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Using equations to graph pictures on calculator

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Calculators: Casio Afx 1.0, Casio fx-9860GII SD, Casio Classpad 330, Casio fx-CG20, Casio Classpad fx-CP400

Using equations to graph pictures on calculator

Postby helder7 » Wed Feb 20, 2013 8:43 pm

A friend of mine started trying to draw pictures on the calculator only with equation types and math functions (ln, log, cos, tan, sin, abs...) available in casio calculators.

It's an interesting challenge. Many of the equations available in web to draw pictures are not compatible with casio calculators.

Below is the list of images made with equations until now (left: prizm; right: fx9860):

1 - Leaf

Author: A friend of mine

Image Image

Equations: Show
Y1 = Image

Y2 = Image

Y3 = Image

Y4 = Image

Y5 = Image

Y6 = Image

Y7 = Image

Y8 = Image

Y9 = Image

Y10 = Image

Y11 = Image

Y12 = Image

Y13 = Image

Y14 = Image

Y15 = Image

Y16 = Image

Y17 = Image


2 - Heart

Author: Casio Poland

Image Image

Equations: Show
Y1 = Image
Y2 = Image
Y3 = Image
Y4 = Image


3 - Nike Logo

Image Image

Equations: Show
Y1 = Image
Y2 = Image


4 - Butterfly

Author: Niel Kelcey

Image Image

Equations: Show
Y1 = Image

Y2 = Image

Y3 = Image

Y4 = Image

Y5 = Image

Y6 = Image

Y7 = Image

Y8 = Image

Y9 = Image

Y10 = Image

Y11 = Image


5 - Star

Image Image

Equations: Show
Y1 = Image

Y2 = Image

Y3 = Image

Y4 = Image

Y5 = Image


If you have more equations to graph pictures on calculator, you can share here.
SiO2 + CaCO3 ----------> CaSiO3 + CO2

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Re: Using equations to graph pictures on calculator

Postby nsg » Thu Feb 21, 2013 12:33 am

This is very interesting and creative excersize.
However, if you remember that cubic splines are functions, you can take any artwork digitized as not too many splines and turn it into parametric polynomial plots.

Here is what I mean. To draw a cubic spline with control points (A,B), (C,D), (E,F), (G,H) set the folowing parametric plots:
"A(1-T)^3+3CT(1-T)^2+3ET^2(1-T)+GT^3"->Xt1
"B(1-T)^3+3DT(1-T)^2+3FT^2(1-T)+HT^3"->Yt1

Also, coefficients can be lists, so you can prefill several of them with control point coordinates and draw many splines using just one command. Unfortunately, i did not figure out how to make them all same color -- when taking coordinates from lists, the graphs system seems to rotate colors.

Another practical matter: you can use spline approximations of special curve to draw them. Like parabolas, ellipses, circular arcs -- which do not have their own casio basic routines.

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Re: Using equations to graph pictures on calculator

Postby aapman55 » Fri Feb 22, 2013 10:36 am

how did you do the interval thing on the 9860?

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Re: Using equations to graph pictures on calculator

Postby helder7 » Fri Feb 22, 2013 4:10 pm

First I write the equation:
Exemple: Y1=X

After, at the end of the equation I put a comma (Image) and a parenthesis ( Image + Image)

Now I have: Y1=X,[

I can write the first interval value:

Y1=X,[-5

before adding the second value I need to put another comma (Image), and only then I can write the second value:

Y1=X,[-5,5

to finish, I need to close parenthesis ( Image + Image)

Done: Y1=X,[-5,5]
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Re: Using equations to graph pictures on calculator

Postby nsg » Sat Feb 23, 2013 7:04 am

Amazing. Is it in the manual? I somehow missed it.
BTW, this domain specification works all the way back. I just tried it with 7700G and it is there.

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Re: Using equations to graph pictures on calculator

Postby helder7 » Sat Feb 23, 2013 9:42 pm

nsg wrote:Is it in the manual? I somehow missed it.

Maybe yes, but I learned this in class. :)
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Joined: Sat Feb 02, 2013 4:29 am
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Re: Using equations to graph pictures on calculator

Postby nsg » Mon Feb 25, 2013 1:35 am

Here is example of a program (fxCG) that draws family of splines using equation graph.

Code: Select all
'ProgramMode:RUN
ParamType
"A(1-T)^3+3C(1-T)_^<2>_T+3E(1-T)T_^<2>_+GT^3"->GraphXt1
"B(1-T)^3+3D(1-T)_^<2>_T+3F(1-T)T_^<2>_+HT^3"->GraphYt1
0->TThetamin
1->TThetamax
0.05->TThetaptch
G SelOff
G SelOn 1
ThinG 1
For 0->I To 5 Step 0.5
(-)6->A:(-)3->B:(-)3->C:6-I->D:0+I->E:(-)3->F:6->G:3->H
DrawGraph
Next


Instead of assinging functions to graph memory, I tried to use Graph(X,Y)=( function which works great, except I do not know how to specify line styles for it.

Code: Select all
'ProgramMode:RUN
0->TThetamin
1->TThetamax
0.05->TThetaptch
For 0->I To 5 Step 0.5
(-)6->A:(-)3->B:(-)3->C:6-I->D:0+I->E:(-)3->F:6->G:3->H
Graph(X,Y)=(_A(1-T)^3+3C(1-T)_^<2>_T+3E(1-T)T_^<2>_+GT^3,B(1-T)^3+3D(1-T)_^<2>_T+3F(1-T)T_^<2>_+HT^3)
Next

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Posts: 369
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Re: Using equations to graph pictures on calculator

Postby helder7 » Sun May 05, 2013 12:00 am

Graphing with white color: :P (and with a black .g3p behind).

Image Image
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