The circle is a two-dimensional geometric figure. It is the set of all points on a plane that are the same distance from a point on that plane, the center. The distance between a circle point and the center represents the radius, which is expressed by a positive real number. Thus, the diameter of a circle is twice the radius. A circle plane in three-dimensional space can be defined by three individual circle points. The circle is a fundamental object of Euclidean geometry, and the mathematics of circles is also an important basis for metrology. Many workpieces are wholly or partially circular, and form elements such as holes often have a circular shape as well. Thus, it is essential that roundness deviations can also be checked with the devices and methods of metrology. Measuring machines also almost always calculate geometrically ideal substitute elements, with free-form surface technology being an exception. Various so-called compensation methods are available for this purpose, such as the Gauss circle, the pen circle or the enveloping circle.

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