Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces

Abstract

We introduce an algorithm to remesh meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips aligned to principal curvature directions and closely approximating the curved parts of the input developable, along with planar polygons representing the flat parts of the input. Such developable PQ-strip meshes are useful in many areas of shape modeling thanks to the simplicity of fabrication from flat sheet material. However, they are difficult to use in the modeling phase due to their restrictive combinatorics and locking issues. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling but generally have non-planar faces or are not aligned to principal curvature. Our method enables one to leverage the modeling flexibility of non-ruling based representations of developable surfaces but still obtain developable, curvature-aligned PQ-strip meshes. Our algorithm optimizes a scalar function on the input mesh, such that its level sets are straight and align well to the locally estimated ruling directions. The condition that guarantees straight level sets is nonlinear of high order and numerically difficult to enforce in a straightforward manner. We devise a dedicated optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle based interactive freeform modeling of developable shapes.