School Project: Draw a Picture

[Dman979]

Hi All! For my math class, I have to draw a picture using Desmos Graphing Calculator. I would like to set the bar pretty high for my class, and I want your help. I plan on making THIS:

The background is irrelevant here. What is important is the shuttle stack; ie the SRBs, External Tank, Orbiter, and smoke.

I don't know all of the functions I need for this to work, so I'm hoping that you can help. If you find a function which will solve for a part of the picture, please post it here. I'll put them up in order and you can copy and paste to see what has already been done.

If you're interested in helping, let me know on this thread and I'll put your name up, along with any details you would like to draw.

Thanks in advance for everyone's help!

Contributors:

Functions:

-1.225x – 15.6 {-26.4≤x≤-4.5}

-1.225x – 4.6 {-20.4≤x≤-12.4}

-1.225x – 4.6 {-6.8≤x≤0}

0.04x+4.1 {-14.5≤x≤-7.5}

0.04x+4.1 {-6.8≤x≤0.5}

-2.3x–12 {-7.6≤x≤-6.9}

-(2.3x–12)–6 {-0.21≤x≤0.8}

-2.3x–13 {-8.04≤x≤-7.3}

-2.3x–30 {-15.05≤x≤-14.569}

1/8x+6.5 {-15.05≤x≤0.2}

x=-15.06 {7.5≥y≥4.6}

x+22.55 {=15.06≤x≤-8.4}

x=-8.4 {14.14≤y≤15}

-2x–1.9 {-13≤x≤-8.4}

Edited May 12, 2015 by Dman979

[Dman979]

anybody want to help? Please?

[kenbobo]

Aye lad, it seems difficult. I cannae help you with this as my coordinate grid skills are limited.

[HafCoJoe]

Good luck!

[Dman979]

Thanks! What I've done so far is to paste the pic into Desmos and play with the lines until they match the pic.

[Dman979]

I'm still looking for help. Please?

[Bill Phil]

Can you set limits to lines???

Can a matrix be used to define shapes? If so, can you use them in Desmos?

[Dman979]

I don't know about using matrices(?), I haven't tried to yet.

You can limit the lines. I've done that on every line so far, that's what the brackets are for.

[Starwhip]

Step one: draw reference points.

Step two: draw lines to connect points.

Step three: define equations.

I cannot help much on mobile. Sorry!

[Dman979]

Step one: draw reference points.

Step two: draw lines to connect points.

Step three: define equations.

Actually, with the wonderful "Import Picture" feature, I'm using the original as my reference. So I'm skipping to step 3 and translating the graphs around a lot.

[Dman979]

Please help! Bump!

[FishInferno]

I think a Saturn V would be easier. simpler shapes

[Dman979]

Hmm, OK. Will you help? Pleaseeeeee?

[pincushionman]

Are you just using a sequence of y=mx+n line segments? That's the simplest approach, but it will be very time-consuming for the curves.

Step one: draw reference points.

Step two: draw lines to connect points.

Step three: define equations.

This is still valid. Define your point cloud first, then identify the line segments that connect which points.

The y=mx+n equation for a line that connects (a, to (c,d) is

y = ((d-b)/(c-a))*(x-a) + d

Well, not quite; I simplified too far.

y = ((d--(c-a))x + (b - ((d-b)/(c-a))a)

Simplify as necessary.

I would use Excel to input your points for each segment and determine your m and n. The CONCATENATE() function or the "&" string-add operator could then be used to give complete equations for cut-and-paste.

[SpaceExplorer]

Hey Dman979,

From the looks of your pictures you are going to need some of these equations:

1. The Parabola

This is a great way to create curved lines in your picture. I would suggest just plugging in this exact formula into Desmos and use the sliders. Play around with it for a bit and see which variable does what. (If you switch the x with the y you can alter the axis of symmetry and have it reflect along the x axis versus the y).

2. The Circle

You are going to need circles to draw in your boosters and the Shuttle's main engines (or the Saturn V's depending on what you plan on drawing) as well. Again, I suggest that you put this formula into Desmos too and play with the variables.

​3. The Ellipse

Squished circles are fun! You are going to need some of these too!

4. Inequalities

I don't know if you need to shade in certain areas of the picture for your project, but if you have to these will for sure help you out. It seems to me that you already know how to do these since you have been limiting the length of your line segments.

5. The Linear Equation

This also seems to me that you know about these as well.

I hope that this helps, or at least gives you some ideas for your picture. (I want to thank Wikipedia's math function for the equation pictures)

All the best to you, and if you have any questions feel free to ask!

Edited May 15, 2015 by SpaceExplorer

[pincushionman]

I was going to suggest that ellipses might be useful too, but all his ellipses are likely to be oriented at funny angles, which makes it more complicated. I also find curve-fitting to be a major PITA, especially if we have easy tools to brute-force a piecewise-linear solution with enough precision you can't tell the difference by eye.

[Dman979]

Oh, the entire picture is a PITA. But the best one gets the most points!

pincushenman, I need to use more than just linear equations. Also, I'd rather not have to make 30 lines for a 2.5 Cm segment

[SpaceExplorer]

but all his ellipses are likely to be oriented at funny angles

Very true. Do you have another idea?

I also find curve-fitting to be a major PITA, especially if we have easy tools to brute-force a piecewise-linear solution with enough precision you can't tell the difference by eye.

I forgot about piecewise functions... That may be a better alternative instead of putting restrictions on each the line segments.

EDIT: Just checked out Desmos and it looks like piecewise functions are tough to do, but are still possible.

Edited May 15, 2015 by SpaceExplorer
Added some stuff

[theend3r]

deleted

Edit: Sorry, it was a nonsense that wouldn't help you.

Edited May 15, 2015 by theend3r

[pincushionman]

pincushenman, I need to use more than just linear equations. Also, I'd rather not have to make 30 lines for a 2.5 Cm segment

Makes sense for a math project. Six o' one, half dozen o' the other - curves will be harder to fit, but you'll have far fewer to do.

Here's a suggestion for the curves: Identify the start, end, and a few points along. Put those coordinates into Excel and make a "scatter" plot from them. Add a trendline. Play with the different options until you get something you're satisfied with. Then have it display the equation for the curve. Don't be afraid to edit your points here, because your coordinates are guesses, and some of the regression options are very sensitive to small changes.

I don't think you can get a good ellipse or a circle with this method. And near-vertical curves will be extra-problematic. But if you're careful, it may look good.

[Dman979]

Makes sense for a math project. Six o' one, half dozen o' the other - curves will be harder to fit, but you'll have far fewer to do.

Exactly what the teacher was thinking.

Here's a suggestion for the curves: Identify the start, end, and a few points along. Put those coordinates into Excel and make a "scatter" plot from them. Add a trendline. Play with the different options until you get something you're satisfied with. Then have it display the equation for the curve. Don't be afraid to edit your points here, because your coordinates are guesses, and some of the regression options are very sensitive to small changes.

Hmm, an option I didn't even know existed! Thanks! I will try using this and see how it goes.

I don't think you can get a good ellipse or a circle with this method. And near-vertical curves will be extra-problematic. But if you're careful, it may look good.

Well, for the elipises and circles, I can use the regular equations above. If I'm careful, anything can look good. Thanks again!