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From Geometry to Motion: inverse modeling of complex mechanical structures

Periodic Reporting for period 3 - GEM (From Geometry to Motion: inverse modeling of complex mechanical structures)

Reporting period: 2018-09-01 to 2020-02-29

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.
At the mid-term of the project, we have made two major achievements:

1. The proof of the existence of an unique solution to the inverse static Kirchhoff problem. These theoretical and numerical results have just been published in the journal Proceedings of the Royal Society A;

2. The development of a frictional contact solver for cloth/shells with an unpreceding level of realism compared to previous cloth simulators. This contribution has just been accepted for publication at ACM SIGGRAPH 2018 (journal Transactions on Graphics);
Uniqueness result for the natural shape of a suspended Kirchhoff rod