In geometry, the symmetry set is a method for representing the local symmetries of a curve, and can be used as a method for representing the shape of objects by finding the topological skeleton. The medial axis, a subset of the symmetry set is a set of curves which roughly run along the middle of an object.
... The symmetry set is then the bifurcation set of the family of distance squared functions ... it is the set of such that has a repeated singularity for some The symmetry set is then the set of such that there exist with, and together with the ...
... The medial axis of an object is the set of all points having more than one closest point on the object's boundary ... The medial axis is a subset of the symmetry set, which is defined similarly, except that it also includes circles not contained in S ... (Hence, the symmetry set of S generally extends to infinity, similar to the Voronoi diagram of a point set.) If S is given by a unit speed parametrisation, and is the unit tangent vector at each point ...
Famous quotes containing the words set and/or symmetry:
“He could walk, or rather turn about in his little garden, and feel more solid happiness from the flourishing of a cabbage or the growing of a turnip than was ever received from the most ostentatious show the vanity of man could possibly invent. He could delight himself with thinking, Here will I set such a root, because my Camilla likes it; here, such another, because it is my little Davids favorite.”
—Sarah Fielding (17101768)
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (17881824)