Modeling generic polyhedral objects with constraints

A generic polyhedral model is represented as a network of nodes and constraints. Nodes are 3-D vectors representing the location and orientation of the geometric entities, or measure variables such as length or cosine. Constraints are polynomial equations in the node parameters. Modeling and recognition are viewed as solving for values of the node parameters such that all the constraint equations are satisfied and the mean square error between the model and the observed shape is minimized. Buchberger´s Grobner basis algorithm and Ritt-Wu´s triangulation algorithm can be used for eliminating dependent parameters as well as for detecting inconsistency among constraints. Numerical techniques are used to find the best-fit model subject to constraints