Animations
The program ANIMATE below requires a matrix [I] containing coordinates of points in your drawing (if there are n points, [I] will have 2 rows and n columns, as in the DRAW program). It also requires matrix [J], containing pairs of points that are to be connected. [J] has 2 rows, and as many columns as there are to be segments. And it requires the DRAW program.
What ANIMATE does:
It animates a rotation of the figure drawn by DRAW counterclockwise around angle A about the origin, with a “growth” or “shrink” factor C. (If C>1. the drawing increases in size. If C < 1, the drawing shrinks. If C = 1, the drawing size does not change.) So you see picture after picture in an animated sequence. There is a delay D between each two pictures. You set D between 0 (fast) and 10 (slow).
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Drawing Program |
Explanation |
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PrgmANIMATE |
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:While 1 :For (L,1,D) |
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:π2→Z |
Computing π2→Z takes a while, and causes a delay. |
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:End |
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:ClrDraw |
Erases screen |
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:C[[cos(A),-sin (A)][sin(A),cos(A)]]*[I] →[I] |
Rotates picture by angle A, and changes its size by factor C |
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:PrgmDRAW |
Draws a new picture |
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:End |
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To run the program, you need [I] and [J]. Also, from the home screen, choose values for A, C, and D. For example,
20→A (rotate by 20 degree angle)
.95→C (this will decrease the size of the picture)
5→D (this will cause an intermediate delay between pictures)
Now choose PrgmANIMATE, and press ENTER.
Some tasks.
1. Experiment with different values for A, C, and D for a drawing.
2. Can you design a beginning drawing (with two points and one segment) that will result in a square being drawn, segment by segment?
3. Can you design a beginning drawing that will result in an n-sided regular polygon being drawn?
4. In order to compute p, Archimedes used a 96-gon. Can you design 2 points and one edge of a polygon, so that you will get a 96-gon?
Solutions for tasks 3 and 4. (To draw a regular
n-gon.)
Modify program ANIMATE by blocking ClrDraw by putting it in quotes:
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Drawing Program |
Explanation |
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PrgmANIMATE |
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:While 1 :For (L,1,D) |
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:π2→Z |
Computing π2→Z takes a while, and causes a delay. |
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:End |
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:"ClrDraw" |
Now it does nothing. |
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:C[[cos(A),-sin (A)][sin(A),cos(A)]]*[I] →[I] |
Rotates picture by angle A, and changes its size by factor C |
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:PrgmDRAW |
Draws a new picture |
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:End |
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Set the variables as follows:
[I] = 10*[[1, cos(360/n)][0, sin(360/n)]]
[J] = [[1][2]]
A = 360/n
C = 1
D = any including 0.
After you interrupt it by [ON][ENTER], just press [GRAPH].
You can clear it by ClrDraw, or put another picture on top of it.
In order to draw stars, change only [I], choosing k < n (and preferably relatively prime to n):
[I] = 10*[[1, cos(k*A)][0, sin(k*A)]]