| 释义 |
Cone-Sphere IntersectionLet a Cone of opening parameter  and vertex at  intersect a Sphere ofRadius  centered at  , with the Cone oriented such that its axis does not pass through thecenter of the Sphere. Then the equations of the curve of intersection are
Combining (1) and (2) gives
 | (3) |
 | |  | (4) |
Therefore,  and  are connected by a complicated Quartic Equation, and , , and  by a QuadraticEquation.
If the Cone-Sphere intersection is on-axis so that a Cone of opening parameter and vertex at is oriented with its Axis along a radial of the Sphere of radius centered at , thenthe equations of the curve of intersection are
Combining (5) and (6) gives
 | (7) |
 | (8) |
 | (9) |
So the curve of intersection is planar. Plugging (10) into (5) shows that the curve is actually a Circle,with Radius given by
 | (11) |
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