public Parametrisation FindNearest(
IParametricSurface surface,
Point3D referencePoint
)
{
Parametrisation closestParametrisation = new Parametrisation();
var closestDistance = double.MaxValue;
for (var u = 0; u < SamplesU; ++u)
{
for (var v = 0; v < SamplesV; ++v)
{
var paramU = u / (SamplesU - 1.0);
var paramV = v / (SamplesV - 1.0);
var location = surface.Evaluate(paramU, paramV);
var distance = (referencePoint - location).Length;
if (closestDistance > distance)
{
closestDistance = distance;
closestParametrisation = new Parametrisation(
paramU,
paramV
);
}
}
}
return(closestParametrisation);
}
public void Build(IParametricSurface surface)
{
_sampledSurface = surface;
var samplesU =
GlobalSettings.QualitySettingsViewModel.SurfaceHSubdivisions;
var samplesV =
GlobalSettings.QualitySettingsViewModel.SurfaceWSubdivisions;
var lineSamples = 32;
Func <int, double> uCoordGenerator = (i) => i / (samplesU - 1.0);
Func <int, double> vCoordGenerator = (i) => i / (samplesV - 1.0);
Func <int, double> lineGenerator = (i) => i / (lineSamples - 1.0);
for (var i = 0; i < samplesU; ++i)
{
var uCoord = uCoordGenerator(i);
ScanConstantParameter(
(unused) => uCoord,
lineGenerator,
lineSamples
);
}
for (var i = 0; i < samplesV; ++i)
{
var vCoord = vCoordGenerator(i);
ScanConstantParameter(
lineGenerator,
(unused) => vCoord,
lineSamples
);
}
}
public static Point3D Evaluate(
this IParametricSurface surface,
Parametrisation parametrisation
)
{
return(surface.Evaluate(
parametrisation.U,
parametrisation.V
));
}
public PolygonIntersection FindIntersectionPolygon(
IParametricSurface firstSurface,
IParametricSurface secondSurface,
Point3D intersectionNearPoint
)
{
_surfaces[0] = firstSurface;
_surfaces[1] = secondSurface;
var firstGuessParametrisation = NearestPointFinder.FindNearest(
_surfaces[0],
intersectionNearPoint
);
var secondGuessParametrisation = NearestPointFinder.FindNearest(
_surfaces[1],
intersectionNearPoint
);
firstGuessParametrisation.Boundaries =
firstSurface.ParametrisationBoundaries;
secondGuessParametrisation.Boundaries =
secondSurface.ParametrisationBoundaries;
var trackingDistanceSetting = TrackingDistance;
TrackingDistance = -trackingDistanceSetting;
var polygonPart = GetDirectionalPolygonPart(
firstGuessParametrisation,
secondGuessParametrisation
);
if (polygonPart.IsLooped)
{
return(polygonPart);
}
TrackingDistance = trackingDistanceSetting;
var polygonRemainingPart = GetDirectionalPolygonPart(
firstGuessParametrisation,
secondGuessParametrisation
);
if (polygonRemainingPart.IsLooped)
{
return(polygonRemainingPart);
}
return(PolygonIntersection.JoinFromSamePoint(
polygonPart,
polygonRemainingPart
));
}
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 static Vector3D Normal(
this IParametricSurface surface,
Parametrisation parametrisation)
{
var du = surface.Derivative(
parametrisation,
DerivativeParameter.U
);
var dv = surface.Derivative(
parametrisation,
DerivativeParameter.V
);
return(Vector3D.CrossProduct(du, dv));
}
/// <summary>
/// Calculates F(u,v) = dot(P(u,v) - P, t) - d
/// </summary>
/// <param name="surface"></param>
/// <param name="parametrisation"></param>
/// <param name="previousPoint"></param>
/// <param name="tangentVector"></param>
/// <returns></returns>
private DenseVector EvaluatePlaneEquation(
IParametricSurface surface,
Parametrisation parametrisation,
Vector previousPoint,
Vector tangentVector
)
{
var surfacePosition =
((Vector3D)surface.Evaluate(parametrisation)).ToMathVector();
var position = surfacePosition - previousPoint;
var dot = position.DotProduct(tangentVector);
var tangentZeroEquationValue = dot - TrackingDistance;
var tantentPlaneEquationVector = DenseVector.OfArray(new[]
{
tangentZeroEquationValue,
tangentZeroEquationValue,
tangentZeroEquationValue
});
return(tantentPlaneEquationVector);
}
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);
}