  Direct modeling is a very recent CAD modeling paradigm featuring direct,
intuitive push-pull interactions with the geometry of the model to much
increase model editing flexibility. The major issue for push-pull direct
modeling is the possible inconsistency between the altered geometry of the
model and its unchanged topology. The challenge of resolving the
geometry-topology inconsistency lies in ensuring that the resulting model
remains as a valid solid model and that the model shape follows a continuous
change pattern. Although push-pull direct modeling has been implemented in
several CAD software packages, robustness towards generating valid modeling
results and continuous shape changes still remains an open issue. This paper
proposes a systematic method to handle the resolution of any possible
inconsistent situation. The method formulates the continuous shape change
requirement as successive Boolean operations on the model volume, thereby
guaranteeing valid solid models and continuous shape changes. Further, this
formulation allows for an easy implementation of push-pull direct modeling
using existing CAD research and engineering results. In order to show the
effectiveness of the proposed method, a software prototype is developed and the
modeling results are compared with those of five leading CAD software packages.
