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，研究了微分几何中高斯曲率和平均曲率等不变量的最优值的计算方法。在构建几何模型的过程中，事实证明，它是有效的，包括在每个点的法线方向的信息，我们建立了技术来构建模型的基础上，这种增强的数据。我们成功地构建了高精度的立方体表面和铝制成的恒定负曲率表面上的27条线的模型。我们得到了一个令人满意的过程，建立一个接口，从离散数据构建模型。

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.