The Art of Computer Graphics

ICMS

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The Art Of Computer Graphics

Modern computer programs use graphics intensively. All popular products in the computer market, be it Windows 98, Microsoft Word, CorelDraw! or even PaintBrush have one thing in common their attractive, colourful, graphical interface.

The two main applications of computer graphics are

Building up new images from scratch using basic geometrical principles.

Displaying real-life photographs.

Mathematics plays a major role in the creation and display of graphics. This project gives a brief description of some of the mathematics used in the creation of three-dimensional graphics.

Image Creation And Manipulation

As an example, we create a vase using basic geometrical concepts (see our computer display).

We first define control points in the XY plane and draw a curve controlled by these points. The curve is then rotated about an axis to produce a surface. The surface is then scaled to produce a vase of the right proportions, which is then translated to the desired position on the screen. Since the vase is a three-dimensional object, perspective plotting is being used at every stage to plot it on the 2-D screen.

Drawing a Curve

Spline Curves

Spline Curves are smooth curves which are drawn through a large number of control points approximated by drawing many small curves through consecutive pairs of points. They are used when the shape is almost pre-determined, e.g., in designing aircraft wings. Even Microsoft Word uses splines to draw curves. Most commonly used splines are the cubic splines where the curves fitted between any two consecutive points is a cubic.

Bezier Curves

In contrast to a spline curve, Bezier curves, are defined by a set of points such that the smooth curve may not pass through any other point except the first and the last. These curves are used when a vague idea of the shape is known and an added sense of aesthetic appeal is required, e.g., in designing ship hulls, furniture and glassware. The points determine the slope of the curve section. These curves are named after Pierre Bezier who used them to design the bodies of Renault cars.