In this article, we introduce a novel reconstruction and modeling pipeline to create polygonal models from unstructured point clouds. We propose an automatic polygonal reconstruction that can then be interactively refined by the user. An initial model is automatically created by extracting a set of RANSAC-based locally fitted planar primitives along with their boundary polygons, and then searching for local adjacency relations among parts of the polygons. The extracted set of adjacency relations is enforced to snap polygon elements together, while simultaneously fitting to the input point cloud and ensuring the planarity of the polygons. This optimization-based snapping algorithm may also be interleaved with user interaction. This allows the user to sketch modifications with coarse and loose 2D strokes, as the exact alignment of the polygons is automatically performed by the snapping. The generated models are coarse, offer simple editing possibilities by design, and are suitable for interactive 3D applications like games, virtual environments, etc. The main innovation in our approach lies in the tight coupling between interactive input and automatic optimization, as well as in an algorithm that robustly discovers the set of adjacency relations.

Fascinating and elegant shapes may be folded from a single planar sheet of material without stretching, tearing or cutting, if one incorporates curved folds into the design. We present an optimization-based computational framework for design and digital reconstruction of surfaces which can be produced by curved folding. Our work not only contributes to applications in architecture and industrial design, but it also provides a new way to study the complex and largely unexplored phenomena arising in curved folding.

We present a system for automatic reassembly of broken 3D solids. Given as input 3D digital models of the broken fragments, we analyze the geometry of the fracture surfaces to find a globally consistent reconstruction of the original object. Our reconstruction pipeline consists of a graph-cuts based segmentation algorithm for identifying potential fracture surfaces, feature-based robust global registration for pairwise matching of fragments, and simultaneous constrained local registration of multiple fragments. We develop several new techniques in the area of geometry processing, including the novel integral invariants for computing multi-scale surface characteristics, registration based on forward search techniques and surface consistency, and a non-penetrating iterated closest point algorithm. We illustrate the performance of our algorithms on a number of real-world examples.