The Research And Development Of The Algorithms Used To Disperse And Display NURBS Curves And Surfaces In Surface Modeling

The surface modeling is one of the most active and pivotal embranchments in Computer Aided Geometric Design, having been developing with the in-depth application of the CAD/CAM technology.During the course of defining product shape, the NURBS way is always adopted as an industrial standard because of its outstanding merits, and applied to industrial product design widely, witch leads to geometric process problems of free form surfaces.Moreover,the curve and surface subdivision occurs in 3D object rendering, surface approximation,wireframe displaying, finite element analysis and computing surface intersections,and so on. Therefor, it is important significance to study a practical, steady and efficient algorithm to disperse curves and surfaces.At the same time, 3D object models are often expressed with triangular meshs in computer graphics and geometric shaping. With the advance of metrical equipment precision, the triangular mesh model obtained by the way of three dimensional model reconstruction usually comprises millions of triangular facets, and that slowers the speed of real time graphics rendering that the applications require. So 3D acceleration of real time graphics rendering is becoming a focus in computer graphics research areas, for example, in Virtual Reality. To reduce rendering time, in addition to utilizing faster and more powerful hardware function, another way is to decrease time consumption during geometric process by reducing the number of triangular facets. Thereby, it also has an important significance to study a simplification algorithm based on triangular mesh model, which can lessen some inconsequential details according to requirement of precision and consequently improve rendering speed.The problems which come forth when we disperse NURBS curves or surfaces and display them in surface modeling are discussed in this dissertation.The principle content studied in this thesis includes:??The theory of dispersing NURBS curves and confirming approximating precision; based on these, an adaptive binary-tree subdivision method to disperse a NURBS curve is put forward.??The theory and method of dispersing NURBS surfaces, including confirming approximating precision, the uniform dispersing in common borders, producing inner nodes, producing cells and computing normal unit vector for NURBS surface; a boundery process algorithm for triangulation of multi-trimmed surfaces are broughtforward, and a rapid and effective approach of subdividing the parametric space of trimmed NURBS surfaces is adopted. The theory of a mesh simplification algorithm based on edge convergence and a vertex-spliting algorithm; based on this mesh simplification algorithm, the author brings forward a way to process the mesh models with inner border, and provides detailed description of how to build a Multiple Resolution Model.Finally, the author implements the above curve and surface subdivision and mesh simplification algorithms in a 3D graphics browser system by utilizing Visual C++ 6.0, OpenGL, Windows2000.