Graphics Reference
In-Depth Information
(1) To what class of shapes is a user restricted?
(2) How does a user describe and edit the possible shapes and how easy is this?
(a) How shapes are described can easily limit the user's ability to use good
designs and even to think up a good design in the first place.
(b) How much input is required for each shape?
(c) Can a user easily predict the output from the input?
(d) How accurate are the representations with respect to what the user wants?
(e) Are the operations that a user can perform on shapes closed in the sense
that the output to an operation can be the input to another?
(3) How fast and how realistically can the shapes be generated on a display?
(4) What operations can a user perform on shapes and how fast can they be
carried out?
Of course, the type of user representation that one wants depends on the user. Here
we have in mind a more technical type of user. Later in Section 5.6 we consider a user
in the context of a manufacturing environment.
5.3.1
Early Representation Schemes
Approaches to geometric modeling have changed over the years. These changes began
before computers existed and all one had was pencil and paper. Since the advent
of computers, these changes were largely influenced by their power, the essential
mathematics behind the changes being basically not new. As computers become more
and more powerful, it gradually becomes possible to implement mathematical repre-
sentations that mathematicians have used in their studies. The history of the devel-
opment of geometric modeling shows this trend. Of course, the new ways of
interactively visualizing data that was not possible before will undoubtedly cause its
own share of advances in knowledge. We shall comment more on this at the end of
this chapter.
Engineering Drawings.
Engineering drawings were the earliest attempts to model
objects. Computers were not involved and they were intended as a means of com-
munication among
humans
. They often had errors but humans were able to use
common sense to end up with correct result. There was no formal definition of such
drawings as a representation scheme. The basic idea was to represent objects by a
collection of planar projections. As such it is a highly ambiguous representation
scheme because if one were to try to implement it on a computer, it is very difficult
to determine how many two-dimensional projections would be needed to completely
represent a three-dimensional object. Constructing an object from some two-dimen-
sional projections of it is a highly interesting and difficult problem. We touched on
two small aspects of this problem in Section 4.12. For more, see [RogA90], [BoeP94],
[PenP86], or [Egga98].
Wireframe Representations.
Wireframe representations were the first representa-
tion schemes for three-dimensional linear polyhedra. It is a natural approach, the idea
