private double _distance_cicle_to_sphere(Circle3d c1, Sphere c2, out Point3d p1, out Point3d p2)
// Use quadratic interpolation to find closest point on circle
// p1 and p2 - closest points on circle and sphere respectively
{
double d1 = 1e20;
double t1 = 0;
Point3d p;
for (int i = 0; i < 16; i++)
{
double t = i * Math.PI / 8;
p = c1.ParametricForm(t);
double dist = p.DistanceTo(c2);
if (dist < d1)
{
d1 = dist;
t1 = t;
}
}
double t2 = t1 - Math.PI / 8;
p = c1.ParametricForm(t2);
double d2 = p.DistanceTo(c2);
double t3 = t1 + Math.PI / 8;
p = c1.ParametricForm(t3);
double d3 = p.DistanceTo(c2);
int iter = 0;
while (d2 - d1 > 0.2 * GeometRi3D.DefaultTolerance && d1 > GeometRi3D.DefaultTolerance)
{
if (++iter > 100)
{
break;
}
double ax = 2.0 * d1 / (t1 - t2) / (t1 - t3);
double aa = 0.5 * ax * (t2 + t3);
double bx = 2.0 * d2 / (t2 - t1) / (t2 - t3);
double bb = 0.5 * bx * (t1 + t3);
double cx = 2.0 * d3 / (t3 - t1) / (t3 - t2);
double cc = 0.5 * cx * (t1 + t2);
double t = (aa + bb + cc) / (ax + bx + cx);
p = c1.ParametricForm(t);
double d = p.DistanceTo(c2);
if (d < d1)
{
if (t > t2 & t < t1)
{
t3 = t1; d3 = d1;
}
else
{
t2 = t1; d2 = d1;
}
t1 = t; d1 = d;
}
else
{
if (t < t1)
{
t2 = t; d2 = d;
}
else
{
t3 = t; d3 = d;
}
}
}
p1 = c1.ParametricForm(t1);
p2 = c2.ClosestPoint(p1);
return(d1);
}
/// <summary>
/// Get intersection of ray with sphere.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Sphere s)
{
return(s.IntersectionWith(this));
}
/// <summary>
/// Get intersection of two spheres.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Circle3d'.
/// </summary>
public object IntersectionWith(Sphere s)
{
// Relative tolerance ================================
if (!GeometRi3D.UseAbsoluteTolerance)
{
double tol = GeometRi3D.Tolerance;
GeometRi3D.Tolerance = tol * Max(this.R, s.R);
GeometRi3D.UseAbsoluteTolerance = true;
object result = this.IntersectionWith(s);
GeometRi3D.UseAbsoluteTolerance = false;
GeometRi3D.Tolerance = tol;
return(result);
}
//====================================================
Point3d p = s.Center.ConvertTo(this.Center.Coord);
double Dist = Sqrt(Math.Pow((this.X - p.X), 2) + Math.Pow((this.Y - p.Y), 2) + Math.Pow((this.Z - p.Z), 2));
// Separated spheres
if (Dist > this.R + s.R + GeometRi3D.Tolerance)
{
return(null);
}
// One sphere inside the other
if (Dist < Abs(this.R - s.R) - GeometRi3D.Tolerance)
{
return(null);
}
// Intersection plane
double A = 2 * (p.X - this.X);
double B = 2 * (p.Y - this.Y);
double C = 2 * (p.Z - this.Z);
double D = Math.Pow(this.X, 2) - Math.Pow(p.X, 2) + Math.Pow(this.Y, 2) - Math.Pow(p.Y, 2) + Math.Pow(this.Z, 2) - Math.Pow(p.Z, 2) - Math.Pow(this.R, 2) + Math.Pow(s.R, 2);
// Intersection center
double t = (this.X * A + this.Y * B + this.Z * C + D) / (A * (this.X - p.X) + B * (this.Y - p.Y) + C * (this.Z - p.Z));
double x = this.X + t * (p.X - this.X);
double y = this.Y + t * (p.Y - this.Y);
double z = this.Z + t * (p.Z - this.Z);
// Outer tangency
if (Abs(this.R + s.R - D) < GeometRi3D.Tolerance)
{
return(new Point3d(x, y, z, this.Center.Coord));
}
// Inner tangency
if (Abs(Abs(this.R - s.R) - D) < GeometRi3D.Tolerance)
{
return(new Point3d(x, y, z, this.Center.Coord));
}
// Intersection
double alpha = Acos((Math.Pow(this.R, 2) + Math.Pow(Dist, 2) - Math.Pow(s.R, 2)) / (2 * this.R * Dist));
double R = this.R * Sin(alpha);
Vector3d v = new Vector3d(this.Center, s.Center);
return(new Circle3d(new Point3d(x, y, z, this.Center.Coord), R, v));
}