## Metrology

Metrology is the science of measurement of objects at all scales.
The NIST's project on "Computational Geometry and Metrology"
includes the use of geometric techniques including
mesh generation in computer simulations
to study the accuracy and precision of coordinate measuring machines
(machines which measure the dimensions of parts in a three-dimensional
coordinate system). There are also connections with
geographic information systems relating
to problems of surveying or otherwise measuring large areas of land.
One type of problem of particular interest in
manufacturing is determining
from a sequence of measurements the tolerance of a part;
that is, its departure from the Platonic ideal form of its design.
There has been some related work in the computational geometry community,
on problems such as constructing the minimum width annulus containing the
boundary of an input figure (a measure of its roundness) however there
has been little systematic treatment of such problems.
Chee Yap recently spoke on this subject at the 5th MSI
Worksh. on Computational Geometry; his talk pointed out the possibility
of designing algorithms
that take advantage of some known structure in a sequence of measurements,
and of coupling measurement and computation in an adaptive probing algorithm.

- Aspects of Dimensional Tolerancing,
Chee Yap, 5th MSI Worksh. Comp. Geom.

- Exact Computational Geometry and Tolerancing Metrology,
survey by Chee Yap, NYU, Feb. 1995

- Gatling guns.
Computational questions related to Matousek's work on violated constraints,
from a problem of testing guns.

- Guaranteeing
bounds on uncertainty in metrology. A. Neumaier advocates interval
arithmetic as an approach to robustness in geometric computation.

- NIST projects in computational geometry and metrology

- NIST Yearly Reports, 1995: Computational Geometry and Metrology

- Open
Problems in Computational Metrology,
C. Duncan, Johns Hopkins.

- A Review
of Current Geometric Tolerancing Theories and Inspection
Data Analysis Algorithms, S. Feng and T. Hopp, US Dept. Commerce, 1991.

- US
Patent 5465221 describes a part inspection system including the use
of convex hulls to determine stable orientations.

Part of
Geometry in Action,
a collection of applications of computational geometry.

David Eppstein,
Theory Group,
ICS,
UC Irvine.

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