/// <summary>
/// Check if two objects are orthogonal
/// </summary>
public bool IsOrthogonalTo(ILinearObject obj)
{
Vector3d v = obj.Direction;
if ((this._coord != v._coord))
{
v = v.ConvertTo(this._coord);
}
double this_norm = this.Norm;
double v_norm = v.Norm;
if (GeometRi3D.UseAbsoluteTolerance)
{
if (GeometRi3D.Greater(this_norm, 0.0) && GeometRi3D.Greater(v_norm, 0.0))
{
return(GeometRi3D.AlmostEqual(Abs(this * v), 0.0));
}
else
{
return(false);
}
}
else
{
if (this_norm > 0.0 && v_norm > 0.0)
{
return(GeometRi3D.AlmostEqual(Abs(this * v) / (this_norm * v_norm), 0.0));
}
else
{
return(false);
}
}
}
internal int _AxialPointLocation(Point3d p)
{
if (GeometRi3D.UseAbsoluteTolerance)
{
if (GeometRi3D.AlmostEqual(p.DistanceTo(this._p1), 0) || GeometRi3D.AlmostEqual(p.DistanceTo(this._p2), 0))
{
return(0); // Point is on boundary
}
else if (Abs(new Vector3d(p, this._p1).Normalized.AngleTo(new Vector3d(p, this._p2).Normalized)) < PI / 2)
{
return(-1); // Point is outside
}
else
{
return(1); // // Point is strictly inside
}
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * this.Length;
GeometRi3D.UseAbsoluteTolerance = true;
int result = this._AxialPointLocation(p);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
/// <summary>
/// Determines whether two objects are equal.
/// </summary>
public override bool Equals(object obj)
{
if (obj == null || (!object.ReferenceEquals(this.GetType(), obj.GetType())))
{
return(false);
}
Box3d b = (Box3d)obj;
if (GeometRi3D.UseAbsoluteTolerance)
{
return(this.Center == b.Center && _r == b.Orientation &&
GeometRi3D.AlmostEqual(L1, b.L1) &&
GeometRi3D.AlmostEqual(L2, b.L2) &&
GeometRi3D.AlmostEqual(L3, b.L3));
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * this.Diagonal;
GeometRi3D.UseAbsoluteTolerance = true;
bool result = this.Equals(b);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
internal override int _PointLocation(Point3d p)
{
Coord3d lc = new Coord3d(this.Center, this.SemiaxisA, this.SemiaxisB);
p = p.ConvertTo(lc);
if (GeometRi3D.UseAbsoluteTolerance)
{
double dist = this.ClosestPoint(p).DistanceTo(p);
if (GeometRi3D.AlmostEqual(dist, 0))
{
return(0); // Point is on boundary
}
if (GeometRi3D.Smaller(p.X * p.X / (A * A) + p.Y * p.Y / (B * B) + p.Z * p.Z / (C * C), 1.0))
{
return(1); // Point is strictly inside box
}
return(-1); // Point is outside
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * this.A;
GeometRi3D.UseAbsoluteTolerance = true;
int result = this._PointLocation(p);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
/// <summary>
/// Point on axis aligned box (including interior points) closest to target point "p".
/// </summary>
public Point3d AABBClosestPoint(Point3d p)
{
p = p.ConvertToGlobal();
double x = GeometRi3D.Clamp(p.X, this._center.X - _lx / 2, this._center.X + _lx / 2);
double y = GeometRi3D.Clamp(p.Y, this._center.Y - _ly / 2, this._center.Y + _ly / 2);
double z = GeometRi3D.Clamp(p.Z, this._center.Z - _lz / 2, this._center.Z + _lz / 2);
return(new Point3d(x, y, z));
}
/// <summary>
/// Intersection of circle with plane.
/// Returns 'null' (no intersection) or object of type 'Circle3d', 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Plane3d s)
{
// Relative tolerance ================================
if (!GeometRi3D.UseAbsoluteTolerance)
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * this.R;
GeometRi3D.UseAbsoluteTolerance = true;
object result = this.IntersectionWith(s);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return result;
}
//====================================================
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);
}
}
}
//////////////////////////////////////////
#region "ParallelMethods"
/// <summary>
/// Check if two objects are parallel
/// </summary>
public bool IsParallelTo(ILinearObject obj)
{
Vector3d v = obj.Direction;
if ((this._coord != v._coord))
{
v = v.ConvertTo(this._coord);
}
return(GeometRi3D.AlmostEqual(this.Normalized.Cross(v.Normalized).Norm, 0.0));
}
/// <summary>
/// Point on box (including interior points) closest to target point "p".
/// </summary>
public Point3d ClosestPoint(Point3d p)
{
Coord3d local_coord = this.LocalCoord();
p = p.ConvertTo(local_coord);
double x = GeometRi3D.Clamp(p.X, -_lx / 2, _lx / 2);
double y = GeometRi3D.Clamp(p.Y, -_ly / 2, _ly / 2);
double z = GeometRi3D.Clamp(p.Z, -_lz / 2, _lz / 2);
return(new Point3d(x, y, z, local_coord));
}
/// <summary>
/// Check if point belongs to the sphere surface
/// </summary>
/// <returns>True, if the point belongs to the sphere surface</returns>
public bool BelongsTo(Sphere s)
{
if (GeometRi3D.UseAbsoluteTolerance)
{
return(GeometRi3D.AlmostEqual(this.DistanceTo(s.Center), s.R));
}
else
{
return(GeometRi3D.AlmostEqual((this.DistanceTo(s.Center) - s.R) / s.R, 0.0));
}
}
/// <summary>
/// Check if point belongs to the circle
/// </summary>
/// <returns>True, if the point belongs to the circle</returns>
public bool BelongsTo(Circle3d c)
{
if (GeometRi3D.UseAbsoluteTolerance)
{
return(GeometRi3D.AlmostEqual(this.DistanceTo(c.Center), c.R) && c.Normal.Normalized.IsOrthogonalTo(new Vector3d(c.Center, this)));
}
else
{
return(GeometRi3D.AlmostEqual((this.DistanceTo(c.Center) - c.R) / c.R, 0.0) &&
c.Normal.Normalized.IsOrthogonalTo(new Vector3d(c.Center, this)));
}
}
/// <summary>
/// Check if two objects are orthogonal
/// </summary>
public bool IsOrthogonalTo(ILinearObject obj)
{
Vector3d v = obj.Direction;
if ((this._coord != v._coord))
{
v = v.ConvertTo(this._coord);
}
double this_norm = this.Norm;
double v_norm = v.Norm;
return(GeometRi3D.AlmostEqual(Abs(this * v) / (this_norm * v_norm), 0.0));
}
internal override int _PointLocation(Point3d p)
{
if (GeometRi3D.UseAbsoluteTolerance)
{
Plane3d s = new Plane3d(this.A, this.Normal);
Point3d proj = p.ProjectionTo(s);
if (GeometRi3D.AlmostEqual(p.DistanceTo(proj), 0))
{
if (p.BelongsTo(new Segment3d(_a, _b)) || p.BelongsTo(new Segment3d(_a, _c)) || p.BelongsTo(new Segment3d(_c, _b)))
{
return(0); // Point is on boundary
}
else
{
double area = this.Area;
double alpha = new Vector3d(proj, _b).Cross(new Vector3d(proj, _c)).Norm / (2 * area);
double beta = new Vector3d(proj, _c).Cross(new Vector3d(proj, _a)).Norm / (2 * area);
double gamma = new Vector3d(proj, _a).Cross(new Vector3d(proj, _b)).Norm / (2 * area);
if (GeometRi3D.AlmostEqual(((alpha + beta + gamma) - 1.0) * (AB + BC + AC) / 3, 0.0))
{
return(1); // Point is strictly inside
}
else
{
return(-1);
}
}
}
else
{
return(-1); // Point is outside
}
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * (AB + BC + AC) / 3;
GeometRi3D.UseAbsoluteTolerance = true;
int result = this._PointLocation(p);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
/// <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>
/// Check if point is inside ellipsoid
/// </summary>
public bool IsInside(Ellipsoid e)
{
Coord3d lc = new Coord3d(e.Center, e.SemiaxisA, e.SemiaxisB);
Point3d p = this.ConvertTo(lc);
if (GeometRi3D.UseAbsoluteTolerance)
{
return(GeometRi3D.Smaller(p.X * p.X / e.A / e.A + p.Y * p.Y / e.B / e.B + p.Z * p.Z / e.C / e.C, 1.0));
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * e.SemiaxisA.Norm;
GeometRi3D.UseAbsoluteTolerance = true;
bool result = this.IsInside(e);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
//////////////////////////////////////////
#region "ParallelMethods"
/// <summary>
/// Check if two objects are parallel
/// </summary>
public bool IsParallelTo(ILinearObject obj)
{
Vector3d v = obj.Direction;
if ((this._coord != v._coord))
{
v = v.ConvertTo(this._coord);
}
double this_norm = this.Norm;
double v_norm = v.Norm;
if (GeometRi3D.Greater(this_norm, 0.0) && GeometRi3D.Greater(v_norm, 0.0))
{
return(GeometRi3D.AlmostEqual(this.Normalized.Cross(v.Normalized).Norm, 0.0));
}
else
{
return(false);
}
}
/// <summary>
/// Calculates the point on the ellipse's boundary closest to given point.
/// </summary>
public Point3d ClosestPoint(Point3d p)
{
// Algorithm by Dr. Robert Nurnberg
// http://wwwf.imperial.ac.uk/~rn/distance2ellipse.pdf
// Does not work for interior points
Coord3d local_coord = new Coord3d(this.Center, this._v1, this._v2);
p = p.ConvertTo(local_coord);
if (GeometRi3D.AlmostEqual(p.X, 0) && GeometRi3D.AlmostEqual(p.Y, 0))
{
// Center point, choose any minor-axis
return(new Point3d(0, this.B, 0, local_coord));
}
double theta = Atan2(this.A * p.Y, this.B * p.X);
int iter = 0;
int max_iter = 100;
Point3d n0 = p.Copy();
while (iter < max_iter)
{
iter += 1;
double f = (A * A - B * B) * Cos(theta) * Sin(theta) - p.X * A * Sin(theta) + p.Y * B * Cos(theta);
double f_prim = (A * A - B * B) * (Cos(theta) * Cos(theta) - Sin(theta) * Sin(theta))
- p.X * A * Cos(theta) - p.Y * B * Sin(theta);
theta = theta - f / f_prim;
Point3d n = new Point3d(A * Cos(theta), B * Sin(theta), 0, local_coord);
if (n0.DistanceTo(n) < GeometRi3D.Tolerance)
{
return(n);
}
n0 = n.Copy();
}
return(n0);
}
/// <summary>
/// Check if two objects are orthogonal
/// </summary>
public bool IsOrthogonalTo(ILinearObject obj)
{
Vector3d v = obj.Direction;
if ((this._coord != v._coord))
{
v = v.ConvertTo(this._coord);
}
double this_norm = this.Norm;
double v_norm = v.Norm;
return(GeometRi3D.AlmostEqual(Abs(this * v) / (this_norm * v_norm), 0.0));
//if (GeometRi3D.Greater(this_norm, 0.0) && GeometRi3D.Greater(v_norm, 0.0))
//{
// return GeometRi3D.AlmostEqual(Abs(this * v) / (this_norm * v_norm), 0.0);
//}
//else
//{
// return false;
//}
}
internal override int _PointLocation(Point3d p)
{
if (GeometRi3D.UseAbsoluteTolerance)
{
Point3d proj = p.ProjectionTo(this.ToLine);
if (GeometRi3D.AlmostEqual(p.DistanceTo(proj), 0))
{
if (GeometRi3D.AlmostEqual(p.DistanceTo(this.P1), 0) || GeometRi3D.AlmostEqual(p.DistanceTo(this.P2), 0))
{
return(0); // Point is on boundary
}
else if (Abs(new Vector3d(proj, this.P1).AngleTo(new Vector3d(proj, this.P2))) < 2e-8)
// Need to decrease accuracy due to Acos calculations
{
return(-1); // Point is outside
}
else
{
return(1); // // Point is strictly inside
}
}
else
{
return(-1); // Point is outside
}
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * this.Length;
GeometRi3D.UseAbsoluteTolerance = true;
int result = this._PointLocation(p);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
internal override int _PointLocation(Point3d p)
{
if (GeometRi3D.UseAbsoluteTolerance)
{
Plane3d s = new Plane3d(this.Center, this.Normal);
Point3d proj = p.ProjectionTo(s);
if (GeometRi3D.AlmostEqual(p.DistanceTo(proj), 0))
{
if (GeometRi3D.Smaller(p.DistanceTo(this.Center), this.R))
{
return(1); // Point is strictly inside
}
else if (GeometRi3D.AlmostEqual(p.DistanceTo(this.Center), this.R))
{
return(0); // Point is on boundary
}
else
{
return(-1); // Point is outside
}
}
else
{
return(-1); // Point is outside
}
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * this.R;
GeometRi3D.UseAbsoluteTolerance = true;
int result = this._PointLocation(p);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
/// <summary>
/// Check if point is inside circle
/// </summary>
/// <returns>True, if the point is inside circle</returns>
public bool IsInside(Circle3d c)
{
if (GeometRi3D.UseAbsoluteTolerance)
{
if (this.BelongsTo(new Plane3d(c.Center, c.Normal)))
{
return(GeometRi3D.Smaller(this.DistanceTo(c.Center), c.R));
}
else
{
return(false);
}
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * c.R;
GeometRi3D.UseAbsoluteTolerance = true;
bool result = this.IsInside(c);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
/// <summary>
/// Check if point is inside ellipse
/// </summary>
/// <returns>True, if the point is inside ellipse</returns>
public bool IsInside(Ellipse e)
{
if (GeometRi3D.UseAbsoluteTolerance)
{
if (this.BelongsTo(new Plane3d(e.Center, e.MajorSemiaxis, e.MinorSemiaxis)))
{
return(GeometRi3D.Smaller(this.DistanceTo(e.F1) + this.DistanceTo(e.F2), 2 * e.A));
}
else
{
return(false);
}
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * e.MajorSemiaxis.Norm;
GeometRi3D.UseAbsoluteTolerance = true;
bool result = this.IsInside(e);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
}
private object _line_intersection(Line3d l, double t0, double t1)
{
// Smith's algorithm:
// "An Efficient and Robust Ray–Box Intersection Algorithm"
// Amy Williams, Steve Barrus, R. Keith Morley, Peter Shirley
// http://www.cs.utah.edu/~awilliam/box/box.pdf
// Modified to allow tolerance based checks
// Relative tolerance ================================
if (!GeometRi3D.UseAbsoluteTolerance)
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * this.Diagonal;
GeometRi3D.UseAbsoluteTolerance = true;
object result = _line_intersection(l, t0, t1);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
//====================================================
// Define local CS aligned with box
Coord3d local_CS = new Coord3d(this.Center, this.Orientation.ConvertToGlobal().ToRotationMatrix, "local_CS");
Point3d Pmin = this.P1.ConvertTo(local_CS);
Point3d Pmax = this.P7.ConvertTo(local_CS);
l = new Line3d(l.Point.ConvertTo(local_CS), l.Direction.ConvertTo(local_CS).Normalized);
double tmin, tmax, tymin, tymax, tzmin, tzmax;
double divx = 1 / l.Direction.X;
if (divx >= 0)
{
tmin = (Pmin.X - l.Point.X) * divx;
tmax = (Pmax.X - l.Point.X) * divx;
}
else
{
tmin = (Pmax.X - l.Point.X) * divx;
tmax = (Pmin.X - l.Point.X) * divx;
}
double divy = 1 / l.Direction.Y;
if (divy >= 0)
{
tymin = (Pmin.Y - l.Point.Y) * divy;
tymax = (Pmax.Y - l.Point.Y) * divy;
}
else
{
tymin = (Pmax.Y - l.Point.Y) * divy;
tymax = (Pmin.Y - l.Point.Y) * divy;
}
if (GeometRi3D.Greater(tmin, tymax) || GeometRi3D.Greater(tymin, tmax))
{
return(null);
}
if (GeometRi3D.Greater(tymin, tmin))
{
tmin = tymin;
}
if (GeometRi3D.Smaller(tymax, tmax))
{
tmax = tymax;
}
double divz = 1 / l.Direction.Z;
if (divz >= 0)
{
tzmin = (Pmin.Z - l.Point.Z) * divz;
tzmax = (Pmax.Z - l.Point.Z) * divz;
}
else
{
tzmin = (Pmax.Z - l.Point.Z) * divz;
tzmax = (Pmin.Z - l.Point.Z) * divz;
}
if (GeometRi3D.Greater(tmin, tzmax) || GeometRi3D.Greater(tzmin, tmax))
{
return(null);
}
if (GeometRi3D.Greater(tzmin, tmin))
{
tmin = tzmin;
}
if (GeometRi3D.Smaller(tzmax, tmax))
{
tmax = tzmax;
}
// Now check the overlapping portion of the segments
// This part is missing in the original algorithm
if (GeometRi3D.Greater(tmin, t1))
{
return(null);
}
if (GeometRi3D.Smaller(tmax, t0))
{
return(null);
}
if (GeometRi3D.Smaller(tmin, t0))
{
tmin = t0;
}
if (GeometRi3D.Greater(tmax, t1))
{
tmax = t1;
}
if (GeometRi3D.AlmostEqual(tmin, tmax))
{
return(l.Point.Translate(tmin * l.Direction));
}
else
{
return(new Segment3d(l.Point.Translate(tmin * l.Direction), l.Point.Translate(tmax * l.Direction)));
}
}
/// <summary>
/// Returns the hashcode for the object.
/// </summary>
public override int GetHashCode()
{
return(GeometRi3D.HashFunction(_point.GetHashCode(), _r.GetHashCode(), _normal.GetHashCode()));
}
/// <summary>
/// Angle between two objects in radians (0 < angle < Pi)
/// </summary>
public double AngleTo(IPlanarObject obj)
{
return(GeometRi3D.GetAngle(this, 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>
/// Check if two objects are coplanar
/// </summary>
public bool IsCoplanarTo(ILinearObject obj)
{
return(GeometRi3D._coplanar(this, obj));
}
/// <summary>
/// Determines whether two objects are equal.
/// </summary>
public override bool Equals(object obj)
{
if (obj == null || (!object.ReferenceEquals(this.GetType(), obj.GetType())))
{
return(false);
}
Ellipse e = (Ellipse)obj;
if (GeometRi3D.UseAbsoluteTolerance)
{
if (GeometRi3D.AlmostEqual(this.A, this.B))
{
// Ellipse is circle
if (GeometRi3D.AlmostEqual(e.A, e.B))
{
// Second ellipse also circle
return(this.Center == e.Center && GeometRi3D.AlmostEqual(this.A, e.A) && e.Normal.IsParallelTo(this.Normal));
}
else
{
return(false);
}
}
else
{
return(this.Center == e.Center && GeometRi3D.AlmostEqual(this.A, e.A) && GeometRi3D.AlmostEqual(this.B, e.B) &&
e.MajorSemiaxis.IsParallelTo(this.MajorSemiaxis) && e.MinorSemiaxis.IsParallelTo(this.MinorSemiaxis));
}
}
else
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * e.MajorSemiaxis.Norm;
GeometRi3D.UseAbsoluteTolerance = true;
if (GeometRi3D.AlmostEqual(this.A, this.B))
{
// Ellipse is circle
if (GeometRi3D.AlmostEqual(e.A, e.B))
{
// Second ellipse also circle
bool res1 = this.Center == e.Center && GeometRi3D.AlmostEqual(this.A, e.A);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
bool res2 = e.Normal.IsParallelTo(this.Normal);
return(res1 && res2);
}
else
{
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(false);
}
}
else
{
bool res1 = this.Center == e.Center && GeometRi3D.AlmostEqual(this.A, e.A) && GeometRi3D.AlmostEqual(this.B, e.B);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
bool res2 = e.MajorSemiaxis.IsParallelTo(this.MajorSemiaxis) && e.MinorSemiaxis.IsParallelTo(this.MinorSemiaxis);
return(res1 && res2);
}
}
}
/// <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>
/// Returns the hashcode for the object.
/// </summary>
public override int GetHashCode()
{
int hash_code = GeometRi3D.HashFunction(_lx.GetHashCode(), _ly.GetHashCode(), _lz.GetHashCode());
return(GeometRi3D.HashFunction(_center.GetHashCode(), _r.GetHashCode(), hash_code));
}
/// <summary>
/// Returns the hashcode for the object.
/// </summary>
public override int GetHashCode()
{
return(GeometRi3D.HashFunction(_a.GetHashCode(), _b.GetHashCode(), _c.GetHashCode()));
}
