Kokichi Sugihara's Homepage (Japanese)

Comments on Lecture 6 "Multiple Silhouette Objects"

Comment 1. Constructability Condition for Two Silhouettes with Holes

For two connected shapes without holes, the associated multiple silhouette object can be constructed if they have the same height. This is the only condition. This condition is valid also in the case where the silhouettes have holes. This can be understood in the following way. Suppose that we consider a sufficiently long cylinder with the section of the first silhouette. No matter whether it has holes or not, this cylinder gives a rectangular canvas when we see it from side. So on this canvas we can draw the second silhouette with the same height, construct the second cylinder by sweeping this silhouette in the perpendicular direction, and compute the intersection of the two cylinders.

Comment 2. Object with Three Silhouettes

There are trials to increase the number of silhouettes from two to three. One method is to realize three silhouettes in three mutually orthogonal view directions by adding the vertical direction. On the front cover of the next book, an object with silhouettes "G", "E" and "B" is shown. [Reference]　D. R. Hofstadter, "Godel, Escher, Bach: An Eternal Golden Braid." Vintage Books, Random House, Inc., New York, 1989.
Another trial is to realize three silhouettes all in the horizontal view directions. The left figure shows an example of an object constructed in our research group. See the next reference for the detail. [Reference]　T. Ohgami and K. Sugihara: Realizability of solids from three silhouettes. Collection of Abstracts of the 24th European Workshop on Computational Geometry (Nancy, France, March 18-20, 2008), pp. 233--236.