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Can’t be done
In the early times of the Nspire I spent some time on some forums discussing Nspire. Quite many people were angry that Nspire could not do this or could not do that. What most of those people missed was that the Nspire is not designed as a tool for engineers but as an educational tool.
On the other hand, what I that TI missed is how little extra would be added to satisfy nerds or geeks (like me to a bit) too. A few more functions, like the Gamma function (maths geeks love the gamma function), possibly some FFT and Laplace transforms, and 3D graphs (that the Nspire have now but not then).
Having added this would have turned the geeks more positive – and the value of that cannot be underestimated.
Anyhow, one of the things people complained about was the lack of a plot command. I.e. a command that would allow you to, under program control, add graphics elements to a window, like a point or a line. One reason for this anger was that people thought it made it impossible to at least write their own 3D-plot functionality since it was (then) missing.
Anyhow, the geek (or perhaps nerd) part of me thought of that as a challenge, so I wrote a “program” that could do just that.
I remember a particular discussion on a forum where someone, yet again, said that the Nspire was a bad product because you could not even program it to do 3D plots. So I said, yes you can, I have just done it, and was immediately called a liar. Would it not have been better to ask me “OK, could you show me”? Internet is at times a dark place. I was by the way also called evil just because I defended the Nspire as an educational tool.
Anyhow, back on track…
How to do what can’t be done
My idea was to use the scatter plot functionality on the Nspire, together with the dynamic coupling between the data and the graph. When changing the data in the built-in spreadsheet, the graph would change too, as in Excel. Then one can choose to connect the dots in the scatter plot. To make several separate parts one can put “_” as data in between the parts. This acts as a “Not a number” and will not be plotted.
The little table above could be used to make the following graph.
Not overly impressive, but at least a start. The idea is now that we could add and remove rows in the tables to add and remove points and change the numbers to other values to change coordinates. The values could for example be changed by adding a slider, and then use the variable values to change the values in the table.
The 3D plotter
This is basically what I did to make the 3D plotter. I calculated a bunch of points on a square grid using a function of the form z=f(x,y), Then I transformed the points to new coordinates using ordinary coordinate transformations (in this case rotations), and then I did a perspective transform from 3D to 2D to get the where to plot the points on the screen. The result looks like this.
The user can change the function, and it will automatically replot the graph. The user can also rotate the graph along all three axes. If you want to try it you can download a copy here: 3d16.tns.
It was written before the Nspire had colours + I would have done it using more program control if I had done it again. But anyhow, it shows what can be done.
The program won some kind of “best program” prize “back in the day”.
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