The University of Edinburgh -
Division of Informatics
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Research Paper #946

Title:Shape Reconstruction Incorporating Multiple Non-linear Geometric Constraints
Authors:Werghi,N; Fisher,RB; Robertson,C; Ashbrook,A
Date:Feb 1999
Keywords:reverse engineering, geometric constraints, constrained shape reconstruction
Abstract:This paper deals with the reconstruction of 3D geometric shapes based on observed noisy 3D measurements and multiple coupled non-linear shape constraints. Here a shape could be a complete object, a portion of an object, a part of a building etc. The paper suggests a general incremental framework whereby constraints can be added and integrated in the model reconstruction process, resulting in an optimal trade-off between minimization of the shape fitting error and the constraint tolerances. After defining sets of main constraints for objects containing planar and quadric surfaces, the paper shows that our scheme is well behaved and the approach is valid through application on different real parts. This work is the first to give such a large framework for the integration of numerical geometric relationships in object modelling from range data. The technique is expected to have a great impact in reverse eingineering applications and manufactured object modelling where the majority of parts are designed with intended feature relationships.

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