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Miura-Ori, a celebrated origami pattern that facilitates functionality in matter, has found multiple applications in the field of mechanical metamaterials. Modifications of Miura-Ori pattern can produce curved configurations during folding,…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3-manifolds which it bounds. Gluing along S defines a Hermitian pairing on this space with values in the complex vector space…
Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…
We introduce 3inGAN, an unconditional 3D generative model trained from 2D images of a single self-similar 3D scene. Such a model can be used to produce 3D "remixes" of a given scene, by mapping spatial latent codes into a 3D volumetric…
Let $(M^3, g)$ be an asymptotically flat 3-manifold with positive ADM mass. In this paper, we show that each leaf of the canonical foliation is the unique isoperimetric surface for the volume it encloses. Our proof is based on the "fill-in"…
Most existing 3D assembly methods treat the problem as pure pose estimation, rearranging observed parts via rigid transformations. In contrast, human assembly naturally couples structural reasoning with holistic shape inference. Inspired by…
Reconstructing 3D geometry and appearance from a sparse set of fixed cameras is a foundational task with broad applications, yet it remains fundamentally constrained by the limited viewpoints. We show that this bound can be broken by…
Here we describe an ultra-low-cost origami-based approach for large-scale manufacturing of microscopes, specifically demonstrating brightfield, darkfield, and fluorescence microscopes. Merging principles of optical design with origami…
3D objectness estimation, namely discovering semantic objects from 3D scene, is a challenging and significant task in 3D understanding. In this paper, we propose a 3D objectness method working in a bottom-up manner. Beginning with…
Rigid origami has shown potential in large diversity of practical applications. However, current rigid origami crease pattern design mostly relies on known tessellations. This strongly limits the diversity and novelty of patterns that can…
For centuries, human civilizations devised metal forming techniques to make tools and items; yet, customized metal forming remains costly and intricate. Laser-forming origami} (lasergami) is a metal forming process where a laser beam cuts…
We present a framework for learning 3D object shapes and dense cross-object 3D correspondences from just an unaligned category-specific image collection. The 3D shapes are generated implicitly as deformations to a category-specific signed…
It is well known that several classical geometry problems (e.g., angle trisection) are unsolvable by compass and straightedge constructions. But what kind of object is proven to be non-existing by usual arguments? These arguments refer to…
Accurate 3D reconstruction using multi-camera RGB-D systems critically depends on precise extrinsic calibration to achieve proper alignment between captured views. In this paper, we introduce an iterative extrinsic calibration method that…
Rotational erection system (RES) represents an origami-based design method for generating a three-dimensional (3D) structure from a planar sheet without compression. Its rotational and translational kinematics is fully encoded in a form of…
We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…
Given a monocular face image as input, 3D face geometry reconstruction aims to recover a corresponding 3D face mesh. Recently, both optimization-based and learning-based face reconstruction methods have taken advantage of the emerging…
Generating animatable human avatars from a single image is essential for various digital human modeling applications. Existing 3D reconstruction methods often struggle to capture fine details in animatable models, while generative…
Optical imaging technologies are central to discovery in the life and physical sciences, yet their impact depends on how readily they can be built, adapted, and sustained across laboratories. Digital fabrication, including desktop 3D…