TABLE OF CONTENTS The need to plot contour maps over complex-shaped domains arises frequently in the course of analysis of stress and strain distributions with respect to different coordinate systems. This appendix is dedicated to the construction of a series of graphics tools to build parametric meshes and to plot functions over new domains.
A mesh is defined in cartesian coordinates by the function
and a series of three increments du, dv, dz on each of the coordinate lines. We propose to colour each mesh element using a colour function defined as
The tools constructed here stand in a close relationship with the already existing commands of the ParametricPlot type or the ComplexMap package, which are standard with the MATHEMATICA distribution.
The main ingredients of the parametric plot package are presented next. The collection of commands and their assembly can be further understood by looking at the ParametricMesh package that is provided together with this book. Further insight into the techniques of command and package building can be found in Maeder (1997).
The sequence of commands introduced below shows how the mesh is first built up from rectangular elements, and then colour is associated with each element.
We start by defining a rectangular domain of the parameters
and associating a standard spacing with each of the parametric axes, ndu and ndv.
Then the function defining the deformation of the domain is introduced:
<b class="bold">Thread[{u0, u1, ndu} = {0, 1, 0.1}];</b><b class="bold">Thread[{v0, v1,...
