int ON_Intersect( const ON_Sphere& sphere0,
const ON_Sphere& sphere1,
ON_Circle& circle
)
{
double r0 = sphere0.Radius();
double r1 = sphere1.Radius();
ON_3dPoint C0 = sphere0.Center();
ON_3dPoint C1 = sphere1.Center();
ON_3dVector D = C1-C0;
double d = D.Length();
if (!D.Unitize()){
if (fabs(r1-r0) > ON_ZERO_TOLERANCE)
return 0;//Same center, different radii
return 3;//Same sphere.
}
//Spheres are appart.
if (d > r0 + r1)
return 0;
//Spheres tangent and appart
if (d == r0+r1){
ON_3dPoint P = C0 + r0*D;
circle.Create(P, 0.0);
return 1;
}
//Spheres tangent, one inside the other
if (d == fabs(r0-r1)){
ON_3dPoint P = (r0 > r1) ? C0 + r0*D : C0 - r0*D;
circle.Create(P, 0.0);
return 1;
}
//Spheres don't intersect, one inside the other.
if (d < fabs(r0-r1))
return 0;
//Intersection is a circle
double x = 0.5*(d*d + r0*r0 - r1*r1)/d;
if (x >= r0){//Shouldn't happen
ON_3dPoint P = C0 + r0*D;
circle.Create(P, 0.0);
return 1;
}
if (x <= -r0){//Shouldn't happen
ON_3dPoint P = C0 - r0*D;
circle.Create(P, 0.0);
return 1;
}
double y = r0*r0 - x*x;
if (y < 0.0)//Shouldn't happen
return 0;
y = sqrt(y);
ON_3dPoint P = C0 + x*D;
ON_Plane plane(P, D);
circle.Create(plane, y);
return 2;
}
// Copied from opennurbs_intersect.cpp but with a bug fix.
// We can remove it once the bug is fixed in OpenNurbs and once
// Grasshopper has dropped Rhino4 support.
int PS_Intersect(
const ON_Plane& plane,
const ON_Sphere& sphere,
ON_Circle& circle
)
{
// 16 April 2011 Dale Lear
// Prior to this date, this function did not return the correct answer.
int rc = 0;
const double sphere_radius = fabs(sphere.radius);
double tol = sphere_radius*ON_SQRT_EPSILON;
if ( !(tol >= ON_ZERO_TOLERANCE) )
tol = ON_ZERO_TOLERANCE;
const ON_3dPoint sphere_center = sphere.Center();
ON_3dPoint circle_center = plane.ClosestPointTo(sphere_center);
double d = circle_center.DistanceTo(sphere_center);
circle.radius = 0.0;
if ( ON_IsValid(sphere_radius) && ON_IsValid(d) && d <= sphere_radius + tol )
{
if ( sphere_radius > 0.0 )
{
d /= sphere_radius;
d = 1.0 - d*d;
// The d > 4.0*ON_EPSILON was picked by testing spheres with
// radius = 1 and center = (0,0,0). Do not make 4.0*ON_EPSILON
// any smaller and please discuss changes with Dale Lear.
circle.radius = (d > 4.0*ON_EPSILON) ? sphere_radius*sqrt(d) : 0.0;
}
else
circle.radius = 0.0;
if ( circle.radius <= ON_ZERO_TOLERANCE )
{
// return a single point
rc = 1;
circle.radius = 0.0;
// When tolerance is in play, put the point on the sphere.
// If the caller prefers the plane, then they can adjust the
// returned answer to get the plane.
ON_3dVector R = circle_center - sphere_center;
double r0 = R.Length();
if ( r0 > 0.0 )
{
R.Unitize();
ON_3dPoint C1 = sphere_center + sphere_radius*R;
double r1 = C1.DistanceTo(sphere_center);
if ( fabs(sphere.radius-r1) < fabs(sphere.radius-r0) )
circle_center = C1;
}
}
else
{
// return a circle
rc = 2;
}
}
// Update circle's plane here in case the input plane
// is the circle's plane member.
circle.plane = plane;
circle.plane.origin = circle_center;
circle.plane.UpdateEquation();
return rc;
}