Chinese Journal of Computers   Full Text
Title	Feature Preserving Mesh Simplification Algorithm Based on Square Volume Measure
Authors	ZHOU Yuan-Feng1) ZHANG Cai-Ming1),2) HE Ping1)
Address	1)(School of Computer Science and Technology, Shandong University, Jinan 250101) 2)(School of Computer Science and Technology, Shandong Economic University, Jinan 250014)
Year	2009
Issue	No.2(203—212)
Abstract &   Background	Abstract A new algorithm for mesh simplification with triangle collapse based on square volume measure is presented in this paper. Models can be simplified by minimizing error objective function. Square volume error, shape factor and normal constraint factor of triangles are combined together to define the simplification error, which can be described as a quadratic objective function. New vertices replaced collapsed triangles can be determined linearly. Comparing with the QEM method which is the most effective method so far, computation complexity will not be increased. Gaussian curvature factor is computed for each collapsed triangle and used to identify strong feature triangle. For non-strong feature triangle, new vertex position is determined by minimizing the error objective function. For strong feature triangle, new vertex is taken the strong feature vertex of the three triangle vertices for preserving the model feature. Each collapsed triangle is processed as inner triangle or boundary triangle to keep the boundary feature. Experiments for the efficiency of the new algorithm are included. Keywords mesh simplification; triangle collapse; SVE; feature factor; objective function; Gaussian curvature Background Polygonal meshes are widely used in computer graphics, visualization and CAD/CAM systems. Triangular mesh and quadrangular mesh are two common mesh presentation forms. Triangular mesh is used more widely for its simple expression and steady topology. For more complex models, the current graphics systems are hard to handle them. As models get larger, they are more difficult to store, transfer, render and modify. One of the best solution is to represent the complex model in multi-resolution models via mesh simplification. Mesh simplification should use less Polygons to express the original models, and keep less distortion comparing with original models. Most of existing methods can’t give good performance both in simplification quality and simplification speed. In this paper, a new method is presented for mesh simplification based on triangle collapse. For preserving the given model as far as possible and improving the quality of model together, square volume error (SVE) is used to define mesh variation after simplification. Combining with triangle shape factor and normal constraint factor to define the collapse error of a triangle which is a quadratic objective function. New vertex which replaces collapsed triangle is determined linearly by minimizing this objective function. Gaussian curvature filter factor is used to judge the strong feature triangles so that the strong feature triangles can be preserved. This method is computationally efficient and easy to implement. Experimental results show that the method can produce ideal mesh simplification results. This work was supported by the National Basic Research Program (973 Program) of China (No.2006CB303102) and the National Nature Science Foundation of China (Nos.60673003, 60573180).