Pictures
 

Calculator: TI-83.

 

Most computer drawings are made from segments. Here we learn some basic techniques of making such pictures on the screen of the TI-83 calculator. To create pictures we use analytic geometry. Each point will have two coordinates, x and y, and each segment will be determined by two points (its ends). In order to avoid a messy choice of window settings, set the window to ZStandard, ZSquare. The x-coordinate ranges from -15 to 15, and the y-coordinate ranges from -10 to 10. In order to see the whole picture, you have to keep the coordinates of all points within these limits. Also set 2nd FORMAT to put coordinates and axes OFF.

 

To start, get a sheet of paper with a square-centimeter grid (click here). Sketch a drawing using straight segments, and write the coordinates of all your points on it. It is much better to write too many digits than too few. Also you may use arithmetic expressions for describing coordinates; √(2) and sin(65) are as good numbers as -5.4 or 8.9. It also helps to number the points (in any order) from 1 to n, and to number all the segments from 1 to m.

Here is an example:

 

Data structures.

We are going to keep all our points in one table (matrix), [I], and all our segments in a second table [J].

 

Make [I] a 2 by n matrix, where n is the number of points in your picture. The x coordinates are in the first row, and the y coordinates are in the second. For example, five points, p1 = (x1, y2), ..., p5 = (x5, y5), would be represented by:

  [[x1  x2  x3   x4  x5]

   [y1  y2  y3  y4  y5]]

 

Matrix [J] is a 2 by m matrix, where m is the number of segments. Each column will hold the numbers of two end-points of one segment. For example, if we have four segments, (p1, p2) (p1, p3) (p2, p4) and (p4, p5), the [J] matrix would be (the order of the columns is not important):

   [[1   1   2   4]

   [2   3   4   5]]

 

Task 1.

Choose the coordinates of 5 points and create matrices [I] and [J].

 

Drawing program. Explanation
PROGRAM:DRAW  
:dim([J])→L1 Get the dimension of table J of pairs of points to be connected.This dimension consists of 2 numbers, e.g., {2,4} is 2 rows and 4 columns. This 2 means 2 points will be connected at one time, and 4 means we have 4 pairs of points, so we will make 4 segments. We will connect 2 points at one time.L1(2) is the number of segments (the number of pairs of points to be connected).
:For(K,1,L1(2)) Each point has a number, 1, 2, 3, 4, & 5; and their coordinates are in matrix I.
:[J](1,K)→P

Points numbered P and Q are end-points of the Kth segment.
:[J](2,K)→Q They need to be connected at this time.
:Line([I](1,P),[I](2,P),[I](1,Q),[I](2,Q)):End

Segment P Q is drawn. In order to draw the segment, we have togive 2 coordinates of the 1st point, x and y, and 2 coordinates of the 2nd point, x and y. [I](1,P) gives the 1st coord. of point P

[I](2,P) gives the 2nd coord. of point P.

[I](1,Q) gives the 1st coord. of point Q.

[I](2,Q) gives the 2nd coord. of point Q.

So the segment between the two points P and Q is drawn. End of for loop

Task 2.

Execute DRAW.

 

Remark.

To erase the picture from the screen, use ClrDraw. Just to return to the home screen (without erasing the drawing), press CLEAR.

 

Task 3.

Set MODE to Degree. In matrix [A] store:

   [[cos(45)   sin(45)]

   [-sin(45)   cos(45)]]   Values, not expressions, are stored.

 

Enter on the home screen:

[A][I]→[I]

and then repeat,

PrgmDRAW

ENTER

CLEAR

[A][I]→[I]

 

What do you see? 

Webpage by Owen Ramsey
Lesson Index