Generalized distance functions
Generalized distance functions
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广义距离函数
DOI：
10.1109/sma.1999.749326
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Jianer Chen
中科院分区：
文献类型：
--
作者：
E. Akleman;Jianer Chen
我们得到了一个广义版本的著名的距离函数家庭L/子p/范数。我们证明了新的函数满足距离函数的性质。通过使用这些函数，凸对称形状可以被描述为轨迹，从给定点等距离的点的集合。我们还表明，这些对称的凸形状可以很容易地参数化。我们还证明了这些距离函数满足Lipschitz型条件。我们提供了一个快速的光线行进算法来绘制这些距离函数所描述的形状。这些距离函数可以用作一些隐式建模工具的构建块，例如软对象，构造性软几何，函数表示（freps）或光线二次曲面。
We obtain a generalized version of the well-known distance function family L/sub p/ norm. We prove that the new functions satisfy distance function properties. By using these functions, convex symmetric shapes can be described as loci, the set of points which are in equal distance from a given point. We also show that these symmetric convex shapes can be easily parameterized. We also show these distance functions satisfy a Lipschitz-type condition. We provide a fast ray marching algorithm for rendering shapes described by these distance functions. These distance functions can be used as building blocks for some implicit modeling tools such as soft objects, constructive soft geometry, function representations (freps) or ray quadrics.