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Interpolation over arbitrary topology meshes using a two-phase subdivision scheme

机译:使用两阶段细分方案对任意拓扑网格进行插值

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The construction of a smooth surface interpolating a mesh of arbitrary topological type is an important problem in many graphics applications. This paper presents a two-phase process, based on a topological modification of the control mesh and a subsequent Catmull-Clark subdivision, to construct a smooth surface that interpolates some or all of the vertices of a mesh with arbitrary topology. It is also possible to constrain the surface to have specified tangent planes at an arbitrary subset of the vertices to be interpolated. The method has the following features: 1) it is guaranteed to always work and the computation is numerically stable, 2) there is no need to solve a system of linear equations and the whole computation complexity is O(K) where K is the number of the vertices, and 3) each vertex can be associated with a scalar shape handle for local shape control. These features make interpolation using Catmull-Clark surfaces simple and, thus, make the new method itself suitable for interactive free-form shape design.
机译:内插任意拓扑类型的网格的平滑表面的构造是许多图形应用程序中的重要问题。本文基于控制网格的拓扑修改和随后的Catmull-Clark细分,提出了一个两阶段过程,以构造平滑表面,该表面插值具有任意拓扑的网格的部分或全部顶点。也可以将曲面约束为在要插值的顶点的任意子集处具有指定的切平面。该方法具有以下特点:1)保证始终工作并且计算是数值稳定的; 2)无需求解线性方程组,并且整个计算复杂度为O(K),其中K为数3)每个顶点可以与标量形状手柄关联以进行局部形状控制。这些功能使使用Catmull-Clark曲面进行插值变得简单,因此使新方法本身适用于交互式自由形状设计。

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