Is there a name for a mesh has 4 vertices that is not flat Is this good to keep or should i avoid them?
Flat quads (or, why is my mesh so funky?) I think my question relates to a fundamental of 3D modeling that I haven't picked up on yet. It's very simple:  Let's say I have a flat quad. A plane on the XY plane inserted into am empty blender file is a great example. Now let's say I start moving each of the 4 vertices around on in any direction, especially the Z axis.   At this point, there would still be one face, but its extremely unlikely that the face would be planar (I just learned this word). So blender does its best to make sense of what this should look like.  The problem I'm having is that it seems like my quads are always like this, but they never look the way I want. There are edges and seams that look like they are dangling in space, and what tends to happen is that my mesh looks great when viewed from most angles, but if you look at it from just the right angle, you notice the dangling edges or sometimes even some kind of impossible geometry. And so I might try to nudge the problematic vertices around, but this often seems to either make it worse, or just hide the bad geometry until you see it from a different angle.  For me, this always seems to happen whenever I'm trying to move vertices to add roundness to something that is originally square.   There is another question on here about how to actually flatten the quads. That's great, and I might use some of the techniques mentioned there. My question is:   Why does this happen? (Can someone explain this better?) What are some tips and tricks to avoid this situation? What are some tips and tricks to mitigate this situation?   EDIT Here is an illustration:  The overall mesh as viewed from a distance looks decent (for my skill level)    But if you get closer and look from a certain angle...    Super close up:    The "edge" that is pointed to by the arrow is not actually an edge, but some kind of artifact created when blender tries to show the quad. The way the vertices are positioned, it shouldn't actually be possible to see the sliver of the face that I marked in red, since this face is supposed to be around the corner from the edges. The edges should form the silhouette on the right side of my figure.     Here is the side view. Maybe it is the angled topology that skews the face in a funny way?  But I'm not looking for help with this one particular issue, but rather a better understanding of why this happens, and ideas to prevent this in future models.
Is there an comparison of the various mapping libraries for Android? I am currently looking at the various libraries that I can use to show a map in my custom Android App. I have found several like Mapsforge, OSMDroid, ArcGIS runtime for Android, Google Maps for Android and so on. I'm sure that I am missing a few.   Is there a comparison chart somewhere about the differences in functionalities and pros and cons of each one?   If there isn't one, we could make this question community wiki, to serve alongside  &amp; . Usage of "they" / "them" / "their" when the person's gender is not known Bibliography in Texmaker I'm having some problems with my bibliography in Texmaker. My code is:  \documentclass[11pt, a4paper]{article} \usepackage{graphicx} \usepackage{amsmath} \usepackage{natbib} \usepackage[utf8]{inputenc}     \usepackage{natbib} \usepackage[usenames,dvipsnames]{xcolor} \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry} \begin{document}  ....  \cite{Johnson} \bibliographystyle{plain} \bibliography{mybib}  \end{document}   I also created a new file (File > New) that I saved as mybib.bib:  @Article{Johnson, author = {Edgar G. Johnson and Alfred O. Nier}, title = {Angular Aberrations in Sector Shaped Electromagnetic Lenses for Focusing Beams of  Charged Particles}, journal = {Physical Review}, year = {1953}, volume = {91}, number = {1}, }  @phdthesis{Zoran, author = {Zoran Racic}, title = {\'Etude et essais du spectromÃ¨tre Ã  plasma {DYMIO} de la  mission {MARS 96}}, publisher = {UniversitÃ© Pierre et Marie Curie}, year = {1996} }   When I compile my .tex file, I only have a [?] appearing.  Could you tell me what my mistake is? Does English have any singularia tantum besides mass nouns? How to display quick-updating images without large memory allocation? Is the force which throws a body on a rotating disk outwards centrifugal force? If some object is kept in a radial groove made on a disk and the disk is rotated with say constant angular velocity.   Now as we know that the object moves outwards ie away from the centre of the disk. I want to know which force is it which throws the object outwards.   As centrifugal force is a pseudo force and hence when the observer is in ground frame it shouldn't be present so which force exactly pulls it out. Having recently reviewed a few suggested edits, I've found that not being able to see the comments on the post is hindering my understanding of the context of some edits.  In particular, there have been a few posts where someone has made a substantial edit to a question or answer which significantly alters its meaning. Typically I'd reject that as "too radical", since it can't be known that the new meaning of the post was what the original author intended.  However, in some cases it is clear from the comments that the original author is aware of the intended change, and as such the editor is not in fact misrepresenting the author's intentions. In these cases, it would have been useful to see the comments when making the review decision.  As an example, a common cause of this is when an inexperienced user is asked to clarify their question, and ends up writing a comment that would be better off as an edit to the question (due to length, excess code content, etc), presumably due to lack of awareness that the question can be edited. Often, other users will helpfully edit the question to include the information the OP put in the comment (see ,  and  for examples). In this situation, it is clear that the edit reflects the OP's intentions, but this information is only present in the comments which are not visible in the review interface.  Following is the suggested edit screen showing the suggested edit. It seems indentation is increased and one line is moved a few lines upwards and some empty lines added to increase readability. But it look like an invalid edit since changing the related line may cause alteration on the runtime. So not looks lie a valid edit. Better open the answer and examine it        Checking the Q&amp;A itself reveals that a talk had taken place between the OP and the answerer and revision done by the OP with the permission of the answerer. So it was indeed a valid edit.        In short: is there any particular reason comments are not displayed in the suggested edit review interface? I think it would add useful contextual information when making review decisions, and presumably this would be trivial to implement.  Note: this is not a dupe of , as it does not concern comments posted after the suggested edit. FTPS versus SFTP versus SCP In case, if I get a multiple-entry Schengen visa in one of the embassies in Ukraine, Kyiv - should my first trip be to the country which issued the visa?  Any there any requirements of this sort? Does this condition vary depending on embassy which issued the visa?  What are the possible consequences on not visiting that country first? Does it somehow depend on country where the embassy is (i.e. non-Schengen and not EU members)? Estimator for $\theta$ using the method of moments Exercise :     Using the method of moments, find the estimator for $\theta$ for a random sample $X_1, \dots, X_n$ that follows the distribution with pdf $f(x) = \theta x^{-2}, \; 0 &lt; \theta \leq x &lt; \infty$, where $\theta$ is the unknown parameter.   Attempt :  $$m_1' = \bar{X}$$  $$μ_1' = \int_\theta^xu\theta u^{-2}\mathrm{d}u=\int_\theta^x\theta u^{-1}\mathrm{d}u=\big[\theta \ln u\big]_\theta^x =\theta\ln x - \theta\ln\theta$$  Thus, the estimator is given by :  $$m_1' = μ_1' \Rightarrow \theta\ln x - \theta\ln\theta = \bar{X}$$  But we cannot solve that equation with respect to $\theta$, so we'll take the moments of bigger order :  $$m_2' = \frac{1}{n}\sum_{i=1}^nX_i^2$$ $$μ_2' = \int_\theta^x u^2 \theta u^{-2} \mathrm{d}u = \int_\theta^x \theta \mathrm{d}u = \big[\theta u\big]_\theta^x =\theta x - \theta ^2 $$  Thus the solution of the following quadratic equation for $\theta &gt;0$, gives as the estimator of $\theta$ :  $$\theta^2-x\theta +\frac{1}{n}\sum_{i=1}^nX_i^2$$  Question : Is my solution correct ? Shall the upper bound be $x$ or $\infty$ ? How do you calculate the likelihood of drawing certain cards in your opening hand? In Magic, at the start of the game, you draw 7 cards. How would you calculate the likelihood of drawing a specific card in your opening hand?  For example, let's say I have a 60 card deck, and I'm running 4 . What is the percent chance that I will have at least one Bird in my opening hand? Is it normal for focal length to change while focusing? When I change the focus distance on my Pentax 55-300mm lens, the focal length appears to change.  More specifically, the lens appears to zoom in as I focus towards the minimum focusing distance.  This is most noticeable at the 55mm end of the lens.  Is this normal? Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. Prove  that the function $\displaystyle f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. You should give a proof that is directly based on the  definition of continuity.   I saw many similar questions on this website, but none of them gave me a satisfactory answer. I more or less understand how epsilon-delta proofs work but my problem lies more in the algebraic manipulations probably. So here's my "attempt".  Definition of continuity; for $f:A \to \mathbb{R}$     $$\forall \varepsilon &gt;0 \ \exists\delta&gt;0\ \forall x \forall x_0 \in A:|x-x_0|&lt;\delta \Rightarrow |f(x)-f(x_0)|&lt;\varepsilon$$   So from what I understand, the procedure for epsilon-delta proofs are as follows: 1. Plug the point of interest $x_0$ into $|f(x)-f(x_0)|&lt;\varepsilon$ 2. Write $x$ in terms of $\varepsilon$ 3. Then plug $x$ into $|x-x_0|&lt;\delta$ 4. Find $\delta$ in terms of $\varepsilon$. Done    At step 1, we have $\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Step 2 is where I'm stuck because of the 2nd degree polynomial in the denominator. First, I did this: $\left|\dfrac{x}{x^2+1}\right|&lt;\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Then, I wasn't too sure about what to do, I thought about getting rid of the "$1$", but that would screw up my inequality. I thought about factoring $x^2+1$, but it doesn't have any real roots. I tried inverting the fraction, but that led me to nowhere. And I've already exhausted the tools I have. How do I proceed?  Apparently, epsilon-delta proofs are the most basic building blocks of analysis. And I'm already failing, this is both embarrassing and depressing... Negative logLikelihood Kalman filter Drawing users' attention to unrecoverable actions? How to compare the differences between two PDF files on Windows? This is probably pretty basic, but to save me an hour or so of grief can anyone tell me how you can work out the number of bits required to represent a given positive integer in Java?  e.g. I get a decimal 11, (1011). I need to get the answer, 4.  I figured if I could work out how to set all the bits other than the most significant bit to 0, and then >>> it, I'd get my answer. But... I can't. It is much more convenient and cleaner to use a single statement like  import java.awt.*;   than to import a bunch of individual classes  import java.awt.Panel; import java.awt.Graphics; import java.awt.Canvas; ...   What is wrong with using a wildcard in the import statement? Justify text in moderncv cover letter I am writing a cover letter and CV using moderncv. Everything works fine so far, but the text in the cover letter is not justified. I think it is good that it is not hyphenated, but it would look much nicer if the text was justified.  Here is a minimal example:  \documentclass{moderncv} \moderncvstyle{classic}  \usepackage{lipsum} % just for dummy text  \firstname{John} \familyname{Doe}  \begin{document} \recipient{Prof.\ Dr.\ Foo Bar}{} \opening{Dear Professor Dr.\ Bar,} \closing{Yours sincerely,} \enclosure[Attached]{curriculum vit\ae}  \makelettertitle \lipsum[1] \makeletterclosing  \clearpage  \makecvtitle  \section{Education} \cventry{2009--present}{PhD Student}{here}{and}{there}{} \end{document} Cross tabulation of two categorical variables: recommended techniques