Motion planning in three dimensions using cyclides

We describe a novel technique for generating collision-free volumes in three dimensions for navigating a spherical object amidst obstacles. The volumetric path is composed of smoothly joined pieces of a low degree algebraic primitive called cyclide. The cyclide is a torus like primitive that incorporates a variable radius. In computer aided geometric design, it has been used as a blending surface and in freeform surface modeling. The present paper extends the use of cyclides into a new domain that of motion planning in 3D. The method is conceptually simple and stems from the original definition of a cyclide. We also provide two implemented examples.

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