We introduce a new type of subdivision-based multiresolution representation for triangle meshes, kite trees, which has the flexibility to represent arbitrary triangle meshes losslessly. We also develop an algorithm for extracting a balanced kite tree representation of an arbitrary input mesh that preserves mesh topology and regularities in the subdivision structure. Our scheme allows us to combine surface information automatically extracted from input data with algorithmically-generated information in a single multiresolution representation and to represent the results of adaptive refinement of regular subdivision surfaces.
Regular subdivision in $\mathbf{Z}[\frac{1+\sqrt{5}}{2}]$