Related papers: Algebraic Representations for Volumetric Frame Fie…
Vessels are complex structures in the body that have been studied extensively in multiple representations. While voxelization is the most common of them, meshes and parametric models are critical in various applications due to their…
Framework materials and their deformations provide a compelling relation between materials science and algebraic geometry. Physical distance constraints within the material transform into polynomial constraints, making algebraic geometry…
We propose Medial Atom Ray Fields (MARFs), a novel neural object representation that enables accurate differentiable surface rendering with a single network evaluation per camera ray. Existing neural ray fields struggle with multi-view…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
Subdivision methods such as quadtrees, octrees, and higher-dimensional orthrees are standard practice in different domains of computer science. We can use these methods to represent given geometries, such as curves, meshes, or surfaces.…
Electromagnetic metasurfaces offer the capability to realize almost arbitrary power conserving field transformations. These field transformations are governed by the generalized sheet transition conditions, which relate the tangential…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Recent work has demonstrated that volumetric scene representations combined with differentiable volume rendering can enable photo-realistic rendering for challenging scenes that mesh reconstruction fails on. However, these methods entangle…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
In modern computer vision, the optimal representation of 3D shape continues to be task-dependent. One fundamental operation applied to such representations is differentiable rendering, as it enables inverse graphics approaches in learning…
We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities,…
We propose a novel explicit dense 3D reconstruction approach that processes a set of images of a scene with sensor poses and calibrations and estimates a photo-real digital model. One of the key innovations is that the underlying volumetric…
The ability to accurately produce geometries with specified properties is perhaps the most important characteristic of a manufacturing process. 3D printing is marked by exceptional design freedom and complexity but is also prone to…
In this paper we introduce three complementary three-dimensional weighted quadratic enrichment strategies to improve the accuracy of local histopolation on tetrahedral meshes. The first combines face and interior weighted moments…
Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical…
A mesh-based parametrization is a parametrization of a geometric object that is defined solely from a mesh of the object, e.g., without an analytical expression or computer-aided design (CAD) representation of the object. In this work, we…