
CSG ModelsWeight functions for models in constructive solid geometry (CSG) can be constructed with the aid of Rvachev's Rfunctions. This technique provides a fully automatic mechanism for combining ``primitive'' weight functions (defining, e.g. halfspaces, ellipsoids, cubes, etc.) according to specified set operations.
A drawback of the standard Rfunction method is the global impact of each primitive function, e.g. modifying a local feature of the model changes the entire weight function w. Moreover, for complicated models, evaluating the weight function requires many recursive steps. These disadvantages can be overcome using local Rweights w_{k}. Each w_{k} is constructed via the Rfunction method with respect to a small part of the object. Then the w_{k} are combined with a suitable blending technique, e.g., using BSplines: . The CSG description of the cog wheel, shown above, involves 32 primitives. With BSpline blending this number is reduced to 4 primitive weights for a local Rweight w_{k}, as shown on the left below. The corresponding global weight function w is visualized on a cross section on the right. Local Rweights provide efficient tools for modeling essential boundary conditions in finite element simulations with websplines. Depending on the number of primitives, substantial savings in computing time are possible compared to a global approach. Author: IVM Fuchs GmbH ; Last modification: 2003/11/10 18:23:13 UTC.
