论文标题
通过隐式，多面表面近似三角形网格
Approximating triangular meshes by implicit, multi-sided surfaces
论文作者
论文摘要
i-patch是一种多面表面表示，定义为隐式色带和边界表面的组合，其成对的相交决定了斑块的自然边界。我们的目标是展示如何使用平稳连接的I-Patches集合来近似三角形网格。我们从一个粗糙的用户定义的顶点图开始，该图指定了表面的初始细分。基于此，我们创建的丝带在位置和切向意义上都沿其边缘紧密地贴合，然后我们优化贴片的自由参数，以更好地近似内部。如果表面不够准确，则需要完善网络；在这里，我们利用I-Patch构造自然支持T节点。我们还描述了一种很好地近似欧几里得距离场的归一化方法，并且可以进行有效评估。通过几个示例分析了该方法的功能和局限性。
The I-patch is a multi-sided surface representation, defined as a combination of implicit ribbon and bounding surfaces, whose pairwise intersections determine the natural boundaries of the patch. Our goal is to show how a collection of smoothly connected I-patches can be used to approximate triangular meshes. We start from a coarse, user-defined vertex graph which specifies an initial subdivision of the surface. Based on this, we create ribbons that tightly fit the mesh along its edges in both positional and tangential sense, then we optimize the free parameters of the patch to better approximate the interior. If the surfaces are not sufficiently accurate, the network needs to be refined; here we exploit that the I-patch construction naturally supports T-nodes. We also describe a normalization method that nicely approximates the Euclidean distance field, and can be efficiently evaluated. The capabilities and limitations of the approach are analyzed through several examples.
