Differential and Topological Properties of Medial Axis Transforms (original) (raw)

1996, Graphical Models and Image Processing

It has several properties which neither B-Rep nor CSG directly provide. First, because it elicits important symmet-The medial axis transform is a representation of an object which has been shown to be useful in design, interrogation, aniries of an object, it facilitates the design and interrogation mation, finite element mesh generation, performance analysis, of symmetrical objects [6]. Second, the MAT exhibits dimanufacturing simulation, path planning, and tolerance specimensional reduction [14]; for example, it transforms a 3-D fication. In this paper, the theory of the medial axis transform solid region into a connected set of points, curves, and for 3-D objects is developed. For objects with piecewise C 2 boundsurfaces, along with an associated radius function described aries, relationships between the curvature of the boundary and in more detail below. Third, once a region is expressed the position of the medial axis are developed. For n-dimensional with the MAT, the skeleton and radius function themselves submanifolds of ᑬ ᑬ n with boundaries which are piecewise C 2 and may be manipulated, and the boundary will deform in a completely G 1 , a deformation retract is set up between each object natural way, suggesting applications in computer animaand its medial axis, which demonstrates that if the object is path tion. Fourth, the skeleton may be used to facilitate the connected, then so is its medial axis. Finally, it is proven that path connected polyhedral solids without cavities have path con-creation of coarse and fine finite element meshes of the nected medial axes.