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Title: Shape-preserving algorithms for curve and surface design
Author: Iqbal, Rafhat
ISNI:       0000 0001 3586 9337
Awarding Body: Newcastle University
Current Institution: University of Newcastle upon Tyne
Date of Award: 1998
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This thesis investigates, develops and implements algorithms for shape- preserving curve and surface design that aim to reflect the shape characteristics of the underlying geometry by achieving a visually pleasing interpolant to a set of data points in one or two dimensions. All considered algorithms are local and useful in computer graphics applications. The thesis begins with an introduction to existing methods which attempt to solve the shape-preserving 1 curve interpolation problem using C cubic and quadratic splines. Next, a new generalized slope estimation method involving a parameter t, which is used to control the size of the estimated slope and, in turn, produces a more visually pleasing shape of the resulting curve, is proposed. Based on this slope generation formula, new automatic and interactive algorithms for constructing 1 shape-preserving curves from C quadratic and cubic splines are developed and demonstrated on a number of data sets. The results of these numerical experiments are also presented. Finally, a method suggested by Roulier which 1 generates C surfaces interpolating arbitrary sets of convex data on rectangular grids is considered in detail and modified to achieve more visually pleasing surfaces. Some numerical examples are given to demonstrate the performance of the method.
Supervisor: Not available Sponsor: Ministry of Education, Government of Pakistan
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Computer graphics; Convexity preserving