Algorithms Of Surface Modeling In Spatial Structure And Their Program Realization

Spatial structure presents colorful shape surface, which can be classified as function surface and free surface. The function surface can be expressed by analytic expression and constructed easily. Most function surface in spatial structure is conicoid. Modeling of free surface is difficult because it has no analytic expression. However, free surface has been applied widely in spatial structure due to its vivid shape. This paper mainly researched on algorithms of surface modeling and mesh methods in spatial structure and their program realization.First, application and taxonomy of surface in spatial surface were introduced. Some problems and relevant research actuality were also expounded.A fitting algorithm based on Least Square method is raised to achieve unknown expression of conicoid. For solving the non-linear equations generated by least square method, Newton-Raphson method was combined with Negative-Grad method. Both methods are illustrated in detail, as well as their advantage and demerit. By solving Lagrange equations, a data point can be projected to a function surface including conicoid.Research on free surface is mature in Computer Aided Geometric Design (CAGD). Some of basic theories and concepts in CAGD were presented. Bezier method and B-Spline method in CAGD can be handled in surface modeling in spatial structure. Algorithm of Bicubic B-Spline Interpolation Surface was studied as an approach to build free surface. Control points and knot vectors of closed surface were discussed specially.To interpolate those data points which can not make up of topographic rectangle grid, an algorithm of interpolation surface base on Triangular Bernstein-B ezier Surface was suggested. The algorithm can handle scattered data points, Cline-Renka method was improved for three-dimensional data points.Surface in Spatial Lattice Structure is comprised of a lot of grids. Some mesh methods in Finite Element Method (FEM) are also suit to spatial structure. A grid quality criterion based on grid shape and element length was proposed.A surface modeling program orient to spatial structure was developed. In this program, the algorithms and criterion above were demonstrated by some examples.