ECCOMAS Congress 2016
Finite Transformation Rigid Motion Mesh Morpher
1, 3*
George Eleftheriou
2, 3
, Athanasios Liatsikouras
1, 4
, Gabriel Fougeron
1
, Guillaume Pierrot
1
ESI Group
99 rue des Solets, 94513 Rungis CEDEX, France
{george.eleftheriou,gabriel.fougeron,guillaume.pierrot}@esi-group.com
2
ESI Software Germany GmbH
Kruppstr. 90, ETEC H4, 3.OG 45145, Essen, Germany
[email protected]
3
National Technical University of Athens
P.O. Box 64069, 15710 Athens, Greece
{gel,liatsi}@central.ntua.gr
4
CentraleSupélec Laboratoire MSSMat
UMR CNRS 8579 Grande Voie des Vignes 92290 Châtenay-Malabry, France
[email protected]
ABSTRACT
A complete discrete adjoint optimization process necessitates the use of a reliable and robust mesh
deformation tool. The Rigid Motion Mesh Morpher has already been introduced in [2]. This article extends
this tool and its respective underlying theory.
The Rigid Motion Mesh Morpher is a mesh deformation tool based on the principle of gracefully deforming
the mesh in a way that keeps the motion of its parts (groups of nodes) as-rigid-as-possible. This is achieved
by minimizing a distortion metric, hence solving the problem of minimization of a mesh deformation energy
functional. Furthermore, if combined with a surface parameterization involving handle nodes with target
displacements [3] instead of just having prescribed-motion surface nodes, then it proves to be a promising
addition to a shape optimization toolchain.
An improvement upon this concept, is the development of a non-linear variant, namely, the Finite
Transformation Rigid Motion Mesh Morpher, that eliminates the need for subcycling and keeping track of
the "rigid-motion" history of the stencils for all subcycles. It employs the Polar Decomposition [4] to
compute a rotation matrix and bears some similarity to [1]. Finally, there is a significant gain in terms of
morphing efficiency and the quality of the resulting mesh. Mid-size industrial test cases have been run and
the results are hereby presented.
References
[1] Isaac Chao, Ulrich Pinkall, Patrick Sanan, and Peter Schröder. A simple geometric model for elastic
deformations. In ACM Transactions on Graphics (TOG), volume 29, page 38. ACM, 2010.
[2] George S. Eleftheriou and Guillaume Pierrot. Rigid Motion Mesh Morpher: A novel approach for
mesh deformation. In OPT-i International conference on Engineering and Applied Sciences Optimization,
June 2014.
[3] Athanasios G. Liatsikouras, George S. Eleftheriou, and Guillaume Pierrot. CAD-free soft handle
constraint parameterization tool. In ECCOMAS Congress, Crete, June 2016.
[4] Nicholas J Higham. Computing the polar decomposition-with applications. SIAM Journal on
Scientific and Statistical Computing, 7(4):1160-1174, 1986.
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