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So,  Each of my polygons is a separate object. Their default normals point like this:   But their orientation or local axes are like so:   How can I make their local axes to be like so, but automatically?   I guess particles might be one solution for this exact case (if you emit new objects on top of the existing ones) but let's say the original objects are triangles and I wouldn't want to change their shape and pointing direction at all, only their local orientation axes, would that be possible?  Cheers! How to tell the probability of failure if there were no failures? I was wondering if there is a way to tell the probability of something failing (a product) if we have 100,000 products in the field for 1 year and with no failures? What is the probability that one of the next 10,000 products sold fail? Can I kill the Golem pre-hardmode? How can I get back a system file after deleting it from my Mac? I've deleted a system file from my Mac and need to get it back.  System files can include:   hidden files in the root of / - especially unix files in /private  /System files /Library files /Applications files that ship with the core OS   System files are not any app, user files or files that can be regenerated by a known sequence such as cache files, Spotlight index files, etc…    Canonical question and answer for . Defining my own None-like Python constant What I am working with: I am running my self-made Arduino board (in the sense that I use the Arduino bootloader and code editor) at 3.3V, and powered from a Lithium ion battery, which is USB-charged by a corresponding Microchip charger IC.  What I am trying to achieve: I want to measure battery capacity once every minute or so. I have an LCD attached, so the idea is that the overall setup lets me know how the battery is doing at a given moment. The datasheet of the battery has a voltage versus discharge-level curve, and so by measuring the voltage of the battery, I can estimate the remaining capacity (very roughly but enough for me!).  What I did:   (EDIT: Resistor values updated and P-MOSFET switch added based on @stevenvh and @Jonny's suggestions).  I connected a voltage divider from the battery V_plus, with the larger "portion" going to an analog-read-pin (i.e., ADC) on the Arduino/Atmega chip. The divider is 33 KOhm-to-10 KOhm, thus allowing measurement up to 4.1 Volts maximum of the Li-ion battery from my 3.3V level microcontroller. Also, using one of the I/O pins connected to an n-channel MOSFET, I can switch the current through the divider only when I need the measurement. Here is a rough schematic (updated for a 2nd time based on suggestions of @stevenvh and @Nick):     My question:   How is my current setup? My only constraints are: (1) I would like to make a rough measurement of the battery capacity based on the voltage reading, as described above. (2) I would like to prevent the voltage divider from interfering with my charging IC's reading of battery presence (in my original setup, the divider sometimes caused the IC to misread presence even when the battery was absent). Order of execution of jquery document ready How are ssl certificates verified? What is the series of steps needed to securely verify a ssl certificate?  My (very limited) understanding is that when you visit an https site, the server sends a certificate to the client (the browser) and the browser gets the certificate's issuer information from that certificate, then uses that to contact the issuerer, and somehow compares certificates for validity.     How exactly is this done?  What about the process makes it immune to man-in-the-middle attacks? What prevents some random person from setting up their own verification service to use in man-in-the-middle attacks, so everything "looks" secure? How do I know if an ability is magical? Often confusion arises when the  spell is used, an  is worn, or the 's anti-magic ray is employed, whether a given character's ability will still function.   The spell does give you some guidelines on how to adjudicate the effects of the loss of magic but says very little about how to determine what is affected.  In short, how do I tell if an ability is magical? How long can I stay in the UK during a 1-year period? I am a Chinese citizen holding a HK SAR passport. How long am I able to visit the UK within a 365-day period?  My stamp is for 6 months. Could I leave within 6 months but re-enter again a couple of weeks for another 6 months? Find all the values of $w$ ∈ C that satisfy the equation. Realtek RTL8723BE Wi-Fi incredibly weak If every polynomial of degree 2 is reducible then $K$ is algebraically closed? Consider the following 2-variable function:     $$f(x,y) = \frac{x^2y}{x^4+y^2}$$   I would like to find the limit of this function as $(x,y) \rightarrow (0,0)$.   I used polar coordinates instead of solving explicitly in $\mathbb R^2 $, and it went as the following:  $$ x = r \cos \theta, \qquad y = r\sin\theta $$   Hence,  $$\lim_{(x,y) \to (0,0)} \frac{x^2y}{x^4 + y^2} = \lim_{r \to 0}\frac{r^2\cos^2\theta(r\sin\theta)}{r^4\cos^4\theta + r^2\sin^2\theta}$$  This simplifies to,  $$ \lim_{r \to 0} \frac{r^3 \cos^2\theta\sin\theta}{r^2(r^2\cos^4\theta + \sin^2\theta)}$$  Simplifying $r^3/r^2$, we finally get;  $$\lim_{r \to 0} \frac{r (\cos^2\theta\sin\theta)}{r^2\cos^4\theta + \sin^2\theta}$$  Now from the above, we find that as $r \to 0$ the limit is $0$.   I wanted to verify this answer so I checked on Wolfram Alpha. Explicitly without changing to polar coordinates, it said that the limit does not exist at $(0,0)$ and rightly so. Then how is it that with polar coordinates, the limit exists and is $0$? Am I doing something wrong in this method?  Also, what should I do in this situation, and when should I NOT use polar coordinates to find limits of multi-variable functions? Formal basis for variable substitution in limits So we do a lot of variable substitution in limits at school. Stuff like $\lim\limits_{x\to5}\ (x+1)^2\ =\ \lim\limits_{y\to6}\ y^2$, where we define the substitution $y = x + 1$.  But I've never been clear on what exactly the theoretical basis for this is. What is the formula that you're actually applying when you do variable substitution? What are the formal conditions under which it is possible?  My conjecture would be the following:  For all continuous $f$, and all real $a$: $\lim\limits_{x\to a}\ (f\circ g)(x)\ =\lim\limits_{x\to g(a)}\ f(x)$, where $g$ is a continuous function  So to take my first example, $f$ would be $x^2$, $g$ would be $x + 1$, and $a$ would be $5$.  Am I in the right area? If this is correct, can it be proven using $\epsilon$-$\delta$? I had a half-hearted shot at it the other night and didn't get anywhere. Where and why do I have to put the "template" and "typename" keywords? In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template &lt;typename T, typename Tail&gt; // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template&lt;typename U&gt; struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion&lt;U&gt; dummy;      };     template&lt; &gt; struct inUnion&lt;T&gt; {     }; }; template &lt;typename T&gt; // For the last node Tn. struct UnionNode&lt;T, void&gt; {     // ...     template&lt;typename U&gt; struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template&lt; &gt; struct inUnion&lt;T&gt; {     }; };   The problem I have is in the typedef Tail::inUnion&lt;U&gt; dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion&lt;U&gt; names a type and not a function? Cause of black artifacts in render? I do not have much experience in table design. My goal is to create one or more product tables that meet the requirements below:   Support many kinds of products (TV, Phone, PC, ...). Each kind of product has a different set of parameters, like:   Phone will have Color, Size, Weight, OS... PC will have CPU, HDD, RAM...  The set of parameters must be dynamic. You can add or edit any parameter you like.   How can I meet these requirements without a separate table for each kind of product? How to Export this animation as a gif file for powerpoint presentation I recently traveled from India to USA. I am on H1B. I entered USA on 29th December 2016. As my Visa extension is due in August 2017, I was gathering documents for Visa Extension. It was required to provide a scanned copy of passport page with all entry and exit stamps.  Myself and my wife both travelled back from India. My wife's passport has a entry stamp with date as 29th December 2016. But the same is missing from my passport. I guess the officer missed putting the entry stamp on my passport. My I 94 reflects the correct date of entry as 29th December. Somehow I still have my boarding pass from this trip (usually I throw them once trip is complete).   Want to know what could be implications of missing entry stamp when I travel to India next time (somewhere towards early next year)? Does this impact my H1B Visa extension ? Also what can I do to correct this information on my passport?