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Nordic Track Ellipse Elliptical
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Nordic Track Ellipse Elliptical

HARD parametricly defined ellipse problem?

I have such question Given a point P that is coplanar to an ellipse, which is defined by the function R( t ) = C + A * cos( t ) + B * sin ( t ) where A, B, and C are given vectors in space and A and B are NOT orgthogonal to each other, determine if P is "inside" the ellipse. Point P is inside the ellipse if ||P - C|| ||Q - C|, Q is a point on the ellipse and also on the line formed by C and P. The t value of the point on the ellipse is unknown, as well as the point Q. If this can not be done, please tell me why and thanks for trying, otherwise I would like a general algorithm to find out if ||P - C|| > ||Q - C|. Another, equivalent elliptical shape may be generated where A and B are orthogonal, but I have to know how to get that ellipse (I can easily complete the problem with the new shape if I have the equation for it). C can be ignored if it is assumed to be on the origin.

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