Slicing boxes in higher dimensional Euclidean
Linear scaling higher dimensional Euclidean box slicing!? O(n) speed for O(n!) complexity, can you believe it?
Slicing boxes in higher dimensional Euclidean
Linear scaling higher dimensional Euclidean box slicing!? O(n) speed for O(n!) complexity, can you believe it?
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Transcript
At this point in time we have seen 710 dimensional Objects.
with slicing, 300 dimensional.
Objects.
with sign distance fields.
Today I'm going to show you
How to do...
My version of it.
So we have this screen here.
Pixel 1, Pixel 2, Pixel 3.
Okay, they're big.
But you get the idea.
We go pixel by pixel.
we find
Where?
So that's the viewpoint.
So pixel one, Goes this direction.
takes old two
Goes past it.
Thank you.
but barely hits.
that sort of thing, what we can do.
Is...
minimums and maximums of possibility.
Thank you.
Thank you.
And...
when we find those, we can find maximum minimums and minimum of maximums.
we can discard the ones that cannot be in Thank you.
the view area.
But that...
Thank you.
That is O.
Ask for screen pixels.
Times.
n.
Times.
Oh, for objects.
But that's linear.
Thank you.
Thank you.
Thank you.
Thank you.
Thank you.
Thank you.
Tetrahedra.
Thank you.
That...
Edge.
equals
Oh.
2 to the power of n.
That's edges of of the
thing where
doing.
So what are we doing?
We are finding...
Thank you.
you
No.
Oh, I'll just write it.
Thank you.
Okay.
So, boxes.
Basically...
It's defined as like...
From a minimum to a maximum.
So, Bye.
within a minimum or a maximum
where the minimum or maximum for a rally with travel could be
Yes.
What we are finding.
Thank you.
Thank you.
Now this is well and good.
but,
for this approach.
Storage.
is approximately
Thank you.
Thank you.
That's also storage.
which is possibly not good.
But what we can do
is
See, that's one line.
of them.
in pixels.
We then.
Go.
pixel by pixel, Finding.
Only one dimension.
Whether it could be in, whether it could not be in.
The first thing...
that could be from that one.
Recheck.
in more dimensions.
until it is not or be discarded.
And similarly,
for the other direction.
Thank you.
Thank you.
So, I'm going to go ahead and get it.
Storage is really
Thank you.
Thank you.
More like...
Jess.
Oh.
times n.
plus some negligible amount.
Thank you.
Thank you.
Thank you.
Thank you.
Thank you.
Thank you.
Thank you.
Thank you for watching.
And of course, feel free to use this.
It's amazing.
Also, I'm going to make you happy and mad at me.
