter,
Color?color = null
)
{
var point = surface.Evaluate(u, v);
var derivative = surface.Derivative(u, v, parameter);
DrawVector(point, derivative, derivative.Length, color);
}
public Vector3D Derivative(
double u,
double v,
DerivativeParameter parameter)
{
AdjustCoorinates(ref u, ref v);
AdjustDerivativeParameter(ref parameter);
var flip = (FlipU && parameter == DerivativeParameter.U) ||
(FlipV && parameter == DerivativeParameter.V);
var flipFactor = flip ? -1.0 : 1.0;
return(flipFactor * Surface.Derivative(u, v, parameter));
}
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 Vector3D Derivative(
double u,
double v,
DerivativeParameter parameter
)
{
switch (parameter)
{
case DerivativeParameter.U:
return(DerivativeU(u, v));
case DerivativeParameter.V:
return(DerivativeV(u, v));
default:
throw new ArgumentOutOfRangeException(
nameof(parameter),
parameter,
null
);
}
}
public Vector3D Derivative(
double u,
double v,
DerivativeParameter parameter
)
{
double patchU, patchV;
var patch = GetPatchWithAdjustedCoords(
u,
v,
out patchU,
out patchV
);
double innerDerivative;
switch (parameter)
{
case DerivativeParameter.U:
innerDerivative = SegmentsU;
break;
case DerivativeParameter.V:
innerDerivative = SegmentsV;
break;
default:
throw new ArgumentOutOfRangeException(
nameof(parameter),
parameter,
null
);
}
return(innerDerivative * patch.Derivative(patchU, patchV, parameter));
}
public Vector3D Derivative(
double u, double v,
DerivativeParameter parameter)
{
throw new NotImplementedException();
}
private DenseVector EvaluateNumericalDerivativeForPlaneEquation(
IParametricSurface surface,
Parametrisation parametrisation,
Vector previousPoint,
Vector tangentVector,
DerivativeParameter parameter
)
{
var parametrisationStep = 0.01;
Parametrisation newParametrisation;
switch (parameter)
{
case DerivativeParameter.U:
if (parametrisation.U > 1 - parametrisationStep - 0.001)
{
parametrisationStep = -parametrisationStep;
}
newParametrisation = parametrisation + new Parametrisation(
parametrisationStep,
0.0
);
break;
case DerivativeParameter.V:
if (parametrisation.V > 1 - parametrisationStep - 0.001)
{
parametrisationStep = -parametrisationStep;
}
newParametrisation = parametrisation + new Parametrisation(
0.0,
parametrisationStep
);
break;
default:
throw new ArgumentOutOfRangeException(
nameof(parameter),
parameter,
null
);
}
var currentValues = EvaluatePlaneEquation(
surface,
parametrisation,
previousPoint,
tangentVector
);
var shiftedValues = EvaluatePlaneEquation(
surface,
newParametrisation,
previousPoint,
tangentVector
);
return((shiftedValues - currentValues) / parametrisationStep);
}
