Research On Modeling Technology Of Subdivision Surface

Subdivision scheme is a new discrete modeling technology. Subdivision surface canexpress modeling surface through control mesh and subdivision rules. This technology notonly preserves several advantages of traditional B-spline surface, especially the propertiesof localness and affine–invariance, but also has some special advantages such asadaptability to arbitrary topology which parameter surfaces don't have. These leadsubdivision surface into one of the most powerful geometric modeling tools. However,without global analytic representation, the research about subdivision surface is difficult.The main focus of this paper is the further study of modeling technology in subdivisionsurface. Its main contents and contributions are as follows: Based on the analyses of subdivision schemes in common use, an improvedwinged-edge data structure suitable for subdivision is developed. The principle to choosesubdivision schemes in practice is presented. Surface offset is one of the basic methods in surface modeling. The algorithm ispresented for offsetting Loop subdivision surface with boundary. An approach to displacethe vertex of control mesh is utilized, which makes it still available to represent the offsetsurface of Loop subdivision surface with boundary through Loop subdivision surface. Thelinear equation system concerning Loop subdivision is established. The reason to bringerrors in offsetting process has been analyzed, and its error band has been calculated byway of the technique of sphere bounding box. The offset precision is guaranteed bysubdividing the basic control mesh properly, together with offsetting once more. By meansof detecting the self-intersection of control mesh, which has been offset, the detectionabout the self-intersection of subdivision surface and its trimming are all fulfilled. Calculating surface intersection and trimming are two important functions in surfacemodeling. Intersection and trimming of subdivision surface have been implemented in thisthesis. An idea is put forward, which converts the calculation of subdivision surfaceintersection into that of control mesh intersection. The first operation is to continuouslysubdivide the 1-neighborhood zone of intersecting triangles. When the given precision isguaranteed, the intersection lines of corresponding triangles are linked to generatesubdivision surface intersection curves. In addition, the subdivision surface is trimmed vialocally modifying topology and vertices positions of control mesh at those intersectionpoints. Though subdivision surfaces have good smoothness, some non-smooth effects arerequired in engineering surface modeling. Combined with adaptive subdivision scheme, analgorithm to modify topology of control mesh is presented and implemented for generatingthe sharp features over hybrid subdivision surface adaptively. It makes sharp features likecrease, cone, dart and corner. Based on modifying subdivision mask, the adaptivealgorithm to generate the sharp and semi-sharp features over Loop subdivision surface isimplemented. Owing to the adaptability to arbitrary topology, subdivision surface is suitable forconstructing model of product with complicated shape in reverse engineering. Analgorithm is put forward to fit Loop subdivision surfaces from an irregular and densetriangle mesh of arbitrary topology type. All features of original mesh model are firstidentified. A topology- and shape-optimization mesh simplification method is presented tofurther simplify the dense triangle mesh into an initial control mesh. The vertex withincontrol mesh of fitting subdivision surface is located by iterative modification, mesh shapeoptimization and local adaptive subdivision. This method makes it feasible to avoid thesolution of linear equation system, at the same time the distortion of fitting control mesh isovercome. Moreover, the size of control mesh, which is corresponding to the fitting Loopsubdivision surface, is smaller. The surface is reconstructed according to the givenprecision. It can represent detail characteristics of original model, a...