TY - GEN
T1 - New geometric constraint solving formulation
T2 - 6th International Conference on Image and Signal Processing, ICISP 2014
AU - Barki, Hichem
AU - Cane, Jean Marc
AU - Michelucci, Dominique
AU - Foufou, Sebti
PY - 2014
Y1 - 2014
N2 - Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient way, through a new formulation that reduces the underlying algebraic formulation to a well-constrained system of three equations in three unknowns, and avoids at the same time the use of placement rules that resolve the under-constrained original formulation. We show that geometric constraints can be specified in many ways and that some formulations are much better than others, because they are much smaller and they avoid spurious degenerate solutions. Several experimentations showing a considerable performance enhancement (x42) are reported in this paper to consolidate our theoretical findings.
AB - Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient way, through a new formulation that reduces the underlying algebraic formulation to a well-constrained system of three equations in three unknowns, and avoids at the same time the use of placement rules that resolve the under-constrained original formulation. We show that geometric constraints can be specified in many ways and that some formulations are much better than others, because they are much smaller and they avoid spurious degenerate solutions. Several experimentations showing a considerable performance enhancement (x42) are reported in this paper to consolidate our theoretical findings.
KW - 3D Pentahedron
KW - Geometric Constraint Solving Problems
KW - Parametrization
UR - http://www.scopus.com/inward/record.url?scp=84903624797&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84903624797&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-07998-1_68
DO - 10.1007/978-3-319-07998-1_68
M3 - Conference contribution
AN - SCOPUS:84903624797
SN - 9783319079974
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 594
EP - 601
BT - Image and Signal Processing - 6th International Conference, ICISP 2014, Proceedings
PB - Springer Verlag
Y2 - 30 June 2014 through 2 July 2014
ER -