Graphics Reference
In-Depth Information
picture of the slice is then obtained from a reconstruction process applied to all this
data. Radiologists were apparently good at seeing three-dimensional models from
these two-dimensional slices, but surgeons and doctors were not. Fortunately, there
exist algorithms that, when applied to a stack of such slices, produce a representation
of the whole organ and volume rendering makes it possible to display it. One is able
to remove uninteresting tissues to see those parts that one wants to see. At this point
in time, three-dimensional medical graphics is not yet widely used, mainly because
of the cost. Also, the slices are more accurate and have more information than the
three-dimensional reconstruction, so that radiologists tend to refer to them more.
In another recent development, surgeons can now also use haptic systems to prac-
tice surgeries beforehand. “Haptic” means that one gets physical touch feedback from
the system.
Modeling Natural Phenomena.
Understanding the flow of air over an airplane
wing is important for its design. A similar understanding is needed for designing
intake or exhaust manifolds in engines. This is where fluid dynamics enters. Fluid
dynamics deals with fluid flow, which is governed by a set of differential equations
called the Navier-Stokes equations. These equations define the velocity and vorticity
of the fluid. The
vorticity
describes the rotational part of the flow and is defined by
a vector at each point of the fluid. Understanding vector-valued functions is not
easy, but volume-rendering techniques have enabled scientists to get a better visual
understanding of what happens inside a flow. Volume modeling has been helpful in
modeling other phenomena such as ocean turbulence and hurricanes. Oil exploration
has been greatly aided by the ability to use volume modeling to analyze geological
data.
Education.
Volume modeling has been used to avoid having to use actual bodies in
dissection experiments. As a result of the visible human project sponsored by the
National Library of Medicine, there now exist models of a human male and female.
If one tried to model a human in the more traditional way by means of facets, it would
take millions of triangles to do so.
Nondestructive Testing.
Volume modeling has been used to enable mechanical and
materials engineers to find structural flaws in objects without having to take them
apart.
This ends our brief overview of volume modeling. We return to the very interest-
ing topic of volume rendering in Section 10.4. There is a large body of literature on
volume modeling and the related subject of scientific visualization. A good place to
begin more reading is [LiCN98], [ScML98], and various ACM SIGGRAPH course notes
such as [Kauf98].
5.3.9
The Medial Axis Representation
In mathematics, when one tries to characterize or classify geometric objects, one first
looks for coarse invariants (topology) and then successively refines the classification
by adding metric criteria, differentiability criteria, etc. For example, at a very top level,
