I'm making a 2D retro-style pixel game and I'd like to know how big my sprites should be. I'm not talking about the size of my image files (which I decided to use a 32x32-based artstyle), but the actual size of them once they are in Unity. Should I keep a 1:1 scale and import all of my usually 32x32 sprites into Unity? Is there a special scale up or down process I need to do before or after import them? I'm saying this because when I'm working with HUD elements, they are drastically really big compared to my tiny sprites, so I'm worried if this could affect implementing something like RigidBody or collisions,  and I should indeed scale up my sprites, or if this is normal and I'm being paranoic. I'll append an image showing my concern. BTW, the game looks so far as I wanted to, and it's working well, but right now it's more like a proto, so I'd like to resolve this doubt before continuing. Also, I test this usually in a 1920x1080 resolution, so maybe that's why the HUD looks so big. Thanks!
I try to create a 2D game for Android. It looks like Cut the rope (it isn't a clone but it have same level representation) if it has a value. My problem that I can't understand that optimal sprite sizes I should use. I.e. what target screen resolution should I use to sprites didn't have anomalies on HD-devices (like Samsung Galaxy S7 and etc., phones and tablets)?    To make my question is clearer I ask about this 1 unit = X pixels for xxhdpi-screens. What is X?    P.S. Sorry if it's a duplicate I will be grateful for link on this post cuz I couldn't find it.
How to solve this limit: $\lim\limits_{x\to0}\frac{(1+x)^{1/x}-e}x$? I tried to evaluate $$\lim_{x\to0}\frac{(1+x)^{1/x}-e}x$$but all my efforts were in vain . L'Hospital rule becomes very complicated. This doesn't work:  tar xf /tmp/foo.tar.gz foo/bar tar: foo/bar: Not found in archive   It's not obvious to me what would do this beyond extracting it in place and moving the files over. Reference request: Standard textbook for first-order predicate logic in english I am writing my bachelor thesis in english, but I have studied logic in my different native language. Since a rely on elementary results from first-order predicate logic (especially satisfaction in structures), I should reference the reader to a textbook for details.   Is there a standard textbook that starts with elementary propositional logic and goes to Incompleteness theorems? Can't find boot-repair package for the newest version of Ubuntu Anonymous Types - Are there any distingushing characteristics? Is there anything to use, to determine if a type is actually a anonymous type? For example an interface, etc?  The goal is to create something like the following...  //defined like... public static T Get&lt;T&gt;(this IAnonymous obj, string prop) {     return (T)obj.GetType().GetProperty(prop).GetValue(obj, null); } //...  //And then used like... var something = new { name = "John", age = 25 }; int age = something.Get&lt;int&gt;("age");   Or is that just the beauty of an anonymous type? Nothing to identify it self because it takes a new shape?  Note - I realize that you can write an extension method for the object class, but that seems like a little overkill, in my opinion. How to write in bibliography (package natbib) letter "a" with two dots above? Specially, I mean the word Birkhäuser.  Is there a general rule or way how to write such umlauts or other accented letters in bibliographies? I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$.  Okay, fine.  You write down the action functional, require that it be a minimum (or maximum), and arrive at the Euler-Lagrange equations.  Great.  But now you want these Euler-Lagrange equations to not just be derivable from the Principle of Least Action, but you want it to be equivalent to the Principle of Least Action.  After thinking about it for awhile, you realize that this implies that the Principle of Least Action isn't really the Principle of Least Action at all:  it's the "Principle of Stationary Action".  Maybe this is just me, but as generous as I may be, I will not grant you that it is "natural" to assume that nature tends to choose the path that is stationary point of the action functional.  Not to mention, it isn't even obvious that there is such a path, or if there is one, that it is unique.  But the problems don't stop there.  Even if you grant the "Principle of Stationary Action" as fundamentally and universally true, you realize that not all the equations of motions that you would like to have are derivable from this if you restrict yourself to a Lagrangian of the form $T-V$.  As far as I can tell, from here it's a matter of playing around until you get a Lagrangian that produces the equations of motion you want.  From my (perhaps naive point of view), there is nothing at all particularly natural (although I will admit, it is quite useful) about the formulation of classical mechanics this way.  Of course, this wouldn't be such a big deal if these classical ideas stayed with the classical physics, but these ideas are absolutely fundamental to how we think about things as modern as quantum field theory.  Could someone please convince me that there is something natural about the choice of the Lagrangian formulation of classical mechanics (I don't mean in comparison with the Hamiltonian formulation; I mean period), and in fact, that it is so natural that we would not even dare abandon these ideas? I am solving a clustering problem on a trivial dataset with the k-means algorithm. I am running a couple of tests and, from time to time, one centroid doesn't attract any points, i.e. I've got an empty cluster (see the purple "x" in the picture).  What should I do? Shall I delete it or just stop updating its value? Why?    I am aware that built-in functions (e.g., kmeans() in R) have automatic ways of dealing with this situation, but I am trying to write the standard algorithm from scratch. As soon as I fix it I'll be able to compare my results to built-in functions. At this moment I'm looking for some theoretical reasons why I should prefer one solution or another.  In the picture each colour represents a cluster according to the current iteration and each "X" is its centroid (old ones have been kept and marked with the number of the iteration in which they were computed).      [Some related links about empty cluster case, added later by @ttnphns: ; ; ; ; ; ; ; ; ] Change Folder Permissions I started off with changing to the folder I want to change permissions for, and that is the opt folder.  $ cd /opt/ test@testVM:/opt$   So I tried changing the permissions for this folder now using:  sudo chmod 775   And that hasn't worked. It showed this message:  Try 'chmod --help' for more information.   There is something I am forgetting or leaving out.  Please can you show me what I am doing wrong?  Thanks in advance. If $|a| = 12, |b| = 22$ and $\langle a \rangle\cap \langle b\rangle \ne e$, prove that $a^6 = b^{11}$ Showing that $\frac{z^n}{1+z^{2n}}$ is real for $|z|=1$. Calculate $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$ How can I calculate the integral $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$ by substituting $t=\frac{1-x}{1+x}$. If no spell can reawaken the dead, how did the resurrection stone work? Dumbledore himself said that no spell can reawaken the dead. Isn't that the main objective of the resurrection stone? If one can't reawaken the dead then what is the use of the stone? Surely then one of the Hallows is flawed? Should a user be forced to add a comment when they vote to close? How to remove ubuntu partitions and use them to install windows How to remove the top horizontal bar in fancyhdr? When using fancyhdr, how do you remove the top horizontal rule?  I do not want a header at all, just a footer.  This is what I do now:  \documentclass{article} \usepackage{fancyhdr} \pagestyle{fancy}  \lfoot{text} \cfoot{text 2} \rfoot{text 3}  \begin{document} Foo Bar \end{document} I overseasoned my food, what can I do to remove the strong smell? Traveling to the US with new passport, visa on the old one How do I map a network drive to the root of a server (\\server)? In Windows XP I can very easily map a network drive to the root of my NAS server. I browse to it in Explorer (\\192.168.1.70), choose "Map Network Drive", then choose the drive letter.  In Windows Vista, mapping the root of a server doesn't seem possible. I have to go "Map Network Drive" from 'Computer', then enter the address, but it will only let me map to specific shares (sub-folders off of the server root) and NOT to the server root share.   Since my NAS has built-in shares (music, photo, video, etc.) then I would have to have drive letters for all of these, which I absolutely don't want.  Why can I easily map a network drive to the server root in Windows XP, but not in Vista? Is there something fundamentally different in the networking across the two OS's? Or do I need to do things a different way? I have been reading Men With Brooms for a few days. I read a sentence which did not make any sense to me, so I landed here to get some help on it. I have pasted the sentence from the novel. Please go through it and let me know your valuable feedback on it.  An excerpt from the novel (Men With Brooms: A Sweeping Epic, paperback 2002, a novelization by Diane Baker Mason):     Gordon was about to walk away from the Impala when he saw it stop and his son get out. So it was real the boy had come.   As per my opinion it should have been:     Gordon was about to walk away from the Impala when he saw it stopped and his son got out. So it was real the boy had come.   I have two questions here:   Why did the writer use stop and get instead of stopped and got? As she is telling us a story which happened in the past. Let's say the writer is telling us her mind's situation and she used the present tense for it but why did she use stop and get instead of stops and gets?