Profile

Computing maps between data sequences is a fundamental problem with various applications in the fields of geometry and signal processing. As such, a multitude of approaches exist, that make trade-offs between flexibility, performance, and accuracy. Even recent approaches cannot be applied to periodic data, such as contours, without significant compromises due to their map representation or method of optimization. We propose a universal method to optimize maps between periodic and non periodic univariate sequences. By continuously optimizing a piecewise linear approximation of the smooth map on a common intermediate domain, we decouple the map and input resolution. Our optimization offers bijectivity guarantees and flexibility with regards to applications and data modality. To robustly converge towards a high quality solution we initially apply a low-pass filter to the input. This creates a scale space that suppresses local features in the early phase of the optimization (global phase) and gradually adds them back later (local phase). We demonstrate the versatility of our method on various scenarios with different types of sequences, including multi-contour morphing, signature prototypes, symmetry detection, and 3D motion-capture-data alignment.

• P&G Best Presentation Award

Fast, flexible, and cost efficient production of 3D models from 2D material sheets is a key component in digital fabrication and prototyping. In order to achieve high quality approximations of freeform shapes, a common set of methods aim to produce bendable 2D cutouts that are then assembled. So far bent surfaces are achieved automatically by computing developable patches of the input surface, e.g. in the context of papercraft. For stiff materials such as medium-density fibreboard (MDF) or plywood, the 2D cutouts require the application of additional cutting patterns (“kerfing”) to make them bendable. Such kerf patterns are commonly constructed with considerable user input, e.g. in architectural design. We propose a fully automatic method that produces kerfed cutouts suitable for the assembly of freeform shapes from stiff material sheets. By exploring the degrees of freedom emerging from the choice of bending directions, the creation of box joints at the patch boundaries as well as the application of kerf cuts with adaptive density, our method is able to achieve a high quality approximation of the input.