Toric degenerations of Bézier patches
Toric degenerations of Bézier patches
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DOI：
10.1145/2019627.2019629
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
L. García-Puente;F. Sottile;Chungang Zhu
中科院分区：
文献类型：
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作者：
L. García-Puente;F. Sottile;Chungang Zhu
有理bassazier曲线的控制多边形定义良好，具有几何意义；有一系列权值，在这些权值下，曲线的极限位置是控制多边形。对于一个合理的bassazier曲面块，有许多可能的多面体控制结构，没有一个是规范的。我们提出了一种不一定是多面体的合理曲面块控制结构，规则控制曲面是一定的C0样条曲面。虽然不是唯一的，但当权重变化时，规则的控制面正是合理bsamzier补丁的可能限制位置。
The control polygon of a rational Bézier curve is well-defined and has geometric significance; there is a sequence of weights under which the limiting position of the curve is the control polygon. For a rational Bézier surface patch, there are many possible polyhedral control structures, and none is canonical. We propose a not necessarily polyhedral control structure for rational surface patches, regular control surfaces, which are certain C0 spline surfaces. While not unique, regular control surfaces are exactly the possible limiting positions of a rational Bézier patch when the weights vary.