〈 Berger | Dillon 〉

One of the reasons I use my own drawing library is to make arrows, surfaces and shapes feel "physical". This is so I can play with our visual/spatial intuition. Here's a good example: the "thick" surface in this animation allows you to instantly "get" the complex 3D shape.pic.twitter.com/XfAgZ496en

Another great example of this technique to convey physical structure to 3D surfaces is in this animation depicting a "Fourier transform surface", something I never saw fully visualized before. Without this approach, using thin surfaces, this would likely look like garbage.pic.twitter.com/G4kG2g2E0L

I always try to find a middle ground between flatness/3D. Naive 3D rendering, with shadows & etc, produce unnecessary visual noise. You can convey depth by simply treating flat shapes as actual tridimensional objects, like the arrows here. The grid adds extra information.pic.twitter.com/uofY2nKafr

This cross product GIF also illustrates how the flat-rendered vectors are always drawn as physical, 3D objects. If I didn't treat the arrowheads as cones, you wouldn't get the same depth effect. Notice that I also don't typically treat the arrow body as cylinders unless needed.pic.twitter.com/V4XO31VLid

Another way I mix flatness with depth is to smoothly alternate between orthographic and perspective projections. You'd probably never notice it, but I do it all the time. The camera motion in this line integral animation switches from orthographic to perspetive, then back.pic.twitter.com/AyOybRddVk

The torus is my favorite 3D solid, which explains why I have so many torus stuff. This one showing Villarceau circles, also using physical intuition with the "slicing", was inspired by the "Villarceau Circles" rendering in the POV-Ray Hall of Fame, by Tor Olav Kristensen.pic.twitter.com/sCyZyKKq9E