Geometric Optimization for Developable Panel Approximation

This paper presents a type of surface approximation problem that commonly arises in relation to design for manufacturing of complex architectural surfaces. The engineering context of the problem is introduced by a real-world example. The problem requires approximation of each facet of a surface subdivision by a simpler surface that is economical to fabricate into a panel. However, apart from the fitting accuracy, it is also required to manage the gaps between neighboring panels. We show that the concept of shape features is useful in modeling such problems into a global optimization problem. When such non-linear optimization formulations can be solved, we obtain better solutions that the two stage method currently used by the industry. © 2014 CAD Solutions, LLC.