A method for the construction of bijective volumetric maps between 3D shapes is presented. Arbitrary shapes of ball-topology are supported, overcoming restrictions of previous methods to convex or star-shaped targets. In essence, the mapping problem is decomposed into a set of simpler mapping problems, each of which can be solved with previous methods for discrete star-shaped mapping problems. Addressing the key challenges in this endeavor, algorithms are described to reliably construct structurally compatible partitions of two shapes with constraints regarding star-shapedness and to compute a parsimonious common refinement of two triangulations.

中文翻译：

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通过星形分解进行双射体积映射


提出了一种在 3D 形状之间构建双射体积图的方法。支持任意形状的球形拓扑，克服了以前方法对凸形或星形目标的限制。从本质上讲，映射问题被分解为一组更简单的映射问题，每个问题都可以用以前的离散星形映射问题方法来解决。为了解决这项工作中的关键挑战，描述了算法来可靠地构建两个形状的结构兼容的分区，并对星形有约束，并计算两个三角剖分的简洁公共细化。