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中文摘要：
为了使平面形状混合得到较好的结果，提出了一种新的构造2个多边形的高质量同构三角剖分的有效方法．通过加入一定数目的Steiner点生成其中一个多边形的质量较好的三角剖分，根据此三角网格中顶点之间的相对位置关系和邻接关系确定另一个多边形的三角剖分，然后利用面积均等方法和其他优化方法对同构的三角剖分同时进行优化．此算法将同构三角剖分的构造转化为一个稀疏线性方程组的求解，可以通过已有的程序库进行快速求解；同时通过约束一些对应特征点的位置，使生成的同构三角剖分具有较好的特征对应．此算法计算量小，运行效率高，对形状复杂的多边形仍然可以得到满意的结果，适合于morphing等实时性的应用要求．
英文摘要：
A novel and efficient approach for building high quality compatible triangulations between two simple polygons was presented to obtain good results of planar shape blending. A high quality triangulation was easily constructed for the first polygon by adding some Steiner points on the boundary of and inside the polygon. Then the connectivity of the triangulation vertices was transferred into the second polygon, whose vertices＇ positions were determined by the relative geometric relationship in the first triangulation. Some efficient approaches including area equalization, edge swap, and Laplace smoothing were used to optimize the triangles in both triangulations. The construction of compatible triangulation was formulated as a sparse linear system, which could be easily solved by some solver library. Furthermore, the fea- tures of the triangulations could be preserved by adding linear constraints in the linear system. This approach is simple and fast and can obtain satisfied results for complex polygons. Experimental results were presented to show the applicability and flexibility of the approach.
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