Artist-created meshes in-the-wild often do not have a well defined interior. We observe that they typically consist of a mix of solid elements, faces that bound a volume, and shell elements that represent the medial surface of a thin shell. The lack of a well-defined interior prevents downstream applications, such as solid-modeling, simulation, and manufacturing. We present a method that takes as input a surface mesh and assigns to each face a label determining whether it belongs to a solid or shell. These labels reduce ambiguity by defining the interior for solid faces through thresholding the generalized winding number field, and for shell faces as the volume within an offset. We cast the labeling problem as an optimization that outputs a solid/shell label for each face, guided by a sparse set of user inputs. Once labeling is complete, we show how the shape can be volume meshed by passing the shell faces through an offset mesher and the solid faces to an off-the-shelf tetrahedral mesher, producing a final volumetric mesh by taking their union. Experiments on diverse meshes with defects and multiple solid and shell components demonstrate that our approach delivers the desired labels, enabling modeling and simulation on wild meshes in a way that respects the user intent.

Abstract Effective representation of 2D images is fundamental in digital image processing, where traditional methods like raster and vector graphics struggle with sharpness and textural complexity, respectively. Current neural fields offer high fidelity and resolution independence but require predefined meshes with known discontinuities, restricting their utility. We observe that by treating all mesh edges as potential discontinuities, we can represent the discontinuity magnitudes as continuous variables and optimize. We further introduce a novel discontinuous neural field model that jointly approximates the target image and recovers discontinuities. Through systematic evaluations, our neural field outperforms other methods that fit unknown discontinuities with discontinuous representations, exceeding Field of Junction and Boundary Attention by over 11dB in both denoising and super‐resolution tasks and achieving 3.5× smaller Chamfer distances than Mumford–Shah‐based methods. It also surpasses InstantNGP with improvements of more than 5dB (denoising) and 10dB (super‐resolution). Additionally, our approach shows remarkable capability in approximating complex artistic and natural images and cleaning up diffusion‐generated depth maps.

Inspired by surface mesh simplification methods, we present a technique for reducing the number of Bézier curves in a vector graphics while maintaining high fidelity. We propose a curve-to-curve distance metric to repeatedly conduct local segment removal operations. By construction, we identify all possible lossless removal operations ensuring the smallest possible zero-error representation of a given design. Subsequent lossy operations are computed via local Gauss-Newton optimization and processed in a priority queue. We tested our method on the OpenClipArts dataset of 20,000 real-world vector graphics images and show significant improvements over representative previous methods. The generality of our method allows us to show results for curves with varying thickness and for vector graphics animations.

Textures are encountered often on various common objects and surfaces. Many textures combine visual and tactile aspects, each serving important purposes; most obviously, a texture alters the object's appearance or tactile feeling as well as serving for visual or tactile identification and improving usability. The tactile feel and visual appearance of objects are often linked, but they may interact in unpredictable ways. Advances in high-resolution 3D printing enable highly flexible control of geometry to permit manipulation of both visual appearance and tactile properties. In this paper, we propose an optimization method to independently control the tactile properties and visual appearance of a texture. Our optimization is enabled by neural network-based models, and allows the creation of textures with a desired tactile feeling while preserving a desired visual appearance at a relatively low computational cost, for use in a variety of applications.

Enabling adaptivity on a uniform Cartesian grid is challenging due to its highly structured grid cells and axis-aligned grid lines. In this paper, we propose a new grid structure - the adaptive staggered-tilted (AST) grid - to conduct adaptive fluid simulations on a regular discretization. The key mechanics underpinning our new grid structure is to allow the emergence of a new set of tilted grid cells from the nodal positions on a background uniform grid. The original axis-aligned cells, in conjunction with the populated axis-tilted cells, jointly function as the geometric primitives to enable adaptivity on a regular spatial discretization. By controlling the states of the tilted cells both temporally and spatially, we can dynamically evolve the adaptive discretizations on an Eulerian domain. Our grid structure preserves almost all the computational merits of a uniform Cartesian grid, including the cache-coherent data layout, the easiness for parallelization, and the existence of high-performance numerical solvers. Further, our grid structure can be integrated into other adaptive grid structures, such as an Octree or a sparsely populated grid, to accommodate the T-junction-free hierarchy. We demonstrate the efficacy of our AST grid by showing examples of large-scale incompressible flow simulation in domains with irregular boundaries.