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@m_schuetz @CianNoonan The superior distribution is demonstrated by the vertical lines in this diagram from Foundations of Game Engine Development, Vol. 2. (a) Depth is mapped from 0 to 1. (b) Depth is mapped from 1 to 0.… Image

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More from @EricLengyel

Jan 19
The 8 basis elements for the 3D geometric algebra correspond to the 8 ways that three dimensions x, y, and z can be partitioned into two groups, shown as red and blue here. The symmetries of duality arise from an operation that simply swaps the two colors. Image
Quaternions are multivectors only with components having an even number of red dimensions, and they look like this. Quaternions perform rotations, and they correspond to all possible proper isometries in 3D space that leave the origin fixed. Image
What about the basis elements with an odd number of red dimensions? They look like this, and they perform *rotoreflections*. These correspond to all possible improper isometries in 3D space that leave the origin fixed. Image
Read 4 tweets
May 3, 2021
Back in 1993, I was taking a number theory class, and there was a semester-long factorization contest that we could participate in. I implemented a distributed multiple polynomial quadratic sieve (MPQS) for the Mac, and I needed a cluster of computers to run it on.
The computer lab in the math building had a bunch of Mac Centris 650s on an AppleTalk network. But they were running some kind of secure software that didn't give you access to the Finder, only specific software, so I couldn't pop in a disk and run my own programs.
You can see in this picture that the Centris had two little buttons on the front. One was a reset button, and the other generated a non-maskable interrupt (NMI). If Macsbug was installed, the NMI button froze everything and dropped you into the system debugger.
Read 9 tweets

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