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Clarification of the Relative Minimum Distance (RMD) Theorems
  • Valere Huypens
Valere Huypens

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The well-known Bresenham and the midpoint algorithm of Pitteway and Van Aken belong to the RMD algorithms. The RMD theorem proves why they have the highest accuracy and the fastest real time execution time. Nowadays the RMD’s have constant feedrate and they even measure the rounded arclength in real time. That was until now a main property of the Pythagorean-hodograph curves of Farouki, which also have applications in offsetting curves. The RMD algorithms implement the basic offset curves from the connected points, the implementation with the high degree PH-curves is complex. This paper proves that everyone can generate a “classic” OoA error and that everyone can correct that OoA error at an amazingly straightforward way, and furthermore the OoARange is inversely proportional with the rounded radius. Therefore, rejecting RMD algorithms for the sake of OoA is hair-splitting.