Transfinite interpolation over implicity defined sets
Computer Aided Geometric Design
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Real-time GPU rendering of piecewise algebraic surfaces
ACM SIGGRAPH 2006 Papers
Periodic surface modeling for computer aided nano design
Computer-Aided Design
Interactive Ray Tracing of Arbitrary Implicits with SIMD Interval Arithmetic
RT '07 Proceedings of the 2007 IEEE Symposium on Interactive Ray Tracing
Bio-CAD modeling and its applications in computer-aided tissue engineering
Computer-Aided Design
Real-Time Ray Tracing of Implicit Surfaces on the GPU
IEEE Transactions on Visualization and Computer Graphics
Procedural Function-Based Spatial Microstructures
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
SMI 2011: Full Paper: Feature based volumes for implicit intersections
Computers and Graphics
Functionally heterogeneous porous scaffold design for tissue engineering
Computer-Aided Design
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Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel representations.