Parametric surface
View article
AtlasNet: A Papier-M\\^ach\\'e Approach to Learning 3D Surface Generation Open
We introduce a method for learning to generate the surface of 3D shapes. Our\napproach represents a 3D shape as a collection of parametric surface elements\nand, in contrast to methods generating voxel grids or point clouds, naturally\ninf…
View article
Creation of Parametric BIM Objects from Point Clouds Using Nurbs Open
This paper presents an innovative procedure to create parametric building information modelling ( BIM ) objects from point clouds of complex architectural features. BIM technology requires an advanced parametric representation of the geome…
View article
Surface Reconstruction from Point Clouds without Normals by Parametrizing the Gauss Formula Open
We propose Parametric Gauss Reconstruction (PGR) for surface reconstruction from point clouds without normals. Our insight builds on the Gauss formula in potential theory, which represents the indicator function of a region as an integral …
View article
DeepSpline: Data-Driven Reconstruction of Parametric Curves and Surfaces Open
Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have traditio…
View article
A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization Open
Summary A framework to validate and generate curved nodal high‐order meshes on Computer‐Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin‐shell and 3D finite element …
View article
AtlasNet: A Papier-Mâché Approach to Learning 3D Surface Generation Open
We introduce a method for learning to generate the surface of 3D shapes. Our approach represents a 3D shape as a collection of parametric surface elements and, in contrast to methods generating voxel grids or point clouds, naturally infers…
View article
Approximating 3D surfaces using generalized waterbomb tessellations Open
Origami has received much attention in geometry, mathematics, and engineering due to its potential to construct 3D developable shapes from designed crease patterns on a flat sheet. Waterbomb tessellation, which is one type of traditional o…
View article
EyeNeRF Open
A unique challenge in creating high-quality animatable and relightable 3D avatars of real people is modeling human eyes, particularly in conjunction with the surrounding periocular face region. The challenge of synthesizing eyes is multifo…
View article
3D Parametric and Nonparametric Description of Surface Topography in Manufacturing Processes Open
Surface topography has a profound influence on the function of a surface [...]
View article
SurfNet: Generating 3D shape surfaces using deep residual networks Open
3D shape models are naturally parameterized using vertices and faces, \ie, composed of polygons forming a surface. However, current 3D learning paradigms for predictive and generative tasks using convolutional neural networks focus on a vo…
View article
Using Multistep Methods in Slicing 2 ½ Dimensional Parametric Surfaces for Additive Manufacturing Applications Open
Parametric surfaces such as Bezier are commonly used in the industrial applications and academic research. In additive manufacturing, surfaces are constructed by layering. For this reason, a method is needed to slice the surfaces. In this …
View article
Model Selection for Parametric Surfaces Approximating 3D Point Clouds for Deformation Analysis Open
Deformation monitoring of structures is a common application and one of the major tasks of engineering surveying. Terrestrial laser scanning (TLS) has become a popular method for detecting deformations due to high precision and spatial res…
View article
Human-in-the-loop fabrication of 3D surfaces with natural tree branches Open
We propose a design and fabrication system leveraging the diverse shapes of natural wood. With our system, precise geometries are fabricated from non-standardized, naturally curved branches. In this way, low-valued tree branches are up-cyc…
View article
PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parametric PDEs on Irregular Domain Open
Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all differe…
View article
Iso-Planar Feed Vector-Fields-Based Streamline Tool Path Generation for Five-Axis Compound Surface Machining With Torus-End Cutters Open
This paper presents a new vector-field-based streamline smoothing method in the parametric space and a tool orientation optimization technique for five-axis machining of complex compound surfaces with torus-end cutters. Iso-planar tool pat…
View article
Guiding Vector Fields for the Distributed Motion Coordination of Mobile Robots Open
In this article, we propose coordinating guiding vector fields to achieve two tasks simultaneously with a team of robots: first, the guidance and navigation of multiple robots to possibly different paths or surfaces typically embedded in 2…
View article
A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation Open
We establish a new connection between metric Diophantine approximation and the parametric geometry of numbers by proving a variational principle facilitating the computation of the Hausdorff and packing dimensions of many sets of interest …
View article
A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters Open
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points lines,…
View article
Constrained willmore surfaces Open
Smooth curves and surfaces can be characterized as minimizers of squared curvature bending energies subject to constraints. In the univariate case with an isometry (length) constraint this leads to classic non-linear splines. For surfaces,…
View article
On the Construction of a Surface Family with Common Geodesic in Galilean Space G<sub>3</sub> Open
In this paper, we investigate the parametric representation for a family of surfaces through a given geodesic curve G 3 . We provide necessary and sufficient conditions for this curve to be an isogeodesic curve on the parametric surfaces u…
View article
A novel representation method of non-ideal surface morphologies and its application in shaft-hole sealing simulation analysis Open
Assembly process simulation has been recognized as an effective tool for design verification. The representation of actual part surfaces produced by manufacturing processes is an important issue for assembly simulation. Manufactured part s…
View article
Influence of the geometrical researches of ruled surfaces on design of unique structures Open
Aims of research. Due to the growing interest in the design, calculation and application of architectural structures and structures in the form of a variety of smooth and composite surfaces, it is interesting to illustrate the use of analy…
View article
Curves and ruled surfaces according to alternative frame in dual space Open
In this paper, the vectorial moments of the alternative vectors are expressed in terms of alternative frame. According to the new versions of these vectorial moments, the parametric equations of the closed ruled surfaces corresponding to t…
View article
Fast variable density node generation on parametric surfaces with application to mesh-free methods Open
Domain discretization is considered a dominant part of solution procedures for solving partial differential equations. It is widely accepted that mesh generation is among the most cumbersome parts of the FEM analysis and often requires hum…
View article
Influence of the geometrical researches of surfaces of revolution and translation surfaces on design of unique structures Open
Aims of research. The use, design and analysis of architectural and building structures in the form of smooth and composite surfaces have become relevant and in demand lately, which determined the purpose of this article - to analyze the u…
View article
Stable numerical approximation of two-phase flow with a Boussinesq–Scriven surface fluid Open
We consider two-phase Navier--Stokes flow with a Boussinesq--Scriven surface\nfluid. In such a fluid the rheological behaviour at the interface includes\nsurface viscosity effects, in addition to the classical surface tension\neffects. We …
View article
Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions Open
Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex s…
View article
Matlab-based Calculation Method for Partitioning a Free-form Surface into Regions Open
A Matlab-based calculation method which can be used to partition a free-form surface into regions is presented in this paper. Based on surface curvatures and Freeman chain code technique, a free-form surface can be devided into convex, con…
View article
INFLUENCE OF THE GEOMETRICAL RESEARCHES OF RARE TYPE SURFACES ON DESIGN OF NEW AND UNIQUE STRUCTURES Open
The aim of the paper is to illustrate using of analytical surfaces, i.e. surfaces, which can be given by vector, parametric or explicit equations, in real structures, i.e. in parametric architecture.Parametric architecture is a unique styl…
View article
Kerf bending: ruled double curved surfaces manufacturing Open
Knowledge of geometric properties of surfaces is crucial for resolution of many manufacturing problems. Developability is an important feature of a surface that allows its manufacture from a flat "strip" of a "flexible" and "non-deformable…