What about normalized gaps?

[Chris M. Thomasson]

To normalize the distance between two points in n-ary space. p0 and p1
can be n-ary vectors.

p0 = 1/2
p1 = 1/1
pdif = p1 - p0

the mid point would use the unit fraction 1/2 at:

pmid = p0 + pdif * 1/2

right?

For say a 3d vector of the above would be:

p0 = (1/2, 0, 0)
p1 = (1/1, 0, 0)

We can plot these. Say


p0 = (1/2, 1/4, 1/1)
p1 = (1/2, 1/3, -1/8)

That is a line in pure 3d space, yet the line normalization still works.
The unit fraction 1/2 is half way in between p0 and p1...

pdif = p1 - p0
pmid = p0 + pdif * 1/2

Right?

[Chris M. Thomasson]

Post by Chris M. Thomasson
To normalize the distance between two points in n-ary space. p0 and p1
can be n-ary vectors.
p0 = 1/2
p1 = 1/1
pdif = p1 - p0
pmid = p0 + pdif * 1/2
right?
p0 = (1/2, 0, 0)
p1 = (1/1, 0, 0)
We can plot these. Say
p0 = (1/2, 1/4, 1/1)
p1 = (1/2, 1/3, -1/8)
That is a line in pure 3d space, yet the line normalization still works.
The unit fraction 1/2 is half way in between p0 and p1...
pdif = p1 - p0
pmid = p0 + pdif * 1/2
Right?

Wrt normalizing it where p0 + pdif * 0 = p0 and p0 + pdif * 1 = p1
allows us to use unit fractions to find points on the line from p0 to
p1? For instance p2 would be 1/4 across from p0 to p1 where:

p2 = p0 + pdif * 1/4

Draw a line from p0 to p2.