The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application,...The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.展开更多
In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 cont...In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves.展开更多
基金Project supported by the Outstanding Youth Grant of Natural Science Foundation of China (No. 60225002), the National Basic Research Program (973) of China (No. 2004CB318000), the National Natural Science Foundation of China (Nos. 60533060 and 60473132)
文摘The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.
基金Supported by the National Key Basic Research Project of China (No. 2004CB318000)the NSF of China(No. 60533060/60872095)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education (No.20060358055)the Subject Foundation in Ningbo University(No. xkl09046)
文摘In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves.
