Progressive combined B-reps - multi-resolution meshes for interactive real-time shape design

We present the Combined B-rep (cB-rep) as a multiresolution data structure suitable for interactive modeling and visualization of models composed of both free-form and polygonal parts. It is based on a half-edge data structure combined with Catmull/Clark subdivision surfaces. In addition to displaying the curved parts of the surface at an adaptive level-of-detail, the control mesh itself can be changed interactively at runtime using Euler operators. The tessellation of changed parts of the mesh is incrementally updated in real time. All changes in the mesh are logged, so that a complete undo/redo mechanism can be provided. We introduce Euler macros as a grouping mechanism for Euler operator sequences. The macro dependency graph, a directed acyclic graph, can be used for creating progressively increasing resolutions of the control mesh, and to guide the view-dependent refinement (pcB-rep). We consider Progessive Combined B-reps to be of use for data visualization and interactive 3D modeling, as well as a compact representation of synthetic 3D models.