bool ON_Arc::Create( // arc through 3 3d points
const ON_3dPoint& P, // point P
const ON_3dPoint& Q, // point Q
const ON_3dPoint& R // point R
)
{
ON_Circle c;
double a = 0.0;
for (;;)
{
if ( !c.Create(P,Q,R) )
break;
if ( !c.ClosestPointTo( R, &a ) )
break;
if ( !(a > 0.0) )
break;
if ( !Create( c, ON_Interval(0.0,a) ) )
break;
return true;
}
plane = ON_Plane::World_xy;
radius = 0.0;
m_angle.Set(0.0,0.0);
return false;
}
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;
}