/// <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))
{
// Coplanar line and triangle
// Check intersection in one corner
// or in corner and opposite side
if (_a.BelongsTo(l))
{
object obj2 = new Segment3d(_b, _c).IntersectionWith(l);
if (obj2 != null && obj2.GetType() == typeof(Point3d))
{
return(new Segment3d(_a, (Point3d)obj2));
}
else
{
return(A);
}
}
if (_b.BelongsTo(l))
{
object obj2 = new Segment3d(_a, _c).IntersectionWith(l);
if (obj2 != null && obj2.GetType() == typeof(Point3d))
{
return(new Segment3d(_b, (Point3d)obj2));
}
else
{
return(B);
}
}
if (_c.BelongsTo(l))
{
object obj2 = new Segment3d(_a, _b).IntersectionWith(l);
if (obj2 != null && obj2.GetType() == typeof(Point3d))
{
return(new Segment3d(_c, (Point3d)obj2));
}
else
{
return(C);
}
}
// Check intersection with two sides
object objAB = new Segment3d(_a, _b).IntersectionWith(l);
object objBC = new Segment3d(_b, _c).IntersectionWith(l);
if (objAB != null && objAB.GetType() == typeof(Point3d))
{
if (objBC != null && objBC.GetType() == typeof(Point3d))
{
return(new Segment3d((Point3d)objAB, (Point3d)objBC));
}
else
{
object objAC = new Segment3d(_a, _c).IntersectionWith(l);
if (objAC != null && objAC.GetType() == typeof(Point3d))
{
return(new Segment3d((Point3d)objAB, (Point3d)objAC));
}
else
{
return((Point3d)objAB);
}
}
}
if (objBC != null && objBC.GetType() == typeof(Point3d))
{
object objAC = new Segment3d(_a, _c).IntersectionWith(l);
if (objAC != null && objAC.GetType() == typeof(Point3d))
{
return(new Segment3d((Point3d)objBC, (Point3d)objAC));
}
else
{
return((Point3d)objBC);
}
}
object objAC2 = new Segment3d(_a, _c).IntersectionWith(l);
if (objAC2 != null && objAC2.GetType() == typeof(Point3d))
{
return((Point3d)objAC2);
}
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 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>
/// Intersection of ellipse with line.
/// 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 * this.A;
GeometRi3D.UseAbsoluteTolerance = true;
object result = this.IntersectionWith(l);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
//====================================================
if (l.Direction.IsOrthogonalTo(this.Normal))
{
if (l.Point.BelongsTo(new Plane3d(this.Center, this.Normal)))
{
// coplanar objects
// Find intersection of line and ellipse (2D)
// Solution from: http://www.ambrsoft.com/TrigoCalc/Circles2/Ellipse/EllipseLine.htm
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;
}
// 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 (det > 1e-12)
{
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)));
}
else
{
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
{
// parallel objects
return(null);
}
}
else
{
// Line intersects ellipse' plane
Point3d p = (Point3d)l.IntersectionWith(new Plane3d(this.Center, this.Normal));
if (p.BelongsTo(this))
{
return(p);
}
else
{
return(null);
}
}
}