Related papers: 3D POLYLLA: Polyhedral meshing algorithm based on …
We investigate the combinatorics of max-pooling layers, which are functions that downsample input arrays by taking the maximum over shifted windows of input coordinates, and which are commonly used in convolutional neural networks. We…
Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling. In our former work, we have…
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…
Volume approximation is an important problem found in many applications of computer graphics, vision, and image processing. The problem is about computing an accurate and compact approximate representation of 3D volumes using some simple…
In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study…
Fringe projection profilometry (FPP) has become increasingly important in dynamic 3-D shape measurement. In FPP, it is necessary to retrieve the phase of the measured object before shape profiling. However, traditional phase retrieval…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
Two important classes of three-dimensional elements in computational meshes are hexahedra and tetrahedra. While several efficient methods exist that convert a hexahedral element to a tetrahedral elements, the existing algorithm for…
Particle shape is a critical parameter that plays an important role in self-assembly, for example, in designing targeted complex structures with desired properties. In the last decades an unprecedented range of monodisperse nanoparticle…
If all tiles in a tiling are congruent, the tiling is called monohedral. Tiling by convex polygons is called edge-to-edge if any two convex polygons are either disjoint or share one vertex or one entire edge in common. In this paper, we…
We present Picasso, a CUDA-based library comprising novel modules for deep learning over complex real-world 3D meshes. Hierarchical neural architectures have proved effective in multi-scale feature extraction which signifies the need for…
We introduce a new practical and more general definition of local symmetry-preserving operations on polyhedra. These can be applied to arbitrary plane graphs and result in plane graphs with the same symmetry. With some additional properties…
Polygonal mesh reconstruction of a raw point cloud is a valuable topic in the field of computer graphics and 3D vision. Especially to 3D architectural models, polygonal mesh provides concise expressions for fundamental geometric structures…
A surface is considered flexible if it allows a continuous deformation that preserves both metric and smoothness. We introduce a novel construction method, called 'base + crinkle,' for generating a broad class of non-self-intersecting…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
Reconstructing and processing the 3D objects are popular activities in the research field of computer graphics, image processing and computer vision. The 3D objects are processed based on the methods like geometric modeling, a branch of…
Three-dimensional (3D) printing is a powerful development tool both in industry, as well as in biomedical research. Additive-lathe 3D printing is an emerging sub-class of 3D printing whereby material is layered outward from the surface of a…
Quad meshes are essential in geometric modeling and computational mechanics. Although learning-based methods for triangle mesh demonstrate considerable advancements, quad mesh generation remains less explored due to the challenge of…
We present a method for the efficient processing of contact and collision in volumetric elastic models simulated using the Projective Dynamics paradigm. Our approach enables interactive simulation of tetrahedral meshes with more than half a…