We characterize the solution of the following problem and describe an algorithm for numerically solving it. Two sets ofN points in the plane, labeled 1,...,N, are given: a fixed set of nominal points and a set of measured points. We wish to transform the messured points as a whole, by translation and rotation, so that the maximal distance between corresponding points in the two sets is minimized. This algorthm provides an accept-reject criterion that may be used together with a coordinate measuring machine to determine if two mating parts will fit, or if a part is sufficiently close to its ideal measurements. A weighted version, suitable for point-dependent tolerances, is also discussed, as is optimal joint scalling of the data.
[1]
H. Keller,et al.
Analysis of Numerical Methods
,
1969
.
[2]
Saharon Shelah,et al.
On the Complexity of the Elzinga-Hearn Algorithm for the 1-Center Problem
,
1987,
Math. Oper. Res..
[3]
Michael Ian Shamos,et al.
Computational geometry: an introduction
,
1985
.
[4]
E. Cheney.
Introduction to approximation theory
,
1966
.
[5]
R. Hanson,et al.
Analysis of Measurements Based on the Singular Value Decomposition
,
1981
.
[6]
Donald W. Hearn,et al.
Efficient Algorithms for the (Weighted) Minimum Circle Problem
,
1982,
Oper. Res..