/***************************************************/
/**** Split curve at points ****/
/***************************************************/
public static List <Arc> SplitAtPoints(this Arc arc, List <Point> points, double tolerance = Tolerance.Distance)
{
if (!points.Any())
{
return new List <Arc> {
arc.DeepClone()
}
}
;
List <Arc> result = new List <Arc>();
List <Point> cPts = new List <Point>();
Vector normal = arc.Normal();
foreach (Point point in points)
{
if (point.IsOnCurve(arc, tolerance))
{
cPts.Add(point);
}
}
cPts.Add(arc.StartPoint());
cPts.Add(arc.EndPoint());
cPts = cPts.CullDuplicates(tolerance);
cPts = cPts.SortAlongCurve(arc, tolerance);
if (arc.EndAngle - 2 * Math.PI < tolerance && arc.EndAngle - 2 * Math.PI > -tolerance)
{
cPts.Add(arc.EndPoint());
}
if (cPts.Count > 2)
{
Double startAng = arc.StartAngle;
Double endAng = arc.EndAngle;
Double tmpAng = 0;
Arc tmpArc;
for (int i = 1; i < cPts.Count; i++)
{
tmpArc = arc.DeepClone();
tmpArc.StartAngle = startAng;
tmpAng = (2 * Math.PI + (cPts[i - 1] - arc.Centre()).SignedAngle(cPts[i] - arc.Centre(), normal)) % (2 * Math.PI);
endAng = startAng + tmpAng;
tmpArc.EndAngle = endAng;
result.Add(tmpArc);
startAng = endAng;
}
}
else
{
result.Add(arc.DeepClone());
}
return(result);
}
/***************************************************/
/**** Public Methods - Curves ****/
/***************************************************/
public static Point ClosestPoint(this Arc curve, Point point, double tolerance = Tolerance.Distance)
{
if (point.SquareDistance(curve.Centre()) <= tolerance * tolerance)
{
return(curve.StartPoint());
}
Point center = curve.Centre();
Point midPoint = curve.PointAtParameter(0.5);
Plane p = curve.FitPlane();
Point onCircle = center + (point.Project(p) - center).Normalise() * curve.Radius;
double sqrd = midPoint.SquareDistance(curve.StartPoint());
return(midPoint.SquareDistance(onCircle) <= sqrd ? onCircle : onCircle.ClosestPoint(new List <Point> {
curve.StartPoint(), curve.EndPoint()
}));
}
/***************************************************/
/**** Public Methods - Curve / curve ****/
/***************************************************/
public static bool IsContaining(this Arc curve1, ICurve curve2, bool acceptOnEdge = true, double tolerance = Tolerance.Distance)
{
if (!curve1.IsClosed(tolerance))
{
return(false);
}
Circle circle = new Circle {
Centre = curve1.Centre(), Radius = curve1.Radius(), Normal = curve1.FitPlane().Normal
};
return(circle.IsContaining(curve2));
}
/***************************************************/
/**** Public Methods - Curve / points ****/
/***************************************************/
public static bool IsContaining(this Arc curve, List <Point> points, bool acceptOnEdge = true, double tolerance = Tolerance.Distance)
{
if (!curve.IsClosed(tolerance))
{
return(false);
}
Circle circle = new Circle {
Centre = curve.Centre(), Radius = curve.Radius(), Normal = curve.FitPlane().Normal
};
return(circle.IsContaining(points, acceptOnEdge, tolerance));
}
/***************************************************/
/**** Public Methods - Curves ****/
/***************************************************/
public static Point ClosestPoint(this Arc arc, Point point)
{
Point center = arc.Centre();
Point midPoint = arc.PointAtParameter(0.5);
Plane p = arc.FitPlane();
Point onCircle = center + (point.Project(p) - center).Normalise() * arc.Radius;
double sqrd = midPoint.SquareDistance(arc.StartPoint());
return(midPoint.SquareDistance(onCircle) <= sqrd ? onCircle : onCircle.ClosestPoint(new List <Point> {
arc.StartPoint(), arc.EndPoint()
}));
}
/***************************************************/
public static List <Point> LineIntersections(this Arc arc, Line line, bool useInfiniteLine = false, double tolerance = Tolerance.Distance)
{
Line l = line.DeepClone();
l.Infinite = useInfiniteLine ? true : l.Infinite;
List <Point> iPts = new List <Point>();
Point midPoint = arc.PointAtParameter(0.5);
Point center = arc.Centre();
//Check if curves are coplanar
if (Math.Abs(arc.CoordinateSystem.Z.DotProduct(l.Direction())) > Tolerance.Angle)
{
//Curves not coplanar
Point pt = l.PlaneIntersection((Plane)arc.CoordinateSystem);
if (pt != null && Math.Abs(pt.Distance(center) - arc.Radius) <= tolerance)
{
iPts.Add(pt);
}
}
else
{
//Curves coplanar
Circle c = new Circle {
Centre = center, Normal = arc.CoordinateSystem.Z, Radius = arc.Radius
};
iPts = c.LineIntersections(l);
}
List <Point> output = new List <Point>();
double halfAngle = arc.Angle() / 2;
double tolAngle = tolerance / arc.Radius;
double sqrd = 2 * Math.Pow(arc.Radius, 2) * (1 - Math.Cos(Math.Abs(halfAngle + tolAngle))); // Cosine rule
{
foreach (Point pt in iPts)
{
if ((l.Infinite || pt.Distance(l) <= tolerance) && midPoint.SquareDistance(pt) <= sqrd)
{
output.Add(pt);
}
}
}
return(output);
}
/***************************************************/
/**** Public Methods - Curves ****/
/***************************************************/
public static NurbsCurve ToNurbsCurve(this Arc arc)
{
{
double angle = arc.EndAngle - arc.StartAngle;
Point centre = arc.Centre();
int nbPts = 1 + 2 * (int)Math.Ceiling(2 * angle / Math.PI);
double factor = Math.Cos(angle / (nbPts - 1));
// Create the points
List <Point> points = new List <Point>();
for (int i = 0; i < nbPts; i++)
{
double t = i * 1.0 / (nbPts - 1);
Point pt = arc.PointAtParameter(t);
if (i % 2 == 1)
{
pt = centre + (pt - centre) / factor;
}
points.Add(pt);
}
// Create the knots
double knotStep = 2.0 / (nbPts - 1);
List <double> knots = new List <double>();
for (int i = 0; i < (nbPts + 1) / 2; i++)
{
knots.Add(i * knotStep);
knots.Add(i * knotStep);
}
// Create the weights
List <double> weights = new List <double>();
for (int i = 0; i < nbPts; i++)
{
double w = (i % 2 == 0) ? 1.0 : factor;
weights.Add(w);
}
return(new NurbsCurve {
ControlPoints = points, Knots = knots, Weights = weights
});
}
}
/***************************************************/
public static Output <Point, Point> CurveProximity(this Arc curve1, Circle curve2, double tolerance = Tolerance.Distance)
{
List <Point> cIntersections = curve1.CurveIntersections(curve2);
if (cIntersections.Count > 0)
{
return new Output <Point, Point> {
Item1 = cIntersections[0], Item2 = cIntersections[0]
}
}
;
Output <Point, Point> result = new Output <Point, Point>();
Plane ftPln1 = curve1.FitPlane();
Plane ftPln2 = curve2.FitPlane();
List <Point> intPts = new List <Point>();
Point tmp = null;
if ((intPts = curve1.PlaneIntersections(ftPln2)).Count != 0)
{
if (intPts.Count == 1)
{
tmp = intPts[0];
}
else
{
if (intPts[0].Distance(curve2) < intPts[1].Distance(curve2))
{
tmp = intPts[0];
}
else
{
tmp = intPts[1];
}
}
}
else if ((intPts = curve2.PlaneIntersections(ftPln1)).Count != 0)
{
if (intPts.Count == 1)
{
if (tmp == null)
{
tmp = intPts[0];
}
else if (tmp.Distance(curve2) > intPts[0].Distance(curve1))
{
tmp = intPts[0];
}
}
else
{
if (intPts[0].Distance(curve1) < intPts[1].Distance(curve1))
{
if (tmp == null)
{
tmp = intPts[0];
}
else if (tmp.Distance(curve2) > intPts[0].Distance(curve1))
{
tmp = intPts[0];
}
}
else
{
if (tmp == null)
{
tmp = intPts[1];
}
else if (tmp.Distance(curve2) > intPts[1].Distance(curve1))
{
tmp = intPts[1];
}
}
}
}
Output <Point, Point> oldresult = new Output <Point, Point>();
Output <Point, Point> oldresult2 = new Output <Point, Point>();
Output <Point, Point> result2 = new Output <Point, Point>();
if (tmp != null)
{
if (tmp.IsOnCurve(curve1))
{
result.Item1 = tmp;
result.Item2 = curve2.ClosestPoint(result.Item1);
}
else
{
result.Item2 = tmp;
result.Item1 = curve1.ClosestPoint(result.Item2);
}
do
{
oldresult.Item1 = result.Item1;
oldresult.Item2 = result.Item2;
result.Item1 = curve2.ClosestPoint(result.Item2);
result.Item2 = curve1.ClosestPoint(result.Item1);
}while (oldresult.Item2.Distance(result.Item2) > tolerance * tolerance && oldresult.Item1.Distance(result.Item1) > tolerance * tolerance);
}
else
{
Line intersect = new Line {
Start = curve1.Centre(), End = curve2.Centre
};
Point tmp1 = intersect.CurveProximity(curve1).Item1;
Point tmp2 = intersect.CurveProximity(curve2).Item1;
if (tmp == null)
{
tmp = tmp1;
}
if (tmp1.Distance(curve2) < tmp.Distance(curve1) || tmp1.Distance(curve2) < tmp.Distance(curve2))
{
tmp = tmp1;
}
if (tmp2.Distance(curve1) < tmp.Distance(curve1) || tmp2.Distance(curve1) < tmp.Distance(curve2))
{
tmp = tmp2;
}
if (tmp.IsOnCurve(curve1))
{
result.Item1 = tmp;
result.Item2 = curve2.ClosestPoint(tmp);
}
else
{
result.Item2 = tmp;
result.Item1 = curve1.ClosestPoint(tmp);
}
do
{
oldresult.Item1 = result.Item1;
oldresult.Item2 = result.Item2;
result.Item1 = curve2.ClosestPoint(result.Item2);
result.Item2 = curve1.ClosestPoint(result.Item1);
}while (oldresult.Item2.Distance(result.Item2) > tolerance * tolerance && oldresult.Item1.Distance(result.Item1) > tolerance * tolerance);
}
if (curve1.EndPoint().Distance(curve2.ClosestPoint(curve1.EndPoint())) < result.Item1.Distance(result.Item2))
{
result.Item1 = curve1.EndPoint();
result.Item2 = curve2.ClosestPoint(result.Item1);
}
if (curve1.StartPoint().Distance(curve2.ClosestPoint(curve1.StartPoint())) < result.Item1.Distance(result.Item2))
{
result.Item1 = curve1.StartPoint();
result.Item2 = curve2.ClosestPoint(result.Item1);
}
tmp = curve1.PointAtParameter((curve1.ParameterAtPoint(result.Item1) + 0.6) % 1);
result2.Item1 = tmp;
result2.Item2 = curve2.ClosestPoint(tmp);
do
{
oldresult2.Item1 = result2.Item1;
oldresult2.Item2 = result2.Item2;
result2.Item1 = curve2.ClosestPoint(result2.Item2);
result2.Item2 = curve1.ClosestPoint(result2.Item1);
}while (oldresult2.Item2.Distance(result2.Item2) > tolerance * tolerance && oldresult2.Item1.Distance(result2.Item1) > tolerance * tolerance);
if (result.Item1.Distance(result.Item2) > result2.Item1.Distance(result2.Item2))
{
result = result2;
}
return(result);
}
/***************************************************/
public static Output <Point, Point> CurveProximity(this Arc curve1, Arc curve2, double tolerance = Tolerance.Distance)
{
List <Point> cIntersections = curve1.CurveIntersections(curve2);
if (cIntersections.Count > 0)
{
return new Output <Point, Point> {
Item1 = cIntersections[0], Item2 = cIntersections[0]
}
}
;
Output <Point, Point> result = new Output <Point, Point>();
Output <Point, Point> oldresult = new Output <Point, Point>();
Output <Point, Point> result2 = new Output <Point, Point>();
Output <Point, Point> result3 = new Output <Point, Point>();
Output <Point, Point> result4 = new Output <Point, Point>();
Output <Point, Point> result5 = new Output <Point, Point>();
Output <Point, Point> result6 = new Output <Point, Point>();
Plane ftPln1 = curve1.FitPlane();
Plane ftPln2 = curve2.FitPlane();
List <Point> fitPoints = new List <Point>();
bool check = false;
if ((fitPoints = curve1.PlaneIntersections(ftPln2)).Count > 0)
{
if (fitPoints.Count == 1)
{
result.Item1 = fitPoints[0];
result.Item2 = curve2.ClosestPoint(fitPoints[0]);
check = true;
}
else if (fitPoints.Count > 1)
{
if (fitPoints[0].Distance(curve2) < fitPoints[1].Distance(curve2))
{
result.Item1 = fitPoints[0];
result.Item2 = curve2.ClosestPoint(fitPoints[0]);
check = true;
}
else
{
result.Item1 = fitPoints[1];
result.Item2 = curve2.ClosestPoint(fitPoints[1]);
check = true;
}
}
}
if ((fitPoints = curve2.PlaneIntersections(ftPln1)).Count > 0)
{
if (check)
{
if (fitPoints.Count == 1 && (fitPoints[0].Distance(curve1) < result.Item1.Distance(curve2)))
{
result.Item2 = fitPoints[0];
result.Item1 = curve1.ClosestPoint(fitPoints[0]);
}
else if (fitPoints.Count > 1)
{
if (fitPoints[0].Distance(curve1) < fitPoints[1].Distance(curve1))
{
if (fitPoints[0].Distance(curve1) < result.Item1.Distance(curve2))
{
result.Item2 = fitPoints[0];
result.Item1 = curve1.ClosestPoint(fitPoints[0]);
}
}
else
{
if (fitPoints[1].Distance(curve1) < result.Item1.Distance(curve2))
{
result.Item2 = fitPoints[1];
result.Item1 = curve1.ClosestPoint(fitPoints[1]);
}
}
}
}
else if (fitPoints.Count == 1)
{
result.Item2 = fitPoints[0];
result.Item1 = curve1.ClosestPoint(fitPoints[0]);
check = true;
}
else if (fitPoints.Count > 1)
{
if (fitPoints[0].Distance(curve1) < fitPoints[1].Distance(curve1))
{
result.Item2 = fitPoints[0];
result.Item1 = curve1.ClosestPoint(fitPoints[0]);
check = true;
}
else
{
result.Item2 = fitPoints[1];
result.Item1 = curve1.ClosestPoint(fitPoints[1]);
check = true;
}
}
}
if (check)
{
do
{
oldresult.Item1 = result.Item1;
oldresult.Item2 = result.Item2;
result.Item1 = curve2.ClosestPoint(result.Item2);
result.Item2 = curve1.ClosestPoint(result.Item1);
}while (oldresult.Item2.Distance(result.Item2) > tolerance * tolerance && oldresult.Item1.Distance(result.Item1) > tolerance * tolerance);
}
check = false;
Line intersect = new Line {
Start = curve1.Centre(), End = curve2.Centre()
};
Point tmp1 = intersect.CurveProximity(curve1).Item2;
Point tmp2 = intersect.CurveProximity(curve2).Item2;
if (tmp1.Distance(curve2) < tmp2.Distance(curve1))
{
result2.Item1 = tmp1;
result2.Item2 = curve2.ClosestPoint(tmp1);
}
else
{
result2.Item2 = tmp2;
result2.Item1 = curve1.ClosestPoint(tmp2);
}
do
{
oldresult.Item1 = result2.Item1;
oldresult.Item2 = result2.Item2;
result2.Item1 = curve2.ClosestPoint(result2.Item2);
result2.Item2 = curve1.ClosestPoint(result2.Item1);
}while (oldresult.Item2.Distance(result2.Item2) > tolerance * tolerance && oldresult.Item1.Distance(result2.Item1) > tolerance * tolerance);
if (curve1.EndPoint().Distance(curve2.ClosestPoint(curve1.EndPoint())) < curve1.StartPoint().Distance(curve2.ClosestPoint(curve1.StartPoint())))
{
result3.Item1 = curve1.EndPoint();
result3.Item2 = curve2.ClosestPoint(result3.Item1);
}
else
{
result3.Item1 = curve1.StartPoint();
result3.Item2 = curve2.ClosestPoint(result3.Item1);
}
if (curve2.EndPoint().Distance(curve1.ClosestPoint(curve2.EndPoint())) < curve2.StartPoint().Distance(curve1.ClosestPoint(curve2.StartPoint())))
{
result4.Item2 = curve2.EndPoint();
result4.Item1 = curve1.ClosestPoint(result4.Item2);
}
else
{
result4.Item2 = curve2.StartPoint();
result4.Item1 = curve1.ClosestPoint(result4.Item2);
}
do
{
oldresult.Item1 = result3.Item1;
oldresult.Item2 = result3.Item2;
result3.Item1 = curve2.ClosestPoint(result3.Item2);
result3.Item2 = curve1.ClosestPoint(result3.Item1);
}while (oldresult.Item2.Distance(result3.Item2) > tolerance * tolerance && oldresult.Item1.Distance(result3.Item1) > tolerance * tolerance);
do
{
oldresult.Item1 = result4.Item1;
oldresult.Item2 = result4.Item2;
result4.Item1 = curve2.ClosestPoint(result4.Item2);
result4.Item2 = curve1.ClosestPoint(result4.Item1);
}while (oldresult.Item2.Distance(result4.Item2) > tolerance * tolerance && oldresult.Item1.Distance(result4.Item1) > tolerance * tolerance);
result5.Item2 = curve2.PointAtParameter(0.5);
result5.Item1 = curve1.ClosestPoint(result5.Item2);
result6.Item1 = curve1.PointAtParameter(0.5);
result6.Item2 = curve2.ClosestPoint(result6.Item1);
do
{
oldresult.Item1 = result5.Item1;
oldresult.Item2 = result5.Item2;
result5.Item1 = curve2.ClosestPoint(result5.Item2);
result5.Item2 = curve1.ClosestPoint(result5.Item1);
}while (oldresult.Item2.Distance(result5.Item2) > tolerance * tolerance && oldresult.Item1.Distance(result5.Item1) > tolerance * tolerance);
do
{
oldresult.Item1 = result6.Item1;
oldresult.Item2 = result6.Item2;
result6.Item1 = curve2.ClosestPoint(result6.Item2);
result6.Item2 = curve1.ClosestPoint(result6.Item1);
}while (oldresult.Item2.Distance(result6.Item2) > tolerance * tolerance && oldresult.Item1.Distance(result6.Item1) > tolerance * tolerance);
if (result.Item1 == null || result.Item2 == null)
{
result = result2;
}
if (result2.Item2.Distance(result2.Item1) < result.Item1.Distance(result.Item2))
{
result = result2;
}
if (result3.Item2.Distance(result3.Item1) < result.Item1.Distance(result.Item2))
{
result = result3;
}
if (result4.Item2.Distance(result4.Item1) < result.Item1.Distance(result.Item2))
{
result = result4;
}
if (result5.Item2.Distance(result5.Item1) < result.Item1.Distance(result.Item2))
{
result = result5;
}
if (result6.Item2.Distance(result6.Item1) < result.Item1.Distance(result.Item2))
{
result = result6;
}
return(result);
}
/***************************************************/
public static Output <Point, Point> CurveProximity(this Line curve1, Arc curve2, double tolerance = Tolerance.Distance)
{
List <Point> cIntersections = curve1.CurveIntersections(curve2);
if (cIntersections.Count > 0)
{
return new Output <Point, Point> {
Item1 = cIntersections[0], Item2 = cIntersections[0]
}
}
;
List <Point> plnPts = new List <Point>();
plnPts.Add(curve1.Start);
plnPts.Add(curve1.End);
plnPts.Add(curve2.Centre());
Point tmp;
Plane ftPln = plnPts.FitPlane();
if (ftPln != null)
{
List <Point> intersecting = curve2.PlaneIntersections(ftPln);
if (intersecting.Count > 1)
{
if (intersecting[0].Distance(curve1) < intersecting[1].Distance(curve1))
{
tmp = intersecting[0];
}
else
{
tmp = intersecting[1];
}
}
else if (intersecting.Count == 1)
{
tmp = intersecting[0];
}
else
{
tmp = curve2.StartPoint();
}
}
else
{
tmp = curve2.StartPoint();
}
if (curve2.StartPoint().Distance(curve1) < tmp.Distance(curve1))
{
tmp = curve2.StartPoint();
}
if (curve2.EndPoint().Distance(curve1) < tmp.Distance(curve1))
{
tmp = curve2.EndPoint();
}
Line prLn = curve1.Project(curve2.FitPlane());
List <Point> lnInt = prLn.CurveIntersections(curve2);
if (lnInt.Count > 0)
{
if (lnInt.Count > 1)
{
if (lnInt[0].Distance(curve1) > lnInt[0].Distance(curve1))
{
lnInt[0] = lnInt[1];
}
}
if (lnInt[0].Distance(curve1) < tmp.Distance(curve1))
{
tmp = lnInt[0];
}
}
Output <Point, Point> result = new Output <Point, Point>();
result.Item1 = curve1.ClosestPoint(tmp);
result.Item2 = curve2.ClosestPoint(result.Item1);
result.Item1 = curve1.ClosestPoint(result.Item2);
Output <Point, Point> oldfinal = new Output <Point, Point>();
Output <Point, Point> result2 = new Output <Point, Point>();
if (curve1.Start.Distance(curve2) < curve1.End.Distance(curve2))
{
result2.Item1 = curve1.Start;
}
else
{
result2.Item1 = curve1.End;
}
result2.Item2 = curve2.ClosestPoint(result2.Item1);
result2.Item1 = curve1.ClosestPoint(result2.Item2);
Output <Point, Point> final = new Output <Point, Point>();
if (result.Item1.Distance(result.Item2) < result2.Item1.Distance(result2.Item2))
{
final = result;
}
else
{
final = result2;
}
do
{
oldfinal.Item1 = final.Item1;
oldfinal.Item2 = final.Item2;
final.Item2 = curve2.ClosestPoint(final.Item1);
final.Item1 = curve1.ClosestPoint(final.Item2);
}while (Math.Abs(oldfinal.Item1.Distance(oldfinal.Item2) - final.Item1.Distance(final.Item2)) > tolerance * tolerance);
return(final);
}