Deformation with Enforced Metrics on Length, Area and Volume

Abstract

Techniques have been developed to deform a mesh with multiple types of constraints. One limitation of prior methods is that the accuracy of demanded metrics on the resultant model cannot be guaranteed. Adding metrics directly as hard constraints to an optimization functional often leads to unexpected distortion when target metrics differ significant from what are on the input model. In this paper, we present an effective framework to deform mesh models by enforcing demanded metrics on length, area and volume. To approach target metrics stably and minimize distortion, an iterative scale-driven deformation is investigated, and a global optimization functional is exploited to balance the scaling effect at different parts of a model. Examples demonstrate that our approach provides a user-friendly tool for designers who are used to semantic input.