After seeing the results obtained with LuxRender , I was curious to try and reproduce beautiful caustics in Cycles such as these:    I created a scene and added some lights, following the advice given  to create the materials, and also trying out other materials.  I find it hard to find much documentation on caustics within Cycles; some people advise to use Sun Lamps, some other recommend emitter planes. Sometimes large emitter planes seem to work, sometimes people recommend smaller emitter planes. Besides from this confusion, in my various tests, the light that goes through the objects and hits the ground plane is usually very diffuse, of an evenly brightness, and doesn't have many sharp areas.  Here's an example of what I get the closest I get being the shape on the left):    Moreover, in the example given above, caustics appear on two sides of the object, probably due to the light bouncing inside the object and being projected out on both sides.  How should I set up materials and lights for sharp and realistic caustics, in Cycles?  File:
Working in Cycles.  Say I have a "disco ball" with a glossy shader. I'm pointing a spot light to it, and I'm trying to have the reflections of that light illuminate the diffuse material on the walls with the patterns from the ball.    I get this:    but I'd like to get something like:    For the illustration I placed a point light inside the ball an removed faces. But what I'd like to do is move the light around the ball so that the light reflected from it changes like it would do in real life.   Is that possible at this point?  EDIT:  Just for the record here's the image rendered in LuxRender (yet another program to learn...)
I am trying to find ways to quantitatively describe the shapes of various polygons. For my project, these polygons represent lakes, rivers, lagoons, and parks. So they can be almost any shape. One easy metric is to calculate perimeter vs. area, which is at best an only slightly useful metric. But I would also very much like to be able to say something about the 'roundness' of a polygon. Or how 'compact' the shape is on a map.  The only way I can think of doing this easily is to calculate the area of each polygon in relation to a bounding box for that polygon (which I already have). But this seems like a poor solution.  So now I am thinking of something more like this - take the centroid of the polygon, add on a series of buffers of increasing areas (say 50%, 100%, 150%), then compare how much overlap there is between each buffer and the original polygon. A perfect circle will have perfect overlap at 100%, and I can use the 50% and 150% buffers to judge how much and in what way each polygon differs.  But even that feels cumbersome, and like a poor workaround for what somebody else has probably already figured out far better.  For reference, at a minimum I will need to be able to look at the resulting indices for the shape of various polygons, and be able to make an educated guess as to their source (River? Reservoir with dendritic shape? Lake/Lagoon? Park?) The electroweak and strong forces seem to be completely different types of forces to gravity. The latter is geometric while the former are not (as far as I'm aware!). So why should they all be described in the same way? - Why are gravitons needed?  Alternatively, I suppose my question is why a theory of everything has to be some form of quantum gravity. Is there a reason why a theory of everything requires gravity to be quantised? Is it possible for the quantum world and gravity to be described by some overarching theory which does not require gravity to be quantised? Or is there some reason why this is not the case? Present Perfect or simple past? Cutting a circular hole in a hollow cylinder without distorting the cylinder Whenever I try to cut out a circular hole in either a cylinder or sphere the polygons around the circular hole always have distorted normals after smoothing. Is there anyway to fix this. I've tried using the remesh modifier but wind up with some pretty ugly results. Question 1: Let $x,y \in S$ such that $x\sim y$ if $x^2 =y^2\pmod6 $. Show that $\sim$ is an equivalence relation.    This is what I tried: Reflexive: $x^2\pmod6 = x^2$  implying $x\sim x$ Symmetry: suppose $x\sim y$, then  $x^2 =y^2\pmod6$ Operating by inverse of $x^2$ both sides we have $e=(x^2)^{-1} y^2\pmod6$ Then I have $y^2=x^2\pmod6$, hence $y\sim x$ I would like to get some corrections up to here because am not sure with this     Question 2. Find the orbits of the given permutation:    $$v:\mathbb{Z}\to\mathbb{Z}\quad\text{ defined by }\quad v(n)=n+3$$   Here is my solution which I would also want somebody to correct me! Let the relation $\sim$ be defined on $\mathbb{Z}$ by $a\sim b$ if $b=a+3$ I consider that the orbits of $v$ are the classes of $\mathbb{Z}$ with respect to $\sim$ given by  $\{b\mid b=a+3\}$. Thus I get only three orbits which are $\{1,4,7,10,…,3n-2\mid n\in \mathbb{Z}\}$, $\{2,5,8,…,3n-1\mid n\in \mathbb{Z}\}$, and $\{3,6,9,…,3n \mid n\in \mathbb{Z}\}$. Why only light nuclei are able to undergo nuclear fusion not heavy nuclei? Is it because of the binding energy or the binding energy per nuclei .  I am having trouble with this whole binding energy and nuclear fusion concept. Could "them" mean "those"? Background Nowadays, I see &quot;them&quot; used to mean &quot;those&quot; a lot. I don't know if it was as common in the past. For example, take &quot;one of &quot;. On researching about it, I found some people say it comes from a dialect of British English. Some others say it is a &quot;non-standard&quot; usage. I see this usage in Canadian English also, and it seems some people use it in a sarcastic way. Moreover, I have seen a song titled &quot;one of them days&quot;. I also read, in the book called &quot;A Broken Promise&quot;, &quot;&quot; Finally, Wikipedia says that it is a usage in  (a common name for the Southern Midland dialect of American English):  Pronouns and demonstratives &quot;Them&quot; is sometimes used in place of &quot;those&quot; as a demonstrative in both nominative and oblique constructions. Examples are &quot;Them are the pants I want&quot; and &quot;Give me some of them crackers.&quot;    Question(s): What would you say about the usage of this word? Is it correct? Could we use it in daily speech? Could this usage go beyond a specific dialect and be used in other dialects, regions, etc.? Does it really originate from Appalachian English? Why did this usage become popular among other English speakers? Note: I have already seen a similar question:  However, it only says, &quot;ungrammatical,&quot; there. This question is specific to this situation only, and there is more to it. If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric Let $(X,d)$ be a metric space and for $x,y \in X$ define $$d_b(x,y) = \dfrac{d(x,y)}{1 + d(x,y)}$$ a) show that $d_b$ is a metric on $X$  Hint: consider the derivative of $f(t)$ = $\dfrac{t}{1+t}$  b) show that $ d$ and $ d_b $ are equivalent metrics. c) let $(X,d) $ be $(\mathbb{R}, |\cdot|)$ Show that there exists no $ M&gt;0$ such that $ |x-y| $ $\leq$ $Md_b$ $(x,y)$ for all $ x,y$ $\in$ $\mathbb{R}$  I have calculated $f(t)$ and $f'(t)$ and from this I know $f(t)$ is an increasing function as $f'(t)$ is strictly positive. But I don't know where to go from here or how to do parts b) and c) How can I accept the Microsoft EULA agreement for ttf-mscorefonts-installer? After a recent update, ttf-mscorefonts-installer prompted me to accept its license agreement.     ┌─────────────────┤ Configuring ttf-mscorefonts-installer ├─────────────────┐  │                                                                           │   │ TrueType core fonts for the Web EULA                                          │                                                                               │ END-USER LICENSE AGREEMENT FOR MICROSOFT SOFTWARE                             │                                                                               │ IMPORTANT-READ CAREFULLY: This Microsoft End-User License Agreement           │ ("EULA") is a legal agreement between you (either an individual or a          │ single entity) and Microsoft Corporation for the Microsoft software           │ accompanying this EULA, which includes computer software and may include      │ associated media, printed materials, and "on-line" or electronic              │ documentation ("SOFTWARE PRODUCT" or "SOFTWARE"). By exercising your          │ rights to make and use copies of the SOFTWARE PRODUCT, you agree to be        │ bound by the terms of this EULA. If you do not agree to the terms of          │ this EULA, you may not use the SOFTWARE PRODUCT.                              │                                                                               │                                  &lt;Ok&gt;                                         │                                                                           │   └───────────────────────────────────────────────────────────────────────────┘    Screenshot:   For some reason my terminal will not allow me to accept, or for some reason I am pressing the wrong hotkey...  I've tried every letter on the keyboard and Enter among others...  I'm sure there is a very simple and obvious solution to this.  I've also just tried to remove the package completely however the terminal states that due to the package not being correctly installed, I should reinstall the package before removing it.  Very frustrating!  Essentially, because I cannot successfully install this package, I can't really ever upgrade my system because I always have to end up terminating the terminal with the license agreement (thus the upgrade fails). Can a service written in .NET self-terminate? I have a service application written in C# and under certain circumstances, I would like it to terminate itself.  This would happen after the service has been running for a while, so this would not be happening in the OnStart() event.  Everything that I have read so far suggests that the only safe way to terminate a service is through the Service Control Manager.  My service runs as Local Service and does not have the rights to start or stop services, so I can't access the SCM from the service itself.  Is there another way to self-terminate while still playing by the rules of the SCM? Since I first learned English, I have been holding this understanding that "and", as a conj. but unlike "but",  can only connect two clauses, not two sentences ended with periods.  But recently, I have seen so many prints, either in entertainment or in academia, where "And" is popularly used in the beginning of a sentence. It seems like the author is trying to connect the sentence just right before and the sentence following "And" in some intended meaning which I don't quite get.  I was wondering if I have been wrong all the time, or if there is a new trend that I fail to understand and accept? How to understand such usage of "and" in rigorous English grammar? If I am right, why it is used differently from "but" in terms of what I mentioned at the beginning of this post? Why the rows returns by "explain" is not equal to count()? Can't change mouse influence in proportional editing mode I press O and I see it change to Proportional Editing mode, but when I press G and mouse wheel down/up, or arrow keys down/up, it doesn't change the influence area.    And I am, I press G and then I tried to scroll to change influence, but it's not working.    Done this aswell and it's not working I generally know how to use a hyphen, but when should I use an en-dash (–) instead of an em-dash, or when should I use a hyphen (-) instead of an em-dash (—)? I'm trying to get images in my document in two different ways:   On top of the entire page, centered On top of a single column   I tried it with both twocols and multicols. I ruled out twocols because it forces a new page every time you turn it on, because I need the abstract to be wide and the rest of the cover page to be two columns.  Here are some examples of both points (screenshot from a downloaded PDF):   I want to achieve both, but somehow I can only solve the first point with:  \end{multicols}  \begin{figure}   \centering     \includegraphics[width=0.5\textwidth]{figure}   \caption{Dataflow pipeline of the edge detector}   \label{fig:workflowedge} \end{figure}  \begin{multicols}{2}   Is it awkward to turn off multicols, then turn it back on again?  For my second point, I've tried everything, but almost always, the image doesn't show up at all! The only way I can get it to show at all is by specifying the H placement specifier, but that places the image inside the text where I defined it, not on top of the column.  This is my best try, but it hides the image and breaks all references to ??:  \begin{figure}[t!]   \centering     \includegraphics[width=0.25\textwidth]{figure}   \caption{Dataflow pipeline of the edge detector}   \label{fig:workflowedge} \end{figure}   and I'm getting the warning:  Package multicol Warning: Floats and marginpars not allowed inside `multicols' environment!.   How can I make a figure a non-float?  I also tried the figure* environment, but that just creates an image centered on top of the page, like my first point. Here is a quesion that has been bugging me. You know how you can set up a program to run on start up right?  Well, how can i tell it to start minimized, like you would do in windows?   TeamViewer starts open, but I need it minimized, and Tray-it just doesn't seem as elegant of a way to do it. When documenting a style file, it would be nice to be able to easily put side by side different examples of code, side-by-side with the output they produce.  What recommendations to people have to do this efficiently, and &aelig;sthetically? I'm trying out  with gnuplot to generate the data.  This works by having pgfplots write some stuff to an external file, run gnuplot on the file, and then use the generated data to plot the graph.  The problem I'm having is that I get different behaviour under xelatex as pdflatex or lualatex.  In xelatex, the data file is littered with ^^I whereas in the other two formats these are tabs.  It appears that the code ^^I is getting stored as a macro which then gets written out to the file, so possibly there's something funny going on with the ^^I syntax: xelatex is reading it literally.  Indeed, when I do \show\pgfplots@TAB (the macro in question) then for pdflatex and lualatex then I get a literal tab whereas for xelatex I get ^^I.  So how do I get a tab in xelatex?  And why isn't \gdef\pgfplots@TAB{^^I} working?  (The previous line in the code, by the way, is \catcode`\^^I=12 - I don't know if that has anything to do with it.) My mother is a quite famous researcher (she has a PhD) on the field I want to do a PhD in. She works on the industry (not academia). I helped her on successful projects. She knows more about my work than my professors since we have worked much longer together.  Is it a good idea to ask for a recommendation letter from her? Since our personalities are very similar she can point out the high probability that I will be successful like her? What's the subject of "There is my biscuit!" ? And how about "There is one biscuit left"? What's the subject, grammatically speaking, of these sentences?   There is my biscuit! My biscuit is there! There is one biscuit left.   I don't really know how to analyze these. The following observations seem to be relevant, though:   The verb to be doesn't take an object. In the first two sentences, there is a demonstrative pronoun. It is therefore potentially a subject, I think. I don't know what part of speech is taken by there in the third sentence. In favour of reading my biscuit and one biscuit as the subjects is that if there were more than one biscuit then, in each case, the verb would become plural (There are my biscuits! etc.) In favour of reading one biscuit as the subject of the third sentence is that if we recast it as (the slightly unidiomatic) There remains one biscuit, it seems that one biscuit would have to be the subject.   All of this leads me tentatively towards thinking that my biscuit and one biscuit are the subjects here, but I'm not totally confident about this.  One other possibility: since to be doesn't take an object, does that mean it can have two subjects? In I am he, presumably both I and he are subjects, if neither is an object?