/// <summary>
/// Point on sphere's surface closest to target point "p".
/// </summary>
public Point3d ClosestPoint(Sphere s)
{
return(s.ClosestPoint(this));
}
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);
}
