提出了一种基于变分隐函数插值的连续多分辨率模型生成算法,通过递归地删除网格模型中的边得到连续的简化模型.算法采用变分隐函数插值的方法对网格模型分区域插值,生成原始模型的区域插值隐函数曲面，并以对应隐函数曲面上的采样点作为边折叠的目标点.算法建立了可调加权控制函数来控制边的简化顺序.在模型简化过程中,可通过交互调节控制函数的权值执行不同的简化原则,使得重要度低的边优先删除.此外,通过建立独立集,避免了模型的局部过度简化.实验结果表明,此算法能实现较理想的简化效果.

In this paper, the authors present a new multiresolution modeling algorithm, which generates the full set of simplified polygonal models by progressively removing insignificant edges from previous models. This algorithm first divides the polygonal mesh of the model into regions and interpolates each region with a variation implicit surface. When an edge is collapsed, its target point is obtained by sampling the relative implicit surface. A weighted control function is adopted to determine the order of edge collapse operation. The algorithm dynamically adjusts the weights of the control function in different simplification phases so that the less important edges for appearance preservation are always removed earlier than other edge candidates. Furthermore, independent sets are defined to avoid excessive local simplification. Experimental results show that the proposed algorithm can achieve satisfactory result.

本文研究得到国家自然科学基金(No.69823003)、国家杰出青年基金(No.69925204)和高等学校骨干教师基金资助.