I'm making a game in SDL2 and C++. I want a way to make any game object move in a specific direction. I've thought of assigning each object a direction in radians, from 0 until 2 PI where 0 would represent movement in the positive x direction, and PI movement in the negative x direction (0.5 PI would be positive y, 1.5 PI negative y, etc).   My problem occurs when trying to translate these directions into actually moving an object on the screen - moving objects with directions of 0, 0.25 PI, 0.5 PI, 0.75 PI, etc are trivial, as one would either decrement or increment only x, or only y, or alternate x and y.   To approximate other angles of movement in x and y, I figured I could calculate how much each object should move in x, before it increments y, (or vice versa, depending on whether the direction is bigger or smaller than 0.25 PI, and assuming we're only considering the positive x and y quadrant ). And then restricting how many moves in x and y the object makes each time it is moved, in an attempt to preserve the speed of the object, though this would still result in an object moving along an axis moving slower than one moving in at an angle. Is this a reasonable solution?  Is there a more elegant or precise way of accomplishing this problem?
I'm playing around with height maps (bitmaps), trying to create some of my own in my game, and for that I need to implement some basic drawing methods. I've quickly realized that drawing straight lines isn't as basic as I thought.  It simple's if your points share an X or Y coordinate, or if they are aligned so you can draw a perfectly diagonal line. But in all other cases its trickier.  What algorithm do you use to determine what pixels need to be coloured for it to become a "straight" line ?
Does there exist an $a_0$ such that the sequence $a_{n+1} = 2a_n + 1$ is prime for all $n \ge 0$? I'm from Western Pennsylvania. Until I moved away, I never realized that when I omitted the to be from phrases like needs to be cleaned, my usage was different than what most English speakers are accustomed to. Is it wrong? Holomorphic function has at most countably zeros Let $f$ be holomorphic in a domain $U$, then $f$ has at most countably zeros.  How can I prove this statement? I have seen it in Sheng Gong  explicitly, but without any indications. I am trying to prove the following statement.     If a field $K$ is not algebraically closed, then any $K$-variety $V\subset\mathbb{A}^n$ can be written as the zero set of a single polynomial in $K[X_1,X_2,...,X_n].$     Suppose $V=V(f_1,f_2,...,f_n)$, and I would want to find a polynomial $g\in K[X_1,X_2,...,X_n]$ such that $V=V(g)$.  I know that if I can find a polynomial $\phi\in K[X_1,X_2,...,X_n]$ whose only zero is $(0,0,...,0)$, then it is done, since we could take $g=\phi(f_1,f_2,...,f_n)$.  For $n=1$, then I would just choose $\phi=X$, but I do not even know how to proceed to the case $n=2$. Maybe we could choose an irreducible polynomial of degree $&gt;1$.  Any help will be appreciated. Updating VS Code in ubuntu 18.04 show all my unanswered questions from SE Any way how to get    my all un-answered questions  from across all SE sites? "Coming soon" pages & SEO I am setting up my personal website, and I have designed a simple "Coming Soon / Under Construction" page which basically has nothing but a small notice for the users.   What kind of SEO can I make on this page such that it won't harm the full website's ranking later on? Is there a fast way to get to the bottom of the Death Star? In Tiny Death Star, you can get to the top of your tower by tapping on the top of the screen while avoiding the "Add Level" button. However, the only way I can find to go to the bottom of the tower is to wait for someone to want an elevator ride, and tap on the button to give them that ride. Is there any other hot-spot for getting to the bottom of your Death Star? Generic Parse Method without Boxing I am trying to write a generic Parse method that converts and returns a strongly typed value from a NamedValueCollection.  I tried two methods but both of these methods are going through boxing and unboxing to get the value.  Does anyone know a way to avoid the boxing?  If you saw this in production would you not like it, how bad is it for performance?  Usuage:  var id = Request.QueryString.Parse&lt;int&gt;("id");   Attempt #1:  public static T Parse&lt;T&gt;(this NameValueCollection col, string key) {     string value = col[key];      if (string.IsNullOrEmpty(value))         return default(T);      if (typeof(T) == typeof(int))     {         //return int.Parse(value); // cannot convert int to T         //return (T)int.Parse(value); // cannot convert int to T         return (T)(object)int.Parse(value); // works but boxes     }     if (typeof(T) == typeof(long))     {         return (T)(object)long.Parse(value); // works but boxes     }     ...      return default(T); }   Attempt #2 (using reflection):  public static T Parse&lt;T&gt;(this NameValueCollection col, string key) {     string value = col[key];      if (string.IsNullOrEmpty(value))         return default(T);      try     {         var parseMethod = typeof(T).GetMethod("Parse", new Type[] { typeof(string) });          if (parseMethod == null)             return default(T);          // still boxing because invoke returns an object         var parsedVal = parseMethod.Invoke(null, new object[] { value });         return (T)parsedVal;     }     // No Proper Parse Method found     catch(AmbiguousMatchException)      {     }      return default(T); } If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$ If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$   I was practicing quadratic equation questions online but I am stuck on this question.  I found the values of roots $a= 1$, $b= 1/2$ Make a substitution to express the integrand as a rational function and then evaluate the integral  $$\int {\frac{2}{x\sqrt{x+1}}}\, dx$$  What is the substitution that I have to make? I have a managed C# dll that uses an unmanaged C++ dll using DLLImport. All is working great. However, I want to embed that unmanaged DLL inside my managed DLL as explain by Microsoft there:    So I added the unmanaged dll file to my managed dll project, set the property to 'Embedded Resource' and modify the DLLImport to something like:  [DllImport("Unmanaged Driver.dll, Wrapper Engine, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null", CallingConvention = CallingConvention.Winapi)]   where  'Wrapper Engine' is the assembly name of my managed DLL 'Unmanaged Driver.dll' is the unmanaged DLL  When I run, I get:     Access is denied. (Exception from HRESULT: 0x80070005   (E_ACCESSDENIED))   I saw from MSDN and from  that's supposed to be possible... Can the Earth's magnetic field be used to generate electricity? Can you be refused a visitor visa to US if you have bad Credit there? I was coding a physics simulation, and noticed that I was using discrete time. That is, there was an update mechanism advancing the simulation for a fixed amount of time repeatedly, emulating a changing system.  I though that was interesting, and now believe the real world must behave just like my program does. It is actually advancing forward in tiny but discrete time intervals? Why do some websites show the company name next to the URL? Some websites show the company name next to the URL (in Chrome) and some don't.  How do I set this up for my website? Is there a reason why or why I wouldn't want to do this? Custom action to set emblem in thunar piping in real time This is more a conceptual thing than a current problem.  Would it be possible to do this:  tail -f &lt;file&gt; | grep "string" | sed 's/stuff//g' &gt;&gt; output.txt  The problem I'm thinking is that tail -f never terminates so it won't progress in the command. I'm trying to read and output a file in real-time. If this doesn't work how would I do it? What is the best way to parse html in C#? Product Snippets with JSON-LD + Schema.org - Are there any live examples in Google index? ** EDIT Feb 2016 - Finally JSON-LD seems to be working now in SERPS, with extremely fast changes-to-index time, assuming you have everything with Google merchant center feeds syncd and linked. Make sure the price, stock, and identifier are the same on your JSON-LD as it is on the Google shopping feed. New organization-&gt;localbusiness types are live, organization reviews are live... however JSON-LD feed alt= endpoints still do not exist, the homepage schema defining custom site name is not active, and G support for schema itemList/dateModified is still questionable. You can still get pagination results and date modified snippets by using literal text strings in your view/template Showing 1-28 of 8977 Results (321 Pages)and Last updated on February 3rd 2016. To proceed to a deeper exploration of JSON-LD support, see these:       Original Post Below: Google seems to be flip flopping JSON-LD -&gt; Schema.org product [or other types of] snippets. The snippets verify without error in both the testing tool and long term (10+ months) across 5 properties in GWT search console. The snippets have been applied to index, removed, applied, and removed again, seemingly not being applied again in regards to various facets. Since they worked in the past via microdata, and were applied long term, I assume it's due to the switch to JSON-LD. I have not found any official docs nor examples that say &quot;Google will support and render products snippets that use JSON-LD&quot;. Same thing with breadcrumb snippets and review looping. All I see is a handful of Google examples for events, movies, recipes, very basic [incomplete] organization etc. This seems strange to me considering the sheer amount of ecom pages using product snippets trumps the amount of movies, recipes, and events combined. So the question is, does Google officially support, index, and render product markup using JSON-LD? If so, can anyone point me to a live example to verify this? ** This question is not intended to be &quot;opinion/recommendation based&quot;....im looking for a specific link and subsequent SERP result [evidence] showing that JSON-LD products/etc are indeed rendered within Google.com realm as of late August 2015. ** EDIT Nov 16 2015 - Another annoying caveat has been found. Google merchant center validates certain shopping feed fields such as condition, stock, and price against live microdata. However, it seems to not recognize JSON-LD.... although, as stated above, it's recommended to use in all the G examples, and it validates the snippet test. So due to this, your merchant center account could be suspended because of &quot;differences in presentation data&quot;