Research On Trimming, Shape-modifying And Bounds Of Surfaces In Geometric Modeling

Spline surfaces are the main methods and core contents in CAGD. The following three problems arising from using spline surfaces in geometric modeling are researched in this dissertation.1. The trimming of spline surface. Trimming of surface means how to refine a subdomain of a given surface for further processing of this subdomain and the left parts. Many problems such as subdivision and connection of surfaces can be regarded as the special cases of trimming. By means of blossoms, one united method is given for the problem of trimming with lines firstly. Then this method is generalized to trimming with polynomial curves, which makes more choices for the shape of trimming subdomain. The method is working for both polynomial surfaces and rational cases.2. When the control points are given, the shape of classical Bezier curve or surface is uniquely decided. For remedying this cases, the generalized Bezier curve and surface with multi-shape-parameters are given, which not only hold the excellent properties of classical Bezier curve or surface, but also can changing the shape of the curve or surface with the shape parameters. The geometric significance of shape parameters is clearly, the modifying style can be foreseen and evaluated accurately. And the connecting of generalized Bezier curves and surfaces are also discussed.3. The bound of spline surface means how to evaluate the distance from the surface to a fixed position for deciding a small and accurate topologic bound of this surface. The bounds of Bezier and B-Spline surfaces have some researched achievements. This thesis gives a bound of three direction quartic box spline surface which is well used in geometric modeling with triangular surfaces. The distance from the surface to the central triangular plane patch over control net is described with the direction differences of control points.