Object Modeling with Guaranteed Fulfillment of Geometric Constraints

Object modeling under consideration of geometric constraints is an important task. In this paper we describe a novel approach to achieving this goal. It has the nice property that all geometric constraints can be absolutely satisfied. To our knowledge it seems to be the first one with guaranteed constraint fulfillment. It is realized by integrating these constraints as hard conditions into the fitting process, in contrast to their use as soft optimization criteria in earlier work. We describe the principle behind our approach and give examples to show how it can be applied to practice. Experimental results will be reported on objects with numerous complex constraints. The technique proposed in this paper is expected to have a great impact in reverse engineering applications and manufactured object modeling where the majority of parts are designed with intended feature relationships.