Research On Applications Of Multiresolution Analysis In Geometry Modeling

The technology of geometry modeling refers to how to construct and represent theshapes of models. Parametric curves and surfaces and subdivision are two very importanttechniques in geometry modeling. The theories of parametric curves and surfaces were firstdeveloped in1960s, when the most well-known Bezier curve was created. In1970s B-splinewas well extended to make up the lack of capability of local control of the Bezier curve.And then, in1980s researchers developed non-uniform rational B-spline which canrepresent conic curves such as circle, parabola and so on. This research filed encapsulatesand develops many theories, such as approximation theory, interpolation theory, and spacesplitting. Another important modeling technique is subdivision. In subdivision, a givenoriginal mesh is refined by an assigned tessellation scheme many times, and finally asmoother mesh is created.The rapid development of3D digital geometry model acquisition techniques and thegradually increased requirement of3D model refinement have stimulated a new wave ofresearches on digital geometry processing theories and applications. Among many theories,multi-resolution modeling has gained special attention in many fields of computer graphicsand geometric modeling, and gives a new perspective to solve the problems of colossalgeometry model representation and process.After brief introduction to geometry modeling and multi-resolution, this paper proposesto study subdivision and parametric curves and surfaces within the multiresolutionframework. This paper’s main contributions include:1) induces Catmull-Clark subdivisionscheme from split algorithm of B-spline surface, and implements the multi-levelrepresentation of Catmull-Clark surface. The experiments show the good ability ofmultiresolution, so it gives a new method for solving progressive transmission and level ofdetail rendering. And here a new compression transmission model based on subdivision isproposed;2) introduces multiresolution representation of uniform B-spline curve, andimplements the multi-resolution curves editing. This method can modify the sweep andcharacter of B-spline separately and flexibly, strengthening the ability of B-spline editing.Obviously, Multiresolution techniques have proven their application efficiency andprospect through the above two application in geometry modeling.