1 research outputs found
Shape-preserving algorithms for curve and surface design
PhD ThesisThis 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
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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
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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
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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.Ministry of Education, Government of
Pakista