APPLIED GEOMETRY AND GRAPHICS
FOR INTERACTIVE EDUCATION (AGGIE 1)

Volume I: Lines, Planes, Curves and Surfaces

Preface

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 two volumes.
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.

AGGIE: 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.

References: 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:

Rogers, D.F. and Adams, J.A., Mathematical Elements for Computer Graphics, second edition, McGraw-Hill Inc., 1990.

Adams, J.A. and Billow, L.M., Descriptive Geometry and Geometric Modeling, Holt, Rinehart and Winston, Inc. 1988.

Zeid, I., CAD/CAM Theory and Practice, McGraw-Hill Inc.,1991.