Sphere Intersection

This is an important calculation.

Sphere intersection. The diagram shows the case where the intersection of a cylinder and a sphere consists of two circles. Sphere sphere intersection let two spheres of radii and be located along the x axis centered at and respectively. It also has the advantage because of its simplicity to be very fast. Methods for distinguishing these cases and determining equations for the points in the latter cases are useful in a number of circumstances.

Not surprisingly the analysis is very similar to the case of the circle circle intersection. Otherwise there is an intersection if the distance from p to c is less than or equal to the radius. The distance d between the spheres centers is. The outer intersection points of the two spheres forms a circle ab with radius h which is the base of two spherical caps.

If it s not less than 0 we move on. No intersection at all at exactly one point or in two points. To make calculations easier we choose the center of the first sphere at 0 0 0 and the second sphere. If the result of this is that tc is less than 0 it means that the ray does not intersect the sphere and we can bail out of our intersection test early.

If is equal then the intersection is the point p itself. At d 0 0. In the theory of analytic geometry for real three dimensional space the curve formed from the intersection between a sphere and a cylinder can be a circle a point the empty set or a special type of curve. Intersecting a ray with a sphere is probably the simplest form of ray geometry intersection test which is the reason why so many raytracers show images of spheres.

In analytic geometry a line and a sphere can intersect in three ways. The last thing we need to do with this triangle is solve for the length of d. The center of the sphere is behind the ray.