Geometry in Action


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.

Part of Geometry in Action, a collection of applications of computational geometry.
David Eppstein, Theory Group, ICS, UC Irvine.

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