Parametric Spiral And Its Application As Transition Curve

Lengkung Bezier merupakan suatu perwakilan lengkungan yang paling popular digunakan di dalam applikasi Rekabentuk Berbantukan Komputer (RBK) dan Rekabentuk Geometrik Berbantukan Komputer (RGBK). The Bezier curve representation is frequently utilized in computer-aided design (CAD) and computer-aided geometric design (CAGD) applications. The curve is defined geometrically, which means that the parameters have geometric meaning; they are just points in three-dimensional space

Recursive subdivision algorithms for curve and surface design

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In this thesis, the author studies recursIve subdivision algorithms for curves and surfaces. Several subdivision algorithms are constructed and investigated. Some graphic examples are also presented. Inspired by the Chaikin's algorithm and the Catmull-Clark's algorithm, some non-uniform schemes, the non-uniform corner cutting scheme and the recursive subdivision algorithm for non-uniform B-spline curves, are constructed and analysed. The adapted parametrization is introduced to analyse these non-uniform algorithms. In order to solve the surface interpolation problem, the Dyn-Gregory-Levin's 4-point interpolatory scheme is generalized to surfaces and the 10-point interpolatory subdivision scheme for surfaces is formulated. The so-called Butterfly Scheme, which was firstly introduced by Dyn, Gregory Levin in 1988, is just a special case of the scheme. By studying the Cross-Differences of Directional Divided Differences, a matrix approach for analysing uniform subdivision algorithms for surfaces is established and the convergence of the 10-point scheme over both uniform and non-uniform triangular networks is studied. Another algorithm, the subdivision algorithm for uniform bi-quartic B-spline surfaces over arbitrary topology is introduced and investigated. This algorithm is a generalization of Doo-Sabin's and Catmull-Clark's algorithms. It produces uniform Bi-quartic B-spline patches over uniform data. By studying the local subdivision matrix, which is a circulant, the tangent plane and curvature properties of the limit surfaces at the so-called Extraordinary Points are studied in detail.The Chinese Educational Commission and The British Council (SBFSS/1987

On the capture and representation of fonts

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The commercial need to capture, process and represent the shape and form of an outline has lead to the development of a number of spline routines. These use a mathematical curve format that approximates the contours of a given shape. The modelled outline lends itself to be used on, and for, a variety of purposes. These include graphic screens, laser printers and numerically controlled machines. The latter can be employed for cutting foil, metal. plastic and stone. One of the most widely used software design packages has been the lKARUS system. This, developed by URW of Hamburg (Gennany), employs a number of mathematical descriptions that facilitate the process of both modelling and representation of font characters. It uses a variety of curve formats, including Bezier cubics, general conics and parabolics. The work reported in this dissertation focuses on developing improved techniques, primarily. for the lKARUS system. This includes two algorithms which allow a Bezier cubic description, two for a general conic representation and, yet another, two for the parabolic case. In addition, a number of algorithms are presented which promote conversions between these mathematical forms; for example, Bezier cubics to a general conic form. Furthennore, algorithms are developed to assist the process of rasterising both cubic and quadratic arcs.This study was partly funded by the Science and Education Research Council (SERC)

A Modified Reverse Engineering Approach Using Bezier Curve Approximation

Reverse Engineering is a process of re-producing existing parts by obtaining digital models using a special data taken from the original parts using specific techniques. It can be used to redesign existing parts either due to lost data or the parts are no longer available. In this paper, surface modelling technique using special data taken from CMM (Coordinate Measuring Machine) was employed to redesign a candle holder. Specific MATLAB code was generated to model the data taken from the surface of a candle holder made of glass. Bezier curve technique was implemented in this research to model the curve of the outer surface of the candle holder. Various orders of Bezier curves were discussed and used to give better approximation of the original data curve with error percentage monitoring each time. The thickness of the candle holder was reduced from 5mm to 3mm and the volume reduction was calculated. The amount of reduction in the glass volume when reducing the thickness was found to be 210mm3. In addition, the amount of increase in the area of glass section was calculated to be 138.5mm2. This reduction gives a better vision of the amount of glass saved using this procedure. Two different shapes were found and plotted by varying the control points coordinates

Rational Cubic B-Spline Interpolation and Its Applications in Computer Aided Geometric Design

Because of the flexibility that the weights and the control points provide, NURBS have recently become very popular tools for the design of curves and surfaces. If the weights are positive then the NURB will lie in the convex hull of its control points and will not possess singularities. Thus it is desirable to have positive weights. In utilizing a NURB a designer may desire that it pass through a set of data points {xi} This interpolation problem is solved by the assigning of weights to each data point. Up to now little has been known regarding the relationship between these assigned weights and the weights of the corresponding interpolating NURB. In this thesis this relationship is explored. Sufficient conditions are developed to produce interpolating NURBS which have positive weights. Applications to the problems of degree reduction and curve fairing are presented. Both theoretical and computational results are presented

Intelligent support for knitwear design

Communication between different members of a design team often poses difficulties. The knitwear design process is shared by the designers, who plan the visual and tactile appearance of the garments, and the technicians, who have to realise the garment on a knitting machine and assemble it. This thesis reports a detailed empirical study of over' twenty companies in Britain and Germany, which shows that the communication problem constitutes a major bottleneck. Designers specify their designs inaccurately, incompletely and inconsistently; the technicians interpret these specifications according to their previous experience of similar designs, and produce garments very different from the designers' original intention. Knitwear is inherently difficult to describe, as no simple and complete notation exists for knitted structures; and the relationship between visual appearance and structure and technical properties of knitted fabric is subtle and complex. At the same time the interaction between designers and technicians is badly managed in many companies. This thesis argues that this communication bottleneck can be overcome by enabling designers to produce accurate specifications of technically correct designs, through the help. of an intelligent computer support system that corrects inconsistent input and proposes design suggestions that the user can edit. In this thesis this proposal is elaborated for one aspect of knitwear design: garment shape construction. Garment shapes are modelled using Bezier curves generated using design heuristics drawn from industrial practice, to create curves that look right to a designer and can be easily edited. The development of the garment shape models presented in this thesis involved the solution of unusual problems in numerical analysis. The thesis shows how the mathematical models can be integrated into an intelligent CAD system, and discusses die benefits of such a system could have for the design process

Topologically reliable approximation of curves and surfaces

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1997.Includes bibliographical references (p. [213]-222).by Wonjoon Cho.Ph.D