TI-92 CAS Window -- Points and Rigid Transformations in the Plane

This package consists of seven TI-92 programs. If you haven't already done so, enter them into your TI-92 either by typing them in or by downloading them using the TI-Graph Link. The programs are located at the end of this module. Together they allow you to display and manipulate images made up of a series of line segments. You must set the TI-92 graph MODE to FUNCTION before using these programs.

This package represents an image as a list --

The seven programs described below enable you to display and manipulate images represented in this way.

• setshow(n) -- This program requires one argument n. It sets up the graphics window so that the y-axis runs from -n to n. The scale for the x-axis is automatically set so that each physical unit on the x-axis represents the same change in x that each physical unit of the y-axis represents for y.

• showline(list) -- This program requires one argument which is a list containing 2n elements, each pair representing a point as described above. The program draws a line connecting the points. Note: the program does not clear the screen before drawing. This enables you to display several images on the screen. To clear the screen choose ClrDraw from the Draw menu obtained by pressing F6 while the graphics screen is displayed.

  The next five programs enable you to manipulate images by manipulating the lists describing them.

• mirror(list) -- This program requires one argument, a list describing an image, and returns the list describing the same image after it has been reflected in the x-axis. The two screens below illustrate how mirror is used.

  

• rotate(list, theta) -- This program requires two arguments, a list describing an image and an angle theta, and returns the list describing the same image after it has been rotated counterclockwise by the angle theta. The two screens below illustrate how rotate is used.

  

  Notice that the rotation is about the origin -- that is, the origin is fixed and the plane rotates around the origin.

• translat(list, a, b) -- This program requires three arguments, a list describing an image and two numbers, a and b describing how the image is to be translated. It returns the same image after it has been translated horizontally by a units and vertically by b units. The two screens below illustrate how translat is used.

  

• ident(list) -- This program requires one argument, a list describing an image, and returns exactly the same image. The following two screens illustrate how ident is used.

  

  Notice that the second screen contains just one image because ident doesn't do anything.

• dilate(list, factor) -- The four programs mirror, rotate, translat, and ident are used to perform rigid transformations, transformations that can be done physically using a piece of acetate. This program, dilate, is used for a transformation that is not rigid -- dilation. It requires two arguments. The first argument is a list describing an image and the second is the factor by which the image is to be magnified (if the factor is greater than one) or reduced (if the factor is less than one). Notice if the factor is negative then the image is magnified or reduced and rotated 180 degrees (pi radians) about the origin. The following screens illustrate how dilate is used.

  

setshow

showline

ident

mirror

rotate

translat

dilate