CSG Models

Weight functions for models in constructive solid geometry (CSG) can be constructed with the aid of Rvachev's R-functions. This technique provides a fully automatic mechanism for combining ``primitive'' weight functions (defining, e.g. halfspaces, ellipsoids, cubes, etc.) according to specified set operations.

Set operation	Corresponding standard R-function
Complement:
Intersection:
Union:

A drawback of the standard R-function 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 R-weights w_k. Each w_k is constructed via the R-function method with respect to a small part of the object. Then the w_k are combined with a suitable blending technique, e.g., using B-Splines:

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The CSG description of the cog wheel, shown above, involves 32 primitives. With B-Spline blending this number is reduced to 4 primitive weights for a local R-weight w_k, as shown on the left below. The corresponding global weight function w is visualized on a cross section on the right.

Local R-weights provide efficient tools for modeling essential boundary conditions in finite element simulations with web-splines. 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.