* We unintentionally omitted a relevant prior reference: H. Lin, F. M. Chitalu, and T. Komura: Isotropic ARAP Energy Using Cauchy-Green Invariants. ACM Trans. Graph. 41, 6, 2022, ACM SIGGRAPH Asia 2022, Article 275.
This paper demonstrates how to simulate the ARAP energy with an E-based simulator, and similarly to our work, also connects F-based and E-based materials into one framework. It achieves this by differentiating an implicit function of the sum of the three singular values. Their examples are primarily about volumetric simulation, and the cloth example uses the hinge-based energy for bending; our work is about thin-shells and uses a unified energy formulation for stretching and bending. Their technique uses derivatives of the zeros of a polynomial with respect to the polynomial coefficients, and no special handling was proposed to deal with multiple roots. In general in simulation, multiple roots can be a source of singularities; and F-based simulation methods are popular because the singularities can be enumerated, analyzed and removed.