Liangwang Ruan, Bin Wang, Tiantian Liu, Baoquan Chen
We present an efficient and scalable method for the inverse shape design problem of elastic objects, with broad applicability to diverse materials and interactive editing. The core idea is to decouple material nonlinearity from geometry optimization by introducing the Cauchy stress tensor as an auxiliary variable. We design a three-stage scheme that iteratively optimizes the stress tensors and the rest shape, with each stage being well-posed and efficiently-solvable. To address the lack of a theoretical convergence guarantee arising from the decoupled energy formulation, we incorporate a relaxation method that ensures robust stability in practice. As a result, our method achieves a 3× speedup over the state-of-the-art asymptotic method [Jia21] on a model with 40k vertices and 112k elements (Fig. 2), and exhibits near-linear scalability to large systems (Fig. 8). We demonstrate applications including rest shape design for various materials (ranging from standard models to complex spline-based materials [XSZB15]), interactive material and force editing, and elastic object reconstruction from images.
STAGED: Stress-Tensor Assisted Global-local-global solver for interactive Elastic shape Design