/// <summary>
/// Orthogonal projection of the circle to line
/// </summary>
public Segment3d ProjectionTo(Line3d l)
{
double s = _r * Cos(l.AngleTo(this));
Vector3d v = l.Direction.Normalized;
Point3d p = _point.ProjectionTo(l);
return new Segment3d(p.Translate(-s * v), p.Translate(s * v));
}
/// <summary>
/// Orthogonal projection of the ellipse to plane
/// </summary>
public Ellipse ProjectionTo(Plane3d s)
{
Point3d c = _point.ProjectionTo(s);
Point3d q = _point.Translate(_v1).ProjectionTo(s);
Point3d p = _point.Translate(_v2).ProjectionTo(s);
Vector3d f1 = new Vector3d(c, p);
Vector3d f2 = new Vector3d(c, q);
double t0 = 0.5 * Atan2(2 * f1 * f2, f1 * f1 - f2 * f2);
Vector3d v1 = f1 * Cos(t0) + f2 * Sin(t0);
Vector3d v2 = f1 * Cos(t0 + PI / 2) + f2 * Sin(t0 + PI / 2);
return(new Ellipse(c, v1, v2));
}
/// <summary>
/// Reflect vector in given plane
/// </summary>
public Vector3d ReflectIn(Plane3d s)
{
Point3d p1 = new Point3d(0, 0, 0, this._coord);
Point3d p2 = p1.Translate(this);
return(new Vector3d(p1.ReflectIn(s), p2.ReflectIn(s)));
}
/// <summary>
/// Orthogonal projection of ellipsoid to line.
/// </summary>
public Segment3d ProjectionTo(Line3d l)
{
//Stephen B. Pope "Algorithms for Ellipsoids"
// https://tcg.mae.cornell.edu/pubs/Pope_FDA_08.pdf
Coord3d lc = new Coord3d(_point, _v1, _v2);
Point3d x0 = l.Point.ConvertTo(lc);
Vector3d v = l.Direction.ConvertTo(lc);
Matrix3d L_T = Matrix3d.DiagonalMatrix(this.A, this.B, this.C);
Vector3d c = new Vector3d(0.0, 0.0, 0.0, lc);
double s0 = v * (c - x0.ToVector) / (v * v);
Vector3d w = L_T * v / (v * v);
Point3d P1 = x0.Translate((s0 + w.Norm) * v);
Point3d P2 = x0.Translate((s0 - w.Norm) * v);
return(new Segment3d(P1, P2));
}
/// <summary>
/// Translate box by a vector
/// </summary>
public Box3d Translate(Vector3d v)
{
return(new Box3d(_center.Translate(v), _lx, _ly, _lz));
}
/// <summary>
/// Translate triangle by a vector
/// </summary>
public Triangle Translate(Vector3d v)
{
return(new Triangle(_a.Translate(v), _b.Translate(v), _c.Translate(v)));
}
/// <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)));
}
