The study and understanding of molecules, once the domain of blackboards and stick-and-ball models, has become more and more exclusively linked to the use of computer-aided visualizations. Our project seeks to return the physical facsimile to the biologists, allowing the use of tactile senses while interacting with and manipulating a physical model, thus aiding educational and research endeavors. To increase the effectiveness of such a tool, the model is constructed such that multiple levels of information are viewable within the single physical form, stressing the interaction between the assorted components within the molecule. We use the term 3-D physical visualizations to refer to the fabricated model, to avoid confusion with the common usage of model as a virtual representation on the computer. To effectively combine multiple components into a smooth manufacturable physical visualization, all components of the model must be in a homogeneous format. Our research sets forth a method for converting triangulated mesh data, as provided by the molecular modeling packages, into spline models. Spline models have the attractive qualities that they are smooth without triangular facets, can be combined using traditional boolean operations (and, or, not), and can be directly fabricated using modern CAD/CAM techniques. Our method divides the polyhedral representation into multiple rectangular grids, then fits interpolatory spline surfaces to the data in each region, while focusing on smoothly stitching the boundaries and corners of the spline surfaces in order to create a near G1 continuous model.
Optimal quadratic element on rectangular grids for $$H^1$$ problems
