Interpolating an Unlimited Number of Curves Meeting at Extraordinary Points on Subdivision Surfaces

Authors


  • * This work was supported by a URB grant number 51110-111130 from the American University of Beirut.

  • † This is obtained by replacing the vertices of an edge by their corresponding Chaikin's point, i.e. the vertices 3/4 and 1/4 from each vertex.

  • ‡ The radius r can be chosen arbitrarily.

  • § Indices are considered mod n.

Abstract

Interpolating curves by subdivision surfaces is one of the major constraints that is partially addressed in the literature. So far, no more than two intersecting curves can be interpolated by a subdivision surface such as Doo-Sabin or Catmull-Clark surfaces. One approach that has been used in both of theses surfaces is the polygonal complex approach where a curve can be defined by a control mesh rather than a control polygon. Such a definition allows a curve to carry with it cross derivative information which can be naturally embodied in the mesh of a subdivision surface. This paper extends the use of this approach to interpolate an unlimited number of curves meeting at an extraordinary point on a subdivision surface. At that point, the curves can all meet with eitherC0orC1continuity, yet still have common tangent plane. A straight forward application is the generation of subdivision surfaces through 3-regular meshes of curves for which an easy interface can be used.

Ancillary