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Line–sphere intersection
open-in-new
<p>In <a href="/facts/Analytic_geometry/3qWP0kM0">analytic geometry</a>, a <a href="/facts/Line_(mathematics)/gJqsr4Gj">line</a> and a <a href="/facts/Sphere/jywYLNM2">sphere</a> can <a href="/facts/Intersection/hVW6QFWD">intersect</a> in three ways: </p> <ol><li>No intersection at all</li> <li>Intersection in exactly one point</li> <li>Intersection in two points.</li></ol> <p>Methods for distinguishing these cases, and determining the <a href="/facts/Coordinates/Mtd0q4SP">coordinates</a> for the points in the latter cases, are useful in a number of circumstances. For example, it is a common calculation to perform during <a href="/facts/Ray_tracing_(graphics)/n6qpap2q">ray tracing</a>. </p>