Recognizing projections of algebraic curves

Given two irreducible, algebraic space curves C1C1 and C2,C2, where C2C2 is contained in some plane Π  , we provide algorithms to check whether or not there exist perspective or parallel projections mapping C1C1 onto C2,C2, i.e. to recognize C2C2 as the projection of C1C1. In the affirmative case, the algorithms provide the eye point(s) of the perspective transformation(s), or the direction(s) of the parallel projection(s). Although the problem is mainly discussed for rational curves, an algorithm for implicit curves is also given. The algorithms presented are mostly symbolic; nevertheless, we include an approximate algorithm for rational curves too.

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