/// <summary>
/// Constructs a nurbs curve representation of this arc.<br/>
/// <em>Implementation of Algorithm A7.1 from The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <returns>A nurbs curve shaped like this arc.</returns>
internal void ToNurbs()
{
Vector3 axisX = Plane.XAxis;
Vector3 axisY = Plane.YAxis;
double curveAngle = _domain.Length;
int numberOfArc;
Point3[] pts;
Point4[] ctrPts;
double[] weights;
// Number of arcs.
double piNum = 0.5 * Math.PI;
if ((curveAngle - piNum) <= GSharkMath.Epsilon)
{
numberOfArc = 1;
pts = new Point3[3];
ctrPts = new Point4[3];
weights = new double[3];
}
else if ((curveAngle - piNum * 2) <= GSharkMath.Epsilon)
{
numberOfArc = 2;
pts = new Point3[5];
ctrPts = new Point4[5];
weights = new double[5];
}
else if ((curveAngle - piNum * 3) <= GSharkMath.Epsilon)
{
numberOfArc = 3;
pts = new Point3[7];
ctrPts = new Point4[7];
weights = new double[7];
}
else
{
numberOfArc = 4;
pts = new Point3[9];
ctrPts = new Point4[9];
weights = new double[9];
}
double detTheta = curveAngle / numberOfArc;
double weight = Math.Cos(detTheta / 2);
Point3 p0 = Center + (axisX * (Radius * Math.Cos(_domain.T0)) + axisY * (Radius * Math.Sin(_domain.T0)));
Vector3 t0 = axisY * Math.Cos(_domain.T0) - axisX * Math.Sin(_domain.T0);
KnotVector knots = new KnotVector(CollectionHelpers.RepeatData(0.0, ctrPts.Length + 3));
int index = 0;
double angle = _domain.T0;
pts[0] = p0;
ctrPts[0] = new Point4(p0);
weights[0] = weight;
for (int i = 1; i < numberOfArc + 1; i++)
{
angle += detTheta;
Point3 p2 = Center + (axisX * (Radius * Math.Cos(angle)) + axisY * (Radius * Math.Sin(angle)));
ctrPts[index + 2] = new Point4(p2);
pts[index + 2] = p2;
weights[index + 2] = 1.0;
Vector3 t2 = (axisY * Math.Cos(angle)) - (axisX * Math.Sin(angle));
Line ln0 = new Line(p0, t0.Unitize() + p0);
Line ln1 = new Line(p2, t2.Unitize() + p2);
Intersect.LineLine(ln0, ln1, out _, out _, out double u0, out _);
Point3 p1 = p0 + (t0 * u0);
ctrPts[index + 1] = new Point4(p1, weight);
pts[index + 1] = p1;
weights[index + 1] = weight;
index += 2;
if (i >= numberOfArc)
{
continue;
}
p0 = p2;
t0 = t2;
}
int j = 2 * numberOfArc + 1;
for (int i = 0; i < 3; i++)
{
knots[i] = 0.0;
knots[i + j] = 1.0;
}
switch (numberOfArc)
{
case 2:
knots[3] = knots[4] = 0.5;
break;
case 3:
knots[3] = knots[4] = (double)1 / 3;
knots[5] = knots[6] = (double)2 / 3;
break;
case 4:
knots[3] = knots[4] = 0.25;
knots[5] = knots[6] = 0.5;
knots[7] = knots[8] = 0.75;
break;
}
Weights = weights.ToList();
Degree = 2;
Knots = knots;
ControlPoints = ctrPts.ToList();
ControlPointLocations = pts.ToList();
}
public virtual double ClosestParameter(Point3 pt)
{
return(Analyze.Curve.ClosestParameter(this, pt));
}
/// <summary>
/// Recursively search to find the horizon or lit set.
/// </summary>
private void SearchHorizon(List <Point3> points, Point3 point, int prevFaceIndex, int faceCount, Face face)
{
Assert(prevFaceIndex >= 0);
Assert(_litFaces.Contains(prevFaceIndex));
Assert(!_litFaces.Contains(faceCount));
Assert(_faces[faceCount].Equals(face));
_litFaces.Add(faceCount);
// Use prevFaceIndex to determine what the next face to search will
// be, and what edges we need to cross to get there. It's important
// that the search proceeds in counter-clockwise order from the
// previous face.
int nextFaceIndex0;
int nextFaceIndex1;
int edge0;
int edge1;
int edge2;
if (prevFaceIndex == face.Opposite0)
{
nextFaceIndex0 = face.Opposite1;
nextFaceIndex1 = face.Opposite2;
edge0 = face.Vertex2;
edge1 = face.Vertex0;
edge2 = face.Vertex1;
}
else if (prevFaceIndex == face.Opposite1)
{
nextFaceIndex0 = face.Opposite2;
nextFaceIndex1 = face.Opposite0;
edge0 = face.Vertex0;
edge1 = face.Vertex1;
edge2 = face.Vertex2;
}
else
{
Assert(prevFaceIndex == face.Opposite2);
nextFaceIndex0 = face.Opposite0;
nextFaceIndex1 = face.Opposite1;
edge0 = face.Vertex1;
edge1 = face.Vertex2;
edge2 = face.Vertex0;
}
if (!_litFaces.Contains(nextFaceIndex0))
{
Face oppositeFace = _faces[nextFaceIndex0];
double dist = PointFaceDistance(
point,
points[oppositeFace.Vertex0],
oppositeFace);
if (dist <= 0.0f)
{
_horizon.Add(new HorizonEdge
{
Face = nextFaceIndex0,
Edge0 = edge0,
Edge1 = edge1,
});
}
else
{
SearchHorizon(points, point, faceCount, nextFaceIndex0, oppositeFace);
}
}
if (!_litFaces.Contains(nextFaceIndex1))
{
Face oppositeFace = _faces[nextFaceIndex1];
double dist = PointFaceDistance(
point,
points[oppositeFace.Vertex0],
oppositeFace);
if (dist <= 0.0f)
{
_horizon.Add(new HorizonEdge
{
Face = nextFaceIndex1,
Edge0 = edge1,
Edge1 = edge2,
});
}
else
{
SearchHorizon(points, point, faceCount, nextFaceIndex1, oppositeFace);
}
}
}
/// <summary>
/// Start the search for the horizon.
///
/// The search is a DFS search that searches neighboring triangles in
/// a counter-clockwise fashion. When it find a neighbor which is not
/// lit, that edge will be a line on the horizon. If the search always
/// proceeds counter-clockwise, the edges of the horizon will be found
/// in counter-clockwise order.
///
/// The heart of the search can be found in the recursive
/// SearchHorizon() method, but the the first iteration of the search
/// is special, because it has to visit three neighbors (all the
/// neighbors of the initial triangle), while the rest of the search
/// only has to visit two (because one of them has already been
/// visited, the one you came from).
/// </summary>
private void FindHorizon(List <Point3> points, Point3 point, int fi, Face face)
{
// TODO should I use epsilon in the PointFaceDistance comparisons?
_litFaces.Clear();
_horizon.Clear();
_litFaces.Add(fi);
Assert(PointFaceDistance(point, points[face.Vertex0], face) > 0.0f);
// For the rest of the recursive search calls, we first check if the
// triangle has already been visited and is part of litFaces.
// However, in this first call we can skip that because we know it
// can't possibly have been visited yet, since the only thing in
// litFaces is the current triangle.
{
Face oppositeFace = _faces[face.Opposite0];
double dist = PointFaceDistance(
point,
points[oppositeFace.Vertex0],
oppositeFace);
if (dist <= 0.0f)
{
_horizon.Add(new HorizonEdge
{
Face = face.Opposite0,
Edge0 = face.Vertex1,
Edge1 = face.Vertex2,
});
}
else
{
SearchHorizon(points, point, fi, face.Opposite0, oppositeFace);
}
}
if (!_litFaces.Contains(face.Opposite1))
{
Face oppositeFace = _faces[face.Opposite1];
double dist = PointFaceDistance(
point,
points[oppositeFace.Vertex0],
oppositeFace);
if (dist <= 0.0f)
{
_horizon.Add(new HorizonEdge
{
Face = face.Opposite1,
Edge0 = face.Vertex2,
Edge1 = face.Vertex0,
});
}
else
{
SearchHorizon(points, point, fi, face.Opposite1, oppositeFace);
}
}
if (!_litFaces.Contains(face.Opposite2))
{
Face oppositeFace = _faces[face.Opposite2];
double dist = PointFaceDistance(
point,
points[oppositeFace.Vertex0],
oppositeFace);
if (dist <= 0.0f)
{
_horizon.Add(new HorizonEdge
{
Face = face.Opposite2,
Edge0 = face.Vertex0,
Edge1 = face.Vertex1,
});
}
else
{
SearchHorizon(points, point, fi, face.Opposite2, oppositeFace);
}
}
}
private Vector3 Normal(Point3 v0, Point3 v1, Point3 v2)
{
return(Vector3.CrossProduct(v1 - v0, v2 - v0).Unitize());
}
private double PointFaceDistance(Point3 point, Point3 pointOnFace, Face face)
{
return(Vector3.DotProduct(face.Normal, point - pointOnFace));
}