非退化有理贝塞尔四边形的隐式方程
Implicit equations of non-degenerate rational Bezier quadric triangles
AI总结：
本文研究非退化有理贝塞尔四边形的隐式方程推导，基于投影几何和四面体外切圆锥面构造方法，提出基于控制网和权重列表的双线性形式。
摘要：
本文回顾了非退化二次曲面在有理贝塞尔三角形形式下的隐式方程推导。这些情况对应于二次斯蒂纳面。我们以控制网和权重列表的适当形式，无坐标地推导出此类四边形的双线性形式。我们的构造基于投影几何，并基于由控制网顶点和一个额外点形成的四面体的外切圆锥面族。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
