Line–sphere intersection
In analytic geometry, a line and a sphere can intersect in three ways: no intersection at all, at exactly one point, or in two points. Methods for distinguishing these cases, and determining equations for the points in the latter cases, are useful in a number of circumstances. For example, this is a common calculation to perform during ray tracing.In vector notation, the equations are as follows:
Equation for a sphere
Equation for a line starting at
Searching for points that are on the line and on the sphere means combining the equations and solving for, involving the dot product of vectors:
