The objectives of this research are to develop a theoretical framework and geometrical algorithms for the robust and fast intersection of surfaces used in geometric and solid modeling. Symbolic computation will be used. That is, instead of applying algebraic or numerical techniques, the use of a basic set of geometry routines (line/line intersection, line/circle intersection, etc.) combined with a set of techniques for the easy construction and linkage of intersection points is applied. The research has the following significant output: o a set of robust, fast and reliable intersectors that are capable of handling special cases such as touching and overlapping surfaces, o a set of visually describable algorithms that can be included in an academic course, and o theoretical and computational foundation of robust three-dimensional geometric computations.
