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Recent advances in deep learning have significantly transformed the field of 3D shape generation, enabling the synthesis of complex, diverse, and semantically meaningful 3D objects. This survey provides a comprehensive overview of the…
Rank-2 tensor fields of large-scale structure, e.g. a tensor field inferred from shapes of galaxies, open up a window to directly access 2-scalar, 2-vector and 2-tensor modes, where the scalar fields can be measured independently from the…
Surface graphs have been used in many application domains to represent three-dimensional (3D) data. Another approach to representing 3D data is making projections onto two-dimensional (2D) graphs. This approach will result in multiple…
3D reconstruction of highly deformable surfaces (e.g. cloths) from monocular RGB videos is a challenging problem, and no solution provides a consistent and accurate recovery of fine-grained surface details. To account for the ill-posed…
Using degeneration to scrolls, we give an easy proof of non-existence of curves of low genera on general surfaces in P3 of degree d >=5. We show, along the same lines, boundedness of families of curves of small enough genera on general…
We investigate the vertex curve, that is the set of points in the hyperbolic region of a smooth surface in real 3-space at which there is a circle in the tangent plane having at least 5-point contact with the surface. The vertex curve is…
We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also…
Field inversion and machine learning are implemented in this study to describe three-dimensional separation flow around an axisymmetric hill and augment the Spart-Allmaras model. The discrete adjoint method is used to solve the field…
The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…
This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II…
This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the…
A path independent measure in order parameter space is introduced such that, when integrated along any closed contour in a three dimensional nematic phase, it yields the topological charge of any line defects encircled by the contour. A…
Mesh-based 3D static analysis methods have recently emerged as efficient alternatives to traditional computational numerical solvers, significantly reducing computational costs and runtime for various physics-based analyses. However, these…
Field-guided parametrization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct a discrete mesh. A key challenge in…
Reconstructing soft tissues from stereo endoscope videos is an essential prerequisite for many medical applications. Previous methods struggle to produce high-quality geometry and appearance due to their inadequate representations of 3D…
We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of…
Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition…
Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…