彈性形變模擬： 基於剛性分析取樣的模型簡化法

Abstract

圖學領域中，模型簡化法將複雜的高維度系統降至低維度空間，進而在低維度空間下快速的運算取得近似解。在彈性形變模擬中，過去利用了非受力式分析取得低維度形變空間，可以良好的模擬無外力下的小形變行為，但無法良好模擬物體受外力下產生的劇烈形變。 我們提供一個Data-driven的系統，藉由FEM進行前模擬，取得物體數個形變行為的參考資料，進一步分析足以涵蓋這些形變資料的低維度空間。為了有效降低前模擬的時間，又同時保有一定精確度，我們提出剛性分析取樣法，藉由在前模擬前預測物體的剛性，得以預測物體受力時形變的行為，我們將會產生相同剛性的施力測試點進行群組，這些施力點將預期會產生類似的形變，因此我們僅需對每個群組進行一次的FEM前模擬，便能在更短的時間內更有效率地取得各種形變行為的資料，藉以取得良好的低維度形變空間。

In computer graphics, model reduction method, which utilizes a low-dimensional subspace to approximate the original, high-dimensional deformation space, can simulate deformation well in force-free conditions. However, when external forces are applied to simulated objects, noticeable differences between force-free modal analysis and full-scale FEM simulation can be observed. We introduce a data-driven approach that obtains a low-dimensional subspace from pre-computed deformation snapshots by FEM simulation with external forces applied to different parts of an object. In order to significantly reduce pre-computation time without sacrificing deformation quality at runtime, we propose rigidity guided sampling to efficiently select force points for FEM simulation. Our key observation is that the rigidity field of a force point is related to the potential deformation of an object. By clustering candidate force points according to the similarities of their rigidity fields, we can obtain representative force points that well captures the structural dynamics of an object. As the subspace constructed from these specifically chosen force sample points is more efficient and compact, our results show improved accuracy compared to the results of using only the modal analysis bases.