Related papers: The implicit equation of a canal surface
We study the Gauss map and the dual variety of a real-analytic immersion of a connected compact real-analytic manifold into a sphere or into a hyperbolic space. The dual variety is defined to be the set of all normal directions of the…
Point cloud reconstruction from raw point cloud has been an important topic in computer graphics for decades, especially due to its high demand in modeling and rendering applications. An important way to solve this problem is establishing a…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
The calculation of the volume enclosed by curved surfaces discretized into triangular elements, and a cube is of great importance in different domains, such as computer graphics and multiphase flow simulations. We propose a robust…
This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions. The authors consider a particular system---multiple…
We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…
We consider a surface $M$ immersed in $\mathbb{R}^3$ with induced metric $g=\psi\delta_2$ where $\delta_2$ is the two dimensional Euclidean metric. We then construct a system of partial differential equations that constrain $M$ to lift to a…
In this paper, we propose a feasible algorithm to give an explicit basis of the space of regular differential forms on the nonsingular projective model of any given plane algebraic curve. The algorithm is demonstrated for concrete examples,…
In this paper we consider Hugelschaffer cubic curves which are generated using appropriate geometric constructions. The main result of this work is the mode of explicitly calculating the area of the egg-shaped part of the cubic curve using…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As applications, we show that the PGL(4) orbit closure of a generic cubic surface has degree 96120, and…
In this paper, we formulate a simple algorithm that detects contours around a region of interest in an image. After an initial smoothing, the method is based on viewing an image as a topographic surface and finding convex and/or concave…
Neural implicit surface representations have recently emerged as popular alternative to explicit 3D object encodings, such as polygonal meshes, tabulated points, or voxels. While significant work has improved the geometric fidelity of these…
For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…
We consider the problem of computing the topology and describing the geometry of a parametric curve in $\mathbb{R}^n$. We present an algorithm, PTOPO, that constructs an abstract graph that is isotopic to the curve in the embedding space.…
The normal depth is an important hydraulic element for canal design, operation and management. Curved irrigation canals including parabola, U-shaped and catenary canals have excellent hydraulic performance and strong ability of anti-frost…
Implicit representation of shapes as level sets of multilayer perceptrons has recently flourished in different shape analysis, compression, and reconstruction tasks. In this paper, we introduce an implicit neural representation-based…
A new gridding technique for the solution of partial differential equations in cubical geometry is presented. The method is based on volume penalization, allowing for the imposition of a cubical geometry inside of its circumscribing sphere.…
We present a general method for computing local parameterizations rooted at a point on a surface, where the surface is described only through a signed implicit function and a corresponding projection function. Using a two-stage process, we…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…