NEXT       TOP


Cut Locus and Medial Axis in the Euclidean Space and on Surfaces

by Professor Franz-Erich WOLTER


Illustrative Figures

  • Self-intersection

  • Applications : 3D Modeler

     

     

    The pictures below are of 3D solids generated by a modeler based on the notion of 3D Medial Axis (from A. Howind's Masters' thesis). The boundaries (in green ) of the generated objects are the envelope surface of maximal spheres whose centers are located on the medial axis surface. These examples illustrate that it is possible to create, and modify, the shape of solid objects in an intuitive and systematic manner by modifying the maximal disc radius function associated with the initial medial axis. Growing or shrinking of the max disc radius function results in the solid's growing or shrinking, respectively.
     
     


    Example of an airplane model generated with a 3D modeler based on the 3D Medial Axis concept
    (download a LARGER picture by clicking HERE ).



    Illustration of the potential for the systematic usage of the medial axis as a modeling tool based, e.g., on size modifications of the maximal disc radius function generating, here, the boundary surface of a newly designed solid.



    Example of a "spoon"-like solid with concave and convex bounding surfaces, generated by the 3D medial axis modeler.



    3D Modeling and Self-Intersections

     



    Examples of self-intersecting envelope surfaces. These self-intersections occur if the maximal disc radius is not properly controlled during the construction of the envelope surface supposed to bound the newly designed solid.



    NEXT      TOP