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When to use an object pronoun or a possessive adjective before a gerund Ok, I have to admit, I don't really delve too deep into the semantics of the spatial operators list below, I'm more of a user, I write software to drive the SQL most of the time and don't really think about it too much.  However, I have a situation where a spatial operation I'm doing is going dog slow, on a table that has great indexes on and has never caused a problem before now.  As a result, I'm trying to figure out which of the following is my best bet to use, that will give me the best performance, however, sometimes I find my searches don't return anything when I know they should, and sometimes return stuff when they shouldn't.  SO I'm reaching out, to ask if some one can give me the actual definition, such as criteria to match, fully within enclosing geometry, or within outer ring etc etc of each of the following operations:  Equals(Geom1, Geom2):int Disjoint(Geom1, Geom2):int Touches(Geom1, Geom2):int Within(Geom1, Geom2):int Overlaps(Geom1, Geom2):int Crosses(Geom1, Geom2):int Intersects(Geom1, Geom2):int Contains(Geom1, Geom2):int Relate(Geom1, Geom2):int   If you can give a concrete example of when they will and will not match too, that would be great.  For reference, I'm searching on a table of Linestrings, using a rectangular polygon, rotated to be pointing in the direction of travel (It's part of a traffic managment app)  For further reference, here is a sample of the SQL the app generates to perform a search:  SELECT recordID,AsBinary(geometry) AS geometry,Distance(GeomFromText('POINT(-1.84101 54.85078)',4326), geometry) AS distanceFromGps FROM linegrid WHERE Intersects(GeomFromText('POLYGON ((-1.8413149820810311 54.850782468607292, -1.8409507853094111 54.850952257034713, -1.8408279009723911 54.850864894077496, -1.8411920982612455 54.850695105650068, -1.8413149820810311 54.850782468607292))'), geometry)   You can see in this example I'm using intersects trying the others as mentioned doesn't quite give the results I expect, hence why I'm asking the question.  Please note, I'm not particularly bothered about actual faster/other ways of doing this at the moment, BUT if you do happen to spot a better way do feel free to shout up :-)  For now all I'm mostly trying to understand is the differences between each of the operations.  As for doing it faster/better I intend to open a different question for that at a later date.  For more reference, the Spatial engine this is working against is Spatilite 2.3.0, and I can't upgrade it due to the devices it's running on not having a more up to date build for it (Windows CE)    I'm going to choose mintix'es answer here as that provided a super easy to understand grid and description of all the various operations, which answered my question.  I'm still faced with getting performance on the routines up, but I do now have a few strategies to try on that one, I may still seek advice here from the group with regards to that.  @Vince deserves some credit too, as that white paper is definitely the definitive answer, but it's also quite challenging to read (I had to read through it several times) , for anyone wanting the real I am on these operations The Clementini paper is the way to go, if you need an easy to understand overview while developing solutions however, the FME link should be open in another browser tab. Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$ Why is there no plural 's' after "hundred" or "thousand" in cardinal numbers? Let's say we have the numeral "12,345". Why is it pronounced as "twelve thousand three hundred and forty five" as opposed to "twelve thousands three hundreds and forty five". Are 's's omitted while pronouncing numerals to make the whole thing more succinct and easier to pronounce? how to create a roster sheet in sharepoint 2010 tl;dr : For SEO, should I redirect from one to the other or list both on the DNS records?    It seems that most experts think that both www and non-www should exist. (Please correct me if I'm wrong.) And Google Webmasters Tools lets you choose which is the main one.  But: will a redirect give all SEO weight to one of them instead of splitting it? (There are other search engines after all, so setting the main one in Google Webmasters Tools might not be enough.) Will having both on the DNS records give them more importance? No difference? What is the method to make files in a USB Flash Drive undeletable? Does these method work with USB 3.0 interface?  (I have surveyed some Flash Drive manufacturers, and I only see undeletable files for USB 2.0 drives, and not 3.0 drives. One manufacturer claimed that USB 3.0 cannot do undeletable file, so I am curious whether the claim is correct...) Background notebook template with spiral Why is the sky dark at night? The question is the well-known      If there are so many/infinite stars, in every direction, why is it dark at night? Where goes all the light we don't see?    Discussing with a friend we found different answers.   The first (my friend's answer) is that given the fact that in a finite amount of time (in this case, the age of the universe), light can travel only a certain, finite, distance, we cannot see, if they actually exist, stars farther than such distance (about 13 billions of years, I guess). Then he states (or better, I got him notice he implicitly does this)  that within this radius there aren't enough stars to fill the night sky, and that's why we have darkness without sun's light.   The second answer (mine, or anyway the one I heard from a minutephysics YouTube video) is that despite of the big size of the observable universe, cosmological expansion red shifts most of the light out of the visible radiation range, so that the majority of light can't be seen by our eyes at night, while if we use, for example, an infrared camera, we should see a brighter sky, and lenghtening more and more the wavelength at which we observe the sky, we come to the uniform background radiation.  So my question is, what is the right answer? Is it one of the above-mentioned or even a third one?  EDIT: I've seen both answer may be acceptable, but what is the main contributing phenomenon? Why does my wildcard SSL certificate cause a domain mismatch error on a second level subdomain? "Made out of", "made of" and "made with" I understand the phrases made of and made from from the questions and answers provided  and .  Yet I came across three more phrases: made out of, made of, and made with which I think are related to the subject in question.  Would you please help me understand how to differentiate these phrases too? And how is their usage? It is impossible for $(x-1)^2+x^2+(x+1)^2$ to be a perfect square Prove that it is impossible for three consecutive squares to sum to another perfect square. I have tried for the three numbers $x-1$, $x$, and $x+1$. How can I calculate this limit? ideas? How can I calculate this limit? $$\lim_{n\rightarrow\infty} \frac{7^{\sqrt{n+1}-\sqrt{n}}\cdot(\frac{n+1}{2})!\cdot(\frac{n+1}{2})!}{(n+1)\cdot(\frac{n}{2})!\cdot(\frac{n}{2})!}$$ I don't have idea and I will be happy for help. Can multiple different HTML elements have the same ID if they're different elements? How do I show that all continuous periodic functions are bounded and uniform continuous? A function $f:\mathbb{R}\to \mathbb{R}$ is periodic if there exits $p&gt;0$ such that $f(x+P)=f(x)$ for all $x\in \mathbb{R}$. Show that every continuous periodic function is bounded and uniformly continuous.   For boundedness, I first tried to show that since the a periodic function is continuous, it is continuous for the closed interval $[x_0,x_0+P]$. I know that there is a theorem saying that if it is continuous on a closed interval, then it is bounded. However, I'm not allowed to state that theorem directly. Should I just aim for a contradiction by supposing f is not bounded on the interval stated above? How to return to the GUI? I am very new to Linux and Ubuntu. I use Ubuntu 11.10.  I was trying to exit the X server (in order to install some Nvidia drivers) and I typed in the terminal:  sudo service lightdm stop   How can I return to the Ubuntu interface? Let's say I have Windows installed on drive C, however I install all of my programs on the D drive, and I keep my user profile on the D drive as well (things like My Documents). How can I have Windows use those folders instead of the ones on the C drive? Pre-1980s Sci-fi movie about killer aliens Decoupling capacitors: what size and how many? Evaluation Symbol: Consistent Implementation