In Blender Cycles, can a material be formatted so that, when rendering, it ONLY shows the shadows that were cast upon it by objects? This could be used when using a 360° HDRI as world background, to have an object appear to cast shadows on the background.  As an example, in the picture the plane is added to give the cube a shadow. Unfortunately the entire plane keeps showing up in the rendering. I would like to render the cube and the shadow ONLY, as to generate the impression that the cube is sitting on the road deck. Making the material of the plane (but not the shadow) invisible/transparent would do the job. The question is, how?
I am superimposing CGI over video footage, and have run into a problem in making materials for objects that act as 'shadow catchers'.  Essentially I want a shader that is shadeless—like an emitter—but catches shadows and light from other objects. This is so I can reconstruct objects in footage so other objects in the scene interact convincingly with them.  Here's an overcomplicated diagram to illustrate my point:   (In this particular scenario, the problem could be glossed over by using RGB curves, but that is definitely not the case with more complicated scenes)  Isn't this a common situation? How to the real guys do it? Thank you.  (I am welcome suggestions of other ways of doing this.)
Are the known exoplanets representative of the population of exoplanets? An  states that most of the 715 newly announced exoplanets orbit very close to their host stars.   Do the theories predict that this is a representative sample and that most planets are very close to their host stars? Or is it just that our current detection techniques are predisposed to finding only those planets close to their stars (because the sensors look for dimming of the host star for example)? For $n\geq 3$ there exist $x,y\in S_n$ such that $x$ and $y$ have order $2$ and $xy$ has order $n$. Assume that $n\geq 3$. Let $S_n$ be the symmetric group with $n!$ elements. Prove that there exists $x$ and $y$ in $S_n$ such that $x$ and $y$ have order $2$ and $xy$ has order $n$.  For $n=3$, it is easy to see that $x=(1, 2)$ and $y=(1, 3)$ works. How to prove it for the general case? Is it acceptable to write a thank you in a comment? There have been a number of cases where I would like to thank someone for providing me with a thorough response and give them feedback beyond the vote up. Often I wish people would tell me why they voted me up. Not that the thank you part is necessary but it sets it apart from the other comments related to answering the question itself.  In this type of situation is a "Thank you" acceptable in a comment?     For more information, see  in the . glob() - sort array of files by last modified datetime stamp I am wondering if there is anything in Marvel comic book canon or in the MCU that says that the Infinity Gauntlet has the power to make someone fall in love with the person wearing the Infinity Gauntlet, or that the wearer of the Infinity Gauntlet can use the Infinity Gauntlet to make two strangers fall in love with each other? Perhaps the combined power of the Mind Stone and the Soul Stone would make two people fall in love. How do I install gfortran? I am trying to install gfortran in my computer with Ubuntu 12.04 by using these commands,  sudo -i apt-get update apt-get install gfortran   but I found the program saying "unable to locate package gfortran". Then on a Ubuntu page I found some question regarding the same problem and I went through the solution from them but again I couldn't install the gfortran package.  Can anybody tell me how to install it? Let $n \in ℕ$. Show that the ring $ℤ/nℤ$ is a field if and only if $n$   is prime.   Let $n$ prime. I need to show that if $\bar{a} \neq 0$ then $∃\bar b: \bar{a} \cdot \bar{b} = \bar{1}$. Any hints for this ?  Suppose $ℤ/nℤ$ is a field. Therefore: for every $\bar{a} \neq 0$ $∃\bar b: \bar{a}\cdot \bar{b}=1$. How can I show that $n$ must be prime ? Machine learning cookbook / reference card / cheatsheet? I find resources like the  and  incredibly useful. They obviously serve well as references but also help me to organize my thoughts on a subject and get the lay of the land.   Q: Does anything like these resources exist for machine learning methods?  I'm imagining a reference card which for each ML method would include:   General properties When the method works well When the method does poorly From which or to which other methods the method generalizes. Has it been mostly superseded? Seminal papers on the method Open problems associated with the method Computational intensity   All these things can be found with some minimal digging through textbooks I'm sure. It would just be really convenient to have them on a few pages. How do I put big brackets under different parts of an equation so that I can write, e.g., text specific to these parts? For example: f =  x^3 +  2     |___|  |__|        |     |    text 1  text 2 List the files containing a particular word in their text What are the difference between the following sentence?    I ate apples. I have eaten apples.    When should we use simple past tense? When should we use perfect past tense? Position of a relative clause before/after a verb What is the limit of series $\frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{4 \cdot 5 \cdot 6} + \frac{1}{6 \cdot 7 \cdot 8} + \cdots $?  The $n$th summand is $\frac{1}{(2n)(2n + 1)(2n+2)} = \frac{1}{4} \frac{1}{n(2n+1)(n+1)}$.  I have tried expressing this as a telescoping sum, or as the limit of Riemann sums of a partition (the usual methods I normally try when doing this type of question- what are some other strategies?) Numbering side-by-side equations or inline equations So I have a torus, and I need it to "telescope" open -- kind of like Pacman's death animation, but with a torus instead of a sphere.  I'm very new to 3D modeling/animating so I really have no clue how to tackle this problem.  Any advice to help me get pointed in the right direction would be most appreciated :) What is the highest power of n in $(n^r-1)!$ where $n$, $r$ are positive integers? The answer supplied is $\frac{n^r-nr+r-1}{n-1}$   The highest power of $n$ in $n^r!  = r +$ the highest power of $n$ in $(n^r-1)!$ as $n^r$ contributes $r$ powers.    So,  the highest power of $n$ in $n^r!$ needs to be $\frac{n^r-nr+r-1}{n-1} + r =\sum_{1≤t&lt;r}n^t $.    This is clearly true if $n$ were prime according to .  Again,  if $r=1$, $\frac{n^r-nr+r-1}{n-1}$ becomes $0$.    But according to , the  highest power of composite $n$ in $(n-1)! ≥ 1 $.  So, the answer does not seem to hold for $r=1$ if $n$ is composite. If $n=\prod p_i^{a_i}$, where $p_i$ are distinct primes,  $n^r=\prod p_i^{ra_i}$  So, the highest power $(q_i)$ of $p_i$ in  $n^r!$ is  $$\sum_{1≤t&lt;∞}\left\lfloor\frac{n^r}{p_i^t} \right\rfloor =\sum_{1≤t≤ra_i}\frac{n^r}{p_i^t} +\sum_{ra_i+1≤t&lt;∞}\left\lfloor\frac{n^r}{p_i^t} \right\rfloor$$  as $p^t|n^r$ for $t≤ra_i$.  So, the highest power of $p_i^{a_i}$ in  $n^r!$ is $\left\lfloor \frac{q_i}{a_i} \right\rfloor=P_i$(say).   So, the highest power of n=$\prod p_i^{a_i}$ in  $n^r!$ is $min(P_i)$  I could not proceed anymore. Can I run an HTTP GET directly in SQL under MySQL? I'd love to do this:  UPDATE table SET blobCol = HTTPGET(urlCol) WHERE whatever LIMIT n;   Is there code available to do this? I known this should be possible as the  include an example of adding a function that does a DNS lookup.  MySQL / windows / Preferably without having to compile stuff, but I can.  (If you haven't heard of anything like this but you would expect that you would have if it did exist, A "proly not" would be nice.)  EDIT: I known this would open a whole can-o-worms re security, however in my cases, the only access to the DB is via the mysql console app. Its is not a world accessible system. It is not a web back end. It is only a local data logging system When I use any variation of English, US international (with dead keys,altGr dead keys or alternative) on my Linux Mint machine I always encounter this behaviour. When I press one of these keys: ' " and then follow them with a 'non-accentable' character like a [ or a b no output comes out at all.    Whereas in Windows US-International it would print [ or b. If I wanted to type this I would have to escape each dead key with a space instead of with any 'non-accentable' character. This is annoying when programming (not really, but I trained with the Windows 'Qwerty International' on typing.io and switching back and forth between the systems is irritating).    Is there any way to change that so it works like in Windows? Disable the default app key (super+num) functionality on Ubuntu 17.10 and later I like to switch workspaces via Super+Number. But unfortunately the default behavior in Ubuntu for Super+Number is to select applications from the dock.   Is it possible to disable that functionality? I've tried overriding the keyboard shortcuts but it doesn't appear to be working. Global Inbox -> Global RSS feed for all my questions across all the sites?