Geometric elements and classification of quadrics in rational Bézier form

作者：

Highlights：

• Closed formulas for geometric elements of quadrics in rational Bézier form in terms of their weights and control points, using algebraic projective geometry.

• The results are derived for Bézier triangles, but are applicable to tensor product patches.

• Closed, coordinate-free formulas for implicit equations for quadrics in terms of their weights and control points.

• Affine classification of quadrics in Bézier form.

摘要

•Closed formulas for geometric elements of quadrics in rational Bézier form in terms of their weights and control points, using algebraic projective geometry.•The results are derived for Bézier triangles, but are applicable to tensor product patches.•Closed, coordinate-free formulas for implicit equations for quadrics in terms of their weights and control points.•Affine classification of quadrics in Bézier form.

论文关键词：Algebraic projective geometry,Rational Bézier patches,Quadrics,Steiner surfaces

论文评审过程：Received 2 June 2015, Revised 5 January 2016, Available online 18 January 2016, Version of Record 4 February 2016.

论文官网地址：https://doi.org/10.1016/j.cam.2016.01.006