Is there an algorithm to determine which face of an n-dimensional hypercube is closest to a given point in $O(n\log(n))$?

Given a point in N-dimensional space, I’d like to be able to determine which face of an N-dimensional hypercube of edge length 1 that the point is closest to.

In the 2-dimensional case it’s fairly trivial, you simply split the square along its diagonals:

if (x < y) then     if (x + y < 0) then         // Side 1     else         // Side 2 else     if (x + y < 0) then         // Side 3     else         // Side 4  

In 3-dimensions, this becomes more complex; each face creates a ‘volume’ of points that are closest to it in the shape of a square based pyramid.

Visualisation of the 6 planes that form the 6 pyramids

Of course, given a point, it’s possible to determine which side of the 6 planes it lands on and using that information you can determine which face of the cube is closest. However this would involve running 6 separate checks.

Moving this into higher dimensions, a similar algorithm can be run on hypercubes, however, as the number of faces on a n-cube is $ 2^{n-2}{n \choose 2}$ , this quickly becomes computationally very expensive.

However, theoretically a perfect algorithm could cut the search space in half with every check, discarding half the faces each time.

This would give this hypothetical algorithm a runtime of $ O(\log_2(2^{n-2}{n \choose 2}))$ which can be simplified, if my rate of growth calculations worked out, to $ O(n\log(n))$

Is my logic correct here; can/does such an algorithm exist?

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Is Apple’s Face ID less secure in the dark?

I noticed that Apple’s FaceID works even in the dark. I assume it’s using some kind of infrared light to “illuminate” your face and collect the features.

I’m more concerned that when designing the algorithms that confirm a user’s face, Apple may lower the “validation thresholds” when running in the dark to ensure a better user experience.

So I’m wondering if an attacker trying to fool FaceID with a photo or even a 3D printed head, may be more successful in poor lighting conditions.

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Given a DCEL, how do you identify the unbounded face

I have constructed a DCEL using the procedure described in How do I construct a doubly connected edge list given a set of line segments?.

This correctly identifies all faces, however I’m struggling to come up with a way to identify the unbounded face surrounding my graph.

So far my only idea is that by building a polygonal representation of every face, I could find the face polygon which ‘contains’ all the others, but this seems kind of messy.

When waking up this computer blue wierd face characters appeared

I am running Ubuntu 18.04.3 LTS (GNU/Linux 4.15.0-62-generic i686) and each time the computer lid is closed it goes to sleep and then wakes the screen displays this and it is unresponsive.
I have since disabled the sleep function when the lid is closed and keep it logged in to stop it from coming unresponsive.
It is quite old hardware:

  • CPU: mobile AMD Athlon XP-M 2400+ @ 1.79126GHz
  • GPU: ProSavage8 KM266/KL266
  • RAM: 51MiB / 394MiB

It runs without a Desktop Environment in terminal mode most of the time. It has LXDE Desktop Environment installed (the hardware can’t handle any more intensive).
The problem I have is that I can’t put it to sleep so I either have to have it on (and it is quite loud) or off (it takes a few minutes to boot). I would love to be able to put it to sleep every so often.
I have super user privileges, current access (through ssh) and I know how to use the terminal quite well.

enter image description here Cropped image showing the faces here: enter image description here

Having trouble with getting a image to a fit on a face of a cube

I have little problem from a unity project that I’m working on. I’m making a 3d art gallery which will be further developed to VR application. In the 3d scene I created paint canvas as a game object (cube) but having trouble, getting the images fit through out the whole canvas. When i try to apply image as applying a material it is treated as a texture and only small proposition of image is visible in the canvas

And also i am planing to make a UI so that customer can upload pics and application automatically get the images and render the gallery. So I’m kind of stuck in the image to object part.

Can a Beholder face its Antimagic Cone behind itself?

The text for a Beholder’s Antimagic Cone ability reads as follows (MM, pg. 28):

The beholder’s central eye creates an area of antimagic, as in the antimagic field spell, in a 150-foot cone. At the start of each of its turns, the beholder decides which way the cone faces and whether the cone is active. The area works against the beholder’s own eye rays.

The ability states the beholder decides which way the cone faces, and provides no limitations, so would the Beholder be able to face the cone directly behind itself?

6 Ways Face Verification is Used In Education Sector

Face authentication can be of great help in the education sector from assisting online admission processes to providing a secure environment in schools. The technology is enhancing many sectors and education is one of them. Following are some ways in which this technology is reshaping education sectors:

  • Behaviour Analysis Of Students In Classroom

Face Verification System can be used to judge students' acceptance in the classroom. It tracks facial expressions and…

6 Ways Face Verification is Used In Education Sector