/// <summary>
/// Intersection of circle with plane.
/// Returns 'null' (no intersection) or object of type 'Circle3d', 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Plane3d s)
{
if (this.Normal.IsParallelTo(s.Normal))
{
if (this.Center.BelongsTo(s))
{
// coplanar objects
return(this.Copy());
}
else
{
// parallel objects
return(null);
}
}
else
{
Line3d l = (Line3d)s.IntersectionWith(new Plane3d(this.Center, this.Normal));
Coord3d local_coord = new Coord3d(this.Center, l.Direction, this.Normal.Cross(l.Direction));
Point3d p = l.Point.ConvertTo(local_coord);
if (GeometRi3D.Greater(Abs(p.Y), this.R))
{
return(null);
}
else if (GeometRi3D.AlmostEqual(p.Y, this.R))
{
return(new Point3d(0, this.R, 0, local_coord));
}
else if (GeometRi3D.AlmostEqual(p.Y, -this.R))
{
return(new Point3d(0, -this.R, 0, local_coord));
}
else
{
double d = Sqrt(Math.Pow(this.R, 2) - Math.Pow(p.Y, 2));
Point3d p1 = new Point3d(-d, p.Y, 0, local_coord);
Point3d p2 = new Point3d(d, p.Y, 0, local_coord);
return(new Segment3d(p1, p2));
}
}
}
/// <summary>
/// Intersection of ellipse with plane.
/// Returns 'null' (no intersection) or object of type 'Ellipse', 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Plane3d s)
{
if (this.Normal.IsParallelTo(s.Normal))
{
if (this.Center.BelongsTo(s))
{
// coplanar objects
return(this.Copy());
}
else
{
// parallel objects
return(null);
}
}
else
{
Line3d l = (Line3d)s.IntersectionWith(new Plane3d(this.Center, this.Normal));
Coord3d local_coord = new Coord3d(this.Center, this._v1, this._v2);
Point3d p = l.Point.ConvertTo(local_coord);
Vector3d v = l.Direction.ConvertTo(local_coord);
double a = this.A;
double b = this.B;
if (Abs(v.Y / v.X) > 100)
{
// line is almost vertical, rotate local coord
local_coord = new Coord3d(this.Center, this._v2, this._v1);
p = l.Point.ConvertTo(local_coord);
v = l.Direction.ConvertTo(local_coord);
a = this.B;
b = this.A;
}
// Find intersection of line and ellipse (2D)
// Solution from: http://www.ambrsoft.com/TrigoCalc/Circles2/Ellipse/EllipseLine.htm
// Line equation in form: y = mx + c
double m = v.Y / v.X;
double c = p.Y - m * p.X;
double amb = Math.Pow(a, 2) * Math.Pow(m, 2) + Math.Pow(b, 2);
double det = amb - Math.Pow(c, 2);
if (det < -GeometRi3D.Tolerance)
{
return(null);
}
else if (GeometRi3D.AlmostEqual(det, 0))
{
double x = -Math.Pow(a, 2) * m * c / amb;
double y = Math.Pow(b, 2) * c / amb;
return(new Point3d(x, y, 0, local_coord));
}
else
{
double x1 = (-Math.Pow(a, 2) * m * c + a * b * Sqrt(det)) / amb;
double x2 = (-Math.Pow(a, 2) * m * c - a * b * Sqrt(det)) / amb;
double y1 = (Math.Pow(b, 2) * c + a * b * m * Sqrt(det)) / amb;
double y2 = (Math.Pow(b, 2) * c - a * b * m * Sqrt(det)) / amb;
return(new Segment3d(new Point3d(x1, y1, 0, local_coord), new Point3d(x2, y2, 0, local_coord)));
}
}
}