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arXiv · 1601.03224

Implicit equations of non-degenerate rational Bezier quadric triangles

A. Canton·L. Fernandez-Jambrina·E. Rosado Maria·M. J. Vazquez-Gallo
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Abstract

In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bezier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is grounded on the pencil of quadrics circumscribed to a tetrahedron formed by vertices of the control net and an additional point which is required for the Steiner surface to be a non-degenerate quadric.

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A. Canton, L. Fernandez-Jambrina, E. Rosado Maria, M. J. Vazquez-Gallo. 2016-01-13. Implicit equations of non-degenerate rational Bezier quadric triangles. https://doi.org/10.1007/978-3-319-22804-4_6

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