A Time-independent Deformer for Elastic-rigid Contacts

Abstract

We introduce a new tool that assists artists in deforming an elastic object when it comes in intersection with a rigid one. As opposed to methods that rely on time-resolved simulations, our approach is entirely based on time-independent geometric operators. It thus restarts from scratch at every frame from a pair of objects in intersection and works in two stages: the intersected regions are first matched and a contact region is identified on the rigid object; the elastic object is then deformed to match the contact while producing plausible bulge effects with controllable volume preservation. Our direct deformation approach brings several advantages to 3D animators: it provides instant feedback, permits non-linear editing, allows for the replicability of the deformation in different settings, and grants control over exaggerated or stylized bulging effects.

A time-independent deformer for elastic contacts

“…For the sake of simplicity, we will start in this overview with a pair of distinct objects (e.g., the blue plane and green sphere in Figure 2). In this case, our method follows the general pipeline introduced by Brunel et al [2020] for elastic-rigid contacts, but we entirely revisit the contact surface computation (Section 4), as well as the computation of the displacement direction (Section 5.2).…”

“…To this end, d p q each object is projected onto the other by matching every vertex with the most distant point on the opposite mesh, when it exists, along the associated mapping direction (inset figure). Note that these points (e.g., p in the inset) do not necessarily belong to the intersection zones; unlike [Brunel et al 2020], our mapping regions M 𝑙 can thus be larger than I 𝑙 . The simplest approach to compute this matching consists in casting a ray along d (resp.…”

“…Geometric modelling approaches handling collisions (e.g., [Li and Barbič 2019]) can be applied in this context, but they require expensive optimization and lack artistic controls of the deformation. Recently, Brunel et al [2020] have presented a geometric, timeindependent approach to resolve local contacts between an elastic and a rigid object, producing plausible and art-directable bulge deformations. This method relies on the computation of two regions on the elastic object: the contact zone which corresponds to the part where the two objects in collision will remain in contact, and the deformable region that will be smoothly deformed to counterbalance the volume initially enclosed by the surfaces in intersection.…”

“…However, generalizing this technique to two elastic objects in contact is very challenging because a contact zone and a deformable region need to be defined on both meshes, and most importantly, the contact zones must be consistent with each other since this region is shared by the two surfaces once the collision is resolved. In [Brunel et al 2020], the contact zone is established by computing a bijection between the two surface regions within the intersection, and then extracting the subpart of the matched surfaces that should remain in contact via a ball-testing heuristic. Since this heuristic is highly asymmetric, it cannot be applied nor easily extended to elastic-elastic contacts.…”

“…A subset of them is selected to be part of the contact zones with a novel user-controlled symmetric criterion, ensuring 𝐶 1 continuity at its boundary. The deformation method of Brunel et al [2020] can then be applied, with some improvements, independently on each mesh. The resulting deformation (Figure 1(c)) looks plausible and yet the bulge can be fully controlled by an artist.…”