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X3D: behind-the-scenes

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Here is a look at the 3d technology which drives vrmath behind the scenes. It is called X3D and has its own web site. Understanding this technology not only helps in how vrmath extends turtle graphics into 3d but opens the door to a large world of virtual reality in general (x3dom, web3d). It turns out that the vrmath editor is itself a good tool to get to know X3D. Here is how.

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more gears, fast

4 gears

I updated the involute (curved teeth), helical gear generation procedure to use Extrusion rather than IndexedFaceSets. Extrusion automatically supports the back and front faces of the gears, and a smooth appearance by producing a mesh with points shared by triangles. So the logo code could be streamlined and therefore is now much faster generating gears.

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general smoothness

smooth gear

Getting gears to appear smooth by explicitly assigning indices to the generated facets got me thinking in more detail of how to accomplish this result in general, for any facets drawn in face mode by turtle graphics.

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smoother gears

smoother tooth

Trying to get a smoother appearance for the curved gear teeth involves lessons both in logo programming and in the underlying 3d display technology.

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helical gears

3 helical gears

The real advantage of gear modelling in 3d is that gears in a mesh do not have to parallel each other. It is posible to demonstrate how gears can transfer rotation (and forces) to orientations other than the driving gear. This kind of transfer is possible by use of helical gears.