Overview
This app generates a range of common polyhedra and lets you apply
mathematical operations on them to create some interesting and artistic sculptural forms.
I have tried to include most of the standard operations from Conway polyhedron notation – borrowing heavily from
some of the techniques used in Anselm Levskaya's polyHédronisme
and George Hart's Polyhedron Generator
– as well as a couple of my own for spherical inflation and a bit of randomness.
Once you have selected a base polyhedron, you can either enter a
notation command string directly, minus the polyhedron identifier at the end, or build one
up by adding and editing components in the operator stack immediately below.
Conway Polyhedra Notation
Importantly, you don't need to know anything about Conway polyhedron
notation to have fun with this app. You can just experiment by trying out different operators
one by one to see what they do. Moreover, you can choose one of the examples and then start
enabling/disabling or editing the paramaters in order to experiment.
If you do want to know more, the best place is the
Wikipedia page
linked to above. Hopefully at some point I will get enough time to go back and write a detailed
explanation for each of the operations and what they do, but until then it's up to Wikipedia
and George Hart's original explanations.
As notation strings can sometimes get quite complex, especially when
using bracketed arguments, I have tried to make the operator stack a bit more approachable
by including all the available paramaters as interactive sliders.
To enter a number directly, either click the slider instead of dragging
it, or manually edit the appropriate argument in the notation text. By default, the operator
stack will update whenever you manually change the notation in the text editor.
Background
I have always wanted to do a WebGL version of the polyhedron viewer I
wrote in Processing some years ago, but it was just a folly and there were always higher
priorities. However, I recently needed to include some basic polyhedra in my
Tree Generator app,
so had to convert some of the old code anyway. At the same time I was trying to develop a
bullet-proof closed-shell geometry class for my BIM tools and, having seen and been so
completely inspired by polyHédronisme,
I figured that it might make an excellent visual test suite and provide just the excuse I needed.
Interesting Features
The following are some of this app's features and idiosyncrasies:
- Don't go too beserk, but this app will handle higher-order polyhedra
with several hundred thousand vertices and a similar number of faces. However, anything
above about 200k will start to test your patience when editing it - so best to edit a
simplified base and then add smoothing expansions only when you want to export or visualise.
- The final generated polyhedra always has a maximum radius of 1 metre.
This may mean that some extrusions cause the apparent base polyhedron to shrink in size
relative to the external projections, but this is intended behaviour.
- I have tried to provide a range of different facet colouring options,
based on relative area, number of edges, orientation or a combination of all three to create
a signature for like faces. Different types of polyhedra will look good with some and not
others, so you will need to experiment for best results.
- I have taken some egregious liberties by adding a couple of non-standard
operations such as Jitter (J), Wrinkle (W) and Inflate (I)
© Dr. Andrew J. Marsh, 2019.
View Manipulation
You can interactively adjust the 3D view of the model using a mouse,
pen or stylus, or by touch on a tablet or phone.
You can also use the items in the 3D View Settings popup.
- Rotation:
- Drag with the left/right button or a single finger,
or use the arrow keys.
- Panning:
- Drag with the middle button or two/three fingers,
or use the A and D keys.
- Zooming:
- Use the scroll wheel or pinch with two fingers,
or use the W and S keys.
NOTE: You can use the Shift and Ctrl/Meta keys to adjust the increment
of each scroll event or key press.
Keyboard Modifiers
The Shift and Ctrl/Meta keys are used pretty extensively
to modify interactive data entry. This applies to all increment buttons, scroll wheel motion,
slider controls and input elements.
- Shift Key:
- Increases input to larger values, usually by ten times or significantly larger increments
such as 1 month for dates and 1 hour for times.
- Ctrl or Meta Key:
- Decreases input to smaller values, usually by one tenth or the smallest reasonable increment
such as 1 day for dates or 1 minute for times.
NOTE: You can use the scroll wheel to edit a data value when hovering over any slider,
numeric input or even table rows that indicate their editibility.
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