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• Recommended books on math for programmers

  - by Anto

  Some programmers do, besides programming, like math (others don't). What books on math do you recommend programmers who like math to read? There are books which present concepts which are applicable in programming and/or computer science, other books about things which will fascinate programmers etc. Books on applying math to programming are okey, but they should be mainly about math (and not programming). Motivate your answers, with focus on why programmers should read the book(s).

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• dividing double by double gives weird results - Java

  - by Aly

  Hi, I am trying to do the following 33.33333333333333/100.0 to get 0.333333333333333 however when I run System.out.println(33.33333333333333/100.0); I get 0.33333333333333326 as the output, similarly when I run System.out.println(33.33333333333333/1000.0); I get 0.033333333333333326 as the output. Does anyone know why, and how I can get the correct value (without loss of decimal places). Thanks

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• Math questions at a programmer interview?

  - by anon

  So I went to an interview at Samsung here in Dallas, Texas. The way the recruiter described the job, he didn't make it sound like it was too math-oriented. The job basically involved graphics programming and C++. Yes, math is implied in graphics programming, especially shaders, but I still wasn't expecting this... The whole interview lasted about an hour and a half and they asked me nothing but math-related questions. They didn't ask me a single programming question, which I found odd. About all they did was ask me how to write certain math routines as a C++ function, but that's about it. What about programming philosophy questions? Design patterns? Code-correctness? Constness? Exception safety? Thread safety? There are a zillion topics that they could have covered. But they didn't. The main concern I have is that they didn't ask any programming questions. This basically implies to me that any programmer who is good at math can get a job here, but they might put out terrible code. Of course, I think I bombed the interview because I haven't used any sort of linear algebra in about a year and I forget math easily if I haven't used it in practice for a while. Are any of my other fellow programmers out there this way? I'm a game programmer too, so this seems especially odd. The more I learn, the more old knowledge that gets "popped" out of my "stack" (memory). My question is: Does this interview seem suspicious? Is this a typical interview that large corporations have? During the interview they told me that Google's interview process is similar. They have multiple, consecutive interviews where the math problems get more advanced.

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• Math questions at a programmer interview?

  - by anon

  So I went to an interview at Samsung here in Dallas, Texas. The way the recruiter described the job, he didn't make it sound like it was too math-oriented. The job basically involved graphics programming and C++. Yes, math is implied in graphics programming, especially shaders, but I still wasn't expecting this... The whole interview lasted about an hour and a half and they asked me nothing but math-related questions. They didn't ask me a single programming question, which I found odd. About all they did was ask me how to write certain math routines as a C++ function, but that's about it. What about programming philosophy questions? Design patterns? Code-correctness? Constness? Exception safety? Thread safety? There are a zillion topics that they could have covered. But they didn't. The main concern I have is that they didn't ask any programming questions. This basically implies to me that any programmer who is good at math can get a job here, but they might put out terrible code. Of course, I think I bombed the interview because I haven't used any sort of linear algebra in about a year and I forget math easily if I haven't used it in practice for a while. Are any of my other fellow programmers out there this way? I'm a game programmer too, so this seems especially odd. The more I learn, the more old knowledge that gets "popped" out of my "stack" (memory). My question is: Does this interview seem suspicious? Is this a typical interview that large corporations have? During the interview they told me that Google's interview process is similar. They have multiple, consecutive interviews where the math problems get more advanced.

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• CPU Architecture and floating-point math

  - by Jo-Herman Haugholt

  I'm trying to wrap my head around some details about how floating point math is performed on the CPU, trying to better understand what data types to use etc. I think I have a fairly good understanding of how integer math is performed. If I've understood correctly, and disregarding SIMD, a 32-bit CPU will generally perform integer math at at least 32-bit precision etc. Is it correct that floating-point math is dependent on the presence of a FPU? And that the FPU on the x86 is 80-bit, so floating point math is performed at this precision unless using SIMD? What about ARM?

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• Math major as a viable degree

  - by Zak O'Keefe

  While I realize there are many topics about CS vs software engineering vs game school programs, I haven't found anything relating to whether pure math degrees (with CS minor and electives) would also be a viable program. By this I mean: Would having a math major, CS minor put one at competitive disadvantage as compared to a pure CS program? This relates specifically to game engine programming, more on the graphics side. Background (for those who care): Currently a math major, CS minor at school and looking to land a career doing graphics engine programming. Admittedly, I love math and if at all possible would like to stay my current program as long as it doesn't put me at a competitive disadvantage trying to land a job post-graduation. That being said, I'm strong in the traditional C/C++ languages, strong concurrent programming skills, and currently produce self-made games for iOS. As an employer, how badly is the math major hurting me? Just want to get some advice from people already in the field!

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• Bad at math, feeling limited

  - by Peter Stain

  Currently I'm a java developer, making websites. I'm really bad at math, in high school I got suspened because of it once. I didn't program then and had no interest in math. I started programming after high school and started feeling that my poor math skills are limiting me. I feel like the programming's not that hard for me. Though web development in general is not that hard, i guess. I've been doing Spring and Hibernate a lot. What i'm trying to ask is : if I understand and can manage these technologies and programming overall, would it mean that I have some higher than average prerequisite for math and details? Would there be any point or would it be easy for me to take some courses in high school math and get a BSc in math maybe? This web development is really starting to feel like not my cup of tea anymore, i would like to do something more interesting. I'm 25 now and feel like stuck. Any help appreciated.

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• What math should all game programmers know?

  - by Tetrad

  Simple enough question: What math should all game programmers have a firm grasp of in order to be successful? I'm not specifically talking about rendering math or anything in the niche areas of game programming, more specifically just things that even game programmers should know about, and if they don't they'll probably find it useful. Note: as there is no one correct answer, this question (and its answers) is a community wiki. Also, if you would like fancy latex math equations, feel free to use http://mathurl.com/.

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• Game Institute Math Courses

  - by W3Geek

  I'm 21 years old and I suck at math, I mean really bad. I don't have the necessary logic to apply it towards programming. I would like to learn the math and logic of applying it. I found Game Institute (http://www.gameinstitute.com) awhile back and heard a lot of praise about them. Are there Math courses any good? Thank you. Edit: My high school was terrible and did not prepare me for any math. I am fairly decent at programming, I just don't have the logic to apply any mathematics to programming, as an example I don't understand the algorithm of finding the size of a user's screen. Yes I have heard of KhanAcademy (http://www.khanacademy.org/) and I have completed a lot of maths on his website but I still don't have the logic to apply any of it to programming.

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• Long term plan of attack to learn math?

  - by zhenka

  I am a web-developer with a desire to expand my skill-set to mathematics relevant to programming. As 2nd career, I am stuck in college doing some of the requirements while working. I was hoping the my education will teach me the needed skills to apply math, however I am quickly finding it to be too much easily-testable breadth-based approach very inefficient for the time invested. For example in my calculus 2 class, the only remotely useful mind expanding experience I had was volumes and areas under the curve. The rest was just monotonous glorified algebra, which while comes easy to me, could be done by software like wolfram alpha within seconds. This is not my idea of learning math. So here I am a frustrated student looking for a way to improve my understanding of math in a way that focuses on application, understanding and maximally removed needless tedium. However I cannot find a good long term study strategy with this approach in mind. So for those of like mind, how would you go about learning the necessary math without worrying too much about stuff a computer can do much better?

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• (int) Math.floor(x / TILESIZE) or just (int) (x / TILESIZE)

  - by Aidan Mueller

  I have a Array that stores my map data and my Tiles are 64X64. Sometimes I need to convert from pixels to units of tiles. So I was doing: int x int y public void myFunction() { getTile((int) Math.floor(x / 64), (int) Math.floor(y / 64)).doOperation(); } But I discovered by using (I'm using java BTW) System.out.println((int) (1 / 1.5)) that converting to an int automatically rounds down. This means that I can replace the (int) Math.floor with just x / 64. But if I run this on a different OS do you think it might give a different result? I'm just afraid there might be some case where this would round up and not down. Should I keep doing it the way I was and maybe make a function like convert(int i) to make it easier? Or is it OK to just do x / 64?

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• C# (4): double minus double giving precision problems

  - by thermal7

  I have come across a precision issue with double in .NET I thought this only applied to floats but now I see that double is a float. double test = 278.97 - 90.46; Debug.WriteLine(test) //188.51000000000005 //correct answer is 188.51 What is the correct way to handle this? Round? Lop off the unneeded decimal places?

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• Is there a Math.atan2 substitute for j2ME? Blackberry development

  - by Kai

  I have a wide variety of locations stored in my persistent object that contain latitudes and longitudes in double(43.7389, 7.42577) format. I need to be able to grab the user's latitude and longitude and select all items within, say 1 mile. Walking distance. I have done this in PHP so I snagged my PHP code and transferred it to Java, where everything plugged in fine until I figured out J2ME doesn't support atan2(double, double). So, after some searching, I find a small snippet of code that is supposed to be a substitute for atan2. Here is the code: public double atan2(double y, double x) { double coeff_1 = Math.PI / 4d; double coeff_2 = 3d * coeff_1; double abs_y = Math.abs(y)+ 1e-10f; double r, angle; if (x >= 0d) { r = (x - abs_y) / (x + abs_y); angle = coeff_1; } else { r = (x + abs_y) / (abs_y - x); angle = coeff_2; } angle += (0.1963f * r * r - 0.9817f) * r; return y < 0.0f ? -angle : angle; } I am getting odd results from this. My min and max latitude and longitudes are coming back as incredibly low numbers that can't possibly be right. Like 0.003785746 when I am expecting something closer to the original lat and long values (43.7389, 7.42577). Since I am no master of advanced math, I don't really know what to look for here. Perhaps someone else may have an answer. Here is my complete code: package store_finder; import java.util.Vector; import javax.microedition.location.Criteria; import javax.microedition.location.Location; import javax.microedition.location.LocationException; import javax.microedition.location.LocationListener; import javax.microedition.location.LocationProvider; import javax.microedition.location.QualifiedCoordinates; import net.rim.blackberry.api.invoke.Invoke; import net.rim.blackberry.api.invoke.MapsArguments; import net.rim.device.api.system.Bitmap; import net.rim.device.api.system.Display; import net.rim.device.api.ui.Color; import net.rim.device.api.ui.Field; import net.rim.device.api.ui.Graphics; import net.rim.device.api.ui.Manager; import net.rim.device.api.ui.component.BitmapField; import net.rim.device.api.ui.component.RichTextField; import net.rim.device.api.ui.component.SeparatorField; import net.rim.device.api.ui.container.HorizontalFieldManager; import net.rim.device.api.ui.container.MainScreen; import net.rim.device.api.ui.container.VerticalFieldManager; public class nearBy extends MainScreen { private HorizontalFieldManager _top; private VerticalFieldManager _middle; private int horizontalOffset; private final static long animationTime = 300; private long animationStart = 0; private double latitude = 43.7389; private double longitude = 7.42577; private int _interval = -1; private double max_lat; private double min_lat; private double max_lon; private double min_lon; private double latitude_in_degrees; private double longitude_in_degrees; public nearBy() { super(); horizontalOffset = Display.getWidth(); _top = new HorizontalFieldManager(Manager.USE_ALL_WIDTH | Field.FIELD_HCENTER) { public void paint(Graphics gr) { Bitmap bg = Bitmap.getBitmapResource("bg.png"); gr.drawBitmap(0, 0, Display.getWidth(), Display.getHeight(), bg, 0, 0); subpaint(gr); } }; _middle = new VerticalFieldManager() { public void paint(Graphics graphics) { graphics.setBackgroundColor(0xFFFFFF); graphics.setColor(Color.BLACK); graphics.clear(); super.paint(graphics); } protected void sublayout(int maxWidth, int maxHeight) { int displayWidth = Display.getWidth(); int displayHeight = Display.getHeight(); super.sublayout( displayWidth, displayHeight); setExtent( displayWidth, displayHeight); } }; add(_top); add(_middle); Bitmap lol = Bitmap.getBitmapResource("logo.png"); BitmapField lolfield = new BitmapField(lol); _top.add(lolfield); Criteria cr= new Criteria(); cr.setCostAllowed(true); cr.setPreferredResponseTime(60); cr.setHorizontalAccuracy(5000); cr.setVerticalAccuracy(5000); cr.setAltitudeRequired(true); cr.isSpeedAndCourseRequired(); cr.isAddressInfoRequired(); try{ LocationProvider lp = LocationProvider.getInstance(cr); if( lp!=null ){ lp.setLocationListener(new LocationListenerImpl(), _interval, 1, 1); } } catch(LocationException le) { add(new RichTextField("Location exception "+le)); } //_middle.add(new RichTextField("this is a map " + Double.toString(latitude) + " " + Double.toString(longitude))); int lat = (int) (latitude * 100000); int lon = (int) (longitude * 100000); String document = "<location-document>" + "<location lon='" + lon + "' lat='" + lat + "' label='You are here' description='You' zoom='0' />" + "<location lon='742733' lat='4373930' label='Hotel de Paris' description='Hotel de Paris' address='Palace du Casino' postalCode='98000' phone='37798063000' zoom='0' />" + "</location-document>"; // Invoke.invokeApplication(Invoke.APP_TYPE_MAPS, new MapsArguments( MapsArguments.ARG_LOCATION_DOCUMENT, document)); _middle.add(new SeparatorField()); surroundingVenues(); _middle.add(new RichTextField("max lat: " + max_lat)); _middle.add(new RichTextField("min lat: " + min_lat)); _middle.add(new RichTextField("max lon: " + max_lon)); _middle.add(new RichTextField("min lon: " + min_lon)); } private void surroundingVenues() { double point_1_latitude_in_degrees = latitude; double point_1_longitude_in_degrees= longitude; // diagonal distance + error margin double distance_in_miles = (5 * 1.90359441) + 10; getCords (point_1_latitude_in_degrees, point_1_longitude_in_degrees, distance_in_miles, 45); double lat_limit_1 = latitude_in_degrees; double lon_limit_1 = longitude_in_degrees; getCords (point_1_latitude_in_degrees, point_1_longitude_in_degrees, distance_in_miles, 135); double lat_limit_2 = latitude_in_degrees; double lon_limit_2 = longitude_in_degrees; getCords (point_1_latitude_in_degrees, point_1_longitude_in_degrees, distance_in_miles, -135); double lat_limit_3 = latitude_in_degrees; double lon_limit_3 = longitude_in_degrees; getCords (point_1_latitude_in_degrees, point_1_longitude_in_degrees, distance_in_miles, -45); double lat_limit_4 = latitude_in_degrees; double lon_limit_4 = longitude_in_degrees; double mx1 = Math.max(lat_limit_1, lat_limit_2); double mx2 = Math.max(lat_limit_3, lat_limit_4); max_lat = Math.max(mx1, mx2); double mm1 = Math.min(lat_limit_1, lat_limit_2); double mm2 = Math.min(lat_limit_3, lat_limit_4); min_lat = Math.max(mm1, mm2); double mlon1 = Math.max(lon_limit_1, lon_limit_2); double mlon2 = Math.max(lon_limit_3, lon_limit_4); max_lon = Math.max(mlon1, mlon2); double minl1 = Math.min(lon_limit_1, lon_limit_2); double minl2 = Math.min(lon_limit_3, lon_limit_4); min_lon = Math.max(minl1, minl2); //$qry = "SELECT DISTINCT zip.zipcode, zip.latitude, zip.longitude, sg_stores.* FROM zip JOIN store_finder AS sg_stores ON sg_stores.zip=zip.zipcode WHERE zip.latitude<=$lat_limit_max AND zip.latitude>=$lat_limit_min AND zip.longitude<=$lon_limit_max AND zip.longitude>=$lon_limit_min"; } private void getCords(double point_1_latitude, double point_1_longitude, double distance, int degs) { double m_EquatorialRadiusInMeters = 6366564.86; double m_Flattening=0; double distance_in_meters = distance * 1609.344 ; double direction_in_radians = Math.toRadians( degs ); double eps = 0.000000000000005; double r = 1.0 - m_Flattening; double point_1_latitude_in_radians = Math.toRadians( point_1_latitude ); double point_1_longitude_in_radians = Math.toRadians( point_1_longitude ); double tangent_u = (r * Math.sin( point_1_latitude_in_radians ) ) / Math.cos( point_1_latitude_in_radians ); double sine_of_direction = Math.sin( direction_in_radians ); double cosine_of_direction = Math.cos( direction_in_radians ); double heading_from_point_2_to_point_1_in_radians = 0.0; if ( cosine_of_direction != 0.0 ) { heading_from_point_2_to_point_1_in_radians = atan2( tangent_u, cosine_of_direction ) * 2.0; } double cu = 1.0 / Math.sqrt( ( tangent_u * tangent_u ) + 1.0 ); double su = tangent_u * cu; double sa = cu * sine_of_direction; double c2a = ( (-sa) * sa ) + 1.0; double x= Math.sqrt( ( ( ( 1.0 /r /r ) - 1.0 ) * c2a ) + 1.0 ) + 1.0; x= (x- 2.0 ) / x; double c= 1.0 - x; c= ( ( (x * x) / 4.0 ) + 1.0 ) / c; double d= ( ( 0.375 * (x * x) ) -1.0 ) * x; tangent_u = distance_in_meters /r / m_EquatorialRadiusInMeters /c; double y= tangent_u; boolean exit_loop = false; double cosine_of_y = 0.0; double cz = 0.0; double e = 0.0; double term_1 = 0.0; double term_2 = 0.0; double term_3 = 0.0; double sine_of_y = 0.0; while( exit_loop != true ) { sine_of_y = Math.sin(y); cosine_of_y = Math.cos(y); cz = Math.cos( heading_from_point_2_to_point_1_in_radians + y); e = (cz * cz * 2.0 ) - 1.0; c = y; x = e * cosine_of_y; y = (e + e) - 1.0; term_1 = ( sine_of_y * sine_of_y * 4.0 ) - 3.0; term_2 = ( ( term_1 * y * cz * d) / 6.0 ) + x; term_3 = ( ( term_2 * d) / 4.0 ) -cz; y= ( term_3 * sine_of_y * d) + tangent_u; if ( Math.abs(y - c) > eps ) { exit_loop = false; } else { exit_loop = true; } } heading_from_point_2_to_point_1_in_radians = ( cu * cosine_of_y * cosine_of_direction ) - ( su * sine_of_y ); c = r * Math.sqrt( ( sa * sa ) + ( heading_from_point_2_to_point_1_in_radians * heading_from_point_2_to_point_1_in_radians ) ); d = ( su * cosine_of_y ) + ( cu * sine_of_y * cosine_of_direction ); double point_2_latitude_in_radians = atan2(d, c); c = ( cu * cosine_of_y ) - ( su * sine_of_y * cosine_of_direction ); x = atan2( sine_of_y * sine_of_direction, c); c = ( ( ( ( ( -3.0 * c2a ) + 4.0 ) * m_Flattening ) + 4.0 ) * c2a * m_Flattening ) / 16.0; d = ( ( ( (e * cosine_of_y * c) + cz ) * sine_of_y * c) + y) * sa; double point_2_longitude_in_radians = ( point_1_longitude_in_radians + x) - ( ( 1.0 - c) * d * m_Flattening ); heading_from_point_2_to_point_1_in_radians = atan2( sa, heading_from_point_2_to_point_1_in_radians ) + Math.PI; latitude_in_degrees = Math.toRadians( point_2_latitude_in_radians ); longitude_in_degrees = Math.toRadians( point_2_longitude_in_radians ); } public double atan2(double y, double x) { double coeff_1 = Math.PI / 4d; double coeff_2 = 3d * coeff_1; double abs_y = Math.abs(y)+ 1e-10f; double r, angle; if (x >= 0d) { r = (x - abs_y) / (x + abs_y); angle = coeff_1; } else { r = (x + abs_y) / (abs_y - x); angle = coeff_2; } angle += (0.1963f * r * r - 0.9817f) * r; return y < 0.0f ? -angle : angle; } private Vector fetchVenues(double max_lat, double min_lat, double max_lon, double min_lon) { return new Vector(); } private class LocationListenerImpl implements LocationListener { public void locationUpdated(LocationProvider provider, Location location) { if(location.isValid()) { nearBy.this.longitude = location.getQualifiedCoordinates().getLongitude(); nearBy.this.latitude = location.getQualifiedCoordinates().getLatitude(); //double altitude = location.getQualifiedCoordinates().getAltitude(); //float speed = location.getSpeed(); } } public void providerStateChanged(LocationProvider provider, int newState) { // MUST implement this. Should probably do something useful with it as well. } } } please excuse the mess. I have the user lat long hard coded since I do not have GPS functional yet. You can see the SQL query commented out to know how I plan on using the min and max lat and long values. Any help is appreciated. Thanks

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• auto vectorization on double and ffast-math

  - by wiso

  Why is mandatory to use -ffast-math with g++ to achieve vectorization of loop using doubles? I don't like ffast-math because I don't want to loose precision.

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• Simple Math Multiplayer game - is Ajax sufficient?

  - by Christian Strang

  I'm planning to create a simple math multiplayer game and I plan to just use Ajax for the server/client communication but I'm not sure if this is sufficient or if I need a socket server. The game will look like this: 2-4 users all get a simple math task (like: "37 + 14") they have to solve it as fast as possible first user who solves it is the winner I will track the time for each user, since the game started, on the client side and everytime a user gives an answer, the answer and the passed time will be send to the server. Additionally I'll add a function which will check every 3 seconds if the other users finished, how much time they needed and who won. Do you think this is possible just using Ajax? What alternatives are there?

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• Is there an easy way to type in common math symbols?

  - by srcspider

  Disclaimer: I'm sure someone is going to moan about easy-of-use, for the purpose of this question consider readability to be the only factor that matters So I found this site that converts to easting northing, it's not really important what that even means but here's how the piece of javascript looks. /** * Convert Ordnance Survey grid reference easting/northing coordinate to (OSGB36) latitude/longitude * * @param {OsGridRef} gridref - easting/northing to be converted to latitude/longitude * @returns {LatLonE} latitude/longitude (in OSGB36) of supplied grid reference */ OsGridRef.osGridToLatLong = function(gridref) { var E = gridref.easting; var N = gridref.northing; var a = 6377563.396, b = 6356256.909; // Airy 1830 major & minor semi-axes var F0 = 0.9996012717; // NatGrid scale factor on central meridian var f0 = 49*Math.PI/180, ?0 = -2*Math.PI/180; // NatGrid true origin var N0 = -100000, E0 = 400000; // northing & easting of true origin, metres var e2 = 1 - (b*b)/(a*a); // eccentricity squared var n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n; // n, n², n³ var f=f0, M=0; do { f = (N-N0-M)/(a*F0) + f; var Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (f-f0); var Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(f-f0) * Math.cos(f+f0); var Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(f-f0)) * Math.cos(2*(f+f0)); var Md = (35/24)*n3 * Math.sin(3*(f-f0)) * Math.cos(3*(f+f0)); M = b * F0 * (Ma - Mb + Mc - Md); // meridional arc } while (N-N0-M >= 0.00001); // ie until < 0.01mm var cosf = Math.cos(f), sinf = Math.sin(f); var ? = a*F0/Math.sqrt(1-e2*sinf*sinf); // nu = transverse radius of curvature var ? = a*F0*(1-e2)/Math.pow(1-e2*sinf*sinf, 1.5); // rho = meridional radius of curvature var ?2 = ?/?-1; // eta = ? var tanf = Math.tan(f); var tan2f = tanf*tanf, tan4f = tan2f*tan2f, tan6f = tan4f*tan2f; var secf = 1/cosf; var ?3 = ?*?*?, ?5 = ?3*?*?, ?7 = ?5*?*?; var VII = tanf/(2*?*?); var VIII = tanf/(24*?*?3)*(5+3*tan2f+?2-9*tan2f*?2); var IX = tanf/(720*?*?5)*(61+90*tan2f+45*tan4f); var X = secf/?; var XI = secf/(6*?3)*(?/?+2*tan2f); var XII = secf/(120*?5)*(5+28*tan2f+24*tan4f); var XIIA = secf/(5040*?7)*(61+662*tan2f+1320*tan4f+720*tan6f); var dE = (E-E0), dE2 = dE*dE, dE3 = dE2*dE, dE4 = dE2*dE2, dE5 = dE3*dE2, dE6 = dE4*dE2, dE7 = dE5*dE2; f = f - VII*dE2 + VIII*dE4 - IX*dE6; var ? = ?0 + X*dE - XI*dE3 + XII*dE5 - XIIA*dE7; return new LatLonE(f.toDegrees(), ?.toDegrees(), GeoParams.datum.OSGB36); } I found that to be a really nice way of writing an algorythm, at least as far as redability is concerned. Is there any way to easily write the special symbols. And by easily write I mean NOT copy/paste them.

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• how to make a function recursive

  - by tom smith

  i have this huge function and i am wondering how to make it recursive. i have the base case which should never come true, so it should always go to else and keep calling itself with the variable t increases. any help would be great thanks def draw(x, y, t, planets): if 'Satellites' in planets["Moon"]: print ("fillcircle", x, y, planets["Moon"]['Radius']*scale) else: while True: print("refresh") print("colour 0 0 0") print("clear") print("colour 255 255 255") print("fillcircle",x,y,planets['Sun']['Radius']*scale) print("text ", "\"Sun\"",x+planets['Sun']['Radius']*scale,y) if "Mercury" in planets: r_Mercury=planets['Mercury']['Orbital Radius']*scale; print("circle",x,y,r_Mercury) r_Xmer=x+math.sin(t*2*math.pi/planets['Mercury']['Period'])*r_Mercury r_Ymer=y+math.cos(t*2*math.pi/planets['Mercury']['Period'])*r_Mercury print("fillcircle",r_Xmer,r_Ymer,3) print("text ", "\"Mercury\"",r_Xmer+planets['Mercury']['Radius']*scale,r_Ymer) if "Venus" in planets: r_Venus=planets['Venus']['Orbital Radius']*scale; print("circle",x,y,r_Venus) r_Xven=x+math.sin(t*2*math.pi/planets['Venus']['Period'])*r_Venus r_Yven=y+math.cos(t*2*math.pi/planets['Venus']['Period'])*r_Venus print("fillcircle",r_Xven,r_Yven,3) print("text ", "\"Venus\"",r_Xven+planets['Venus']['Radius']*scale,r_Yven) if "Earth" in planets: r_Earth=planets['Earth']['Orbital Radius']*scale; print("circle",x,y,r_Earth) r_Xe=x+math.sin(t*2*math.pi/planets['Earth']['Period'])*r_Earth r_Ye=y+math.cos(t*2*math.pi/planets['Earth']['Period'])*r_Earth print("fillcircle",r_Xe,r_Ye,3) print("text ", "\"Earth\"",r_Xe+planets['Earth']['Radius']*scale,r_Ye) if "Moon" in planets: r_Moon=planets['Moon']['Orbital Radius']*scale; print("circle",r_Xe,r_Ye,r_Moon) r_Xm=r_Xe+math.sin(t*2*math.pi/planets['Moon']['Period'])*r_Moon r_Ym=r_Ye+math.cos(t*2*math.pi/planets['Moon']['Period'])*r_Moon print("fillcircle",r_Xm,r_Ym,3) print("text ", "\"Moon\"",r_Xm+planets['Moon']['Radius']*scale,r_Ym) if "Mars" in planets: r_Mars=planets['Mars']['Orbital Radius']*scale; print("circle",x,y,r_Mars) r_Xmar=x+math.sin(t*2*math.pi/planets['Mars']['Period'])*r_Mars r_Ymar=y+math.cos(t*2*math.pi/planets['Mars']['Period'])*r_Mars print("fillcircle",r_Xmar,r_Ymar,3) print("text ", "\"Mars\"",r_Xmar+planets['Mars']['Radius']*scale,r_Ymar) if "Phobos" in planets: r_Phobos=planets['Phobos']['Orbital Radius']*scale; print("circle",r_Xmar,r_Ymar,r_Phobos) r_Xpho=r_Xmar+math.sin(t*2*math.pi/planets['Phobos']['Period'])*r_Phobos r_Ypho=r_Ymar+math.cos(t*2*math.pi/planets['Phobos']['Period'])*r_Phobos print("fillcircle",r_Xpho,r_Ypho,3) print("text ", "\"Phobos\"",r_Xpho+planets['Phobos']['Radius']*scale,r_Ypho) if "Deimos" in planets: r_Deimos=planets['Deimos']['Orbital Radius']*scale; print("circle",r_Xmar,r_Ymar,r_Deimos) r_Xdei=r_Xmar+math.sin(t*2*math.pi/planets['Deimos']['Period'])*r_Deimos r_Ydei=r_Ymar+math.cos(t*2*math.pi/planets['Deimos']['Period'])*r_Deimos print("fillcircle",r_Xdei,r_Ydei,3) print("text ", "\"Deimos\"",r_Xpho+planets['Deimos']['Radius']*scale,r_Ydei) if "Ceres" in planets: r_Ceres=planets['Ceres']['Orbital Radius']*scale; print("circle",x,y,r_Ceres) r_Xcer=x+math.sin(t*2*math.pi/planets['Ceres']['Period'])*r_Ceres r_Ycer=y+math.cos(t*2*math.pi/planets['Ceres']['Period'])*r_Ceres print("fillcircle",r_Xcer,r_Ycer,3) print("text ", "\"Ceres\"",r_Xcer+planets['Ceres']['Radius']*scale,r_Ycer) if "Jupiter" in planets: r_Jupiter=planets['Jupiter']['Orbital Radius']*scale; print("circle",x,y,r_Jupiter) r_Xjup=x+math.sin(t*2*math.pi/planets['Jupiter']['Period'])*r_Jupiter r_Yjup=y+math.cos(t*2*math.pi/planets['Jupiter']['Period'])*r_Jupiter print("fillcircle",r_Xjup,r_Yjup,3) print("text ", "\"Jupiter\"",r_Xjup+planets['Jupiter']['Radius']*scale,r_Yjup) if "Io" in planets: r_Io=planets['Io']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Io) r_Xio=r_Xjup+math.sin(t*2*math.pi/planets['Io']['Period'])*r_Io r_Yio=r_Yjup+math.cos(t*2*math.pi/planets['Io']['Period'])*r_Io print("fillcircle",r_Xio,r_Yio,3) print("text ", "\"Io\"",r_Xio+planets['Io']['Radius']*scale,r_Yio) if "Europa" in planets: r_Europa=planets['Europa']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Europa) r_Xeur=r_Xjup+math.sin(t*2*math.pi/planets['Europa']['Period'])*r_Europa r_Yeur=r_Yjup+math.cos(t*2*math.pi/planets['Europa']['Period'])*r_Europa print("fillcircle",r_Xeur,r_Yeur,3) print("text ", "\"Europa\"",r_Xeur+planets['Europa']['Radius']*scale,r_Yeur) if "Ganymede" in planets: r_Ganymede=planets['Ganymede']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Ganymede) r_Xgan=r_Xjup+math.sin(t*2*math.pi/planets['Ganymede']['Period'])*r_Ganymede r_Ygan=r_Yjup+math.cos(t*2*math.pi/planets['Ganymede']['Period'])*r_Ganymede print("fillcircle",r_Xgan,r_Ygan,3) print("text ", "\"Ganymede\"",r_Xgan+planets['Ganymede']['Radius']*scale,r_Ygan) if "Callisto" in planets: r_Callisto=planets['Callisto']['Orbital Radius']*scale; print("circle",r_Xjup,r_Yjup,r_Callisto) r_Xcal=r_Xjup+math.sin(t*2*math.pi/planets['Callisto']['Period'])*r_Callisto r_Ycal=r_Yjup+math.cos(t*2*math.pi/planets['Callisto']['Period'])*r_Callisto print("fillcircle",r_Xcal,r_Ycal,3) print("text ", "\"Callisto\"",r_Xcal+planets['Callisto']['Radius']*scale,r_Ycal) if "Saturn" in planets: r_Saturn=planets['Saturn']['Orbital Radius']*scale; print("circle",x,y,r_Saturn) r_Xsat=x+math.sin(t*2*math.pi/planets['Saturn']['Period'])*r_Saturn r_Ysat=y+math.cos(t*2*math.pi/planets['Saturn']['Period'])*r_Saturn print("fillcircle",r_Xsat,r_Ysat,3) print("text ", "\"Saturn\"",r_Xsat+planets['Saturn']['Radius']*scale,r_Ysat) if "Mimas" in planets: r_Mimas=planets['Mimas']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Mimas) r_Xmim=r_Xsat+math.sin(t*2*math.pi/planets['Mimas']['Period'])*r_Mimas r_Ymim=r_Ysat+math.cos(t*2*math.pi/planets['Mimas']['Period'])*r_Mimas print("fillcircle",r_Xmim,r_Ymim,3) print("text ", "\"Mimas\"",r_Xmim+planets['Mimas']['Radius']*scale,r_Ymim) if "Enceladus" in planets: r_Enceladus=planets['Enceladus']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Enceladus) r_Xenc=r_Xsat+math.sin(t*2*math.pi/planets['Enceladus']['Period'])*r_Enceladus r_Yenc=r_Ysat+math.cos(t*2*math.pi/planets['Enceladus']['Period'])*r_Enceladus print("fillcircle",r_Xenc,r_Yenc,3) print("text ", "\"Enceladus\"",r_Xenc+planets['Enceladus']['Radius']*scale,r_Yenc) if "Tethys" in planets: r_Tethys=planets['Tethys']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Tethys) r_Xtet=r_Xsat+math.sin(t*2*math.pi/planets['Tethys']['Period'])*r_Tethys r_Ytet=r_Ysat+math.cos(t*2*math.pi/planets['Tethys']['Period'])*r_Tethys print("fillcircle",r_Xtet,r_Ytet,3) print("text ", "\"Tethys\"",r_Xtet+planets['Tethys']['Radius']*scale,r_Ytet) if "Dione" in planets: r_Dione=planets['Dione']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Dione) r_Xdio=r_Xsat+math.sin(t*2*math.pi/planets['Dione']['Period'])*r_Dione r_Ydio=r_Ysat+math.cos(t*2*math.pi/planets['Dione']['Period'])*r_Dione print("fillcircle",r_Xdio,r_Ydio,3) print("text ", "\"Dione\"",r_Xdio+planets['Dione']['Radius']*scale,r_Ydio) if "Rhea" in planets: r_Rhea=planets['Rhea']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Rhea) r_Xrhe=r_Xsat+math.sin(t*2*math.pi/planets['Rhea']['Period'])*r_Rhea r_Yrhe=r_Ysat+math.cos(t*2*math.pi/planets['Rhea']['Period'])*r_Rhea print("fillcircle",r_Xrhe,r_Yrhe,3) print("text ", "\"Rhea\"",r_Xrhe+planets['Rhea']['Radius']*scale,r_Yrhe) if "Titan" in planets: r_Titan=planets['Titan']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Titan) r_Xtit=r_Xsat+math.sin(t*2*math.pi/planets['Titan']['Period'])*r_Titan r_Ytit=r_Ysat+math.cos(t*2*math.pi/planets['Titan']['Period'])*r_Titan print("fillcircle",r_Xtit,r_Ytit,3) print("text ", "\"Titan\"",r_Xtit+planets['Titan']['Radius']*scale,r_Ytit) if "Iapetus" in planets: r_Iapetus=planets['Iapetus']['Orbital Radius']*scale; print("circle",r_Xsat,r_Ysat,r_Iapetus) r_Xiap=r_Xsat+math.sin(t*2*math.pi/planets['Iapetus']['Period'])*r_Iapetus r_Yiap=r_Ysat+math.cos(t*2*math.pi/planets['Iapetus']['Period'])*r_Iapetus print("fillcircle",r_Xiap,r_Yiap,3) print("text ", "\"Iapetus\"",r_Xiap+planets['Iapetus']['Radius']*scale,r_Yiap) if "Uranus" in planets: r_Uranus=planets['Uranus']['Orbital Radius']*scale; print("circle",x,y,r_Uranus) r_Xura=x+math.sin(t*2*math.pi/planets['Uranus']['Period'])*r_Uranus r_Yura=y+math.cos(t*2*math.pi/planets['Uranus']['Period'])*r_Uranus print("fillcircle",r_Xura,r_Yura,3) print("text ", "\"Uranus\"",r_Xura+planets['Uranus']['Radius']*scale,r_Yura) if "Puck" in planets: r_Puck=planets['Puck']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Puck) r_Xpuc=r_Xura+math.sin(t*2*math.pi/planets['Puck']['Period'])*r_Puck r_Ypuc=r_Yura+math.cos(t*2*math.pi/planets['Puck']['Period'])*r_Puck print("fillcircle",r_Xpuc,r_Ypuc,3) print("text ", "\"Puck\"",r_Xpuc+planets['Puck']['Radius']*scale,r_Ypuc) if "Miranda" in planets: r_Miranda=planets['Miranda']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Miranda) r_Xmira=r_Xura+math.sin(t*2*math.pi/planets['Miranda']['Period'])*r_Miranda r_Ymira=r_Yura+math.cos(t*2*math.pi/planets['Miranda']['Period'])*r_Miranda print("fillcircle",r_Xmira,r_Ymira,3) print("text ", "\"Miranda\"",r_Xmira+planets['Miranda']['Radius']*scale,r_Ymira) if "Ariel" in planets: r_Ariel=planets['Ariel']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Ariel) r_Xari=r_Xura+math.sin(t*2*math.pi/planets['Ariel']['Period'])*r_Ariel r_Yari=r_Yura+math.cos(t*2*math.pi/planets['Ariel']['Period'])*r_Ariel print("fillcircle",r_Xari,r_Yari,3) print("text ", "\"Ariel\"",r_Xari+planets['Ariel']['Radius']*scale,r_Yari) if "Umbriel" in planets: r_Umbriel=planets['Umbriel']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Umbriel) r_Xumb=r_Xura+math.sin(t*2*math.pi/planets['Umbriel']['Period'])*r_Umbriel r_Yumb=r_Yura+math.cos(t*2*math.pi/planets['Umbriel']['Period'])*r_Umbriel print("fillcircle",r_Xumb,r_Yumb,3) print("text ", "\"Umbriel\"",r_Xumb+planets['Umbriel']['Radius']*scale,r_Yumb) if "Titania" in planets: r_Titania=planets['Titania']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Titania) r_Xtita=r_Xura+math.sin(t*2*math.pi/planets['Titania']['Period'])*r_Titania r_Ytita=r_Yura+math.cos(t*2*math.pi/planets['Titania']['Period'])*r_Titania print("fillcircle",r_Xtita,r_Ytita,3) print("text ", "\"Titania\"",r_Xtita+planets['Titania']['Radius']*scale,r_Ytita) if "Oberon" in planets: r_Oberon=planets['Oberon']['Orbital Radius']*scale; print("circle",r_Xura,r_Yura,r_Oberon) r_Xober=r_Xura+math.sin(t*2*math.pi/planets['Oberon']['Period'])*r_Oberon r_Yober=r_Yura+math.cos(t*2*math.pi/planets['Oberon']['Period'])*r_Oberon print("fillcircle",r_Xober,r_Yober,3) print("text ", "\"Oberon\"",r_Xober+planets['Oberon']['Radius']*scale,r_Yober) if "Neptune" in planets: r_Neptune=planets['Neptune']['Orbital Radius']*scale; print("circle",x,y,r_Neptune) r_Xnep=x+math.sin(t*2*math.pi/planets['Neptune']['Period'])*r_Neptune r_Ynep=y+math.cos(t*2*math.pi/planets['Neptune']['Period'])*r_Neptune print("fillcircle",r_Xnep,r_Ynep,3) print("text ", "\"Neptune\"",r_Xnep+planets['Neptune']['Radius']*scale,r_Ynep) if "Titan" in planets: r_Titan=planets['Titan']['Orbital Radius']*scale; print("circle",r_Xnep,r_Ynep,r_Titan) r_Xtita=r_Xnep+math.sin(t*2*math.pi/planets['Titan']['Period'])*r_Titan r_Ytita=r_Ynep+math.cos(t*2*math.pi/planets['Titan']['Period'])*r_Titan print("fillcircle",r_Xtita,r_Ytita,3) print("text ", "\"Titan\"",r_Xtita+planets['Titan']['Radius']*scale,r_Ytita) t += 0.003 print(draw(x, y, t, planets))

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• Using delegates in C# (Part 2)

  - by rajbk

  Part 1 of this post can be read here. We are now about to see the different syntaxes for invoking a delegate and some c# syntactic sugar which allows you to code faster. We have the following console application. 1: public delegate double Operation(double x, double y); 2:  3: public class Program 4: { 5: [STAThread] 6: static void Main(string[] args) 7: { 8: Operation op1 = new Operation(Division); 9: double result = op1.Invoke(10, 5); 10: 11: Console.WriteLine(result); 12: Console.ReadLine(); 13: } 14: 15: static double Division(double x, double y) { 16: return x / y; 17: } 18: } Line 1 defines a delegate type called Operation with input parameters (double x, double y) and a return type of double. On Line 8, we create an instance of this delegate and set the target to be a static method called Division (Line 15) On Line 9, we invoke the delegate (one entry in the invocation list). The program outputs 5 when run. The language provides shortcuts for creating a delegate and invoking it (see line 9 and 11). Line 9 is a syntactical shortcut for creating an instance of the Delegate. The C# compiler will infer on its own what the delegate type is and produces intermediate language that creates a new instance of that delegate. Line 11 uses a a syntactical shortcut for invoking the delegate by removing the Invoke method. The compiler sees the line and generates intermediate language which invokes the delegate. When this code is compiled, the generated IL will look exactly like the IL of the compiled code above. 1: public delegate double Operation(double x, double y); 2:  3: public class Program 4: { 5: [STAThread] 6: static void Main(string[] args) 7: { 8: //shortcut constructor syntax 9: Operation op1 = Division; 10: //shortcut invoke syntax 11: double result = op1(10, 2); 12: 13: Console.WriteLine(result); 14: Console.ReadLine(); 15: } 16: 17: static double Division(double x, double y) { 18: return x / y; 19: } 20: } C# 2.0 introduced Anonymous Methods. Anonymous methods avoid the need to create a separate method that contains the same signature as the delegate type. Instead you write the method body in-line. There is an interesting fact about Anonymous methods and closures which won’t be covered here. Use your favorite search engine ;-)We rewrite our code to use anonymous methods (see line 9): 1: public delegate double Operation(double x, double y); 2:  3: public class Program 4: { 5: [STAThread] 6: static void Main(string[] args) 7: { 8: //Anonymous method 9: Operation op1 = delegate(double x, double y) { 10: return x / y; 11: }; 12: double result = op1(10, 2); 13: 14: Console.WriteLine(result); 15: Console.ReadLine(); 16: } 17: 18: static double Division(double x, double y) { 19: return x / y; 20: } 21: } We could rewrite our delegate to be of a generic type like so (see line 2 and line 9). You will see why soon. 1: //Generic delegate 2: public delegate T Operation<T>(T x, T y); 3:  4: public class Program 5: { 6: [STAThread] 7: static void Main(string[] args) 8: { 9: Operation<double> op1 = delegate(double x, double y) { 10: return x / y; 11: }; 12: double result = op1(10, 2); 13: 14: Console.WriteLine(result); 15: Console.ReadLine(); 16: } 17: 18: static double Division(double x, double y) { 19: return x / y; 20: } 21: } The .NET 3.5 framework introduced a whole set of predefined delegates for us including public delegate TResult Func<T1, T2, TResult>(T1 arg1, T2 arg2); Our code can be modified to use this delegate instead of the one we declared. Our delegate declaration has been removed and line 7 has been changed to use the Func delegate type. 1: public class Program 2: { 3: [STAThread] 4: static void Main(string[] args) 5: { 6: //Func is a delegate defined in the .NET 3.5 framework 7: Func<double, double, double> op1 = delegate (double x, double y) { 8: return x / y; 9: }; 10: double result = op1(10, 2); 11: 12: Console.WriteLine(result); 13: Console.ReadLine(); 14: } 15: 16: static double Division(double x, double y) { 17: return x / y; 18: } 19: } .NET 3.5 also introduced lambda expressions. A lambda expression is an anonymous function that can contain expressions and statements, and can be used to create delegates or expression tree types. We change our code to use lambda expressions. 1: public class Program 2: { 3: [STAThread] 4: static void Main(string[] args) 5: { 6: //lambda expression 7: Func<double, double, double> op1 = (x, y) => x / y; 8: double result = op1(10, 2); 9: 10: Console.WriteLine(result); 11: Console.ReadLine(); 12: } 13: 14: static double Division(double x, double y) { 15: return x / y; 16: } 17: } C# 3.0 introduced the keyword var (implicitly typed local variable) where the type of the variable is inferred based on the type of the associated initializer expression. We can rewrite our code to use var as shown below (line 7).  The implicitly typed local variable op1 is inferred to be a delegate of type Func<double, double, double> at compile time. 1: public class Program 2: { 3: [STAThread] 4: static void Main(string[] args) 5: { 6: //implicitly typed local variable 7: var op1 = (x, y) => x / y; 8: double result = op1(10, 2); 9: 10: Console.WriteLine(result); 11: Console.ReadLine(); 12: } 13: 14: static double Division(double x, double y) { 15: return x / y; 16: } 17: } You have seen how we can write code in fewer lines by using a combination of the Func delegate type, implicitly typed local variables and lambda expressions.

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• Javas Math.sin() produces NaN all the time

  - by milan1612

  Forgive me if this is a dumb beginners problem, but I really don't get it. I have a member variable declared like so: public Double Value; When I assign 3.14159265 to Value and try to compute the sine of it, this happens: system.out.println(Value.toString()); //outputs 3.14159265 Value = Math.sin(Value); system.out.println(Value.toString()); //outputs NaN In fact, this happens with every single value I tried - even with 0! Math.sin() seems to always produce NaN as a result, regardless of the arguments value. The docs say: If the argument is NaN or an infinity, then the result is NaN. But my argument is clearly not NaN or infinity! What the heck is happening there?

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• How to learn the math behind the code?

  - by Solomon Wise

  I am a 12 year old who has recently gotten into programming. (Although I know that the number of books you have read does not determine your programming competency or ability, just to paint a "map" of where I am in terms of the content I know...) I've finished the books: Python 3 For Absolute Beginners Pro Python Python Standard Library by Example Beautiful Code Agile Web Development With Rails and am about halfway into Programming Ruby. I have written many small programs (One that finds which files have been updated and deleted in a directory, one that compares multiple players' fantasy baseball value, and some text based games, and many more). Obviously, as I'm not some sort of child prodigy, I can't take a formal Computer Science course until high school. I really want to learn computer science to increase my knowledge about the code, and the how the code runs. I've really become interested in the math part after reading the source code for Python's random module. Is there a place where I can learn CS, or programming math online for free, at a level that would be at least partially understandable to a person my age?

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• Java Math.cos() Method Does Not Return 0 When Expected

  - by dimo414

  Using Java on a Windows 7 PC (not sure if that matters) and calling Math.cos() on values that should return 0 (like pi/2) instead returns small values, but small values that, unless I'm misunderstanding, are much greater than 1 ulp off from zero. Math.cos(Math.PI/2) = 6.123233995736766E-17 Math.ulp(Math.cos(Math.PI/2)) = 1.232595164407831E-32 Is this in fact within 1 ulp and I'm simply confused? And would this be an acceptable wrapper method to resolve this minor inaccuracy? public static double cos(double a){ double temp = Math.abs(a % Math.PI); if(temp == Math.PI/2) return 0; return Math.cos(a); }

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• MathType and LibreOffice Math comparison

  - by Agmenor

  In my office my team and I are going to type texts in the future which will include mathematical signs. Two programs are being proposed: LibreOffice Writer + Math or Microsoft Office + MathType. I would like to advocate for the first solution, but I need to know what technical advantages and disadvantages each program has. Compatibility with Ubuntu is an evident and important characteristic for LibreOffice, but could you give some other aspects? As a side question, do you advice any other program, even if not WYSIWYG and thus not my preference in this case?

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• Getting to math applications gradually

  - by den-javamaniac

  I'm currently getting a formal degree related to computation, in particular my current focus is numerical programming, scientific computing and machine learning. I'd love to apply that knowledge in game dev and expand it with statistics, probability theory, and graph theory (probably even linear algebra). The question is: which spheres of gamedev are filled with such math stuff, is it possible to advance in those without being a part of a group of people and how to get to it gradually? P.S.: I've got experience with commercial java dev and am getting my hands on C/C++ at the moment, however, I'm opened to go ahead and try Unity3D and etc.

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• Understanding math used to determine if vector is clockwise / counterclockwise from your vector

  - by MTLPhil

  I'm reading Programming Game AI by Example by Mat Buckland. In the Math & Physics primer chapter there's a listing of the declaration of a class used to represent 2D vectors. This class contains a method called Sign. It's implementation is as follows //------------------------ Sign ------------------------------------------ // // returns positive if v2 is clockwise of this vector, // minus if anticlockwise (Y axis pointing down, X axis to right) //------------------------------------------------------------------------ enum {clockwise = 1, anticlockwise = -1}; inline int Vector2D::Sign(const Vector2D& v2)const { if (y*v2.x > x*v2.y) { return anticlockwise; } else { return clockwise; } } Can someone explain the vector rules that make this hold true? What do the values of y*v2.x and x*v2.y that are being compared actually represent? I'd like to have a solid understanding of why this works rather than just accepting that it does without figuring it out. I feel like it's something really obvious that I'm just not catching on to. Thanks for your help.

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• How to rotate a set of points on z = 0 plane in 3-D, preserving pairwise distances?

  - by cagirici

  I have a set of points double n[] on the plane z = 0. And I have another set of points double[] m on the plane ax + by + cz + d = 0. Length of n is equal to length of m. Also, euclidean distance between n[i] and n[j] is equal to euclidean distance between m[i] and m[j]. I want to rotate n[] in 3-D, such that for all i, n[i] = m[i] would be true. In other words, I want to turn a plane into another plane, preserving the pairwise distances. Here's my code in java. But it does not help so much: double[] rotate(double[] point, double[] currentEquation, double[] targetEquation) { double[] currentNormal = new double[]{currentEquation[0], currentEquation[1], currentEquation[2]}; double[] targetNormal = new double[]{targetEquation[0], targetEquation[1], targetEquation[2]}; targetNormal = normalize(targetNormal); double angle = angleBetween(currentNormal, targetNormal); double[] axis = cross(targetNormal, currentNormal); double[][] R = getRotationMatrix(axis, angle); return rotated; } double[][] getRotationMatrix(double[] axis, double angle) { axis = normalize(axis); double cA = (float)Math.cos(angle); double sA = (float)Math.sin(angle); Matrix I = Matrix.identity(3, 3); Matrix a = new Matrix(axis, 3); Matrix aT = a.transpose(); Matrix a2 = a.times(aT); double[][] B = { {0, axis[2], -1*axis[1]}, {-1*axis[2], 0, axis[0]}, {axis[1], -1*axis[0], 0} }; Matrix A = new Matrix(B); Matrix R = I.minus(a2); R = R.times(cA); R = R.plus(a2); R = R.plus(A.times(sA)); return R.getArray(); } This is what I get. The point set on the right side is actually part of a point set on the left side. But they are on another plane. Here's a 2-D representation of what I try to do: There are two lines. The line on the bottom is the line I have. The line on the top is the target line. The distances are preserved (a, b and c). Edit: I have tried both methods written in answers. They both fail (I guess). Method of Martijn Courteaux public static double[][] getRotationMatrix(double[] v0, double[] v1, double[] v2, double[] u0, double[] u1, double[] u2) { RealMatrix M1 = new Array2DRowRealMatrix(new double[][]{ {1,0,0,-1*v0[0]}, {0,1,0,-1*v0[1]}, {0,0,1,0}, {0,0,0,1} }); RealMatrix M2 = new Array2DRowRealMatrix(new double[][]{ {1,0,0,-1*u0[0]}, {0,1,0,-1*u0[1]}, {0,0,1,-1*u0[2]}, {0,0,0,1} }); Vector3D imX = new Vector3D((v0[1] - v1[1])*(u2[0] - u0[0]) - (v0[1] - v2[1])*(u1[0] - u0[0]), (v0[1] - v1[1])*(u2[1] - u0[1]) - (v0[1] - v2[1])*(u1[1] - u0[1]), (v0[1] - v1[1])*(u2[2] - u0[2]) - (v0[1] - v2[1])*(u1[2] - u0[2]) ).scalarMultiply(1/((v0[0]*v1[1])-(v0[0]*v2[1])-(v1[0]*v0[1])+(v1[0]*v2[1])+(v2[0]*v0[1])-(v2[0]*v1[1]))); Vector3D imZ = new Vector3D(findEquation(u0, u1, u2)); Vector3D imY = Vector3D.crossProduct(imZ, imX); double[] imXn = imX.normalize().toArray(); double[] imYn = imY.normalize().toArray(); double[] imZn = imZ.normalize().toArray(); RealMatrix M = new Array2DRowRealMatrix(new double[][]{ {imXn[0], imXn[1], imXn[2], 0}, {imYn[0], imYn[1], imYn[2], 0}, {imZn[0], imZn[1], imZn[2], 0}, {0, 0, 0, 1} }); RealMatrix rotationMatrix = MatrixUtils.inverse(M2).multiply(M).multiply(M1); return rotationMatrix.getData(); } Method of Sam Hocevar static double[][] makeMatrix(double[] p1, double[] p2, double[] p3) { double[] v1 = normalize(difference(p2,p1)); double[] v2 = normalize(cross(difference(p3,p1), difference(p2,p1))); double[] v3 = cross(v1, v2); double[][] M = { { v1[0], v2[0], v3[0], p1[0] }, { v1[1], v2[1], v3[1], p1[1] }, { v1[2], v2[2], v3[2], p1[2] }, { 0.0, 0.0, 0.0, 1.0 } }; return M; } static double[][] createTransform(double[] A, double[] B, double[] C, double[] P, double[] Q, double[] R) { RealMatrix c = new Array2DRowRealMatrix(makeMatrix(A,B,C)); RealMatrix t = new Array2DRowRealMatrix(makeMatrix(P,Q,R)); return MatrixUtils.inverse(c).multiply(t).getData(); } The blue points are the calculated points. The black lines indicate the offset from the real position.

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