/// <summary>
/// Reflect sphere in given line
/// </summary>
public Sphere ReflectIn(Line3d l)
{
return(new Sphere(this.Center.ReflectIn(l), this.R));
}
/// <summary>
/// Reflect segment in given line
/// </summary>
public virtual Segment3d ReflectIn(Line3d l)
{
return(new Segment3d(P1.ReflectIn(l), P2.ReflectIn(l)));
}
/// <summary>
/// Reflect plane in given line
/// </summary>
public Plane3d ReflectIn(Line3d l)
{
return(new Plane3d(this.Point.ReflectIn(l), this.Normal.ReflectIn(l)));
}
/// <summary>
/// Orthogonal projection of the sphere to the line
/// </summary>
public Segment3d ProjectionTo(Line3d l)
{
Point3d p = this.Center.ProjectionTo(l);
return(new Segment3d(p.Translate(this.R * l.Direction.Normalized), p.Translate(-this.R * l.Direction.Normalized)));
}
/// <summary>
/// Reflect ellipse in given line
/// </summary>
public Ellipse ReflectIn(Line3d l)
{
return(new Ellipse(this.Center.ReflectIn(l), _v1.ReflectIn(l), _v2.ReflectIn(l)));
}
/// <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)));
}
}
}
/// <summary>
/// Intersection of ellipsoid with line.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Line3d s)
{
// Analytical solution from:
// https://johannesbuchner.github.io/intersection/intersection_line_ellipsoid.html
// Define local cordinate system for ellipsoid
// and present line in parametric form in local coordinate system
// x: t + x0
// y: k * t + y0
// z: l * t + z0
// For numerical stability choose local X axis such that k<=1 and l<=1 !!!
Coord3d lc = new Coord3d(_point, _v1, _v2);
Vector3d v0 = s.Direction.ConvertTo(lc);
if (Abs(v0.Y) > Abs(v0.X) || Abs(v0.Z) > Abs(v0.X))
{
// Bad choice of X axis, try again
lc = new Coord3d(_point, _v2, _v3);
v0 = s.Direction.ConvertTo(lc);
if (Abs(v0.Y) > Abs(v0.X) || Abs(v0.Z) > Abs(v0.X))
{
lc = new Coord3d(_point, _v3, _v1);
v0 = s.Direction.ConvertTo(lc);
}
}
// Normalize direction vector
double k = v0.Y / v0.X;
double l = v0.Z / v0.X;
Point3d p0 = s.Point.ConvertTo(lc);
double x0 = p0.X;
double y0 = p0.Y;
double z0 = p0.Z;
double a2b2 = A * A * B * B;
double a2c2 = A * A * C * C;
double b2c2 = B * B * C * C;
double det = a2b2 * C * C * (a2b2 * l * l + a2c2 * k * k - A * A * k * k * z0 * z0 +
2 * A * A * k * l * y0 * z0 - A * A * l * l * y0 * y0 + b2c2 -
B * B * l * l * x0 * x0 + 2 * B * B * l * x0 * z0 - B * B * z0 * z0 -
C * C * k * k * x0 * x0 + 2 * C * C * k * x0 * y0 - C * C * y0 * y0);
if (det < -GeometRi3D.Tolerance)
{
return(null);
}
double sum1 = a2b2 * l * z0 + a2c2 * k * y0 + b2c2 * x0;
double sum2 = a2b2 * l * l + a2c2 * k * k + b2c2;
if (Abs(det) <= GeometRi3D.Tolerance)
{
// Intersection is point
double t = -sum1 / sum2;
return(new Point3d(t + x0, k * t + y0, l * t + z0, lc));
}
else
{
double t = -(sum1 + Sqrt(det)) / sum2;
Point3d p1 = new Point3d(t + x0, k * t + y0, l * t + z0, lc);
t = -(sum1 - Sqrt(det)) / sum2;
Point3d p2 = new Point3d(t + x0, k * t + y0, l * t + z0, lc);
return(new Segment3d(p1, p2));
}
}
/// <summary>
/// Reflect point in given line
/// </summary>
public Point3d ReflectIn(Line3d l)
{
Vector3d v = new Vector3d(this, this.ProjectionTo(l));
return(this.Translate(2 * v));
}
/// <summary>
/// Returns shortest distance to the line
/// </summary>
/// <param name="l"></param>
/// <returns></returns>
public double DistanceTo(Line3d l)
{
Vector3d v = new Vector3d(this, l.Point);
return(v.Cross(l.Direction).Norm / l.Direction.Norm);
}