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);
}
private int FindParametrisationIndex(
IntersectionParametrisation parametrisation
)
{
for (var i = 0; i < Polygon.Count - 10; ++i)
{
var norm1 = Parametrisation.DistanceNormMax(
parametrisation.First,
Polygon[i].First
);
var norm2 = Parametrisation.DistanceNormMax(
parametrisation.Second,
Polygon[i].Second
);
//IntersectionParametrisation.DistanceNormMax(
//parametrisation,
//Polygon[i]
//);
if (norm1 < EqualityEpsilon || norm2 < EqualityEpsilon)
{
return(i);
}
}
return(-1);
}
public static void DrawLine(
WriteableBitmap writeableBitmap,
int previewSize,
int offset,
Parametrisation begin,
Parametrisation end
)
{
var x0 = (int)(begin.U * previewSize);
var y0 = (int)(begin.V * previewSize);
var x1 = (int)(end.U * previewSize);
var y1 = (int)(end.V * previewSize);
var maxDistance = (int)(0.8 * previewSize);
if (Math.Abs(x0 - x1) > maxDistance ||
Math.Abs(y0 - y1) > maxDistance)
{
return;
}
writeableBitmap.DrawLine(
offset + x0,
offset + y0,
offset + x1,
offset + y1,
Colors.Red
);
}
public IntersectionParametrisation(
Parametrisation first,
Parametrisation second
)
{
First = first;
Second = second;
}
public static double DistanceNormMax(
IntersectionParametrisation left,
IntersectionParametrisation right
)
{
return(Math.Max(
Parametrisation.DistanceNormMax(left.First, right.First),
Parametrisation.DistanceNormMax(left.Second, right.Second)
));
}
public IntersectionParametrisation(Vector <double> vector)
{
if (vector.Count != 4)
{
throw new ArgumentException(
"Intersection parametrisation requires exactly 4 parameters"
);
}
First = new Parametrisation(vector[0], vector[1]);
Second = new Parametrisation(vector[2], vector[3]);
}
private PolygonIntersection GetDirectionalPolygonPart(
Parametrisation firstGuessParametrisation,
Parametrisation secondGuessParametrisation
)
{
IntersectionParametrisation?previousParametrisation = null;
var currentIntersectionParametrisation = FindFirstIntersection(
firstGuessParametrisation,
secondGuessParametrisation
);
var polygon = new PolygonIntersection();
polygon.EqualityEpsilon = 0.001;
while (currentIntersectionParametrisation.HasValue &&
!AreEdgeTrackingBoundaryConditionsFullfilled(
previousParametrisation,
currentIntersectionParametrisation
)
)
{
if (polygon.FinishIfLoopedBack(
currentIntersectionParametrisation.Value
))
{
break;
}
polygon.Add(currentIntersectionParametrisation.Value);
var nextGuess = GetNextInitialGuess(
currentIntersectionParametrisation.Value
);
if (!nextGuess.HasValue)
{
break;
}
previousParametrisation = currentIntersectionParametrisation;
currentIntersectionParametrisation = FindFirstIntersection(
nextGuess.Value.First,
nextGuess.Value.Second
);
}
return(polygon);
}
/// <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 IntersectionParametrisation?FindFirstIntersection(
Parametrisation startingParametersFirstSurface,
Parametrisation startingParametersSecondSurface
)
{
var currentParametrisation = new IntersectionParametrisation(
startingParametersFirstSurface,
startingParametersSecondSurface
);
var iterationNumber = 0;
do
{
var nextParametrisation = EvaluateTwoSurfacesNewtonStep(
currentParametrisation
);
if (!nextParametrisation.IsValid())
{
return(null);
}
if (MinimumStepLength >=
IntersectionParametrisation.DistanceNormMax(
nextParametrisation,
currentParametrisation
))
{
return(nextParametrisation);
}
currentParametrisation = nextParametrisation;
} while (++iterationNumber < MaximumNewtonIterations);
return(null);
}
public Point3D Evaluate(Parametrisation parametrisation)
{
return(Evaluate(parametrisation.U, parametrisation.V));
}
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);
}
