Abstract: Provided herein are methods and apparatuses for analyzing a patient's dental arches in order to generate a treatment plan for the dentition. In particular described herein are methods and apparatuses for analyzing a patient's dental arches when the patient is missing one or more teeth. Methods and apparatuses are provided to properly number the teeth of a patient's arches after a dental scan, including automatically detect missing teeth after a dental scan and estimating the dimensions of the missing teeth. Methods and apparatuses are provided to perform an analysis of the patient's arches that uses the estimated dimensions of the missing teeth. Methods and apparatuses for designing and manufacturing the aligner are also provided.

Abstract: A method is disclosed that overcomes the problem in the prior art of requiring the use of a template or base molecule in order to compare the three dimensional configurations of molecules. The disclosed method teaches that the requirement for a template can be eliminated by handling the components of configuration—conformation versus rotation and translation in three-dimensional space—separately. The internal coordinate (torsional) space is explored first using a multi-objective genetic algorithm to minimize strain while maximizing steric and pharmacophoric concordance. Optimal overlays in Cartesian space are then obtained by applying a 3D hypermolecule construction method that makes use of linear assignment to identify optimal feature correspondences between ligands.