Keywords (Extracted from title, table of contents and
abstract of thesis) Data, Visualization, Spline,
Functions, monotonicity, convex, graphically, domain, rational,
bicubic 
Abstract Accurate
visualization of regular and scattered surface data requires that
the surface characteristics or shape is preserved. This is desirable
in most computer aided engineering applications, including;
geometric modelling, sectional drawing, designing pipe systems in
chemical plants, surgery; designing car bodies, ship hulls and
airplanes; physical and chemical processes, geology, meteorology.
Three basic surface data shape characteristics, namely positivity,
monotonicity and convexity are of general interest. For examples
rainfall data is positive, the rate of dissemination of drugs in the
blood is positive and monotone, data generated in an optimization
problem may be convex.
Within a data visualization environment, a user is usually
interested in graphically. This requires the use of interpolating
schemes which themselves must possess certain characteristics like
shape preservation, shape control, etc.
Many authors derived the constraints on derivatives to visualize the
shape of data. These schemes fail to preserve the shape of data,
when data are given with the derivatives at the data points. Some
existing schemes are global, the disadvantages of these schemes:
modification of data or constraints in one of the interval will
affect the graphical display of the data over the whole domain. In
the visualization of monotone scattered data, some existing schemes
transform the scattered data in to the regular data. These schemes
are
not feasible to industrial applications where bulk of data is under
consideration.
The focus of this thesis is on the graphical display of regular and
scattered surface data which possess positive, monotone and convex
shape features. The aim is to develop the data visualization schemes
that are local, computationally economical, visually pleasing that
are applicable to both data and data with derivatives and above all
provide automotive techniques for appropriate choice of parameters.
Data visualization schemes for regular data are developed using
rational bicubic function and rational bicubic partially blended
function to preserve positivity, monotonicity and convexity of
surface data. Simple sufficient data dependent shape preserving
constraints are derived in terms of the free parameters of rational
bicubic and rational bicubic partially blended function.
The problem of data visualization of constrained data is also
addressed when the data is lying above the plane and the
interpolating surface is required to lie on the same side of the
plane. Finally, data visualization schemes are developed for
scattered data arranged over the triangular grid.
