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An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees
July/August 2009 (vol. 15 no. 4)
pp. 596-604
ASCII Text
x 
 
Gershon Elber, Tom Grandine, "An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 4, pp. 596-604, July/August, 2009.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2009.42,
author = {Gershon Elber and Tom Grandine},
title = {An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {15},
number = {4},
issn = {1077-2626},
year = {2009},
pages = {596-604},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2009.42},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees
IS - 4
SN - 1077-2626
SP596
EP604
EPD - 596-604
A1 - Gershon Elber,
A1 - Tom Grandine,
PY - 2009
KW - Interval arithmetic
KW - multivariate polynomial constraint solver
KW - self-bisectors
KW - contact computation
KW - Hausdorff distance.
VL - 15
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
Gershon Elber, Technion - IIT, Haifa
Tom Grandine, The Boeing Company, Seattle
In recent years, several quite successful attempts have been made to solve systems of polynomial constraints, using geometric design tools, exploiting the availability of subdivision-based solvers [7], [11], [12], [15]. This broad range of methods includes both binary domain subdivision as well as the projected polyhedron method of Sherbrooke and Patrikalakis [15]. A prime obstacle in using subdivision solvers is their scalability. When the given constraint is represented as a tensor product of all its independent variables, it grows exponentially in size as a function of the number of variables. In this work, we show that for many applications, especially geometric ones, the exponential complexity of the constraints can be reduced to a polynomial by representing the underlying structure of the problem in the form of expression trees that represent the constraints. We demonstrate the applicability and scalability of this representation and compare its performance to that of tensor product constraint representation through several examples.

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Index Terms:
Interval arithmetic, multivariate polynomial constraint solver, self-bisectors, contact computation, Hausdorff distance.
Citation:
Gershon Elber, Tom Grandine, "An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 4, pp. 596-604, July-Aug. 2009, doi:10.1109/TVCG.2009.42
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