Accurate evaluation of functional roundness from point coordinates

• Accurate new algorithms for circularity or roundness calculation are introduced.
• Min. zone, min. circumscribed and max. inscribed circles under similar methodology.
• Reaching in agreement or outperforming results from previous methods.
• New insights for research and application on roundness uncertainty behavior.

A new analytical method and their algorithms are introduced for the minimum zone, maximum inscribed and minimum circumscribed circles determination. First, two points in the envelope circles are identified based on the circle to polar line transformation. The ordered set of polar lines allows the use of the planar straightness problem solution in the roundness problem. The two remaining points of the solution are identified through vectorial calculus. Next, the algorithms are tested in comparison with selected well-known methods, and agreement or improved solutions are reached. The algorithm speed allows an affordable estimation of its uncertainty through the Monte Carlo method, and additional insights in uncertainty behavior are studied for a practical use in roundness evaluation.