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首页> 外文期刊>IEEE transactions on visualization and computer graphics >Polynomial surfaces interpolating arbitrary triangulations
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Polynomial surfaces interpolating arbitrary triangulations

机译：插值任意三角剖分的多项式曲面

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摘要

Triangular Bezier patches are an important tool for defining smooth surfaces over arbitrary triangular meshes. The previously introduced 4-split method interpolates the vertices of a 2-manifold triangle mesh by a set of tangent plane continuous triangular Bezier patches of degree five. The resulting surface has an explicit closed form representation and is defined locally. In this paper, we introduce a new method for visually smooth interpolation of arbitrary triangle meshes based on a regular 4-split of the domain triangles. Ensuring tangent plane continuity of the surface is not enough for producing an overall fair shape. Interpolation of irregular control-polygons, be that in 1D or in 2D, often yields unwanted undulations. Note that this undulation problem is not particular to parametric interpolation, but also occurs with interpolatory subdivision surfaces. Our new method avoids unwanted undulations by relaxing the constraint of the first derivatives at the input mesh vertices: The tangent directions of the boundary curves at the mesh vertices are now completely free. Irregular triangulations can be handled much better in the sense that unwanted undulations due to flat triangles in the mesh are now avoided.
机译：三角Bezier面片是在任意三角网格上定义光滑表面的重要工具。先前引入的4分割方法通过一组5度的切线平面连续三角形Bezier面片对2流形三角形网格的顶点进行插值。生成的曲面具有显式的闭合形式表示形式，并且在本地定义。在本文中，我们介绍了一种新的方法，该方法基于域三角形的规则4分割对任意三角形网格进行视觉平滑插值。确保表面的切线平面连续性不足以产生总体上良好的形状。在1D或2D中对不规则控制多边形进行插值通常会产生不需要的起伏。请注意，此波动问题并非特定于参数插值，而是在插值细分曲面中也会发生。我们的新方法通过放宽输入网格顶点处的一阶导数的约束来避免不必要的波动：现在，网格顶点处的边界曲线的切线方向是完全自由的。从现在可以避免由于网格中的平坦三角形导致的不希望有的起伏的意义上说，可以更好地处理不规则三角剖分。

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