"...and so the line connecting the points Ga and Gb in gradient space,
which correspond to the planes A and B in image space, is the
set of points representing positions of a plane see-sawing around the
line of intersection between A and B..."
Now I see; then I saw;
The planes of a cube have a linear law.
The endpoints of lines in the gradient space
Show where the see-sawing planes fall into place.
Macrakis, sitting beside me, half-asleep: "COFFEE!"
Caffeine doesn't help me composing this verse.
It only awakes me; my thoughts all disperse.
One thinks better dozing, collapsed in a heap;
Why else are most students in classes asleep?
"...the lines in gradient space are perpendicular to the lines in
image space. This doesn't provide enough constraints, however.
Additional equations may be derived from the intensity information.
One can get one or more solutions for a trihedral vertex. If the
vertex has more than three planes, then there are more constraints
than necessary, and one may have to resort to least squares..."
Alone, the geometry isn't enough:
You also require intensity stuff.
We get enough data if points are tri-planed,
While four leave the gradients over-constrained.
I count the following as more mathematical than physical; maybe I'm just a sucker for double dactyls — YMMV:
> [f] I once read that space has three dimensions because orbits aren't stable in 4-space.
I often have wondered in
What kind of orbit a
Planet proceeds in a
Tesseract space?
Multidimensional,
Hyperelliptical,
Dizzying spacemen in
Trans-solar chase.
“The Square Root of Three”(written by David Feinberg)
I’m sure that I will always be A lonely number like root three
The three is all that’s good and right, Why must my three keep out of sight Beneath the vicious square root sign, I wish instead I were a nine
For nine could thwart this evil trick, with just some quick arithmetic
I know I’ll never see the sun, as 1.7321 Such is my reality, a sad irrationality
When hark! What is this I see, Another square root of a three
As quietly co-waltzing by, Together now we multiply To form a number we prefer, Rejoicing as an integer
We break free from our mortal bonds With the wave of magic wands
Our square root signs become unglued Your love for me has been renewed
source: https://allpoetry.com/poem/4721391--The-Square-Root-of-Three...