Related papers: Vector Field Based Volume Peeling for Multi-Axis M…
Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is…
The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not…
Numerical tests of volume formulae are presented to compute efficiently the volume enclosed between flux surfaces for integrable 3D vector fields with various degrees of symmetry. In the process, a new case is proposed and tested.
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
We introduce AmodalSVG, a new framework for amodal image vectorization that produces semantically organized and geometrically complete SVG representations from natural images. Existing vectorization methods operate under a modal paradigm:…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
Comprehending 3D environments is vital for intelligent systems in domains like robotics and autonomous navigation. Voxel grids offer a structured representation of 3D space, but extracting high-level semantic meaning remains challenging.…
Scalable generation of outdoor driving scenes requires 3D representations that remain consistent across multiple viewpoints and scale to large areas. Existing solutions either rely on image or video generative models distilled to 3D space,…
Neural surface reconstruction aims to reconstruct accurate 3D surfaces based on multi-view images. Previous methods based on neural volume rendering mostly train a fully implicit model with MLPs, which typically require hours of training…
The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be $L^2$-orthogonally decomposed into a curl-free, divergence-free, and a harmonic…
Using a designed vector field to control a mobile robot to follow a given desired path is intuitive and practical, and to build a rigorous theory to guide its implementation is essential. In this paper, we study the properties of a general…
We introduce an approach for selecting objects in neural volumetric 3D representations, such as multi-plane images (MPI) and neural radiance fields (NeRF). Our approach takes a set of foreground and background 2D user scribbles in one view…
Robust and scalable function evaluation at any arbitrary point in the finite/spectral element mesh is required for querying the partial differential equation solution at points of interest, comparison of solution between different meshes,…
Smooth vector fields on $\mathbb{R}^n$ can be decomposed into the sum of a gradient vector field and divergence-free (solenoidal) vector field under suitable hypotheses. This is called the Helmholtz-Hodge decomposition (HHD), which has been…
We present Neural Microfacet Fields, a method for recovering materials, geometry, and environment illumination from images of a scene. Our method uses a microfacet reflectance model within a volumetric setting by treating each sample along…
We construct a polynomial planar vector field of degree two with one invariant algebraic curves of large degree. We exhibit an explicit quadratic vector fields which invariant curves of degree nine, twelve, fifteen and eighteen degree.
We present a method for fabricating general models with multi-directional 3D printing systems by printing different model regions along with different directions. The core of our method is a support-effective volume decomposition algorithm…
A technique using vector Slepian harmonics and multipole fields is presented for a general treatment of the inverse problem of high numerical aperture focusing. A prescribed intensity distribution or electric field distribution in the focal…
We are working on the development of a method for optimizing wide-field X-ray telescope mirror prescriptions, including polynomial coefficients, mirror shell relative displacements, and (assuming 4 focal plane detectors) detector placement…
Vectorization of images is a key concern uniting computer graphics and computer vision communities. In this paper we are presenting a novel idea for efficient, customizable vectorization of raster images, based on Catmull Rom spline…