Polygonica Medial Ball Algorithm Speeds CNC Quoting

Medial ball algorithm Polygonica speeds CNC tool selection

2026-04-10 Source: Machine Works 2 min Reading Time

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With its new medial ball algorithm, Polygonica aims to speed up CNC quoting and manufacturability checks by making curvature and tool accessibility analysis faster for intricate part geometries.

The medial ball analysis tool can compute curvature and local accessibility on large complex parts in seconds. The above image shows the medial ball result for a 20mm diameter cutter.(Source: Machine Works) — The medial ball analysis tool can compute curvature and local accessibility on large complex parts in seconds. The above image shows the medial ball result for a 20mm diameter cutter.
(Source: Machine Works)

Polygonica’s new medial ball algorithm provides fast curvature and local accessibility analysis to facilitate quickly choosing optimal cutting tools for complex parts with many freeform surfaces. The algorithm is aimed at automating CNC quoting algorithms, but can also be used interactively to allow the user to quickly explore regions of critical curvature whilst reviewing a part's manufacturability.

Polygonica is a component software library for working with polygon meshes that helps companies in a range of industrial markets solve complex 2D and 3D geometrical problems.

Despite a rapid growth in decision support software, it still takes a lot of skill, knowledge and experience to understand how best to CNC machine a particular CAD design. It’s not simply a matter of generating a toolpath that produces the correct geometry at the end of the job — setup time, machining time and the physics of tool wear, force and vibrations all come into play.

One of the key starting points in the assessment process is determining what cutting tools can be used, given the size and shape of geometry on the part: pockets, islands, fillets, blends and freeform surfaces with varying curvature.

If you choose a large radius cutter, you can remove more material during each tool motion, but there may be smaller features on the part that you cannot access due to the size of the tool. If you choose a small radius cutter, you can potentially machine those small fillets and pockets, but your machining time is going to increase dramatically. Machining time translates directly into cost.

Polygonica’s medial ball algorithm quickly computes the radius of the maximum sphere that can be fitted at points on the surface, making it easy to determine the maximum curvature of cutting tool that can be used to machine a particular region. Although aimed at parts with many complex freeform surfaces, the algorithm is also very useful for performing a fast assessment of machinability for prismatic parts and regions.

The new algorithm works on a facetted model which means results can usually be delivered for in tens of seconds or less. The algorithm adjusts the ball radius based on inferring the true mathematical surface from analysis of the local facetting in the region. Callbacks are provided so that the host application can provide accurate information from CAD Brep surfaces, when available, to better inform these adjustments. Example code is provided for common CAD import SDKs such as Hoops Exchange from Tech Soft 3D.

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