In recent years, there has been a growing interest in training Neural Networks to approximate Unsigned Distance Fields (UDFs) for representing open surfaces in the context of 3D reconstruction. However, UDFs are non-differentiable at the zero level set which leads to significant errors in distances and gradients, generally resulting in fragmented and discontinuous surfaces. In this paper, we propose to learn a hyperbolic scaling of the unsigned distance field, which defines a new Eikonal problem with distinct boundary conditions. This allows our formulation to integrate seamlessly with state-of-the-art continuously differentiable implicit neural representation networks, largely applied in the literature to represent signed distance fields. Our approach not only addresses the challenge of open surface representation but also demonstrates significant improvement in reconstruction quality and training performance. Moreover, the unlocked field's differentiability allows the accurate computation of essential topological properties such as normal directions and curvatures, pervasive in downstream tasks such as rendering. Through extensive experiments, we validate our approach across various data sets and against competitive baselines. The results demonstrate enhanced accuracy and up to an order of magnitude increase in speed compared to previous methods.

Abstract Finding point‐wise correspondences between images is a long‐standing problem in image analysis. This becomes particularly challenging for sketch images, due to the varying nature of human drawing style, projection distortions and viewport changes. In this paper, we present the first attempt to obtain a learned descriptor for dense registration in line drawings. Based on recent deep learning techniques for corresponding photographs, we designed descriptors to locally match image pairs where the object of interest belongs to the same semantic category, yet still differ drastically in shape, form, and projection angle. To this end, we have specifically crafted a data set of synthetic sketches using non‐photorealistic rendering over a large collection of part‐based registered 3D models. After training, a neural network generates descriptors for every pixel in an input image, which are shown togeneralize correctly in unseen sketches hand‐drawn by humans. We evaluate our method against a baseline of correspondences data collected from expert designers, in addition to comparisons with other descriptors that have been proven effective in sketches. Code, data and further resources will be publicly released by the time of publication.

We propose FlexMaps, a novel framework for fabricating smooth shapes out of flat, flexible panels with tailored mechanical properties. We start by mapping the 3D surface onto a 2D domain as in traditional UV mapping to design a set of deformable flat panels called FlexMaps. For these panels, we design and obtain specific mechanical properties such that, once they are assembled, the static equilibrium configuration matches the desired 3D shape. FlexMaps can be fabricated from an almost rigid material, such as wood or plastic, and are made flexible in a controlled way by using computationally designed spiraling microstructures.

Molding is a popular mass production method, in which the initial expenses for the mold are offset by the low per-unit production cost. However, the physical fabrication constraints of the molding technique commonly restrict the shape of moldable objects. For a complex shape, a decomposition of the object into moldable parts is a common strategy to address these constraints, with plastic model kits being a popular and illustrative example. However, conducting such a decomposition requires considerable expertise, and it depends on the technical aspects of the fabrication technique, as well as aesthetic considerations. We present an interactive technique to create such decompositions for two-piece molding, in which each part of the object is cast between two rigid mold pieces. Given the surface description of an object, we decompose its thin-shell equivalent into moldable parts by first performing a coarse decomposition and then utilizing an active contour model for the boundaries between individual parts. Formulated as an optimization problem, the movement of the contours is guided by an energy reflecting fabrication constraints to ensure the moldability of each part. Simultaneously the user is provided with editing capabilities to enforce aesthetic guidelines. Our interactive interface provides control of the contour positions by allowing, for example, the alignment of part boundaries with object features. Our technique enables a novel workflow, as it empowers novice users to explore the design space, and it generates fabrication-ready two-piece molds that can be used either for casting or industrial injection molding of free-form objects.

Designers frequently draw curvature lines to convey bending of smooth surfaces in concept sketches. We present a method to extrapolate curvature lines in a rough concept sketch, recovering the intended 3D curvature field and surface normal at each pixel of the sketch. This 3D information allows to enrich the sketch with 3D-looking shading and texturing. We first introduce the concept of regularized curvature lines that model the lines designers draw over curved surfaces, encompassing curvature lines and their extension as geodesics over flat or umbilical regions. We build on this concept to define the orthogonal cross field that assigns two regularized curvature lines to each point of a 3D surface. Our algorithm first estimates the projection of this cross field in the drawing, which is nonorthogonal due to foreshortening. We formulate this estimation as a scattered interpolation of the strokes drawn in the sketch, which makes our method robust to sketchy lines that are typical for design sketches. Our interpolation relies on a novel smoothness energy that we derive from our definition of regularized curvature lines. Optimizing this energy subject to the stroke constraints produces a dense nonorthogonal 2D cross field which we then lift to 3D by imposing orthogonality. Thus, one central concept of our approach is the generalization of existing cross field algorithms to the nonorthogonal case. We demonstrate our algorithm on a variety of concept sketches with various levels of sketchiness. We also compare our approach with existing work that takes clean vector drawings as input.

Wire wrapping is a traditional form of handmade jewelry that involves bending metal wire to create intricate shapes. The technique appeals to novices and casual crafters because of its low cost, accessibility and unique aesthetic. We present a computational design tool that addresses the two main challenges of creating 2D wire-wrapped jewelry: decomposing an input drawing into a set of wires, and bending the wires to give them shape. Our main contribution is an automatic wire decomposition algorithm that segments a drawing into a small number of wires based on aesthetic and fabrication principles. We formulate the task as a constrained graph labeling problem and present a stochastic optimization approach that produces good results for a variety of inputs. Given a decomposition, our system generates a 3D-printed custom support structure, or jig , that helps users bend the wire into the appropriate shape. We validated our wire decomposition algorithm against existing wire-wrapped designs, and used our end-to-end system to create new jewelry from clipart drawings. We also evaluated our approach with novice users, who were able to create various pieces of jewelry in less than half an hour.

We present an interactive drawing tool that provides automated guidance over model photographs to help people practice traditional drawing-by-observation techniques. The drawing literature describes a number of techniques to %support this task and help people gain consciousness of the shapes in a scene and their relationships. We compile these techniques and derive a set of construction lines that we automatically extract from a model photograph. We then display these lines over the model to guide its manual reproduction by the user on the drawing canvas. Finally, we use shape-matching to register the user's sketch with the model guides. We use this registration to provide corrective feedback to the user. Our user studies show that automatically extracted construction lines can help users draw more accurately. Furthermore, users report that guidance and corrective feedback help them better understand how to draw.