/// <summary>
/// Returns a new list of points and uvs of an extruded contour, where the uv u-parameters have been undergone convolution filtering to try to smooth out discontinuities.
/// </summary>
/// <param name="extrudedLinePoints">Points comprising the extruded line contour</param>
/// <param name="extrusionAmount">The extrusion amount.</param>
public Vector2WithUV[] GetUvAlteredExtrudedContour(Vector2WithUV[] extrudedLinePoints, float extrusionAmount)
{
Vector2WithUV[] altered;
float sigma = _convolutionWidthExtrusionDistanceFraction * extrusionAmount;
//Integral from segmentStartArcDistance to segmentEndArcDistance of G(pointArcDistance - x')dx'
ConvolutionFunctionIntegral gaussianConvolutionIntegral = (pointArcDistance, segmentStartArcDistance, segmentEndArcDistance) => GaussianConvolutionFunctionIntegral(pointArcDistance, segmentStartArcDistance, segmentEndArcDistance, sigma);
//Integral from pointArcDistance - segmentEndArcDistance to pointArcDistance - segmentStartArcDistance of x'G(x')dx'
ConvolutionFunctionIntegral gaussianLinearConvolutionIntegral = (pointArcDistance, segmentStartArcDistance, segmentEndArcDistance) => GaussianLinearConvolutionFunctionIntegral(pointArcDistance, segmentStartArcDistance, segmentEndArcDistance, sigma);
if (extrudedLinePoints.Length > 2)
{
bool isPeriodic = extrudedLinePoints[0].Equals(extrudedLinePoints[extrudedLinePoints.Length - 1]);
float[] uParameters = GetConvolutionUParameters(extrudedLinePoints, isPeriodic, gaussianConvolutionIntegral, gaussianLinearConvolutionIntegral);
altered = UVAlterationUtil.CopyPointsWithOverriddenUParameters(extrudedLinePoints, uParameters);
}
else
{
altered = extrudedLinePoints;
}
return(altered);
}
/// <summary>
/// Gets the u-parameter of a point determined by arcdistance convolution integral along a contour.
/// </summary>
/// <param name="pointArcDistance">The point's arcdistance.</param>
/// <param name="uParameters">The u-parameters of the contour.</param>
/// <param name="arcDistances">The arcdistances of the contour.</param>
/// <param name="isPeriodic">If the contour is periodic.</param>
/// <param name="convolutionFunctionIntegral">Function for computing arcdistance integral of the convolution function.</param>
/// <param name="convolutionLinearFunctionIntegral">Function for computing arcdistance integral of the convolution function multiplied by arcdistance.</param>
private static float GetConvolutionUParameter(float pointArcDistance, float[] uParameters, float[] arcDistances, bool isPeriodic, ConvolutionFunctionIntegral convolutionFunctionIntegral, ConvolutionFunctionIntegral convolutionLinearFunctionIntegral)
{
if (isPeriodic)
{
arcDistances = PeriodicallyWrappedArcDistances(pointArcDistance, arcDistances);
pointArcDistance = 0;
}
double convolutionSum = 0;
for (int segmentIndex = 0; segmentIndex < uParameters.Length - 1; segmentIndex++)
{
float uStart = uParameters[segmentIndex];
float uEnd = uParameters[segmentIndex + 1];
float arcDistanceSegmentStart = arcDistances[segmentIndex];
float arcDistanceSegmentEnd = arcDistances[segmentIndex + 1];
float segmentLength = arcDistanceSegmentEnd - arcDistanceSegmentStart;
float uDifference = uEnd - uStart;
//In periodic case, we'll ignore the 'furthest-away' segment regardless of how large the convolution kernel is, since we'd need to chop it in two to deal with periodically wrapped arcdistances properly.
if (segmentLength > 0)
{
var integralConvolutionFunction = convolutionFunctionIntegral(pointArcDistance, arcDistanceSegmentStart, arcDistanceSegmentEnd);
var integralConvolutionLinearFunction = convolutionLinearFunctionIntegral(pointArcDistance, arcDistanceSegmentStart, arcDistanceSegmentEnd);
var convolutionIntegralFactor = uStart + uDifference * (pointArcDistance - arcDistanceSegmentStart) / segmentLength;
var convolutionLinearIntegralFactor = -uDifference / segmentLength;
var contribution = convolutionIntegralFactor * integralConvolutionFunction + convolutionLinearIntegralFactor * integralConvolutionLinearFunction;
convolutionSum += contribution;
}
}
return((float)convolutionSum);
}
/// <summary>
/// Returns the u-parameters of an extruded contour determined by arcdistance convolution integral.
/// </summary>
/// <param name="contourPoints">The contour points.</param>
/// <param name="isPeriodic">If the contour is periodic.</param>
/// <param name="convolutionFunctionIntegral">Function for computing arcdistance integral of the convolution function.</param>
/// <param name="convolutionLinearFunctionIntegral">Function for computing arcdistance integral of the convolution function multiplied by arcdistance.</param>
private static float[] GetConvolutionUParameters(Vector2WithUV[] contourPoints, bool isPeriodic, ConvolutionFunctionIntegral convolutionFunctionIntegral, ConvolutionFunctionIntegral convolutionLineareFunctionIntegral)
{
int pointCount = isPeriodic ? contourPoints.Length - 1 : contourPoints.Length;
float[] uParameters = UVAlterationUtil.GetUParameters(contourPoints);
float[] arcDistances = UVAlterationUtil.GetPointArcdistances(contourPoints);
float[] uParametersConvolved = new float[contourPoints.Length];
for (int pointIndex = 0; pointIndex < pointCount; pointIndex++)
{
float pointArcDistance = arcDistances[pointIndex];
uParametersConvolved[pointIndex] = GetConvolutionUParameter(pointArcDistance, uParameters, arcDistances, isPeriodic, convolutionFunctionIntegral, convolutionLineareFunctionIntegral);
}
if (isPeriodic)
{
uParametersConvolved[contourPoints.Length - 1] = uParametersConvolved[0];
}
return(uParametersConvolved);
}
