具有物理互動特性之混合形變模型

Abstract

本論文提出了一種利用質量彈簧系統來模擬模型形狀內插變化的 新方法。將質量彈簧系統應用來模擬物體的移動與變形，在動畫模擬 的領域裡相當常見，尤其是在模擬粒子、衣物，以及紡織物等物體的 時候更是被大量使用。 而在混和形變模型的領域中，要找到兩個物體 中間的形狀，除了最直覺的線性內差以外還有許多其他方法，但至今 尚未有人使用質量彈簧系統這個方法來模擬中間的形狀。我們分別將 來源模型與目標模型建構出有一致性的兩個質量彈簧系統（即頂點、 邊以及面都具有相同的拓樸結構）。要產生一個中間的形狀，我們首 先要創建一個新的質量彈簧系統，其結構也和來源模型與目標模型一 致， 接著根據不同的權重，將相對應的彈簧做線性內插，得到一組新 的彈簧靜長度。再通過計算，找出基於這些內插後產生的彈簧靜長度 在到達平衡時候的系統狀態。經由類似的步驟，此方法也適用於同時 融合多形狀。此外，我們結合適當的碰撞偵測與處理，使得中間產生 出的模型可以與其他的物體做互動。

We present a new technique for physically-plausible shape interpolation by blending the rest lengths of springs in a mass-spring system. The proposed method begins by constructing two consistent mass-spring systems (i.e., with vertex-wise correspondence and the same topology) for the input source and target shapes, respectively, and setting the two systems as in their static states by setting the rest length of each spring as its original edge length. To create an intermediate shape, we generate a new mass-spring system that is consistent with the source and target ones and set its spring rest lengths by a linearly interpolation between them based on an interpolation factor α ∈ [0,1]. The new shape is then synthesized by computing the equilibrium of the new system given the interpolated rest lengths. Blending multiple shapes is also applicable through an analogous fashion. In addition, by combining proper collision detection and handling with the mass-spring system, the blendshape model is able to interact with other objects.