scholarly journals A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabia Hameed ◽  
Ghulam Mustafa ◽  
Dumitru Baleanu ◽  
Yu-Ming Chu
Keyword(s):  
Tensor Product ◽  
3D Models ◽  
Divided Differences ◽  
The Given ◽  
Continuity Analysis ◽  
Arithmetic Expressions

AbstractIn this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of $(m+1)$ ( m + 1 ) -point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The $C^{0}$ C 0 , $C^{1}$ C 1 and $C^{2}$ C 2 continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes.

Automatic Parametric Modeling From Non-Feature Based Designs for Additive Manufacturing

2021 ◽  
Author(s):  
Xinyi Xiao ◽  
Byeong-Min Roh
Keyword(s):  
Additive Manufacturing ◽  
3D Models ◽  
Parametric Modeling ◽  
Parametric Models ◽  
Performance Simulation ◽  
Cad Modeling ◽  
3D Cad ◽  
Feature Based ◽  
And Performance ◽  
The Given

Abstract The integration of Topology optimization (TO) and Generative Design (GD) with additive manufacturing (AM) is becoming advent methods to lightweight parts while maintaining performance under the same loading conditions. However, these models from TO or GD are not in a form that they can be easily edited in a 3D CAD modeling system. These geometries are generally in a form with no surface/plane information, thus having non-editable features. Direct fabricate these non-feature-based designs and their inherent characteristics would lead to non-desired part qualities in terms of shape, GD&T, and mechanical properties. Current commercial software always requires a significant amount of manual work by experienced CAD users to generate a feature-based CAD model from non-feature-based designs for AM and performance simulation. This paper presents fully automated shaping algorithms for building parametric feature-based 3D models from non-feature-based designs for AM. Starting from automatically decomposing the given geometry into “formable” volumes, which is defined as a sweeping feature in the CAD modeling system, each decomposed volume will be described with 2D profiles and sweeping directions for modeling. The Boolean of modeled components will be the final parametric shape. The volumetric difference between the final parametric form and the original geometry is also provided to prove the effectiveness and efficiency of this automatic shaping methodology. Besides, the performance of the parametric models is being simulated to testify the functionality.

scholarly journals CULTURAL HERITAGE MONUMENT DOCUMENTATION THROUGH ADAPTIVE PARAMETRIC DESIGN PROCESS

2021 ◽  
Vol XLVI-M-1-2021 ◽  
pp. 769-776
Author(s):  
G. Tryfonos ◽  
M. Ioannides ◽  
A. G. Anastasi ◽  
V. A. Apostolou ◽  
P. P. Pieri ◽  
...  
Keyword(s):  
Cultural Heritage ◽  
Parametric Design ◽  
3D Models ◽  
Building Information Modelling ◽  
3D Data ◽  
Time Period ◽  
Building Information ◽  
Game Developers ◽  
The Given ◽  
The City

Abstract. The paper presents a novel adaptive parametric documentation, modelling and sharing methodology, which aims to achieve a continuous holistic documentation, data processing and sharing process for cultural heritage community, such as architects, engineers, archaeologists, conservators, programmers, fabricators, contest creators, game developers, scholars and common citizens. Thus, the use of advance parametric and building information modelling software allows the processing and specification of all data by creating the 3D models needed for the multidisciplinary experts. Two Cypriot case studies from the medieval time period have been chosen for the development, and evaluation of our proposed methodology in order to investigate the process of modelling and sharing all the given metadata and 3D data. The first one is the Asinou Church, a UNESCO Heritage stone monument in the Troodos Mountains with a unique interior and the Kolossi Castle, a former Crusader stronghold on the west of the city of Limassol on the island of Cyprus.

Automatic Creation of Virtual Artefacts from Video Sequences

2005 ◽  
Author(s):  
Andrew W. Fitzgibbon ◽  
Geoff Cross ◽  
Andrew Zisserman
Keyword(s):  
Focal Length ◽  
3D Models ◽  
Video Sequences ◽  
Digital Representation ◽  
The Third ◽  
3D Presentation ◽  
Object Features ◽  
The Given ◽  
System Geometry ◽  
2D Images

Digital representation of an artefact is necessary in order to measure, admire and analyse such ancient pieces. For the purpose of storing, recoding and transmitting information, digital photographs may be enough. However, in the examination purposes of an artefact, a 3D presentation is invaluable as it allows the object viewpoint to be modified freely and 3D measurements to be taken on object features. This chapter describes the system by which 3D models from photographs can be acquired, without the need for the calibration of system geometry such as the camera focal length, relative motion of the camera and object, and the relative positions of the camera and object. This system instead computes the representation of all possible objects and camera configurations which are consistent with the given image. The first section discusses how tracking points observed in 2D images allows for the computation of the relative camera and object geometry. The second section discusses the construction of a triangulated 3D model from the object projections. The third section discusses the refinement of the model based on surface texture.

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.

scholarly journals Arithmetic expressions optimisation using dual polarity property

2003 ◽  
Vol 1 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Dragan Jankovic ◽  
Radomir Stankovic ◽  
Claudio Moraga
Keyword(s):  
Order Term ◽  
High Order ◽  
High Order Term ◽  
Experimental Results ◽  
Simple Relationship ◽  
Dual Polarity ◽  
The Given ◽  
Arithmetic Expressions

A method for optimisation of fixed polarity arithmetic expressions (FPAEs) based on dual polarity is proposed. The method exploits a simple relationship between two FPAEs for dual polarities. It starts from the zero polarity FPAE of the given function and calculates all FPAEs using the dual polarity route. Using one-bit check carries out conversion from one FPAE to another. Each term in an FPAE is processed by the proposed processing rule. Terms, which differ in a single position, can be substituted by a high order term (cube). Experimental results show efficiency of proposed method.

scholarly journals Solving Nonsmooth Equations Using Derivative-Free Methods

2012 ◽  
Vol 3 ◽  
pp. 37-45
Author(s):  
M.S.M. Bahgat ◽  
M.A. Hafiz
Keyword(s):  
Error Analysis ◽  
Nonlinear Equations ◽  
Divided Differences ◽  
Nonsmooth Equations ◽  
Linear Combinations ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
The Given

In this paper, a family of derivative-free methods of cubic convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.442. The convergence and error analysis are given. Also, numerical examples are used to show the performance of the presented methods and to compare with other derivative-free methods. And, were applied these methods on smooth and nonsmooth equations.

Speedup Method for Paper-Based 3D Color Printing Based on STL File

2015 ◽  
Vol 731 ◽  
pp. 269-272 ◽  
Author(s):  
Jiang Ping Yuan ◽  
Guang Xue Chen
Keyword(s):  
3D Model ◽  
Lower Cost ◽  
3D Models ◽  
Negative Slope ◽  
Geometric Information ◽  
Stl File ◽  
Color Printing ◽  
The Common ◽  
The Given ◽  
Printing Speed

Most paper-based 3D color printers are plagued by the problem of slow printing speed, which is caused by the double-sided coloration for A4 office paper during the printing process. In order to resolve this issue, we propose a new fast and reliable coloration algorithm using geometric information in STL file, given the existing slicing methods. During the entire process, the colored surface is determined by D value that represents the positive or negative slope of layer in the 3D model after slicing. Colored inks with corresponding permeability are used to print single-sided or double-sided to accelerate the printing speed. For the given 3D models, the efficiency of the speedup is discussed and qualitatively analyzed. The results show that the proposed algorithm can increase the printing speed of paper-based 3D color printers, based on the existing materials and apparatus, at a lower cost than the common approaches.

scholarly journals Shape Preserving Interpolation Using Rational Cubic Ball Function and Its Application in Image Interpolation

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Samsul Ariffin Abdul Karim ◽  
Azizan Saaban
Keyword(s):  
Tensor Product ◽  
Image Interpolation ◽  
Sufficient Condition ◽  
Shape Preserving ◽  
Straight Line ◽  
Shape Preserving Interpolation ◽  
Product Approach ◽  
The Given

New rational cubic Ball interpolation with one parameter is proposed for shape preserving interpolation such as positivity, monotonicity, and convexity preservations and constrained data lie on the same side of the given straight line. To produce shape preserving interpolant, the data dependent sufficient condition is derived on the parameter. The rational bicubic Ball function is constructed by using tensor product approach and it will be used for application in image upscaling. Numerical and graphical results are presented by using Mathematica and MATLAB including comparison with some existing scheme.

Research on Methods of Sheet Blank Shape Optimization for Drawing of Complex Special-Shaped Boxes

2011 ◽  
Vol 399-401 ◽  
pp. 1826-1831
Author(s):  
Wei Xia ◽  
Huan Yang ◽  
Jian Min Zeng
Keyword(s):  
Finite Element ◽  
Material Flow ◽  
3D Models ◽  
Drawing Process ◽  
Forming Quality ◽  
Finite Element Software ◽  
Blank Shape Optimization ◽  
Blank Shape ◽  
The Given

The reasonable blank shape is very important for drawing forming quality of sheet. In this paper, the blank shape is obtained by inverse calculation based on final drawing workpiece, with finite element software. The optimal blank contour is determined by modifying the 3D models of final drawing workpiece and comparing with forming quality of the different inverse calculated blank shapes, according to the stress and the material flow law in drawing process. The results show that, in the case of the given shapes of workpiece, the blank shapes with high precision can be obtained, the formability becomes better, and the number of drawing forming can be reduced by using the method. The method may also contribute to the drawing of large and medium-sized panels, rectangular boxes and special-shaped parts.

Cubic TP B-Spline Curves with a Shape Parameter

2013 ◽  
Vol 11 ◽  
pp. 59-72 ◽  
Author(s):  
Mridula Dube ◽  
Reenu Sharma
Keyword(s):  
Tensor Product ◽  
Shape Parameter ◽  
Control Points ◽  
Shape Parameters ◽  
Special Shape ◽  
B Spline ◽  
Control Polygon ◽  
Spline Curves ◽  
Trigonometric Spline ◽  
The Given

In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.

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