# Nonmanifold Subdivision

Media Research Laboratory

Department of Computer Science

Courant Institute of Mathematical
Sciences

New York University

### Abstract

Commonly used subdivision schemes require manifold control meshes and
produce surfaces which are manifolds, that is, each point on the
surface has a neighborhood which is a continuous one to one
deformation of a disk. However, it is often necessary to model
nonmanifold surfaces: for example, several surface sheets meeting at a
common boundary.

In this paper we describe a subdivision algorithm that makes it
possible to model nonmanifold surfaces. Any triangle mesh, subject to
the only restriction that no two vertices of any triangle coincide,
can serve as an input to the algorithm. Resulting surfaces consist of
collections of manifold patches joined along nonmanifold curves and
vertices; if desired, constraints can be imposed on the tangent planes
of manifold patches sharing a curve or a vertex.

The algorithm is an extension of a well-known Loop subdivision scheme,
and uses techniques developed for piecewise linear surfaces.

Compressed Postscript (6.9MB)

PDF (1.2MB)

Project Page: Subdivision Surfaces

Copyright © 2001 Lexing Ying, Denis Zorin