Line–sphere intersection

The three possible line-sphere intersections:
1. no intersection
2. single-point intersection
3. two-point intersection

In analytic geometry, a line and a sphere can intersect in three ways:

  1. no intersection at all,
  2. intersection at exactly one point, and
  3. intersection at two points.

Methods for distinguishing these cases, and determining the coordinates for the points in the latter cases, are useful in a number of circumstances. For example, it is a common calculation to perform during ray tracing.

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