1.3 Game 2302-0110: updating the game math library for graphics  (Page 2/20)

General background information

So far, we have been dealing with column matrices, points, vectors, and lines. (We will get to other topics in future modules.)

What is a point?

According to Kjell, a point is simply a location in space. It has no width, depth, or height. Therefore, it cannot be seen by the human eye,which means that we can't draw a point on the computer screen. However, it is possible to draw an object on the computer screen that indicates the locationof the point.

What do I mean by this?

Suppose you go out onto your driveway and establish that one corner of the driveway represents the origin in a rectangular Cartesian coordinate framework. Then you usemeasuring devices to identify a specific location on the driveway. You can point to that location with your finger, and others can see your finger, butthey can't see the point. Once again, the point has no width, height, or depth, and therefore cannot be seen by the human eye.

Mark the point

What you can do, however, is to take a piece of chalk and draw a small circle around your finger. Then others can see the mark that you have drawn as anestimate of the location of the point. It is very important however to remember that the chalk mark is not the point. It is simply a visualobject that indicates the location of the point to some degree of accuracy. The actual location of the point is a piece of underlying data . The chalk mark is a graphic object that you have invented to represent thatunderlying data in a visual way to a human observer.

Program output

Both of the sample programs that I will explain in this module will produce the same graphic screen output, which is shown in Figure 1 .

Figure 1 Screen output from both sample programs.

The left image in Figure 1 contains seven small circles. Each of those seven circles marks the location of a point in the 2D space of the image.However, those circles are not the points. The seven points consist solely of coordinate values and are not visible to the human eye. The sevencircles are graphics objects that were placed there to mark the locations in space of the seven points. The points existed in the 2D space before thegraphics objects were created, and would have existed even if I had not caused the circles to be drawn to mark the locations of the points.

What is a line segment?

This can be even more confusing. Kjell tells us that a line segment is the straight path between two points, and that it has no thickness. Sinceit has no thickness, a line cannot be seen by the human eye.

The left image in Figure 1 contains six graphic objects that we are likely to call lines or line segments. True enough, those graphic objects markthe path taken by the lines that represent straight paths between the pairs of points whose locations are indicated by the circles. However,those graphic objects are not lines in the context of this discussion. Rather, they are simply graphic objects that were used to mark the paths ofthe lines in a visual way for the benefit of a human observer.