Chinese Journal of Computers   Full Text
Title	A New Interactive Method for Controlling Implicit Surfaces
Authors	ZHOU Yuan-Feng1) BO Peng-Bo3) ZHANG Cai-Ming1)，2) GAO Shan-Shan2)
Address	1)(School of Computer Science and Technology, Shandong University, Jinan 250101) 2)(School of Computer Science and Technology, Shandong Economic University, Jinan 250014) 3)(Department of Computer Science, The University of Hong Kong, Hong Kong)
Year	2009
Issue	No.6(1206—1213)
Abstract &   Background	Abstract This paper proposes a new interactive method for controlling implicit surfaces. Two interactive controlling tools are introduced: position controlling handle and normal controlling handle. The new implicit surfaces are required to interpolate the adjusted position and normal vector at desired vertices on surfaces, which are appointed by user interaction. Quasi-Newton and SQP methods are applied to solve these optimization problems respectively. Particle system is used for real-time rendering of implicit surface. This provides a real-time and interactive method for controlling the shape of implicit surfaces. Experiences are included in the end to demonstrate the efficiency of the new method. Keywords implicit surface; interactive control; optimization; particle system; objective function Background As the developments of computer graphics and computer aided design, implicit surfaces have been increasingly used for modeling, visualizing and animation. In geometric modeling, comparing with parametric surfaces, implicit surface has three obvious advantages: one is implicit surface’s simple expression form which can be described in the form of f(x)=0, another is it is easy to judge the relative position to a special point, and the third is implicit surface has high smoothness. Implicit surfaces are useful for describing continuous and smoothly blend surfaces with complex topology, and can change the topology of surfaces easily. However, effect of coefficients of an implicit surface is not intuitive. So the main drawback of implicit surfaces is difficult to control and model implicit surfaces interactively. Based on above problems, a new interactive controlling method for implicit surfaces is presented. For general implicit surfaces, shape controlling is essential on how to determine the coefficients of the new implicit surfaces. Position and normal of a selected vertex on surface controlling are used as two interactive tools in new method. Based on the desired position and normal vector offered by user, constraint objective functions are established based on interpolating conditions. Freedom degrees are determined by minimizing objective functions via optimization. Particle system is used for rendering implicit surfaces. 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 (60673003, 60573180).