Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » geometry.college.independent

Topic: Scientific Visualization
Replies: 1   Last Post: Feb 9, 1993 3:39 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Gene Klotz

Posts: 30
Registered: 12/3/04
Re: Scientific Visualization: Book by D. Thalmann
Posted: Feb 9, 1993 3:39 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



Thalmann, Daniel (Ed.), "Scientific Visualization and Graphics
Simulation", Wiley, '90, $50, 264 pages.

"The purpose of this book is to present the techniques of computer
graphics, image synthesis, and computer animation necessary for
visualizing phenomena and mechanisms in sciences and medicine". It's
based on lectures given at the Computer Graphics Laboratory of the Swiss
Federal Institute of Technology in Lausanne. It is a reasonably well
written, indifferently proofread collection of good survey articles.
I'll only speak about the parts which strike me as having interesting
mathematics, and I shan't grouse about those parts which don't, since the
book wasn't really written with us in mind.

Chapter 2 on algorithmic (computational) geometry briefly treats several
fundamental problems which frequently arise: intersection problems,
location problems, convex hulls, and proximity problems.

Chapter 3 on surface visualization. What is a surface and how is it
stored? Level surfaces: unstructured or structured discrete or
parameterized. How to draw a surface and how to recognize its shape.
More computer graphics heuristics than mathematics. A mention of
differential geometric tools. For differential geometry, we're referred
to
Nutbourne, A.W. and Martin, R.R. "Differential Geometry Applied to
Curve and Surface Design", Ellis Horwood, Chichester, '88, and to
Faux, I.D. and Pratt, M.J. "Computational Geometry for Design and
Manufacture", Ellis Horwood, Chichester, '79.
Does anyone know these books? We don't have them locally, and I'd like
to know what's involved in applied differential geometry.

Chapter 4: Solid Modeling. Mentions the use of classical algebraic
topology to decide what should be a "valid object" in solid modeling, and
how it should be represented. Apparently, a seminal reference is
Requicha,A.A.G. "Mathematical Models of Rigid Solid Objects", Technical
Memo TM-28, University of Rochester, '77. Anybody ever looked at it?
Euler's Formula can be used to keep track of "topological validity", but
apparently is expensive for computers.

The chapter also considers "Constructive Solid Geometry", but I didn't
quite get what it is, or find references beyond an article by Laidlaw and
Trumbore in SIGGRAPH, '86. Hints of interesting mathematics in the
background. How 'bout "Computational Topology", anyone? (I'll provide
the reference if you'll try to find and report on it).

Chapter 5 is on the Finite Element Method. This is an ancient
differential equations technique, and this naive reader emerged from a
few minutes immersion in the chapter none the wiser as to how it's
applied to scientific visualization, or as to what (if anything) it has
to do with my quest. Enlightenment, anyone?

Chapter 6: Visualizing Sampled Volume Data, is mostly devoted to standard
3-dimensional techniques, although the author briefly mentions higher
dimensions, and acknowledges the need for imaging methods that can show
multiple parameters. We learn that many volume renderers use parallel
projection, because it's cheaper, and for scientific data it may be
preferable to not alter size with distance. However, some renderers do
offer perspective projection, which is better for depth perception.
Sensory input other than visual can help dealing with multiple
parameters. For example, the frequency rate of repetition of a sound
could be used to indicate density as the user moves through the
environment [Grinstein, G., Pickett, R.M.,. Williams, M.G. "Exvis: an
exploratory visualization environment", Proceedings Graphics Interface
'89, pp.254-261, June '89]

Chapter 7, Special Models for Natural Objects, starts with a brief
discussion of fractals, with some emphasis on Barnsley's Iterated
Function Systems. There is a description of structural modeling of
botanical structures.

Chapter 8 seems a perfectly fine introduction to Computer Animation, but
there's little relating to our quest.

Chapter 10 on Robotic Methods for Task-level and Behavioral Animation is
concerned with robotics techniques which are used or could be used for
the task-level animation of linked figures. In direct kinematics,
position and velocity are transformed from "joint-space" into cartesian
coordinates. Other methods are based on Lagrange's equations for motion
for nonconservative systems, the Gibbs-Appel equations, or on the
Newton-Euler equations. I was expecting more computational geometry, but
it might have passed me by.

The theme of Chapter 11, Visualization of Flow Simulations, seems to be
the necessity of interaction between software and a human with knowledge
of what the solution should be like. Many aspects of computational fluid
dynamics require massive computing power.

Chapter 12 on the visualization and manipulation of medical images,
doesn't have much of overt mathematical interest. Apparently the most
widely used method of measuring left ventricular volume is to model the
ventricle as a three-dimensional ellipsoid. Some things never go out of
fashion.

Chapter 13, the Visualization of Botanical Structures and Processes, is
concerned with Lindenmayer systems, a "topological" description of the
modeled structure, which is drawn by a LOGO-like turtle. Phylotaxis is
given by logic-like production rules, with tiny bits of cylindrical
coordinates, etc. The chapter manages to avoid the two or three neat
things I've picked up about the subject--guess they weren't of practical
importance.

Chapter 14 on molecular computer graphics in chemistry has little overt
mathematics, nor does Chapter 15: Graphics Visualization and Artificial
Vision, or Chapter 16 on Collaboration Between Computer Graphics and
Computer Vision.

Chapter 17 on Graphics Simulation in Robotics has comments and references
of mathematical interest, although frequently in the form of laments that
easy problems lead to surprisingly difficult mathematics. For collision
detection, it is sometimes convenient to treat intersection problems as
occurring in 4-space.

It's interesting that the background assumed for users of scientific
visualization systems seems to vary from zero in medical imaging for
routine clinical evaluations to a good understanding of the solutions to
the partial differential equations governing fluid dymanmics in flow
simulation.






Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.