Smooth Piecewise Polynomial Blending Operations for Implicit Shapes
Smooth Piecewise Polynomial Blending Operations for Implicit Shapes
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DOI：
10.1111/j.1467-8659.2007.01011.x
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发表时间：
2007-06
影响因子：
2.5
通讯作者：
Qingde Li
中科院分区：
文献类型：
--
作者：
Qingde Li
在本文中，我们提出了一套新的混合操作隐式定义的几何形状。所提出的形状算子是分段多项式和混合范围可控的，并且可以构造成任何所需的光滑度。这些技术背后的关键思想是引入光滑绝对函数的概念，这反过来又导致了光滑最大值函数的定义。这些新的广义绝对函数可以递归地构造或通过递归定义的函数，因此可以廉价地计算。此外，这些形状操作的基本数学描述非常简单和优雅。
In this paper, we present a new set of blending operations for implicitly defined geometric shapes. The proposed shape operators are piecewise polynomial and blending range controllable, and can be constructed to any required degree of smoothness. The key idea behind these techniques is the introduction of the concept of the smooth absolute functions, which in turn lead to the definition of smooth maximum functions. These novel generalized absolute functions can be constructed recursively or through a recursively defined functions, and can thus be computed cheaply. In addition, the underlying mathematical descriptions of these shape operations are very simple and elegant.