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Session 2520

Introducing Fundamentals of Computer Graphics Using MATLABTM

Shih-Liang (Sid) Wang

Department of Mechanical Engineering North Carolina A&T State University Greensboro, NC 27411

Introduction

In a technical elective CAD course (MEEN 619) in Department of Mechanical Engineering, North Carolina A&T State University, fundamentals of computer graphics typically account for about one-third of the course material. CAD software-IDEAS and finite element analysis are the other subjects in this course. Introduction of computer graphics addresses, among other topics, geometric transformation and parametric curves and surfaces, including B-spline and Bezier curves. These subjects applied to the design of airfoils, auto bodies and ship hulls, as well as to commercial advertising and movie making. Without good understanding of these graphics fun- damentals, CAD users can not effectively use associated tools.

Most textbooks [1-4] covering these graphics subjects are primarily written for computer science majors. Algorithms to implement these concepts are efficient but difficult to be programmed in the conventional programming languages that engineering students are familiar with. Many en- gineering students feel the complex mathematical expressions and programs hinder the learning of these concepts.

MATLAB [5] is a powerful environment for linear algebra with graphical presentation [6], and is available on a wide range of computer platforms. Unlike a general-purpose language, MATLAB development goes much faster and code is dramatically shorter. In some regards, it is a higher language than most common programming languages like C or FORTRAN. MATLAB is therefore a great computation environment for learning the fundamentals of computer graph- ics. Many MATLAB files have been developed in the past few years by the author and his stu- dents to help effectively presenting key concepts and visualizing these mathematical expres- sions.

Parametric Representation of Analytical Curves

Parametric representation of curves and surfaces is a foundation of computer graphics. It is eas- ier to introduce this format with an analytical curve, an arc of a circle for example. Cartesian form of the equation of an arc of a circle can be expressed as the equation of a circle with joint angle constraints: x = r cos θ (1) y = r sin θ θ 0 ≤ θ ≤ θ1

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Wang, S. (1999, June), Introducing Fundamentals Of Computer Graphics Using Matlab Paper presented at 1999 Annual Conference, Charlotte, North Carolina. 10.18260/1-2--7782