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From Geometry to Motion: inverse modeling of complex mechanical structures

Periodic Reporting for period 4 - GEM (From Geometry to Motion: inverse modeling of complex mechanical structures)

Reporting period: 2020-03-01 to 2022-02-28

With the considerable advance of automatic image-based capture in Computer
Vision and Computer Graphics these latest years, it becomes now affordable to acquire quickly and
precisely the full 3D geometry of many mechanical objects featuring intricate shapes. Yet, while more
and more geometrical data get collected and shared among the communities, there is currently very
little study about how to infer the underlying mechanical properties of the captured objects merely
from their geometrical configurations.
The Gem challenge consists in developing a non-invasive method for inferring the
mechanical properties of complex objects from a minimal set of geometrical poses, in
order to predict their dynamics. In contrast to classical inverse reconstruction methods, my
proposal is built upon the claim that 1/ the mere geometrical shape of physical objects reveals a lot
about their underlying mechanical properties and 2/ this property can be fully leveraged for a wide
range of objects featuring rich geometrical configurations, such as slender structures subject to contact
and friction (e.g. folded cloth or twined filaments).
To achieve this goal, we shall develop an original inverse modeling strategy based upon a/ the
design of reduced and high-order discrete models for slender mechanical structures including rods,
plates and shells, b/ a compact and well-posed mathematical formulation of our nonsmooth inverse
problems, both in the static and dynamic cases, c/ the design of robust and efficient numerical tools
for solving such complex problems, and d/ a thorough experimental validation of our methods relying
on the most recent capturing tools.
In addition to significant advances in fast image-based measurement of diverse mechanical materials
stemming from physics, biology, or manufacturing, this research is expected in the long run to ease
considerably the design of physically realistic virtual worlds, as well as to boost the creation of dynamic
human doubles.
The project led to a diverse set of results, implying multidisciplinary collaborations:

1. A new methodology for validating quantitatively simulators of slender elastic structures and frictional contact. Our work includes validation of theory against experiments, the setting up of new scaling laws for validation, and a thorough benchmarking of popular simulators from graphics and mechanical engineering, against a suite of four selected validation protocols.

2. A new non-invasive protocol for estimating material properties of cloth and friction during dynamic interaction, including cloth-solid and cloth-cloth interaction. The method relies on a neural network fed only with simulated data, after a careful validation of the simulator.

3. Two new accurate and fast frictional contact solvers for cloth:

- Argus, relying on a nodal and adaptive version of an implicit velocity-based formulation of the discrete nonsmooth frictional contact problem.
- Projective Friction, based on a light adaptation of the Projective Dynamics algorithm.

4. A new reduced discrete ribbon model, inspired from the super-clothoid model for thin elastic rods: elements are parameterized by a linear curvature and quadratic torsion. Developability of the mid-surface is accounted for by a constraint. The model has been validated against alternative (finite-differences) ribbon models and experiments.

5. A new optimization procedure for recovering the natural shape of cloth deformed by gravity and frictional contact.

6. A theorem of existence and uniqueness for the natural shape of a rod sagged under gravity.

7. The creation in 2019 of Graphyz, the first Graphics-Physics workshop (

See for the complete set of results of the GEM project.
Uniqueness result for the natural shape of a suspended Kirchhoff rod