A framework for multi-dimensional adaptive subdivision objects
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
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Subdivision has gained popularity in computer graphicsand shape modeling during the past two decades, yet volumetricsubdivision has received much less attention. In thispaper, we develop a new subdivision scheme which can interpolateall of the initial control points in 3D and generatea continuous volume in the limit. We devise a set of solidsubdivision rules to facilitate a simple subdivision procedure.The conversion between the subdivided mesh and asimplicial complex is straightforward and effective, whichcan be directly utilized in solid meshing, finite element simulation,and other numerical processes. In principle, oursolid subdivision process is a combination of simple linearinterpolations in 3D. Affine operations of neighboring controlpoints produce new control points in the next level, yetinherit the original control points and achieve the interpolatoryeffect. A parameter is offered to control the tensionbetween control points. The interpolatory property of oursolid subdivision offers many benefits which are desirablein many design applications and physics simulations, includingintuitive manipulation on control points and easeof constraint enforcement in numerical procedures. We outlinea proof that can guarantee the convergence and C1continuity of our volumetric subdivision and limit volumesin regular cases. In addition to solid subdivision, we derivespecial rules to generate C1 surfaces as B-reps andto model shapes of non-manifold topology. Several examplesdemonstrate the ability of our subdivision to handlecomplex manifolds easily. Numerical experiments and futureresearch suggestions for extraordinary cases are alsopresented.