摘要
提出一种用分片代数曲面构造三角曲面片的方法,利用具有公共边的2个三角形区域的4个顶点的函数值以及公共边2个端点的外法向量来构造一个二次曲面V(g)和一个截面V(h),其交V(g,h)即为2个三角曲面片的公共边界曲线.对每个已确定了边界条件的三角片内部进一步划分成3部分,每部分各自定义一个三次代数曲面.这3个三次代数曲面不仅在其交线处光滑拼接,而且分别沿三角形的边界与V(g)光滑拼接,从而构成一个具有GC1连续性的分片代数曲面.对于只属于一个三角片的边界留有一个自由度,可对曲面形状加以控制.
This paper deals with the problem of reconstructing algebraic surfaces over triangular meshes. Firstly, a quadratic surface and a plane are constructed over every edge of triangle. Their intersection is the edge curve. Secondly, we dividethe triangle into three parts and define three cubic surfaces over every part. These cubic surfaces not only intersect smoothly along there intersection curves, but also meet with quadratic surfaces GC^1 continuity. Then a GC^1 continuous surface is gotten over the whole triangular meshes.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2007年第4期460-463,共4页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(60533060
60573180
60673153)
山东省自然科学基金(Y2005G09)
关键词
代数曲面
GC^1连续
三角曲面片
algebraic surfaces
GC^1 continuity
triangular patches
