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基于点表示的曲面曲率计算方法 被引量:19

Directly Compute Curvatures on Point-based Surface
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摘要 提出两种方法直接在点集模型上计算曲面的局部微分性质,包括平均曲率、高斯曲率、主曲率和主方向.第一种方法利用voronoi元和有限元,将曲率公式离散,再进行计算;第二种方法利用移动最小二乘法(ML S) ,构造局部参数曲面来逼近原始曲面,以局部参数曲面的曲率来近似点集模型的曲率.试验表明这两种方法可以在较小的误差范围内表示曲面的曲率.最后对这两种方法进行了比较,给出了各自的适用场合. Presented two methods to approximate several differential properties, including mean curvature, guass curvature, main curvatures and main directions on point-sampled surfaces. The first method transports voronoi cell and mixed finite-element/finite-volume on triangle mesh to point set. The second one uses moving least square(MLS) projection and fits a series of polynomial patch to the point set surface. Compareing our methods to the analytical results on parametric surfaces. Experiments show that the estimates are satisfying in accuracy.
出处 《小型微型计算机系统》 CSCD 北大核心 2005年第5期813-817,共5页 Journal of Chinese Computer Systems
基金 国家"九七三"重大项目 (G19980 3 0 60 0 )资助 国家自然科学基金(199710 87)资助 教育部青年教师奖励计划和教育部博士点基金 (2 0 0 10 3 5 80 0 3 )资助
关键词 曲面上的曲率 点集模型 voronoi元 移动最小二乘法 curvatures on surface point-based surface voronoi cell moving least square
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