Surfaces Simplification And Subdivision Surfaces Modeling

Now laser range scanners and medical imaging devices can provide vast data ofintricate physical objects. Models produced by surface reconstruction and iso-surfaceextraction methods can often be very densely sampled meshes. These models areburdening in many applications such as real-time display, transmission and storage.Therefore, surface simplification and subdivision surface modeling have been twosubjects of the surfaces modeling research.This thesis mainly describes surface simplification and subdivision surfacesmodeling. Simplification is the act of transforming a detailed 3D polygonal modelinto a simpler version, and a good simplification algorithm reduces the number ofvertices and polygons while trying to retain the good approximation of the originalshape. Subdivision defines a smooth surface as the limit of a sequence of successiverefinements. Then subdivision surfaces are obtained using some schemes to insertnew vertices and modify old vertices.Firstly, this thesis begins with a survey of the most notable available algorithmsof surfaces simplification, such as vertex clustering, vertex decimation, regionmerging, wavelet decomposition and edge collapse. Secondly, the thesis introduces aedge collapse simplification algorithm based on sharp degree. The existing automaticmesh simplification algorithms at present always ignore some important shapefeatures of the original model, such as the corners and high-curvature regions, in thelow-level model. And this will lead to degeneration in the sense of sight. Therefore,we introduce the concept of sharp degree and present our method based on QEMalgorithm, which can not only preserve the important features of model but alsodistribute meshes reasonably. We can get a better simplified model which has densemeshes in the high-curvature regions and sparse meshes in the flat regions. Thirdly,the thesis studies the modeling and application of subdivision surfaces. Subdivisionmethod has become an important tool in computer graphics especially in 3D modelingand animation fields. Two important subdivision schemes based on triangular meshes(Loop subdivision and Modified Butterfly subdivision) are listed in the end. Finally,the thesis presents a method of creating butterfly subdivision surfaces from densemeshes. Surface simplification algorithm is based on QEM which applies a sequenceof edge collapse operation. Through it we obtain subdivision surfaces'control meshes.Then subdivision surfaces that highly approximate to their original surfaces aregenerated by subdividing the control meshes using modified butterfly subdivisionscheme. In the end, thesis introduces the continuous multi-resolution models'construction and the application in web transmission. At present, surfacessimplification and subdivision are the two main method of constructingmulti-resolution models. Therefore, it is needed to continue searching a propersimplification algorithm and a subdivision scheme.