Related papers: A more robust multiparameter conformal mapping met…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
This study presents a spiral-based complete coverage strategy for ball-end milling on freeform surfaces, utilizing conformal slit mapping to generate milling trajectories that are more compact, smoother, and evenly distributed when…
An iterative numerical method to compute the conformal mapping in the context of propagating water waves over uneven topographies is investigated. The map flattens the fluid domain onto a canonical strip in which computations are performed.…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
Over-break and under-break excavation is very common in practical tunnel engineering with asymmetrical cavity contour, while existing conformal mapping schemes of complex variable method generally focus on tunnelling with theoretical and…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
Our goal is to provide a novel method of representing 2D shapes, where each shape will be assigned a unique fingerprint - a computable approximation to a conformal map of the given shape to a canonical shape in 2D or 3D space (see page 22…
We propose a method for designing refractive optical elements for collimated beam shaping. In this method, the problem of finding a ray mapping is formulated as a linear assignment problem, which is a discrete version of the corresponding…
Conformal mapping is an important mathematical tool in many physical and engineering fields, especially in electrostatics, fluid mechanics, classical mechanics, and transformation optics. However in the existing textbooks and literatures,…
Triangle strips have been widely used for efficient rendering. It is NP-complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few…
The conformal mapping problem for the section of a channel filled with porous material under a rectangular dam onto the upper half-plane is considered. Similar problems arise in computing of fluid flow in hydraulic structures. As a solution…
In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial…
The multi-beam measurement system plays a crucial role in ocean mapping and underwater terrain detection. By simultaneously transmitting multiple beams, the system can accurately receive sound waves reflected from the seabed, providing more…
A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free…
We study the path planning problem for continuum-arm robots, in which we are given a starting and an end point, and we need to compute a path for the tip of the continuum arm between the two points. We consider both cases where obstacles…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
A new analytical method for the conformal mapping of a rectangular heptagon with a straight angle at infinity to a half plane and back is proposed. The method is based on the observation that SC integral in this case is an abelian integral…