This week, I commissioned a 3D model of a trigonometric curve from the ETS 3D Print shop and was able to do a quick usability test with some volunteers from the TLT accessibility team on what kinds of information could be gleaned from it. As most people would expect, the test was reasonably successful, but I thought I would document the process to give people a sense of what was involved in making the model.

### The Curve

For a 3D printer, you need a file (e.g. STL file) which specifies the dimensions of the object. For this example, I went online and looked for mathematical models and found this 3DPlot function utility for Open SCAD by dnewman on MakerBot Thingverse, one of the various 3D model download sites online now.

In this case, the curve I chose was (in MathML):

$$z(x,y)=\mathrm{cos}\sqrt{\left({x}^{2}+{y}^{2}\right)}$$#### Mathematica and MatLab

If an instructor would need a curve and had access to either Mathematica or MatLab, the more recent versions of these programs should be able to export a generated curve to an STL file.

#### Other Modeling Programs

To create other types of models (e.g. a gear or pencil jar), a 3D modeling program which exports to and STL or other 3D printer compatible file is needed. The Lynda.com at Penn State service includes some 3D modeling courses.

### Making The Print

I sent the STL file I found to our 3D printing gurus in ETS and after they verified the file, the were able to print a 2 inch x 2 inch version of the model. The resolution was quite good, but there were some caveats.

- Beware of any model with a sharp point. If a blind person is handling them, you don’t want any punctured fingers. In this case, I first covered the point with tape, but discovered you could “sand” down the point by pressing it on on a desktop. It removed some of the extruded plastic and rounded out the tip without too much distortion.
- Depending on your printer, there may be ridges created by the extruded plastic. Your model needs to account for any resolution issues. Expanding the scale could be one option although it will require a longer print time. Another is to select a finer resolution/nozzle – which will also result in a longer printing time.

### Assessment

A question about 3D printing is whether the expenditure is justified by a blind (or sighted) person being able to handle a 3D model. In this case, I would say yes. The model was usable enough so that the testers were able to quickly determine the same (circular ridges with a peak in the center). In fact one person immediately proclaimed “It’s a bullseye!” For the record, the original model was developed precisely to explain math curves to a blind student.

That’s not to say that you might not need some tweaks. One tester asked if there should be labeled axes (i.e. x and y axis). This could be done easily with ether a notch or some Braille labels (in the model or with some other Braille label). If a math problem were done based on the graph, it would be necessary to provide the same key data (such as a “y-intercept” point or values at key coordinates) that a sighted student would have.

You could also begin thinking about how many models would be needed. Would one basic model of a curve be sufficient to describe variations that would occur due to other parameters? At which point would a new curve be needed? And how does 2D tactile printing fit in to the discussion?

It’s an interesting topic and a great justification for experimenting with 3D printing