Visualization in geometry and construction of 3-dimensional mathematical models

目前研究的几何对象以各种形式给出，如代数方程、复解析函数和微分方程。从曲面的离散数据出发，研究了高斯曲率和平均曲率等微分几何不变量最优值的计算方法。在构造几何模型的过程中，发现在每个点上包含法向信息是有效的，并建立了基于这些增强数据的构造模型的技术。我们成功地在一个立方体表面和一个恒定负曲率的铝表面上建立了27条线的模型，并取得了很高的精度。我们得到了一个令人满意的建立离散数据模型的接口的过程。

Geometric objects of present research are given in various forms such as algebraic equations, complex analytic functions and differential equations. Starting from discrete data of surfaces we investigated a method to compute optimal values of invariants in differential geometry such as Gauss curvature and mean curvature. In the process of constructing geometric models it turns out that it is efficient to include information about normal direction at each point and we established techniques to construct models based on such enhanced data. We succeeded in constructing models of 27 lines on a cubic surface and a surface of constant negative curvature made of aluminum with high accuracy. We obtained a satisfactory procedure to establish an interface for constructing models from discrete data.