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Physically based morphing of point-sampled surfaces

机译：点采样曲面的基于物理的变形

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This paper presents an innovative method for naturally and smoothly morphing point-sampled surfaces via dynamic meshless simulation on point-sampled surfaces. While most existing literature on shape morphing emphasizes the issue of finding a good correspondence map between two object representations, this research primarily investigates the challenging problem of how to find a smooth, physically-meaningful transition path between two homeomorphic point-set surfaces. We analyze the deformation of surface involved in the morphing process using concepts in differential geometry and continuum mechanics. The morphing paths can be determined by optimizing an energy functional, which characterizes the intrinsic deformation of the surface away from its rest shape. As demonstrated in the examples, our method automatically produces a series of natural and physically-plausible in-between shapes, which greatly alleviates the shrinking, stretching, and self-intersection problems that often occur when linear interpolation is employed for the morphing of two objects. We envision that our new technique will continue to broaden the application scope of point-set surfaces and their dynamic animation.
机译：本文提出了一种创新的方法，可以通过对点采样表面进行动态无网格模拟，自然平滑地对点采样表面进行变形。虽然大多数有关形状变形的文献都强调在两个对象表示之间找到良好的对应图的问题，但这项研究主要研究如何在两个同胚点集表面之间找到​​平滑的，有意义的过渡路径的难题。我们使用微分几何和连续体力学中的概念分析了变形过程中涉及的表面变形。变形路径可以通过优化能量函数来确定，该函数表征表面远离其静止形状的固有变形。如示例所示，我们的方法会自动生成一系列自然且物理上可行的中间形状，从而大大缓解了在将线性插值用于两个对象的变形时经常发生的收缩，拉伸和自相交问题。我们设想我们的新技术将继续扩大点集曲面及其动态动画的应用范围。

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