Proceedings: GI 1996

Interactive construction of smoothly blended star solids

Ergun Akleman

Proceedings of Graphics Interface '96: Toronto, Ontario, Canada, 22 - 24 May 1996, 159-167

DOI 10.20380/GI1996.19

  • BibTeX

     title = {Interactive construction of smoothly blended star solids},
     author = {Ergun Akleman},
     booktitle = {Proceedings of the Graphics Interface 1996 Conference, May 22-24, 1996, Toronto, Ontario, Canada},
     year = {1996},
     month = {May},
     isbn = {0-9695338-5-3},
     publisher = {Canadian Human-Computer Communications Society},
     url = {},
     pages = {159--167}


We introduce a computationally efficient method for interactive construction of implicitly represented star solids. These solids smoothly approximate control shapes that are defined by exact union and intersections over half-spaces containing the origin. Based on our algorithm, computation of a new solid shape when a new half-space is added or when the position of an existing half-space is changed can be performed in constant time and in space linear in the number of half-spaces.  Our implicit shape construction is based on a family of non-polynomials called ray-linears [Akle93b]. Computation of an implicitly represented shape is a root finding process and in general can be extremely difficult. However since ray-linear implicit representations can easily be parameterized, the computation of any ray-linearly represented shape simplifies to evaluation of a parametric equation instead of root finding. But the related parametric equations are non-polynomials and their complexity increases as the number of building blocks (in this case half-spaces) increases. Our algorithm makes the computation of this parametric equation independent of the number of half-spaces. We develop an interactive platform based on our algorithm with which we are able to construct star solids that resemble human faces.