Research And Applications Of Multiresolution Modeling Technology For Freeform Curves And Surfaces

In recent years, multi-resolution modeling technology has been paid more attentions. It may be presented with a group of algorithms and can be used for decomposing complex objects into simple ones combined with multi-level details. In terms of using the hierarchy of objects, the hardware ability of processing complex scenes is greatly improved. The basic theories and algorithms of multi-resolution modeling researched in this dissertation include three aspects: (1) Subdivision modeling. The rules and evaluation of Catmull-Clark subdivision surface were introduced in detail; (2) Multi-resolution modeling based on wavelet analysis. The wavelet analysis has been used widely for signal and image processing. In this dissertation, the second generation wavelets used for curves and surfaces multi-resolution analysis were studied, and the constructing methods for endpoint-interpolating B-spline wavelet and lifted B-spline wavelet were introduced in detail; (3) Multi-resolution modeling based on mesh simplification. It is concerned with the manifold or non-manifold meshes and constructs multi-resolution models in the "fine-to-coarse" mode. The quadric-based polygonal surface simplifica -tion method was discussed amply. Multi-resolution modeling technology mainly operates linear mesh surface. In order to use the multi-resolution modeling technology in some NURBS-driven CAD/CAM systems, the algorithm of transformation between Catmull-Clark subdivision surfaces and NURBS was proposed. So we can improve the modeling ability of CAD/CAM systems taking advantage of the characteristics of multi-resolution modeling technology, and the application fields of multi-resolution modeling technology were also expanded. The applications of multi-resolution modeling technology can be described as follows: (1) Research on the pretreatment algorithm for measured data based on wavelets analysis. The main tasks are to eliminate outlier data, de-noising and compressing measured data depending on the local property of wavelets in time and frequency; (2) Research on the surface reconstruction for dense scattered data. Surface reconstruction is the main task of reverse engineering. A multi-resolution and adaptive surface reconstruction algorithm was brought forward by means of combining triangulation, mesh simplification, quasi-interpolation and subdivision. The algorithm is simple and fast, applicable for a large amount of scattered data. Furthermore, manifold surfaces with arbitary topology can be reconstructed directly by means of using this algorithm; (3) Research on the wavelet smoothness algorithms for freeform curves and surfaces. Firstly, the multi-layer energy algorithm for curve smoothness was brought forward with combining the energy method and wavelets analysis. The compression function of wavelets analysis can raise the speed of energy method that can process the boundary constraints. So the algorithm is fast and can smooth curves locally. Moreover, in terms of using lifting B-spine wavelet, the complex surface smoothness algorithm was proposed. The algorithm is simple and efficient, and can process manifold surfaces with arbitary topology. This algorithm also has compression function. Another interesting advantage is that sharp corners and edges can be preserved or illuminated during smoothness with this algorithm. Based on the theories mentioned above, a multi-resolution modeling system was developed with OpenGL and Microsoft Visual C++, which can run on Windows platform. As the objects representation method and data structure, we designed a kind of improved radial edge structure. The NURBS-based objects and mesh-based objects can be represented uniformly by means of using this topology structure. In order to implement the system well, we also designed a kind of master-object system model. This model keeps advantages of the object-oriented model and improves the object management ability. In terms of using this master-object model, the system maintenance can be performed easily.