GEOMETRY AND GRAPHICS
INTERACTIVE EDUCATION (AGGIE 1)
Volume I: Lines, Planes, Curves and Surfaces
Alan Adams (www.usna.edu/Users/mecheng/adams)
The Applied Geometry and Graphics for Interactive Education (AGGIE)
series of MATHCAD Software is written to use in a variety of ways. It is
designed to be run with MATHCAD 2001i, or higher, running on a PC under Microsoft Windows. The software is suitable for undergraduate
courses in mathematics, computer science, engineering graphics, and design.
Faculty members can use the material to complement lectures (especially
when classroom projection of computer output is available), for assignments
or exams (by selecting suitable material of interest), for self paced instruction
to provide a more solid foundation in a subject, or as textbook supplements
to provide current applications of geometry and graphics. Students and
professionals can use the software to review basic concepts of geometry
and graphics, to support group design projects or formal presentations,
and to develop a spatial reasoning based upon the abstract concepts of
points, lines, planes, curves and surfaces needed to express the basic
relationships of geometry and graphics. On the job, AGGIE can be used on
an office PC to create and modify surface design ideas which can later
be copied to other software systems if necessary. The series consists of
AGGIE: Volume I: Lines, Planes, Curves and Surfaces
is suitable for use at the freshman, sophomore level after the student
has been introduced to elementary matrix theory and calculus. It is particularly
useful for students who need to develop a better three-dimensional visualization
and spatial reasoning capability, such as that needed in descriptive geometry
or engineering design, or for those who want to understand the mathematical
theory behind the commercially available drawing and computer aided design
software in use today.
Volume II. Applied Surface Design contains dozens of examples of practical
surface design, many taken from the current literature, which allow immediate
interactive creation of surface ideas. For those who want to simply study
methods for surface creation, without a detailed study of the mathematics,
it is easy to modify the many examples to suit the purpose of the user.
Depending upon the needs of the user, this volume can be a course complement
at any college level, from introductory freshman design, geometry or computer
graphics classes, to senior design or theory courses. Examples range from
safety helmet and ship hull design to piping assembly and artistic sculpture.
For those who wish to further study the mathematical theory upon which
the geometry and graphics solutions are based, page numbers from three
references appear throughout the documentation. There are many other good
references which also present the relevant concepts and theory. The references
identified as R&A, A&B and Zeid refer to the following references:
D.F. and Adams, J.A., Mathematical
Elements for Computer Graphics,
second edition, McGraw-Hill Inc., 1990.
J.A. and Billow, L.M., Descriptive
Geometry and Geometric Modeling,
Holt, Rinehart and Winston, Inc. 1988.
I., CAD/CAM Theory and
Practice, McGraw-Hill Inc.,1991.