public static PathSplitData SplitBezierPathEvenly(BezierPath bezierPath, float spacing, float accuracy)
{
PathSplitData splitData = new PathSplitData();
splitData.vertices.Add(bezierPath.GetPoint(0));
splitData.tangents.Add(CubicBezierUtility.EvaluateCurveDerivative(bezierPath.GetPointsInSegment(0), 0).normalized);
splitData.cumulativeLength.Add(0);
splitData.anchorVertexMap.Add(0);
splitData.minMax.AddValue(bezierPath.GetPoint(0));
Vector3 prevPointOnPath = bezierPath.GetPoint(0);
Vector3 lastAddedPoint = bezierPath.GetPoint(0);
float currentPathLength = 0;
float dstSinceLastVertex = 0;
// Go through all segments and split up into vertices
for (int segmentIndex = 0; segmentIndex < bezierPath.NumSegments; segmentIndex++)
{
Vector3[] segmentPoints = bezierPath.GetPointsInSegment(segmentIndex);
float estimatedSegmentLength = CubicBezierUtility.EstimateCurveLength(segmentPoints[0], segmentPoints[1], segmentPoints[2], segmentPoints[3]);
int divisions = Mathf.CeilToInt(estimatedSegmentLength * accuracy);
float increment = 1f / divisions;
for (float t = increment; t <= 1; t += increment)
{
bool isLastPointOnPath = (t + increment > 1 && segmentIndex == bezierPath.NumSegments - 1);
if (isLastPointOnPath)
{
t = 1;
}
Vector3 pointOnPath = CubicBezierUtility.EvaluateCurve(segmentPoints, t);
dstSinceLastVertex += (pointOnPath - prevPointOnPath).magnitude;
// If vertices are now too far apart, go back by amount we overshot by
if (dstSinceLastVertex > spacing)
{
float overshootDst = dstSinceLastVertex - spacing;
pointOnPath += (prevPointOnPath - pointOnPath).normalized * overshootDst;
t -= increment;
}
if (dstSinceLastVertex >= spacing || isLastPointOnPath)
{
currentPathLength += (lastAddedPoint - pointOnPath).magnitude;
splitData.cumulativeLength.Add(currentPathLength);
splitData.vertices.Add(pointOnPath);
splitData.tangents.Add(CubicBezierUtility.EvaluateCurveDerivative(segmentPoints, t).normalized);
splitData.minMax.AddValue(pointOnPath);
dstSinceLastVertex = 0;
lastAddedPoint = pointOnPath;
}
prevPointOnPath = pointOnPath;
}
splitData.anchorVertexMap.Add(splitData.vertices.Count - 1);
}
return(splitData);
}
public static Bounds CalculateSegmentBounds(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3)
{
MinMax3D minMax = new MinMax3D();
minMax.AddValue(p0);
minMax.AddValue(p3);
List <float> extremePointTimes = ExtremePointTimes(p0, p1, p2, p3);
foreach (float t in extremePointTimes)
{
minMax.AddValue(CubicBezierUtility.EvaluateCurve(p0, p1, p2, p3, t));
}
return(new Bounds((minMax.Min + minMax.Max) / 2, minMax.Max - minMax.Min));
}
public static Bounds CalculateBounds(Vector3[] points)
{
MinMax3D minMax = new MinMax3D();
minMax.AddValue(points[0]);
minMax.AddValue(points[3]);
List <float> extremePointTimes = ExtremePointTimes(points[0], points[1], points[2], points[3]);
foreach (float t in extremePointTimes)
{
minMax.AddValue(CubicBezierUtility.EvaluateCurve(points, t));
}
return(new Bounds((minMax.Min + minMax.Max) / 2, minMax.Max - minMax.Min));
}
public static Bounds CalculateBounds(Vector3[] points)
{
Debug.Assert(points.Length == 4, "Incorrect number of points supplied to cubic bezier function (expected 4)");
MinMax3D minMax = new MinMax3D();
if (points.Length >= 4)
{
minMax.AddValue(points[0]);
minMax.AddValue(points[3]);
List <float> extremePointTimes = ExtremePointTimes(points[0], points[1], points[2], points[3]);
foreach (float t in extremePointTimes)
{
minMax.AddValue(CubicBezierUtility.EvaluateCurve(points, t));
}
}
return(new Bounds((minMax.Min + minMax.Max) / 2, minMax.Max - minMax.Min));
}
public static PathSplitData SplitBezierPathByAngleError(BezierPath bezierPath, float maxAngleError, float minVertexDst, float accuracy)
{
PathSplitData splitData = new PathSplitData();
splitData.vertices.Add(bezierPath.GetPoint(0));
splitData.tangents.Add(CubicBezierUtility.EvaluateCurveDerivative(bezierPath.GetPointsInSegment(0), 0).normalized);
splitData.cumulativeLength.Add(0);
splitData.anchorVertexMap.Add(0);
splitData.minMax.AddValue(bezierPath.GetPoint(0));
Vector3 prevPointOnPath = bezierPath.GetPoint(0);
Vector3 lastAddedPoint = bezierPath.GetPoint(0);
float currentPathLength = 0;
float dstSinceLastVertex = 0;
// Go through all segments and split up into vertices
for (int segmentIndex = 0; segmentIndex < bezierPath.NumSegments; segmentIndex++)
{
Vector3[] segmentPoints = bezierPath.GetPointsInSegment(segmentIndex);
float estimatedSegmentLength = CubicBezierUtility.EstimateCurveLength(segmentPoints[0], segmentPoints[1], segmentPoints[2], segmentPoints[3]);
int divisions = Mathf.CeilToInt(estimatedSegmentLength * accuracy);
float increment = 1f / divisions;
for (float t = increment; t <= 1; t += increment)
{
bool isLastPointOnPath = (t + increment > 1 && segmentIndex == bezierPath.NumSegments - 1);
if (isLastPointOnPath)
{
t = 1;
}
Vector3 pointOnPath = CubicBezierUtility.EvaluateCurve(segmentPoints, t);
Vector3 nextPointOnPath = CubicBezierUtility.EvaluateCurve(segmentPoints, t + increment);
// angle at current point on path
float localAngle = 180 - MathUtility.MinAngle(prevPointOnPath, pointOnPath, nextPointOnPath);
// angle between the last added vertex, the current point on the path, and the next point on the path
float angleFromPrevVertex = 180 - MathUtility.MinAngle(lastAddedPoint, pointOnPath, nextPointOnPath);
float angleError = Mathf.Max(localAngle, angleFromPrevVertex);
if ((angleError > maxAngleError && dstSinceLastVertex >= minVertexDst) || isLastPointOnPath)
{
currentPathLength += (lastAddedPoint - pointOnPath).magnitude;
splitData.cumulativeLength.Add(currentPathLength);
splitData.vertices.Add(pointOnPath);
splitData.tangents.Add(CubicBezierUtility.EvaluateCurveDerivative(segmentPoints, t).normalized);
splitData.minMax.AddValue(pointOnPath);
dstSinceLastVertex = 0;
lastAddedPoint = pointOnPath;
}
else
{
dstSinceLastVertex += (pointOnPath - prevPointOnPath).magnitude;
}
prevPointOnPath = pointOnPath;
}
splitData.anchorVertexMap.Add(splitData.vertices.Count - 1);
}
return(splitData);
}