TY - JOUR
T1 - Reference software for finding Chebyshev best-fit geometric elements
AU - Anthony, G. T.
AU - Anthony, H. M.
AU - Bittner, B.
AU - Butler, B. P.
AU - Cox, M. G.
AU - Drieschner, R.
AU - Elligsen, R.
AU - Forbes, A. B.
AU - Gross, H.
AU - Hannaby, S. A.
AU - Harris, P. M.
AU - Kok, J.
N1 - Funding Information:
This paper summarizes work carried out in a project supported by the European Communities" Bureau of Reference (BCR) to develop reference software for finding best-fit geometric elements, under specified criteria, to coordinate data. The geometric elements considered are the line, plane, circle, sphere, cylinder, and cone. The criteria for determining the elements are, generally, minimum zone (MZ) and, where appropriate, minimum circumscribed (MC) and maximum inscribed (MI). The software developed implements methods founded on optimization theory. Two approaches are described: the first implements mathematical programming methods that exploit the particular structure of the problems considered and provide a unified approach to their solution; the second, applicable to the M7_ and, where appropriate, MC problems for the line \[in two-dimensions (2-D)\], plane, circle (in 2-D) and sphere, implements a combinatorial method that returns all global solutions.
PY - 1996/7
Y1 - 1996/7
N2 - This paper summarizes work carried out in a project supported by the European Communities' Bureau of Reference (BCR) to develop reference software for finding best-fit geometric elements, under specified criteria, to coordinate data. The geometric elements considered are the line, plane, circle, sphere, cylinder, and cone. The criteria for determining the elements are, generally, minimum zone (MZ) and, where appropriate, minimum circumscribed (MC) and maximum inscribed (MI). The software developed implements methods founded on optimization theory. Two approaches are described: the first implements mathematical programming methods that exploit the particular structure of the problems considered and provide a unified approach to their solution; the second, applicable to the MZ and, where appropriate, MC problems for the line [in two-dimensions (2-D)], plane, circle (in 2-D) and sphere, implements a combinatorial method that returns all global solutions.
AB - This paper summarizes work carried out in a project supported by the European Communities' Bureau of Reference (BCR) to develop reference software for finding best-fit geometric elements, under specified criteria, to coordinate data. The geometric elements considered are the line, plane, circle, sphere, cylinder, and cone. The criteria for determining the elements are, generally, minimum zone (MZ) and, where appropriate, minimum circumscribed (MC) and maximum inscribed (MI). The software developed implements methods founded on optimization theory. Two approaches are described: the first implements mathematical programming methods that exploit the particular structure of the problems considered and provide a unified approach to their solution; the second, applicable to the MZ and, where appropriate, MC problems for the line [in two-dimensions (2-D)], plane, circle (in 2-D) and sphere, implements a combinatorial method that returns all global solutions.
KW - Best fit
KW - Chebyshev approximation
KW - Combinatorics
KW - Coordinate measuring machines
KW - Geometric elements
KW - Geometric form
KW - Global solutions
KW - Reference software
KW - Substitute elements
UR - http://www.scopus.com/inward/record.url?scp=0030197020&partnerID=8YFLogxK
U2 - 10.1016/0141-6359(96)00005-0
DO - 10.1016/0141-6359(96)00005-0
M3 - Article
AN - SCOPUS:0030197020
VL - 19
SP - 28
EP - 36
JO - Precision Engineering
JF - Precision Engineering
SN - 0141-6359
IS - 1
ER -