Abstract Mesh processing pipelines are mature, but adapting them to newer non‐mesh surface representations—which enable fast rendering with compact file size—requires costly meshing or transmitting bulky meshes, negating their core benefits for streaming applications. We present a compact neural field that enables common geometry processing tasks across diverse surface representations. Given an input surface, our method learns a neural map from its coarse mesh approximation to the surface. The full representation totals only a few hundred kilobytes, making it ideal for lightweight transmission. Our method enables fast extraction of manifold and Delaunay meshes for intrinsic shape analysis, and compresses scalar fields for efficient delivery of costly precomputed results. Experiments and applications show that our fast, compact, and accurate approach opens up new possibilities for interactive geometry processing.

We propose a fast, robust, and user-controllable algorithm for knot untangling and volume-filling curves. We extend prior work on surface-filling curves to the more challenging case of 3D volumes, equipped with a specialized gradient preconditioner that allows larger step sizes. Our method exhibits orders of magnitude faster runtime than existing methods. Our framework provides a whole new set of parameters to guide the shape of the curve, making it ideal for interactive design applications.

We introduce a fast, robust, and user-controllable algorithm to generate surface-filling curves. We compute these curves through the gradient flow of a simple sparse energy, making our method several orders of magnitude faster than previous works. Our algorithm makes minimal assumptions on the topology and resolution of the input surface, achieving improved robustness. Our framework provides tuneable parameters that guide the shape of the output curve, making it ideal for interactive design applications.

Despite the recent trend of computational origami for human-computer interaction (HCI) and digital fabrication, it is still difficult for designers to complete a series of design, simulation, and fabrication of objects leveraging computational origami theory. In this paper, we propose Crane, an integrated origami design platform implemented with Grasshopper. With this platform, users can seamlessly (1) design the 2D and 3D crease pattern, (2) simulate 3D folding transformation from the given crease pattern, (3) inversely find a new pattern under design constraints, (4) thicken the 2D pattern into a 3D volume along with the appropriate hinge structures for different fabrication methods, and (5) optionally connect the resulting design to other Rhinoceros or Grasshopper plugins for post-processes. To help understand how to use our system and demonstrate its feasibility, we showed three examples of origami products designed using our system. We also reported user feedback from the workshop as an evaluation.

We propose Inkjet 4D Print, a self-folding fabrication method of 3D origami tessellations by printing 2D patterns on both sides of a heat-shrinkable base sheet, using a commercialized inkjet ultraviolet (UV) printer. Compared to the previous folding-based 4D printing approach using fused deposition modeling (FDM) 3D printers [An et al. 2018], our method has merits in (1) more than 1200 times higher resolution in terms of the number of self-foldable facets, (2) 2.8 times faster printing speed, and (3) optional full-color decoration. This paper describes the material selection, the folding mechanism, the heating condition, and the printing patterns to self-fold both known and freeform tessellations. We also evaluated the self-folding resolution, the printing and transformation speed, and the shape accuracy of our method. Finally, we demonstrated applications enabled by our self-foldable tessellated objects.

Field-aligned parametrization is a method that maps a scalar function onto a surface, such that the gradient vector of the scalar function matches the input vector field. Using this idea, one can produce a stripe pattern that is convenient for various purposes such as remeshing, texture synthesis, and computational fabrication. In the final outcome, the positions of singularities (i.e., bifurcations of the stripe pattern) are essential for functionalities, manufacturability, or aesthetics. In this paper, we propose an algorithm to allow users to interactively edit the singularity positions of field-aligned stripe patterns. The algorithm computes a stripe pattern from a prescribed set of singularities, without generating any unwanted singularities. The solution of the algorithm is formulated as the global minima of a constrained quadratic optimization, whose computation speed is dominated by solving only two sparse linear systems. Furthermore, once the two matrices in the two linear systems are factorized, any update on singularity positions operates in linear time. We showcase several applications feasible with our fast yet simple algorithm.

Despite recent advancements in 3D printing technology, which allows users to rapidly produce 3D objects, printing tall and/or large objects still consumes more time and large amount of support material. In order to address these problems, we propose Pop-up Print, a method to 3D print an object in a compact "folded" state and then unfold it after printing to achieve the final artifact. Using this method, we can reduce the object's print height and volume, which directly affects the printing time and support material consumption. In addition, thanks to the reversibility of folding/unfolding, we can reversibly minimize the printed object's volume when unused for storage or transportation, and expand it only in use. To achieve Pop-up Print, we first conducted an experiment using selected printed sample objects with several parameters, in order to determine suitable crease patterns that make both the unfolded and folded state mechanically stable. Based on this result, we developed an interactive design tool to convert 3D models - such as a Stanford Bunny or a Huffman's cone - to the folded shape. Our design tool allows users to decide non-intuitive parameters that may affect the form's mechanical stability, while maintaining both functional crease patterns and the object's original form factor. Finally, we demonstrate the feasibility of our method through several examples of folded objects.