Dimensional measurement of surfaces and their sampling

The number of the discrete samples for the dimensional measurement of machined surfaces and their coordinates is investigated. Counter to intuition, there need not be quadratically more samples than in the case for sampling lines or curves. To justify this novel scheme, accuracy is defined as the discrepancy of a finite point set. Then, from number theory, a particular sequence of numbers is used to compute the sampling coordinates, resulting in a number that is linear in 1D, at the same level of accuracy that is achieved by a 2D uniform distribution. Finally, experimental results of the measurement of machined surfaces modeled as random processes are compiled. coordinate measurement, optical scanning, surface roughness, lowdiscrepancy point sets

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