The ability to refine a surface representation in a general and efficient way, while maintaining a smooth appearance, is central to computer graphics. A new approach to this problem that allows editing at all levels of a mesh hierarchy is discussed in this paper.

A triangular mesh, with each triangle mapped to a group of four quintic triangular Bézier patches, is employed. Refinement is done in two stages: first, a local mesh refinement is created that provides an additional point that can be changed without destroying tangent plane continuity, thus preserving the global smooth appearance without affecting the shape beyond the local region. Second, local detail is added using the newly introduced adjustable point.

The use of well-chosen figures to illustrate the sequence of computations enhances the algorithm’s presentation. Implementation details include a description of the forest of quad trees used for efficient hierarchical computation. The efficiency and utility of the approach are demonstrated using a modeler applied to a couple of examples, where editing at various levels is illustrated. This modeler further shows that normal vector adjustment can be incorporated to provide a quite effective interface for interactive surface creation.

This is a well-constructed paper, with excellent use of color figures. Mathematical details are kept brief, with ample references for readers seeking more information.