Select problems in 3d solid modeling with applications

Previous work, current plans
Model rectification: removal of short edges
One of the simplest problems of model rectification is the removal of short edges. The operation may, howewer, result in solids which do not fit in a given tolerance model.The underlying mathematics is shortly introduced. Methods of increasing the robustness of Boolean engines are discussed. Are triangular meshes easy to rectify?
Regularized Boolean set operations, regularization
It is known that instead of set-theoretical operations, the construction operations UNION, DIFFERENCE, INTERSECTION do 'regularized' set operations, because that is what matches expectation. Some non-regular 3d point sets do not even have a trivial boundary representation. It is shortly presented how Boolean engines compute regularized results.

A short excursion to the computation of 2d offsets show an application of regularization.

The question is asked if and how 'epsilon-regularization' could be defined. Even if such an operation would be difficult to implement or prove inefficient in a general setting, it is shown how an understanding of its theory might guide the development of robust algorithms for:

* Boolean set operations in vague cases,
* 3d model simplification,
* Model rectification (cf removal of short edges #above ).

Comparison of slightly different 3d models
A short introduction into the possible algorithms takes to cases where comparison based on topology (on the face/edge/vertex incidence graph) may not be the best solution (even though it is known serve certain practical applications satisfactorily).
Computation of normal vectors of parametric patches at degenerate locations
One of the partial derivatives diminishes, whereas the others may be parallel, etc. Computing a normal vector, which changes smoothly from a degenerate location to a non-degenerate one.