保形几何

Based on conformal mapping and differential geometry theory,a triangular mesh parametrization method by optimizing deformation energy is proposed in the paper.

本文首先基于保形映射和微分几何相关理论，定义了一种统一衡量参数化的角度变形和面积变形的变形能量。

Research on application of conformal mapping in geometric modeling is investigated in this paper.

本文对保形映射理论在几何造型中的某些应用问题进行了研究，提出了基于Mbius变换的圆弧样条曲线构造方法、基于保形映射的变形造型方法以及利用保形映射进行三角网格曲面参数化的新方法。

In other words,conformal mapping has the ability to preserve local rigidity while allowing considerable global deformation.

换句话说，几何对象经过保形变换后，它的整体外形发生改变，同时又局部地保持一定的刚体性质。

In 1986, R.D.Cook proposed differential geometry to assess local influence of minor perturbations of linear statistical models. Poon and Poon(1999) constructed a conformably invariant curvature , the conformal normal curvature, for the same purpose.

Cook(1986)用微分几何的方法评估了线性统计模型微小扰动的局部影响，Poon and Poon(1999)改进了Cook提出的统计曲率概念，定义了保形法曲率。

A method of the surface combination based on classification or Euler Operation and the computation of the surface boundaries of a surface is offered to finish the geometry mapping of surfaces between half-edge model and the closed_shell branch of manifold surface model. Moreover, the concepts of conformal-shape geometrical mapping and topological mapping are given. The bi-directional conformal-shape topological mapping between half-edge model and the closed_shell branch of manifold surface model is proved.

提出了一种基于等价分类和欧拉操作的面片合成和曲面边界计算方法，完成了半边模型到流形曲面模型closed shell枝的曲面几何映射；给出了保形几何和保形拓扑映射概念，证明了半边模型到流形曲面模型的closed_shell分枝的双向保形拓扑映射。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。