The Mathematical Description of Shape and Form - ISBN:0470202548

The Mathematical Description of Shape and Form

Date: 22 April 2011, 09:42

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Neither Pythagoras nor Euclid could have foreseen today's
importance of geometry in modern technological systems
of computer-aided design and manufacture. This work
offers the first survey of the mathematical principles of
shape and form and embraces a very wide spectrum of their
applications. It will stimulate the current and growing
revival of interest in the applications of geometry and will
encourage creative thinking about problems of form, as for
instance, in the behaviour of environmental fields in their
interaction with buildings. It will widen awareness of such
versatility of application in other fields whose workers
can now gain a clearer perception of how these rich mathe-
matical concepts can be utilised.
It is a wide-ranging survey of the applications of mathe-
matics to problems of form description, presenting clearly
and concisely a large number of applied geometrical
methods. A unified viewpoint, based on the concept of
mappings between geometrical spaces, is developed so that
the individual methods are seen in the context of a frame-
work of underlying principles.
The topics treated fall broadly into two major categories:
those based on concepts of continuity (differential and
metrical properties of continuous curves and surfaces,
topology, structure of singularities, etc.) and those based on
concepts of discrete point-sets (crystallographic groups,
graph theory, surface and curve fitting and interpolation,
lattice descriptions in pattern recognition and image pro-
cessing, etc.).
A degree of mathematical expertise on the part of the
reader is assumed, in particular a good knowledge of func-
tions, vectors, matrices and differential equations. However,
the esoteric notation and terminology prevalent in texts
meant for specialist mathematicians is avoided.
The book is the first of its kind; no other known work has
attempted this kind of unified presentation of geometrical
methods taken from a wide range of disciplines. As well as
stimulating further the revival of interest in geometry, it is
intended as a first step towards the future development of
an adequate science of morphology. It contains over 200
diagrams and an extensive bibliography.

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