Smoothing of three dimensional models by convolution
Smoothing of three dimensional models by convolution
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DOI：
10.1109/cgi.1996.511800
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发表时间：
1996-06
期刊：
影响因子：
--
通讯作者：
G. Sealy;G. Wyvill
中科院分区：
文献类型：
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作者：
G. Sealy;G. Wyvill
任何3D形状都可以描述为函数g(x，y，z)，其中g>；0位于形状内部，g<；0位于外部。G与合适的滤镜的卷积描述了一个平滑的形状，其中尖锐的边和角都是圆角的。这个想法提供了一种简单而统一的方法来为工程对象创建混合和圆角，并提供了一种通过平滑理想化的几何形状来构建更有机形状的方法。三维卷积需要太多的计算量，不能直接使用这个想法，但我们可以通过将卷积函数表示在三维网格上的点上并在这些点之间进行内插来进行有用的近似。网格可以是规则的，也可以是自适应的(八叉树)。使用这种方法，我们已经成功地对包括工程部件和动物形状在内的各种对象进行了建模。
Any 3D shape can be described as a function g(x,y,z) where g>0 inside the shape and g<0 outside. The convolution of g with a suitable filter describes a smoothed shape where sharp edges and corners have been rounded. This idea provides a simple and uniform method to create blends and fillets for engineering objects and a way to build more organic shapes by smoothing idealised geometrical shapes. Convolution in three dimensions requires too much computation to use this idea directly but we can make a useful approximation by representing the convolved function at points on a three dimensional grid and interpolating between these points. The grid can be regular or adaptive (octree). Using this approach, we have successfully modelled a variety of objects including engineering parts and animal forms.