Dead Reckoning in a Non-Orientable 3D Space

By Xah Lee. Date:

dead reckoning, is when you drive about without a map.

Or for example, in a first-person shooter game. By memory of past navigation decisions and memory of scenery and sense of direction and traveled distances, you can sort of reconstruct the area's map.

js canvas raycaster dead reckoning
walking a 2D maze without a map

now imagine, dead reckoning in a non-orientable 3D space. This is when, the math wonders of nature sends a chill down your spine.

karcher je st
Karcher JE Saddle Tower. A orientable surface that partitions 3D space into 2.

and that's possible when, math comes into a 3D game setting such as Second Life

for detail, see: Geometry: Requirements for a Visualization System for 2020

the image Karcher JE Saddle Tower isn't a non-orientable surface. What we need is a image for non-orientable 3D space. See: Orientability