The paper focuses on automatic simplification algorithms for the generation of a multiresolution family of solid models from an initial boundary representation of a polyhedral solid. A n algorithm for general polyhedra based on an intermediate octree representation is proposed. Simplified elements of the multiresolution family approximate the initial solid within increasing tolerances. A discussion among different octree-based simplification methods and the standard marching cubes algorithm is presented.

Dynamic geometry systems are tools for geometric visualization. They allow the user to define geometric elements, establish relationships between them and explore the dynamic behavior of the remaining geometric elements when one of them is moved. The main problem in dynamic geometry systems is the ambiguity that arises from operations which lead to more than one possible solution. Most dynamic geometry systems deal with this problem in such a way that the solution selection method leads to a fixed dynamic behavior of the system. This is specially annoying when the behavior observed is not the one the user intended.In this work we propose a modular architecture for dynamic geometry systems built upon a set of functional units which will allow to apply some well known results from the Geometric Constraint Solving field. A functional unit called filter will provide the user with tools to unambiguously capture the expected dynamic behavior of a given geometric problem.encouraged by showing to the user which parts of the construction change and which remain unchanged.

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