/// <summary>
/// Get intersection of segment with triangle.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Segment3d s)
{
// Relative tolerance ================================
if (!GeometRi3D.UseAbsoluteTolerance)
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * Max(s.Length, Max(AB, Max(BC, AC)));
GeometRi3D.UseAbsoluteTolerance = true;
object result = this.IntersectionWith(s);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
//====================================================
object obj = this.IntersectionWith(s.ToLine);
if (obj == null)
{
return(null);
}
else if (obj.GetType() == typeof(Point3d))
{
Point3d p = (Point3d)obj;
if (p.BelongsTo(s))
{
return(p);
}
else
{
return(null);
}
}
else
{
return(s.IntersectionWith((Segment3d)obj));
}
}
/// <summary>
/// Intersection of two circles.
/// Returns 'null' (no intersection) or object of type 'Circle3d', 'Point3d' or 'Segment3d'.
/// In 2D (coplanar circles) the segment will define two intersection points.
/// </summary>
public object IntersectionWith(Circle3d c)
{
// Relative tolerance ================================
if (!GeometRi3D.UseAbsoluteTolerance)
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * Max(this.R, c.R);
GeometRi3D.UseAbsoluteTolerance = true;
object result = this.IntersectionWith(c);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
//====================================================
if (this.Normal.IsParallelTo(c.Normal))
{
if (this.Center.BelongsTo(new Plane3d(c.Center, c.Normal)))
{
// Coplanar objects
// Search 2D intersection of two circles
// Equal circles
if (this.Center == c.Center && GeometRi3D.AlmostEqual(this.R, c.R))
{
return(this.Copy());
}
double d = this.Center.DistanceTo(c.Center);
// Separated circles
if (GeometRi3D.Greater(d, this.R + c.R))
{
return(null);
}
// One circle inside the other
if (d < Abs(this.R - c.R) - GeometRi3D.Tolerance)
{
return(null);
}
// Outer tangency
if (GeometRi3D.AlmostEqual(d, this.R + c.R))
{
Vector3d vec = new Vector3d(this.Center, c.Center);
return(this.Center.Translate(this.R * vec.Normalized));
}
// Inner tangency
if (Abs(Abs(this.R - c.R) - d) < GeometRi3D.Tolerance)
{
Vector3d vec = new Vector3d(this.Center, c.Center);
if (this.R > c.R)
{
return(this.Center.Translate(this.R * vec.Normalized));
}
else
{
return(this.Center.Translate(-this.R * vec.Normalized));
}
}
// intersecting circles
// Create local CS with origin in circle's center
Vector3d vec1 = new Vector3d(this.Center, c.Center);
Vector3d vec2 = vec1.Cross(this.Normal);
Coord3d local_cs = new Coord3d(this.Center, vec1, vec2);
double x = 0.5 * (d * d - c.R * c.R + this.R * this.R) / d;
double y = 0.5 * Sqrt((-d + c.R - this.R) * (-d - c.R + this.R) * (-d + c.R + this.R) * (d + c.R + this.R)) / d;
Point3d p1 = new Point3d(x, y, 0, local_cs);
Point3d p2 = new Point3d(x, -y, 0, local_cs);
return(new Segment3d(p1, p2));
}
else
{
// parallel objects
return(null);
}
}
else
{
// Check 3D intersection
Plane3d plane = new Plane3d(this.Center, this.Normal);
object obj = plane.IntersectionWith(c);
if (obj == null)
{
return(null);
}
else if (obj.GetType() == typeof(Point3d))
{
Point3d p = (Point3d)obj;
if (p.BelongsTo(c))
{
return(p);
}
else
{
return(null);
}
}
else
{
Segment3d s = (Segment3d)obj;
return(s.IntersectionWith(this));
}
}
}
/// <summary>
/// Get intersection of line with triangle.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Line3d l)
{
// Relative tolerance ================================
if (!GeometRi3D.UseAbsoluteTolerance)
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * Max(AB, Max(BC, AC));
GeometRi3D.UseAbsoluteTolerance = true;
object result = this.IntersectionWith(l);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
//====================================================
Plane3d s = new Plane3d(this.A, this.Normal);
object obj = l.IntersectionWith(s);
if (obj == null)
{
return(null);
}
else
{
if (obj.GetType() == typeof(Line3d))
{
Segment3d sAB = new Segment3d(A, B);
Segment3d sBC = new Segment3d(B, C);
Segment3d sAC = new Segment3d(A, C);
// Line coincides with one side, return segment
if (sAB.BelongsTo(l))
{
return(sAB);
}
if (sBC.BelongsTo(l))
{
return(sBC);
}
if (sAC.BelongsTo(l))
{
return(sAC);
}
Point3d pAB = (Point3d)sAB.IntersectionWith(l);
Point3d pBC = (Point3d)sBC.IntersectionWith(l);
Point3d pAC = (Point3d)sAC.IntersectionWith(l);
bool bAB = (object.ReferenceEquals(null, pAB)) ? false : pAB.BelongsTo(sAB);
bool bAC = (object.ReferenceEquals(null, pAC)) ? false : pAC.BelongsTo(sAC);
bool bBC = (object.ReferenceEquals(null, pBC)) ? false : pBC.BelongsTo(sBC);
// Line crosses one corner, return point
if (bAB && bBC && pAB == pBC && !bAC)
{
return(pAB);
}
if (bAB && bAC && pAB == pAC && !bBC)
{
return(pAB);
}
if (bAC && bBC && pAC == pBC && !bAB)
{
return(pAC);
}
// Line crosses two sides, return segment
if (bAB && bBC && !bAC)
{
return(new Segment3d(pAB, pBC));
}
if (bAB && bAC && !bBC)
{
return(new Segment3d(pAB, pAC));
}
if (bAC && bBC && !bAB)
{
return(new Segment3d(pAC, pBC));
}
// Line crosses one corner and one side, return segment
if (pAB == pBC && bAC)
{
return(new Segment3d(pAB, pAC));
}
if (pAB == pAC && bBC)
{
return(new Segment3d(pAB, pBC));
}
if (pAC == pBC && bAB)
{
return(new Segment3d(pAB, pAC));
}
//else
return(null);
}
else
{
// result of intersection is point
Point3d p = (Point3d)obj;
if (p.BelongsTo(this))
{
return(p);
}
else
{
return(null);
}
}
}
}
/// <summary>
/// Get intersection of line with segment.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Segment3d s)
{
return(s.IntersectionWith(this));
}