As we learned earlier, visualization is a key ingredient in the
design and analysis of engineering systems.
Throughout history, scientists and engineers have been using visualization
as a way to better understand their models and analyze their solutions. In
the beginning, and for some time, engineers used hand drawn plots to
graphically illustrate their problems. While this worked fairly well for
static, two-dimensional phenomena, it was often very difficult---if not
impossible---to graphically illustrate dynamic and/or three-dimensional
phenomena. Often, scientists and engineers would have to resort to
actually building a small scale model of the engineering system before they
could grasp some of the inherent complexity and begin to understand the
system.
The next step to visualization came about when large mechanical plotters
were developed. These plotters could graph complex two-dimensional data
and allowed scientists to ``slice'' through three-dimensional data. While
engineers could now obtain some clues into understanding their complex
data, it wasn't until the advent of three-dimensional computer graphics
systems that scientists and engineers could really begin to fully analyze
complex three-dimensional and/or dynamic systems. It may interest you to
know that some of the world's very first visualizations of scientific and
engineering data occurred here at the University of Utah. For example, it
was at Utah that the visualization of complex molecules and results from
finite element analysis were first realized.
When one thinks about scientific visualization, one usually thinks about
ways to view the geometrical model and/or interpret and represent the
computer solution which approximates some real world experiment or design.
And while that is our primary goal in this lesson, we should note that
visualization can also be used in other aspects of engineering analysis,
including checking data entry and integrity. In past two decades,
computing power has increased at an exponential rate such that we can now
simulate highly complex phenomena using millions of pieces of information.
Visualization can be used to check the integrity of our input (and output)
data. Furthermore, graphical means can also be used to enter data as it is
not often feasible (or desirable) to enter large data sets by hand.
Visualization can also be used in the analysis of program performance and
aiding to debug Fortran and/or C code. To analyze large, complex system it
often requires a large number of instructions in the form of Fortran/C
code. Visualization systems have been (and are being) developed which
allow engineers to find places in their code that are inefficient and/or
are in error.
Earlier we investigated how to use some of Mathematica's two-dimensional
plotting feature. In this lesson, we will experiment with more advanced
two-dimensional plotting as well as three-dimensional plotting of an
animation.