public void CircleLineCross() {
// DisplayGeometryGraph.SetShowFunctions();
const double chordLen = 1.5;
const int cy = 3;
const double cx = chordLen / 2;
var r = Math.Sqrt(cy * cy + cx * cx);
var center = new Point(cx, cy);
var circle = new Ellipse(r, r, center);
var a = new Point(-10, 0);
var b = new Point(10, 0);
var ca = a - center;
var cb = b - center;
const double angle = Math.PI / 6;
ca = ca.Rotate(angle);
cb = cb.Rotate(angle);
a = center + ca;
b = center + cb;
var lineSeg = new LineSegment(a, b);
var ii = Curve.GetAllIntersections(lineSeg, circle, true);
// DisplayGeometryGraph.ShowDebugCurves(new DebugCurve(100,0.01,"black", lineSeg), new DebugCurve(100,0.01,"blue", circle));
Assert.IsTrue(ii.Count == 2);
var roundedRect = new RoundedRect(new Rectangle(0, 100, 200, 0), 10, 10);
lineSeg = new LineSegment(0, 0, 200, 100);
// DisplayGeometryGraph.ShowDebugCurves(new DebugCurve(100, 0.01, "black", lineSeg), new DebugCurve(100, 0.01, "blue", roundedRect));
ii = Curve.GetAllIntersections(lineSeg, roundedRect, true);
Assert.IsTrue(ii.Count == 2);
lineSeg = new LineSegment(0, 100, 200, 0);
// DisplayGeometryGraph.ShowDebugCurves(new DebugCurve(100, 0.01, "black", lineSeg), new DebugCurve(100, 0.01, "blue", roundedRect));
ii = Curve.GetAllIntersections(lineSeg, roundedRect, true);
Assert.IsTrue(ii.Count == 2);
lineSeg = new LineSegment(-2.05, 92.9, 8.27, 103.0);
// DisplayGeometryGraph.ShowDebugCurves(new DebugCurve(100, 0.01, "black", lineSeg), new DebugCurve(100, 0.01, "blue", roundedRect));
ii = Curve.GetAllIntersections(lineSeg, roundedRect, true);
Assert.IsTrue(ii.Count == 0);
var d = 10 * (Math.Sqrt(2) - 1) * Math.Sqrt(2);
lineSeg = new LineSegment(d, 0, 0, d);
var seg =
roundedRect.Curve.Segments.Where(s => s is Ellipse).Select(s => (Ellipse)s).Where(
e => e.Center.X < 11 && e.Center.Y < 11).First();
// DisplayGeometryGraph.ShowDebugCurves(new DebugCurve(100, 0.01, "black", lineSeg), new DebugCurve(100, 0.01, "blue", seg));
ii = Curve.GetAllIntersections(lineSeg, seg, true);
Assert.IsTrue(ii.Count == 1);
}
static void Main(string[] args)
{
#if TEST
Microsoft.Msagl.GraphViewerGdi.DisplayGeometryGraph.SetShowFunctions();
#endif
//define a polygone
var polygon=new Polyline(new []{new Point(0,0), new Point(7,8), new Point(7,7), new Point(8,8), new Point(5,0)}){Closed=true};
var point = new Point(3, 3);
var ellipse = new Ellipse(0.5, 0.5, point);//just to show the point
//showing the polygon and the ellipse with the center at the point
#if TEST
LayoutAlgorithmSettings.Show(polygon, ellipse);
#endif
// prints out the location of the point relative ot the polygon
Console.WriteLine(Curve.PointRelativeToCurveLocation(point, polygon));
//=====================================================================//
// find out if one curve intersects another
var polygon0 = new Polyline(new[] { new Point(7.041886, 4.683227), new Point(7.102811, 5.797279), new Point(8.303899, 6.467452), new Point(8.547598, 5.1097) }) { Closed = true };
#if TEST
LayoutAlgorithmSettings.Show(polygon, polygon0);
#endif
if (PolylinesIntersect(polygon0, polygon))
Console.WriteLine("intersects");
else
Console.WriteLine("do not intersects");
(polygon0 as ICurve).Translate(new Point(1, 0));
#if TEST
LayoutAlgorithmSettings.Show(polygon, polygon0);
#endif
if (PolylinesIntersect(polygon0, polygon))
Console.WriteLine("intersect");
else
Console.WriteLine("do not intersect");
}
static ParallelogramNodeOverICurve CreateNodeWithSegmentSplit(double start, double end, Ellipse seg, double eps)
{
var pBNode = new ParallelogramInternalTreeNode(seg, eps);
pBNode.AddChild(CreateParallelogramNodeForCurveSeg(start, 0.5 * (start + end), seg, eps));
pBNode.AddChild(CreateParallelogramNodeForCurveSeg(0.5 * (start + end), end, seg, eps));
var boxes = new List <Parallelogram>();
boxes.Add(pBNode.Children[0].Parallelogram);
boxes.Add(pBNode.Children[1].Parallelogram);
pBNode.Parallelogram = Parallelogram.GetParallelogramOfAGroup(boxes);
return(pBNode);
}
public static float EllipseSweepAngle(Ellipse el) {
return (float)((el.ParEnd - el.ParStart) / Math.PI * 180);
}
private void WriteEllipse(Shape shape, Ellipse ellipse)
{
this.outputFileWriter.WriteLine(RectFileStrings.BeginEllipse);
this.outputFileWriter.WriteLine(RectFileStrings.WriteId, shapeToIdMap[shape]);
this.outputFileWriter.WriteLine(
RectFileStrings.WriteEllipse,
ellipse.AxisA.X,
ellipse.AxisA.Y,
ellipse.AxisB.X,
ellipse.AxisB.Y,
ellipse.Center.X,
ellipse.Center.Y);
this.outputFileWriter.WriteLine(RectFileStrings.EndEllipse);
}
static ParallelogramNodeOverICurve CreateParallelogramNodeForCurveSeg(Ellipse seg)
{
return(CreateParallelogramNodeForCurveSeg(seg.ParStart, seg.ParEnd, seg,
ParallelogramNodeOverICurve.DefaultLeafBoxesOffset));
}
static void WriteEllepticalArc(Ellipse ellipse) {
// ReSharper restore UnusedParameter.Local
throw new NotImplementedException();
}
string EllipseRadiuses(Ellipse ellipse) {
return DoubleToString(ellipse.AxisA.Length) + "," + DoubleToString(ellipse.AxisB.Length);
}
internal static ParallelogramNodeOverICurve CreateParallelogramNodeForCurveSeg(double start, double end,
Ellipse seg, double eps){
bool closedSeg = (start == seg.ParStart && end == seg.ParEnd && ApproximateComparer.Close(seg.Start, seg.End));
if(closedSeg)
return CreateNodeWithSegmentSplit(start, end, seg, eps);
Point s = seg[start];
Point e = seg[end];
Point w = e - s;
Point middle = seg[(start + end) / 2];
if (ParallelogramNodeOverICurve.DistToSegm(middle, s, e) <= ApproximateComparer.IntersectionEpsilon &&
w * w < Curve.LineSegmentThreshold * Curve.LineSegmentThreshold && end - start < Curve.LineSegmentThreshold) {
var ls = new LineSegment(s, e);
var leaf = ls.ParallelogramNodeOverICurve as ParallelogramLeaf;
leaf.Low = start;
leaf.High = end;
leaf.Seg = seg;
leaf.Chord = ls;
return leaf;
}
bool we = WithinEpsilon(seg, start, end, eps);
var box = new Parallelogram();
if(we && CreateParallelogramOnSubSeg(start, end, seg, ref box)){
return new ParallelogramLeaf(start, end, box, seg, eps);
} else{
return CreateNodeWithSegmentSplit(start, end, seg, eps);
}
}
static float EllipseStandardAngle(Ellipse ellipse, double angle)
{
MsaglPoint p = Math.Cos(angle) * ellipse.AxisA + Math.Sin(angle) * ellipse.AxisB;
return (float)Math.Atan2(p.Y, p.X) * toDegrees;
}
static float EllipseSweepAngle(Ellipse el)
{
float sweepAngle = (float)(el.ParEnd - el.ParStart) * toDegrees;
if (!OrientedCounterClockwise(el))
sweepAngle = -sweepAngle;
return sweepAngle;
}
ICurve ReadEllepticalArc(CurveStream curveStream, ref Point currentPoint) {
/*
var rx = "A"+DoubleToString(ellipse.AxisA.Length);
var ry = DoubleToString(ellipse.AxisB.Length);
var xAxisRotation = DoubleToString(180*Point.Angle(new Point(1, 0), ellipse.AxisA)/Math.PI);
var largeArcFlag = Math.Abs(ellipse.ParEnd - ellipse.ParStart) >= Math.PI ? "1" : "0";
var sweepFlag = ellipse.ParEnd > ellipse.ParStart ? "1" : "0"; //it happens because of the y-axis orientation down in SVG
var endPoint=PointToString(ellipse.End);
return string.Join(" ", new[] {rx, ry, xAxisRotation, largeArcFlag, sweepFlag, endPoint});
var endPoint = GetCurveDataPoint(curveStream);
*/
var rx = GetNextDoubleFromCurveData(curveStream);
var ry = GetNextDoubleFromCurveData(curveStream);
var xAxisRotation = GetNextDoubleFromCurveData(curveStream)/180*Math.PI;
var largeArcFlag = (int) GetNextDoubleFromCurveData(curveStream);
var sweepFlag = (int) GetNextDoubleFromCurveData(curveStream);
var endPoint = GetNextPointFromCurveData(curveStream);
//figure out the transform to the circle
//then solve this problem on the circle
if (ApproximateComparer.Close(rx, 0) || ApproximateComparer.Close(ry, 0))
Error("ellipseArc radius is too small");
var yScale = rx/ry;
var rotationMatrix = PlaneTransformation.Rotation(-xAxisRotation);
var scaleMatrix = new PlaneTransformation(1, 0, 0, 0, yScale, 0);
var transform = scaleMatrix*rotationMatrix;
var start = transform*currentPoint;
currentPoint = endPoint;
var end = transform*endPoint;
Point center;
double startAngle;
double endAngle;
Point axisY;
GetArcCenterAndAngles(rx, largeArcFlag, sweepFlag, start, end, out center, out startAngle, out endAngle,
out axisY);
var inverted = transform.Inverse;
center = inverted*center;
var rotation = PlaneTransformation.Rotation(xAxisRotation);
var axisX = rotation*new Point(rx, 0);
axisY = rotation*(axisY/yScale);
var ret = new Ellipse(startAngle, endAngle, axisX, axisY, center);
Debug.Assert(ApproximateComparer.Close(ret.End, endPoint));
return ret;
}
static IList<IntersectionInfo> GetIntersectionsWithArrowheadCircle(ICurve curve, double arrowheadLength, Point circleCenter) {
Debug.Assert(arrowheadLength > 0);
var e = new Ellipse(arrowheadLength, arrowheadLength, circleCenter);
return Curve.GetAllIntersections(e, curve, true);
}
static void TryToAddPointToLineCircleCrossing(LineSegment lineSeg,
Ellipse ellipse, List<IntersectionInfo> ret, Point point, double segLength, Point lineDir) {
Point ds = point - lineSeg.Start;
Point de = point - lineSeg.End;
double t = ds*lineDir;
if (t < -ApproximateComparer.DistanceEpsilon)
return;
t = Math.Max(t, 0);
if (t > segLength + ApproximateComparer.DistanceEpsilon)
return;
t = Math.Min(t, segLength);
t /= segLength;
double angle = Point.Angle(ellipse.AxisA, point - ellipse.Center);
if (ellipse.ParStart - ApproximateComparer.Tolerance <= angle) {
angle = Math.Max(angle, ellipse.ParStart);
if (angle <= ellipse.ParEnd + ApproximateComparer.Tolerance) {
angle = Math.Min(ellipse.ParEnd, angle);
ret.Add(new IntersectionInfo(t, angle, point, lineSeg, ellipse));
}
}
}
static IList<IntersectionInfo> GetAllIntersectionsOfLineAndArc(LineSegment lineSeg, Ellipse ellipse) {
Point lineDir = lineSeg.End - lineSeg.Start;
var ret = new List<IntersectionInfo>();
double segLength = lineDir.Length;
if (segLength < ApproximateComparer.DistanceEpsilon) {
if (ApproximateComparer.Close((lineSeg.Start - ellipse.Center).Length, ellipse.AxisA.Length)) {
double angle = Point.Angle(ellipse.AxisA, lineSeg.Start - ellipse.Center);
if (ellipse.ParStart - ApproximateComparer.Tolerance <= angle) {
angle = Math.Max(angle, ellipse.ParStart);
if (angle <= ellipse.ParEnd + ApproximateComparer.Tolerance) {
angle = Math.Min(ellipse.ParEnd, angle);
ret.Add(new IntersectionInfo(0, angle, lineSeg.Start, lineSeg, ellipse));
}
}
}
return ret;
}
Point perp = lineDir.Rotate90Ccw()/segLength;
double segProjection = (lineSeg.Start - ellipse.Center)*perp;
Point closestPointOnLine = ellipse.Center + perp*segProjection;
double rad = ellipse.AxisA.Length;
double absSegProj = Math.Abs(segProjection);
if (rad < absSegProj - ApproximateComparer.DistanceEpsilon)
return ret; //we don't have an intersection
lineDir = perp.Rotate90Cw();
if (ApproximateComparer.Close(rad, absSegProj))
TryToAddPointToLineCircleCrossing(lineSeg, ellipse, ret, closestPointOnLine, segLength, lineDir);
else {
Debug.Assert(rad > absSegProj);
double otherLeg = Math.Sqrt(rad*rad - segProjection*segProjection);
TryToAddPointToLineCircleCrossing(lineSeg, ellipse, ret, closestPointOnLine + otherLeg*lineDir,
segLength, lineDir);
TryToAddPointToLineCircleCrossing(lineSeg, ellipse, ret, closestPointOnLine - otherLeg*lineDir,
segLength, lineDir);
}
return ret;
}
/// <summary>
/// this code only works for the standard ellipse
/// </summary>
/// <param name="ellipse"></param>
/// <returns></returns>
static Polyline RefineEllipse(Ellipse ellipse) {
Polyline rect = StandardRectBoundary(ellipse);
var dict = new SortedDictionary<double, Point>();
double a = Math.PI/4;
double w = ellipse.BoundingBox.Width;
double h = ellipse.BoundingBox.Height;
double l = Math.Sqrt(w*w + h*h);
for (int i = 0; i < 4; i++) {
double t = a + i*Math.PI/2; // parameter
Point p = ellipse[t]; //point on the ellipse
Point tan = l*(ellipse.Derivative(t).Normalize()); //make it long enough
var ls = new LineSegment(p - tan, p + tan);
//System.Diagnostics.Debug.Assert(ls.Start.X > -10000);
foreach (IntersectionInfo ix in GetAllIntersections(rect, ls, true))
dict[ix.Par0] = ix.IntersectionPoint;
}
Debug.Assert(dict.Count > 0);
return new Polyline(dict.Values) {Closed = true};
}
static bool IsFullEllipse(Ellipse ell) {
return ell.ParEnd == Math.PI * 2 && ell.ParStart == 0;
}
static bool OrientedCounterClockwise(Ellipse ellipse)
{
return ellipse.AxisA.X * ellipse.AxisB.Y - ellipse.AxisB.X * ellipse.AxisA.Y > 0;
}
string EllipseToString(Ellipse ellipse) {
string largeArc = Math.Abs(ellipse.ParEnd-ellipse.ParStart) >= Math.PI? "1":"0";
string sweepFlag= ellipse.OrientedCounterclockwise()?"1":"0";
return String.Join(" ", "A", EllipseRadiuses(ellipse), DoubleToString(Point.Angle(new Point(1, 0), ellipse.AxisA) / (Math.PI / 180.0)), largeArc, sweepFlag, PointsToString(ellipse.End));
}
static bool WithinEpsilon(Ellipse seg, double start, double end, double eps){
int n = 3; //hack !!!! but maybe can be proven for Bezier curves and other regular curves
double d = (end - start)/n;
Point s = seg[start];
Point e = seg[end];
double d0 = ParallelogramNodeOverICurve.DistToSegm(seg[start + d], s, e);
if(d0 > eps)
return false;
double d1 = ParallelogramNodeOverICurve.DistToSegm(seg[start + d*(n - 1)], s, e);
//double d1d1 = seg.d1(start) * seg.d1(end);
return d1 <= eps; // && d1d1 > 0;
}
static ParallelogramNodeOverICurve CreateNodeWithSegmentSplit(double start, double end, Ellipse seg, double eps){
var pBNode = new ParallelogramInternalTreeNode(seg, eps);
pBNode.AddChild(CreateParallelogramNodeForCurveSeg(start, 0.5*(start + end), seg, eps));
pBNode.AddChild(CreateParallelogramNodeForCurveSeg(0.5*(start + end), end, seg, eps));
var boxes = new List<Parallelogram>();
boxes.Add(pBNode.Children[0].Parallelogram);
boxes.Add(pBNode.Children[1].Parallelogram);
pBNode.Parallelogram = Parallelogram.GetParallelogramOfAGroup(boxes);
return pBNode;
}
void WriteEllipseInSvgStyle( Ellipse ellipse) {
if( ApproximateComparer.Close(ellipse.ParStart,0) && ApproximateComparer.Close(ellipse.ParEnd, 2*Math.PI)) { WriteFullEllipse(ellipse); }
else
{
WriteEllepticalArc(ellipse);
}
}
internal static bool CreateParallelogramOnSubSeg(double start, double end, Ellipse seg, ref Parallelogram box){
Point tan1 = seg.Derivative(start);
Point tan2 = seg.Derivative(end);
Point tan2Perp = Point.P(-tan2.Y, tan2.X);
Point corner = seg[start];
Point e = seg[end];
Point p = e - corner;
double numerator = p*tan2Perp;
double denumerator = (tan1*tan2Perp);
double x; // = (p * tan2Perp) / (tan1 * tan2Perp);
if(Math.Abs(numerator) < ApproximateComparer.DistanceEpsilon)
x = 0;
else if(Math.Abs(denumerator) < ApproximateComparer.DistanceEpsilon){
//it is degenerated; adjacent sides are parallel, but
//since p * tan2Perp is big it does not contain e
return false;
} else x = numerator/denumerator;
tan1 *= x;
box = new Parallelogram(corner, tan1, e - corner - tan1);
#if DEBUGCURVES
if (!box.Contains(seg[end]))
{
throw new InvalidOperationException();//"the box does not contain the end of the segment");
}
#endif
return true;
}
internal static ParallelogramNodeOverICurve CreateParallelogramNodeForCurveSeg(double start, double end,
Ellipse seg, double eps)
{
bool closedSeg = (start == seg.ParStart && end == seg.ParEnd && ApproximateComparer.Close(seg.Start, seg.End));
if (closedSeg)
{
return(CreateNodeWithSegmentSplit(start, end, seg, eps));
}
Point s = seg[start];
Point e = seg[end];
Point w = e - s;
Point middle = seg[(start + end) / 2];
if (ParallelogramNodeOverICurve.DistToSegm(middle, s, e) <= ApproximateComparer.IntersectionEpsilon &&
w * w < Curve.LineSegmentThreshold * Curve.LineSegmentThreshold && end - start < Curve.LineSegmentThreshold)
{
var ls = new LineSegment(s, e);
var leaf = ls.ParallelogramNodeOverICurve as ParallelogramLeaf;
leaf.Low = start;
leaf.High = end;
leaf.Seg = seg;
leaf.Chord = ls;
return(leaf);
}
bool we = WithinEpsilon(seg, start, end, eps);
var box = new Parallelogram();
if (we && CreateParallelogramOnSubSeg(start, end, seg, ref box))
{
return(new ParallelogramLeaf(start, end, box, seg, eps));
}
else
{
return(CreateNodeWithSegmentSplit(start, end, seg, eps));
}
}
static ParallelogramNodeOverICurve CreateParallelogramNodeForCurveSeg(Ellipse seg) {
return CreateParallelogramNodeForCurveSeg(seg.ParStart, seg.ParEnd, seg,
ParallelogramNodeOverICurve.DefaultLeafBoxesOffset);
}
public static double EllipseSweepAngle(MEllipse ellipse)
{
double sweepAngle = ellipse.ParEnd - ellipse.ParStart;
return(ellipse.OrientedCounterclockwise() ? sweepAngle : -sweepAngle);
}
void WriteFullEllipse(Ellipse ellipse) {
WriteStartElement(GeometryToken.Ellipse);
WriteAttribute(GeometryToken.Cx, ellipse.Center.X);
WriteAttribute(GeometryToken.Cy, ellipse.Center.Y);
WriteAttribute(GeometryToken.Rx, ellipse.AxisA.Length);
WriteAttribute(GeometryToken.Ry, ellipse.AxisB.Length);
WriteEndElement();
}
static Point CornerPoint(Ellipse ellipse) {
return ellipse.Center + ellipse.AxisA + ellipse.AxisB;
}
string EllipticalArcToString(Ellipse ellipse) {
/*
* rx ry x-axis-rotation large-arc-flag sweep-flag x y
* */
//In general in an Msagl ellipse the axes don't have to be orthogonal: we have a possible bug here
var rx = "A"+DoubleToString(ellipse.AxisA.Length);
var ry = DoubleToString(ellipse.AxisB.Length);
var xAxisRotation = DoubleToString(180*Point.Angle(new Point(1, 0), ellipse.AxisA)/Math.PI);
var largeArcFlag = Math.Abs(ellipse.ParEnd - ellipse.ParStart) >= Math.PI ? "1" : "0";
var sweepFlagInt = ellipse.ParEnd > ellipse.ParStart ? 1 : 0; //it happens because of the y-axis orientation down in SVG
if (AxesSwapped(ellipse.AxisA, ellipse.AxisB)) {
sweepFlagInt = sweepFlagInt == 1 ? 0 : 1;
}
var endPoint=PointToString(ellipse.End);
return string.Join(" ", new[] {rx, ry, xAxisRotation, largeArcFlag, sweepFlagInt.ToString(), endPoint});
}
private static bool EllipseIsAlmostLineSegment(Ellipse ellipse) {
return ellipse.AxisA.LengthSquared < 0.0001 || ellipse.AxisB.LengthSquared<0.0001;
}
public static float EllipseStartAngle(Ellipse el) {
return (float)(el.ParStart / Math.PI * 180);
}
private static IEnumerable<Ellipse> GetFittedArcSegs(double radius, Point[] polyline) {
Point leg = polyline[1] - polyline[0];
Point dir = leg.Normalize();
double rad0 = Math.Min(radius, leg.Length/2);
for (int i = 1; i < polyline.Length - 1; i++) {
Ellipse ret = null;
leg = polyline[i + 1] - polyline[i];
double legLength = leg.Length;
if (legLength < ApproximateComparer.IntersectionEpsilon)
ret = new Ellipse(0, 0, polyline[i]);
Point ndir = leg/legLength;
if (Math.Abs(ndir*dir) > 0.9) //the polyline does't make a 90 degrees turn
ret = new Ellipse(0, 0, polyline[i]);
double nrad0 = Math.Min(radius, leg.Length/2);
Point axis0 = -nrad0*ndir;
Point axis1 = rad0*dir;
yield return ret ?? (new Ellipse(0, Math.PI/2, axis0, axis1, polyline[i] - axis1 - axis0));
dir = ndir;
rad0 = nrad0;
}
}
/// <summary>
/// returns the arc that a,b,c touches
/// </summary>
/// <param name="a">belongs to the arc, the tangent point of ba</param>
/// <param name="b">ba, and bc are tangents to the arc</param>
/// <param name="c">belongs to the arc, the tangent point of bc</param>
/// <returns></returns>
internal static ICurve ArcOn(Point a, Point b, Point c) {
Point center;
if (Math.Abs(Point.SignedDoubledTriangleArea(a, b, c)) < 0.0001 || !FindArcCenter(a, b, c, out center))
return new LineSegment(a, c);
var radius = (a - center).Length;
var chordLength = (a - b).Length;
if (chordLength / radius < 0.0001)//to avoid a floating point error
return new LineSegment(a, c);
var cenA = a - center;
var aAngle = Math.Atan2(cenA.Y, cenA.X);
var cenC = c - center;
var cAngle = Math.Atan2(cenC.Y, cenC.X);
var delac = cAngle - aAngle;
if (delac < 0) {
delac += 2 * Math.PI;
cAngle += 2 * Math.PI;
}
if (delac <= Math.PI) {
//going ccw
var el = new Ellipse(aAngle, cAngle, new Point(radius, 0), new Point(0, radius), center);
return el;
}
//going clockwise
if (cAngle > 2 * Math.PI)
cAngle -= 2 * Math.PI;
aAngle = Math.PI - aAngle;
cAngle = Math.PI - cAngle;
if (aAngle < 0)
aAngle += 2 * Math.PI;
while (cAngle < aAngle)
cAngle += 2 * Math.PI;
delac = cAngle - aAngle;
Debug.Assert(delac <= Math.PI);
return new Ellipse(aAngle, cAngle, new Point(-radius, 0), new Point(0, radius), center);
}
public static double EllipseSweepAngle(Ellipse ellipse) {
double sweepAngle = ellipse.ParEnd - ellipse.ParStart;
return ellipse.OrientedCounterclockwise() ? sweepAngle : -sweepAngle;
}