3D Plot Out of Paper + Bonus

Some time ago I found a nice idea of assembling 3D paper plots. There are some websites You can get an idea how they are done:

• Automation of 3D Paper Modeling - math.stackexchange.com
• Paper Models of 3D Plots - mapleprimes.com
• Paper and Plotter: A 3D Surface - graficaobscura.com
• How To Make a 3D-Paper Model from a Heightfield in Processing - local-guru.net

But only the last one gives some program to generate slices for such a 3D plot.

I wanted to share with You my simple JavaScript code You can run directly in Your browser which will generate printable slices for You automatically.

At the end of this Instructable, there is a bonus "plot" made from scratch without printer.

Materials:

• Thick paper (brostol), I would recommend to avoid a regular paper.

Tools:

• Printer (no need for bonus "plot"),
• Scissors,
• Pencil, marker and eraser (needed for bonus "plot"),
• You.

You can use Wolfram Alpha website to generate some nice 3D plots. It gives an overall view how Your future plot will look like.

The equation I've picked as an example of paper 3D plot was:

z = sin(x) * sin(y)

x range: [-2π, 2π], y range: [-2π, 2π], z range: [-1, 1]

Link to Wolfram Alpha

Splitting 3D plot into layers manually is a time consuming task. I used one of online 2D plot drawing website called RechnerOnline where I have used a function graphs engine. I really recommend this site as it contains many more math stuff.

You need to draw a 2D plot (a slice) of a 3D plot according to an "x" variable with some fixed value of "y" variable. And You need to do it many times, one plot for one slice.

To make it more automatic, I've created a simple HTML page which calls the Rechner Online website automatically generating each slice for You at once. Download attached plot.zip file, extract it and open plot.html file in Your browser (unfortunately it is not possible to attach this file unpacked so I had to ZIP it).

It has a reduced number of parameters than original website. The most important parameter is Your equation. You can also adopt the width and height of Your plot, and number of slices You need. Then click "Generate" and all required slices will be generated for You in one go directly in Your browser.

You just need to print the website and You are ready to go to cut Your 3D paper plot.

It takes around 1-2h to cut everything. For my case I had to cut out 21 2D plots.

These small additional cuts on the bottom of slices and 2 supporting bars need a special treatment. It is tempting to just cut them once and that's it. But it makes them very hard to fit to each other. Another problem is that paper can bend a little making it hard to look nice.

What You need to do is to cut a super-thin piece of paper. It means You need to make 2 cuts around every line (try to cut a printed line out of a paper).

After that, You are ready to assemble it.

If You used a thick paper then assembling should go easy. With a regular printing paper it is sometimes quite hard because such a paper is very delicate the 3D plot is not stable enough during assembling..

Here is a bonus 3D "plot" of a hand. The idea is similar to what we all did in school and is presented in 3D hand or 3D hand silver & black edition Instructables.

I used my son's hand (because it was smaller ;) )

My hand was designed to be 16cm x 16cm. It means I needed 17 slices. The process of creating it is very similar to the 3D paper plot, but there is no need to use a printer. Instead, I used a pencil and a marker to emphasize the edges. There was also no need to measure the tickness of a hand - I roughly assumed something around 1-2 cm. The closer to fingers, the thinner the slice.

Cutting is easy but time consuming. The more layers You want, the better quality of Your 3D hand You get. But it will take much more time then.

After cutting, You can remove all lines done by pencil for a clean look.

Assembling is easy if You've used a thick paper. Adding layers one by one makes Your hand "popping out" from a flat surface.

The view from the back (without marked edges by a marker) is also really nice, but unfortunately it doesn't look good on a photo.

Final results are really nice and I have to admit - I didn't expect such a good result. I will definitely build more 3D paper plots and attach them to this Instructable.