Algorithm Research On Reconstruction Of Triangle Bezier Surface Of Scattered Data Points

The technique of surface reconstruction has extensive applications in surface measuring modeling and visualization and such fields. This paper starts with the problems about surface reconstruction of scattered points, and makes a systematic research on the properties and theory of triangle Bézier surface. And based on domestic and international classical algorithm development, arbitary topological grid picewise G 1continuous geometric reconstruction is carried out.At first, this paper analyses the status of international and domestic research in relative field, derives the practical prospect and advantages of using triangle Bézier surface fitting technique, which makes foundation for the research content of this paper.The local structure of a scattered point set and its classical algorithms are investigated. An algorithm for Delaunay triangulation for scattered points is suggested, which is from points in plane.Then this paper introduces the relavent charictreristic of triangle Bézier surface, stresses the basic principle of Bézier surface and the parametric continuity, geometric continuity. Single surface is hard to meet the requirement when the shape of surface is complicated, connected multiple surfaces are adopted, which requires that there be some limitation in the continuity at the joint. Parametric continuity is replaced by geometric continuity. The surface that is G 1continuous along the boundary needs at least quad power triangle Bézier surface.In the end, two new C-T algorithms are proposed for geometric reconstruction of arbitrary topological surfaces. One of them adopts B-B patches on triangles and the other Bézier patches on rectangles. The first algorithm gives unique result unaffected by the handling order of points concerned, and the control vertexes can be calculated at once without initial estimation and correction. The innovation of the second algorithm is that Bézier patches on rectangles are adopted for the first time for this problem, hence it can be directly adopted by most CAD/CAM software. Because the two algorithms are completely local, and redundant freedoms are assiged reasonably, they are highly efficient and comparatively smooth interpolating surfaces can be constructed.