A Recursive, Line-Intersection Method for Finding the Area of a Mesh Projected Onto a Plane

2004 ◽  
Author(s):  
Yifan Chen ◽  
Pietro Buttolo ◽  
James Rankin ◽  
Basavaraj Tonshal
Keyword(s):  
Model Space ◽  
Grid Resolution ◽  
Projection Area ◽  
Projected Area ◽  
Precision Control ◽  
New Approach ◽  
Subdivision Strategy ◽  
Intersection Method ◽  
The Given ◽  
Graphics Engine

In this paper, we describe a new approach for computing the area of a mesh projected onto a plane. This approach utilizes the graphics hardware’s line/object intersection capability and a recursive subdivision strategy to achieve performance and precision control. This approach starts from digitizing the projection plane into a grid of rectangular elements. For each element the graphics engine is utilized to check whether projection lines passing through the nodes of the element intersect the object in the model space. If all lines intersect the object, the element is considered “inside” and its area will be accounted towards the final projection area. If none of the lines has an intersection, the element is considered “outside” and discarded. For those elements that lay along the boundary of the projected area (which means some of their lines intersect the model while others don’t) we subdivide them until they are sufficiently small and the given area tolerance is met. Heuristics are derived for deciding the initial grid resolution and the level of subdivisions needed to meet/exceed a given area tolerance. Implementation results are demonstrated and compared with a classic polygon-clipping approach.

A Unified Approach to H∞ Control of Singular Markovian Jump Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Guoliang Wang ◽  
Hongyi Li
Keyword(s):  
Transition Probability ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
New Approach ◽  
Control Approach ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Bounded Uncertainties ◽  
The Given

This paper considers the H∞ control problem for a class of singular Markovian jump systems (SMJSs), where the jumping signal is not always available. The main contribution of this paper introduces a new approach to a mode-independent (MI) H∞ controller by exploiting the nonfragile method. Based on the given method, a unified control approach establishing a direct connection between mode-dependent (MD) and mode-independent controllers is presented, where both existence conditions are given in terms of linear matrix inequalities. Moreover, another three cases of transition probability rate matrix (TRPM) with elementwise bounded uncertainties, being partially unknown and to be designed are analyzed, respectively. Numerical examples are used to demonstrate the effectiveness of the proposed methods.

Genetic Algorithms in Fuzzy Engineering Design

1999 ◽  
Author(s):  
Ralf Schleiffer ◽  
Hans-Jürgen Sebastian ◽  
Erik K. Antonsson
Keyword(s):  
Engineering Design ◽  
Clustering Algorithm ◽  
Computer Application ◽  
Test Problems ◽  
Important Class ◽  
New Approach ◽  
Design Task ◽  
Evolutionary Technique ◽  
The Given ◽  
Real World Problems

Abstract Problems in the field of engineering design represent an important class of real world problems that typically require a fuzzy and imprecise representation. This article presents and discusses a new approach to model this type of problem, by incorporating linguistic descriptions together with a variety of user-defined trade-off strategies. An interactive computer application is introduced, using stochastic optimization to solve the design task by producing a specially desired output under the given environmental conditions which are partly caused by the personal preferences of the engineer and by the expectations of the customer. It utilizes a randomized evolutionary technique, made suitable for the class of problems at hand, to generate and to optimize design solutions that are later identified by a clustering algorithm. Moreover test problems that were solved by the application are considered. In all cases the good solutions were obtained by evaluating only an extremely small fraction of all possible designs.

A simultaneous decomposition for three quaternion tensors with applications in color video signal processing

2020 ◽  
pp. 1-35
Author(s):  
Zhuo-Heng He ◽  
Chen Chen ◽  
Xiang-Xiang Wang
Keyword(s):  
Signal Processing ◽  
Video Signal ◽  
New Approach ◽  
Video Signal Processing ◽  
Encryption And Decryption ◽  
Color Video ◽  
The Given ◽  
Einstein Product

In this paper, we establish a simultaneous decomposition for three quaternion tensors via Einstein product. This simultaneous decomposition transforms the given three quaternion tensors into nice forms which have only 1 and 0. We conclude with an application in the color video signal processing. This new approach only need to store four keys to realize the simultaneous encryption and decryption of three videos.

scholarly journals A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Alvaro H. Salas S ◽  
Jairo E. Castillo H ◽  
Darin J. Mosquera P
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytical Solution ◽  
Initial Conditions ◽  
Negative Ions ◽  
Nonlinear Problems ◽  
New Approach ◽  
Weierstrass Elliptic Function ◽  
Electronegative Plasma ◽  
The Given

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z ″ = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.

scholarly journals A New Approach to Newton-Type Polynomial Interpolation with Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Le Zou ◽  
Liangtu Song ◽  
Xiaofeng Wang ◽  
Thomas Weise ◽  
Yanping Chen ◽  
...  
Keyword(s):  
Polynomial Interpolation ◽  
Information Matrix ◽  
Divided Differences ◽  
Mathematical Representation ◽  
Interpolation Algorithm ◽  
New Approach ◽  
Multiple Parameters ◽  
Parameter Values ◽  
The Given ◽  
Interpolation Functions

Newton’s interpolation is a classical polynomial interpolation approach and plays a significant role in numerical analysis and image processing. The interpolation function of most classical approaches is unique to the given data. In this paper, univariate and bivariate parameterized Newton-type polynomial interpolation methods are introduced. In order to express the divided differences tables neatly, the multiplicity of the points can be adjusted by introducing new parameters. Our new polynomial interpolation can be constructed only based on divided differences with one or multiple parameters which satisfy the interpolation conditions. We discuss the interpolation algorithm, theorem, dual interpolation, and information matrix algorithm. Since the proposed novel interpolation functions are parametric, they are not unique to the interpolation data. Therefore, its value in the interpolant region can be adjusted under unaltered interpolant data through the parameter values. Our parameterized Newton-type polynomial interpolating functions have a simple and explicit mathematical representation, and the proposed algorithms are simple and easy to calculate. Various numerical examples are given to demonstrate the efficiency of our method.

A New Approach to the Classification and Measurement of Stuttering

1972 ◽  
Vol 37 (2) ◽  
pp. 242-251 ◽  
Author(s):  
Eleanor S. Wertheim
Keyword(s):  
Quantitative Relationship ◽  
Management Plan ◽  
Clinical Validity ◽  
New Approach ◽  
Quantitative Estimates ◽  
The Social ◽  
Method Of Measurement ◽  
Qualitative Pattern ◽  
The Stability ◽  
The Given

A quantitative, multidimensional approach to clinical diagnosis and management of stuttering is proposed. This approach would involve (1) the measurement of stuttering behavior under a number of contrived social conditions relevant to the given population of stutterers; (2) a method of measurement which provides separate quantitative estimates of the qualitative aspects of the stuttering pattern, for example, total frequency of disfluencies as well as incidence of hard blocking; (3) an analysis of the quantitative relationship between the social context and the qualitative pattern of stuttering and its severity; (4) a diagnostic formulation of “stutterogenic” situations for a given individual and of the stability and severity of the stuttering pattern across the total range of situations; and (5) a management plan geared to these diagnostic considerations. The approach is illustrated, using the findings of an experimental study primarily designed to test the author’s recently postulated bioadaptive theory of stuttering. Further research is needed to refine the proposed diagnostic approach and to establish its clinical validity and usefulness.

The Technology of Mig-Mag Welding with Low-Frequency Modulation of Arc Current

2014 ◽  
Vol 682 ◽  
pp. 426-430 ◽  
Author(s):  
S.A. Solodsky ◽  
N.Yu. Lugovtsova ◽  
I.S. Borisov
Keyword(s):  
Weld Pool ◽  
Theoretical Study ◽  
Low Frequency ◽  
Metal Structure ◽  
New Approach ◽  
Deposited Metal ◽  
Arc Current ◽  
Favorable Conditions ◽  
Pool Formation ◽  
The Given

The given paper suggests a new approach towards implementation of arc current low frequency modulating method in MAG, MIG-welding. The process facilitates controlling heat and crystallization processes, regulates the time of the weld pool formation and crystallization. Theoretical study allowed formulating the main criteria of receiving strong permanent joints to produce structures with advanced reliability as it creates favorable conditions for producing a more balanced deposited metal structure and reducing the heat-affected zone. Regulating the time of weld pool formation and crystallization improves weld formation and increases labor productivity when welding sheet metals.

A Distributed Multi-Robot Map Fusion Algorithm

2014 ◽  
Vol 536-537 ◽  
pp. 917-924
Author(s):  
Liang Zhang ◽  
Pei Yi Shen ◽  
Juan Song ◽  
Luo Bin Dong ◽  
Yan Zheng Zhang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Mahalanobis Distance ◽  
Relative Distance ◽  
Fusion Algorithm ◽  
New Approach ◽  
Unscented Transform ◽  
Covariance Intersection ◽  
Intersection Method ◽  
Initial Knowledge ◽  
Multi Robot

This paper proposes a new approach to the multi-robot map fusion algorithm that enables a team of robots to build a joint map without initial knowledge of their relative pose. First, the relative distance and bearing measurements between two robots are fused together by the covariance intersection method after they detect each other. Second, the transformation equations among multi robots coordinates are derived based on their relative distance and bearing measurements. Third, all the multi robots local maps are merged into one global map by unscented transform based on the transformation equations. Fourth, the possible duplicate features are filtered out by the robots maximal detection area and the features coordinate range, then the Mahalanobis distance is computed to decide the duplicate features correspondence through unscented transform, and the Kalman Filter is used while fusing the duplicate features information. As a means of validation for the proposed method, experimental results obtained from the two robots are presented.

FORMAL PROOFS OF FUNCTIONAL BSP PROGRAMS

2003 ◽  
Vol 13 (03) ◽  
pp. 365-376 ◽  
Author(s):  
FRÉDÉRIC GAVA
Keyword(s):  
Type Theory ◽  
Great Difficulty ◽  
Parallel Applications ◽  
Formal Proofs ◽  
Higher Order Logic ◽  
New Approach ◽  
Bulk Synchronous Parallel ◽  
Parallel Data ◽  
Wide Range ◽  
The Given

The Bulk Synchronous Parallel ML (BSML) is a functional language for BSP programming, a model of computing which allows parallel programs to be ported to a wide range of architectures. It is based on an extension of the ML language by parallel operations on a parallel data structure called parallel vector, which is given by intention. We present a new approach to certifying BSML programs in the context of type theory. Given a specification and a program, an incomplete proof of the specification (of which algorithmic contents corresponds to the given program) is built in the type theory, in which gaps would correspond to the proof obligation. This development demonstrates the usefulness of higher-order logic in the process of software certification of parallel applications. It also shows that the proof of rather complex parallel algorithms may be done with inductive types without great difficulty by using existing certified programs. This work has been implemented in the Coq Proof Assistant, applied on non-trivial examples and is the basis of a certified library of BSML programs.

Cardinal characteristics on graphs

2011 ◽  
Vol 76 (1) ◽  
pp. 1-33
Author(s):  
Nick Haverkamp
Keyword(s):  
Short Proof ◽  
Property A ◽  
New Approach ◽  
Cardinal Characteristics ◽  
Cardinal Characteristic ◽  
The Given ◽  
Bounded Graph

AbstractA cardinal characteristic can often be described as the smallest size of a family of sequences which has a given property. Instead of this traditional concern for a smallest realization of the given property, a basically new approach, taken in [4] and [5], asks for a realization whose members are sequences of labels that correspond to 1-way infinite paths in a labelled graph. We study this approach as such, establishing tools that are applicable to all these cardinal characteristics. As an application, we demonstrate the power of the tools developed by presenting a short proof of the bounded graph conjecture [4].

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