## Batching multiple nearest surface queries: Is it faster? Are there better algorithms?

I’m working on an algorithm that computes lots of "nearest point on a triangulated surface" queries in 3d as a way to resample data sets, and I’m wondering if there is any information out there on speeding up these queries. My gut tells me that partitioning the set of query points in a voxel grid or something, and doing them in batches could be a speedup, but I can’t quite see how I could efficiently use that. Also I’m not sure if the time cost of partitioning would balance the search speedup. Is running N independent queries really the best way?

I found that there are papers and research for the all-knn algorithm, but that’s for searching within a single set. And then, those speedups take advantage of the previously computed neighbors or structure within the single set, so I can’t use them. It feels close though.

Any help is appreciated.

## Firewall for my devices (iPad, iPhone, surface) on a shared home WiFi network?

I am renting a room and using shared home WiFi network. The owner has setup a Netgear WiFi range extender for me. I have another roommate on the same network along with the owners. I use Nord VPN. Since a few months I have been getting weird emails…someone opens accounts (like Snapchat, SoundCloud, Pinterest etc.) in my name constantly. I close one account and two more gets opened. I accessed those accounts and they had photos and stuff, so someone had been using them. I noticed that date of birth in one account was a date of significance to me (not my dob) and year in the username was a significant year related to that date. So it is confirmed that I’m hacked. On top of that yesterday I accessed my new website hosting service and made some changes to start a website, today this person opened an account for hiring employees. I believe someone can access (Hack into) my devices through home WiFi. Is there a way to monitor who is accessing and stop it in real time like a firewall. I use iPad and surface pro. Any advice to secure my devices?

## Gouging holes into a surface with magic damage

I have one player currently stuck in a pit. Another player is attempting to use magical damage to gouge holes, or rather handholds into the surfaces of said pit to make it easier to climb out. As far as I am aware, there are no official rules that allow this. But logically speaking, I think it should be possible.

Are there any rules regarding this? And what would be the consequences of allowing this to happen?

I am not asking for other spells or methods to solve this problem. My question is solely regarding the method proposed here.

## Wall of fire: What’s a ‘solid surface’ and what happens if it stops existing?

Wall of fire has to be cast on a solid surface. What’s a solid surface? Can it be the back of a dragon? Dragon scales are pretty solid..

If the solid surface disappears (ice melts away, roof collapses) does the spell then fail or stay where it was cast for the duration?

## What happens to Wall of Fire if the surface moves

The situation I am wondering about is if Wall of Fire is cast upon a wall and then the wall either falls over or crumbles. Would the wall of fire remain floating in the air? Would it disappear? Would it follow the surface to the ground?

You create a wall of fire on a solid surface within range.

## How can Linux service installation page create an attack surface?

Based on one of the lectures of Planning, Auditing and Maintaining Enterprise system course by Greg Williams (Department of computer science university of Colorado):

Let’s say they were installing a service on a Linux system and we forget to take down the installation page. That installation page has a lot of sensitive information on it. so, if we leave that page up and don’t delete it out of the directory after installation, that’s a way for an attacker to get in.

How It becomes possible?

## Surface area of an Island

how can i calculate the surface area of an island? do you know some method do do this? I can’t find nothing in internet thank you

## 3D Plotting and optimising on the surface area of a spherical gyroid

*this is an equation of a shperical gyroid emphasized texti want to plot it in mathematica and obtain the shapes like those on the picture below. sinxcosy + sinycosz + sinzcosx = 0 i also want to know the code to use and how i can model it to obtain different surface areas. please i am in urgent need for an answer

## Evenly Spaced Points On Smooth Surface

I want to space points evenly (i.e. maximizing minimal distance between two points) on some smooth surface $$S\subseteq\mathbf{R}^n$$ (usually $$n=3$$), where I have a projection operator $$p:\mathbf{R}^n\to S$$ which approximates the closest point on the surface. My idea is to place them randomly first and then let some repelling force act between them and reproject back to the surface after each iteration of the action. This can be rather costly, if there are $$10^3$$ points, I have to compute the distance between $$10^6$$ points in one iterations, and I need a few iteration until everything stabilizes.

How can I imporove this process? My ideas:

• Measure the distance between every pair of points but compute the force only when the distance is smaller than some $$a$$, then do a few iterations (assuming the points don’t move too far in one iteration) and recompute the distance after $$k$$ steps.
• Choose some partition of the surface where each part has a set of ‘neighbours’ (including itself), compute for each point the location in the partition, i.e. the part it lies in, then let only the points in neighbouring parts act on each other, recompute the location after $$k$$ steps.

## Convert a polygon mesh into a b-spline surface

$$\textbf{Problem:}$$

Getting a $$\textit{polygon-mesh}$$ as input, I have to construct a surface that looks exactly to the given input. My task is to generate a $$\textit{b-spline}$$ surface that exactly looks like the connected polygon mesh. It is obvious that my $$\textit{b-spline}$$ surface has to have a degree of one in both directions $$\textit{u}$$ and $$\textit{v}$$.

$$\textbf{Output:}$$

As an output for my solution. I have to generate a matrix of $$\textit{control point}$$ that represent that generated surface.

One property of this matrix is that each elements of each row and column are connected with each others. If our control points matrix is a $$n \times m$$ matrix, then let $$C_i$$ a column of this matrix with $$C_i = $$ then there must exist path in the polygon from $$e_{1i}$$ to $$e_{mi}$$.

One thing to consider if there is no edge between $$e_{ji}$$ to $$e_{(j+1)i}$$, we can construct one as long as this edge lies inside the polygon.

$$\textbf{my trivial idea}$$

Assuming that the polygon has $$n$$ nodes. I create $$n$$ other nodes inside the polygon near each original node. I create then a $$2 \times n$$ matrix. The first row contains all the points constructing the polygon. Second row contains the corresponding additional inserted node. In order to connect two additional inserted nodes, i have to make sure that the line between two nodes is kept inside the polygon.

This idea works only for simple structure and the complexer is the polygon the hard to find these additional points.

Any good solutions maybe ?.