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In this paper we present several formulae for computing the partial degrees of the defining polynomial of the offset curve to an irreducible affine plane curve given implicitly, and we see how these formulae particularize to the case of rational curves. In addition, we present a formula for computing the degree w.r.t the distance variable.
The offset hypersurface <i>O</i><inf><i>d</i></inf>(<i>V</i>), at distance <i>d</i>, to an irreducible hypersurface <i>V</i> is essentially the envelope of the system of spheres centered at the points of <i>V</i> with fixed radius <i>d</i> (for a formal definition, and for basic properties of offsets, see  and ). This type of geometric objects have… (More)
We solve a set of tasks for a general 3D-cube-lattice-based homogeneous robotic system, including self organizing —counting the number of modules, finding a master, computing the bounding box, forming a tree— as well as locomotion and reconfiguration. The algorithms proposed are generic and can be applied to a wide variety of particular systems. The modules… (More)