/// <summary>
/// Gets the points corresponding to the extruded subspace due to extruded segment-by-segment intersection.
/// </summary>
/// <param name="linePointsAndForwardSegments">List of line points with segments connecting to the next point in the line.</param>
/// <param name="lastLinePoint">The final line point.</param>
/// <param name="extrusionAmount">The extrusion amount.</param>
/// <param name="parameterShift">The amount to shift the original line point parameters by when constructing the extruded points.</param>
/// <param name="reverseIndices">Whether line point indices associated with extruded points should be reversed.</param>
/// <param name="includeLast">If final segment should be included in the extrusion.</param>
private static List <ExtrudedPointUV> GetExtrudedSubspace_Points_SegmentIntersections(List <LinePointUVAndSegment> linePointsAndForwardSegments, LinePointUV lastLinePoint, float extrusionAmount, float parameterShift, bool reverseIndices, bool includeLast)
{
var extrudedLinePoints = new List <ExtrudedPointUV>();
GetShiftedScaledParameter findParameter = (originalPointParameter) => parameterShift + originalPointParameter;
var numSegments = linePointsAndForwardSegments.Count;
if (numSegments >= 2)
{
int endCount = includeLast ? numSegments : numSegments - 1;
for (int i = 0; i <= endCount; i++)
{
if (i == 0)
{
int lineSegmentIndex = 0;
var linePointAndSegment = linePointsAndForwardSegments[lineSegmentIndex];
int extrudedPointIndexOnOriginalLine = reverseIndices ? numSegments : 0;
var extrudedStartPoint = new ExtrudedPointUV(linePointAndSegment.LinePoint, findParameter(linePointAndSegment.Parameter), linePointAndSegment.SegmentNormal, extrusionAmount, extrudedPointIndexOnOriginalLine);
extrudedLinePoints.Add(extrudedStartPoint);
}
else if (i == numSegments)
{
int lineSegmentIndex = numSegments - 1;
var lastLinePointAndSegment = linePointsAndForwardSegments[lineSegmentIndex];
int extrudedPointIndexOnOriginalLine = reverseIndices ? 0 : numSegments;
var extrudedEndPoint = new ExtrudedPointUV(lastLinePoint, findParameter(lastLinePoint.Parameter), lastLinePointAndSegment.SegmentNormal, extrusionAmount, extrudedPointIndexOnOriginalLine);
extrudedLinePoints.Add(extrudedEndPoint);
}
else
{
var indexToAssign = reverseIndices ? numSegments - i : i;
var linePointAndSegment = linePointsAndForwardSegments[i];
var nextLinePoint = i + 1 < numSegments ? linePointsAndForwardSegments[i + 1].LinePoint : lastLinePoint;
AddPointExtrusionFromPreviousNextSegments(linePointAndSegment, linePointsAndForwardSegments[i - 1], nextLinePoint, indexToAssign, extrusionAmount, extrudedLinePoints, findParameter);
}
}
}
return(extrudedLinePoints);
}
/// <summary>
/// Atempt to add naively-extruded points when the extrusion from two neighbouring segments would intersect outside of those extruded segments.
/// </summary>
/// <param name="linePointAndForwardSegment">First segment.</param>
/// <param name="previousLinePointAndForwardSegment">Previous segment.</param>
/// <param name="lineSegmentIndexToAssign">Line segment index to assign the extruded point coming from.</param>
/// <param name="extrusionAmount">The extrusion amount.</param>
/// <param name="extrudedLinePoints">The list of all extruded line points.</param>
/// <param name="findParameter">Delegate for determining altered point parameter.</param>
/// <param name="extrusionIntersectionDistanceAlongTangents">The extrusion intersection distance along segment tangent directions.</param>
private static void AttemptAddNaiveExtrudedPointsWhenTheirExtrudedSegmentsDoNotIntersect(LinePointUVAndSegment linePointAndForwardSegment, LinePointUVAndSegment previousLinePointAndForwardSegment, int lineSegmentIndexToAssign, float extrusionAmount, List <ExtrudedPointUV> extrudedLinePoints, GetShiftedScaledParameter findParameter, float extrusionIntersectionDistanceAlongTangents)
{
bool intersectionOccursOutOfBothSegments = extrusionIntersectionDistanceAlongTangents >= Mathf.Max(previousLinePointAndForwardSegment.SegmentLength, linePointAndForwardSegment.SegmentLength);
if (intersectionOccursOutOfBothSegments)
{
//Nothing to do here, since any additional points will not contribute to any chunks that are not too close to the original line.
}
else
{
var extrudedFromCenterPointPreviousSegmentNormal = new ExtrudedPointUV(linePointAndForwardSegment.LinePoint, findParameter(linePointAndForwardSegment.Parameter), previousLinePointAndForwardSegment.SegmentNormal, extrusionAmount, lineSegmentIndexToAssign - 1);//Previous segment's index
extrudedLinePoints.Add(extrudedFromCenterPointPreviousSegmentNormal);
var extrudedFromCenterPointCurrentSegmentNormal = new ExtrudedPointUV(linePointAndForwardSegment.LinePoint, findParameter(linePointAndForwardSegment.Parameter), linePointAndForwardSegment.SegmentNormal, extrusionAmount, lineSegmentIndexToAssign);//Current segment's index
extrudedLinePoints.Add(extrudedFromCenterPointCurrentSegmentNormal);
//NB Here we are just adding the 'naive' points without computing the intersection, and relying on the overall intersection algorithm to take care of the rest.
}
}
/// <summary>
/// Add extruded point(s) based on two neighbouring line segments.
/// </summary>
/// <param name="linePointAndForwardSegment">A line point and its corresponding segment.</param>
/// <param name="previousLinePointAndForwardSegment">The previous line point and its corresponding segment.</param>
/// <param name="nextLinePoint">The next line point (since its parameter, uv etc will be needed).</param>
/// <param name="lineSegmentIndexToAssign">Line segment index to assign the extruded point coming from.</param>
/// <param name="extrusionAmount">The extrusion amount.</param>
/// <param name="extrudedLinePoints">The list of all extruded line points.</param>
/// <param name="findParameter">Delegate for determining altered point parameter.</param>
private static void AddPointExtrusionFromPreviousNextSegments(LinePointUVAndSegment linePointAndForwardSegment, LinePointUVAndSegment previousLinePointAndForwardSegment, LinePointUV nextLinePoint, int lineSegmentIndexToAssign, float extrusionAmount, List <ExtrudedPointUV> extrudedLinePoints, GetShiftedScaledParameter findParameter)
{
double extrusionMagnitudeFractionFirstTangent;
bool segmentIntersection = LineSegmentUtil.DoNeighbouringSegmentTangentsFromCommonPointIntersect(previousLinePointAndForwardSegment.SegmentTangent, linePointAndForwardSegment.SegmentTangent, Mathf.Sign(extrusionAmount), out extrusionMagnitudeFractionFirstTangent);
if (segmentIntersection)
{
//Concave section; expect intersection of neighbouring line segments around this point
var extrusionDistanceAlongTangents = Mathf.Abs((float)extrusionMagnitudeFractionFirstTangent * extrusionAmount);
bool intersectionOccursOutOfSegment = extrusionDistanceAlongTangents >= Mathf.Min(previousLinePointAndForwardSegment.SegmentLength, linePointAndForwardSegment.SegmentLength);
if (intersectionOccursOutOfSegment)
{
AttemptAddNaiveExtrudedPointsWhenTheirExtrudedSegmentsDoNotIntersect(linePointAndForwardSegment, previousLinePointAndForwardSegment, lineSegmentIndexToAssign, extrusionAmount, extrudedLinePoints, findParameter, extrusionDistanceAlongTangents);
}
else
{
var intersection = LineSegmentUtil.GetExtrudedSegmentNeighbouringIntersectionPoint(linePointAndForwardSegment.Point, previousLinePointAndForwardSegment.SegmentTangent, extrusionMagnitudeFractionFirstTangent, extrusionAmount);
var linePointOfThisIntersection = new LinePointUV(findParameter(linePointAndForwardSegment.Parameter), intersection, linePointAndForwardSegment.UV);
extrudedLinePoints.Add(new ExtrudedPointUV(linePointOfThisIntersection, lineSegmentIndexToAssign, lineSegmentIndexToAssign - 1));
}
}
else
{
//Convex section, expect a circular fan of points around this point.
RangeF rangeFromPreviousPoints = new RangeF(findParameter(previousLinePointAndForwardSegment.Parameter), findParameter(linePointAndForwardSegment.Parameter));
RangeF rangeFromNextPoints = new RangeF(findParameter(linePointAndForwardSegment.Parameter), findParameter(nextLinePoint.Parameter));
RangeF parameterRangeToUse = new RangeF(rangeFromPreviousPoints.FromFractionUnclamped(0.6f), rangeFromNextPoints.FromFractionUnclamped(0.4f));
var extrudedFromPreviousNormal = linePointAndForwardSegment.Point + extrusionAmount * previousLinePointAndForwardSegment.SegmentNormal;
var extrudedFromNextNormal = linePointAndForwardSegment.Point + extrusionAmount * linePointAndForwardSegment.SegmentNormal;
var diffBetweenExtrusion = (extrudedFromNextNormal - extrudedFromPreviousNormal).magnitude;
var minNeighbouringSegmentDistance = Mathf.Min(previousLinePointAndForwardSegment.SegmentLength, linePointAndForwardSegment.SegmentLength);
float absExtrusionAmount = Mathf.Abs(extrusionAmount);
var comparisonDistance = Mathf.Min(minNeighbouringSegmentDistance, absExtrusionAmount);
var angleBetweenSegmentNormals = Mathf.Acos(Mathf.Clamp(Vector3.Dot(previousLinePointAndForwardSegment.SegmentNormal, linePointAndForwardSegment.SegmentNormal), -1f, 1f));
int numPointsFromDistance = Mathf.CeilToInt(diffBetweenExtrusion / comparisonDistance);
if (numPointsFromDistance <= 2)
{
numPointsFromDistance++;
} //NB Want at least the end-points, and if distance is large enough to need 2 naturally, 3 seems to looks better.
int numPointsFromAngle = Mathf.CeilToInt(angleBetweenSegmentNormals / _convexExtrusionMinimumAngleRadians);
int numPoints = Mathf.Max(numPointsFromDistance, numPointsFromAngle);
for (int i = 0; i < numPoints; i++)
{
float fraction = numPoints == 1 ? 0.5f : i / (numPoints - 1.0f);
var averageTangent = previousLinePointAndForwardSegment.SegmentTangent.AverageDirectionVector(linePointAndForwardSegment.SegmentTangent, fraction);
var averageNormal = NormalUtil.NormalFromTangent(averageTangent);
var extrudedVector = linePointAndForwardSegment.Point + averageNormal * extrusionAmount;
var parameter = parameterRangeToUse.FromFractionUnclamped(fraction);
Vector2 newUV = GetUVParameterOfFanPoint(linePointAndForwardSegment, previousLinePointAndForwardSegment, nextLinePoint, absExtrusionAmount, angleBetweenSegmentNormals, fraction);
var newLinePointInFan = new LinePointUV(parameter, extrudedVector, newUV);
extrudedLinePoints.Add(new ExtrudedPointUV(newLinePointInFan, lineSegmentIndexToAssign, lineSegmentIndexToAssign - 1));
}
}
}
