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<p><b>Abstract</b>—Up to now, the shortest invariant representation of a quadric has 138 summands and there has been no invariant representation of a twisted cubic in 3D projective space, which limit to some extent the applications of invariants in 3D space. In this paper, we give a very short invariant representation of a quadric cone, a special quadric, which has only two summands similar to the invariant representation of a planar conic, and give a short invariant representation of a twisted cubic. Then, a completely linear algorithm for generating the parametric equations of a twisted cubic is provided also. Finally, we exemplify some applications of our proposed invariant representations in the fields of computer vision and automated geometric theorem proving.</p>
Automated theorem proving, computer vision, invariant representation, quadric cone, twisted cubic.

Y. Wu and Z. Y. Hu, "The Invariant Representations of a Quadric Cone and a Twisted Cubic," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 25, no. , pp. 1329-1332, 2003.
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