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• How can I do fast Triangle/Square vs Triangle collision detection?

  - by Ólafur Waage

  I have a game world where the objects are in a grid based environment with the following restrictions. All of the triangles are 45-90-45 triangles that are unit length. They can only rotate 90°. The squares are of unit length and can not rotate (not that it matters) I have the Square vs Square detection down and it is very very solid and very fast (max vs min on x and y values) Wondering if there are any tricks I can employ since I have these restrictions on the triangles?

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• Voronoi regions of a (convex) polygon.

  - by Xavura

  I'm looking to add circle-polygon collisions to my Separating Axis Theorem collision detection. The metanet software tutorial (http://www.metanetsoftware.com/technique/tutorialA.html#section3) on SAT, which I discovered in the answer to a question I found when searching, talks about voronoi regions. I'm having trouble finding material on how I would calculate these regions for an arbitrary convex polygon and aleo how I would determine if a point is in one + which. The tutorial does contain source code but it's a .fla and I don't have Flash unfortunately.

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• Help with timebased scoring algorithm

  - by Dave

  Im trying to devise an appropriate scoring system for my game. The game in essense has a finite number of tasks to complete (say 20) and the quicker you complete these task, the more points you get. I had devised a basic way of doing this using bands of time multiplied by a score for that band multiplied by the number of tasks solved within that time band i.e. (Time Band) = (Points) 1-5 sec = 15, 5-10 secs = 10, 10-20 secs = 5, 20-30 secs = 3, 40 secs onwards = 1, So for example if I did 3 tasks in the 1-5sec band i'd get 15*3=45points, if i found 10 in the 20-30sec band i'd get 3*10=30 points. Im sure there is a more mathematical way of doing this using powers of some kind but I just can't think how and hoping someone has already done something smilar.. Many thanks in advance

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• Finding maximum number of congruent numbers

  - by Stefan Czarnecki

  Let's say we have a multiset (set with possible duplicates) of integers. We would like to find the size of the largest subset of the multiset such that all numbers in the subset are congruent to each other modulo some m 1. For example: 1 4 7 7 8 10 for m = 2 the subsets are: (1, 7, 7) and (4, 8, 10), both having size 3. for m = 3 the subsets are: (1, 4, 7, 7, 10) and (8), the larger set of size 5. for m = 4 the subsets are: (1), (4, 8), (7, 7), (10), the largest set of size 2. At this moment it is evident that the best answer is 5 for m = 3. Given m we can find the size of the largest subset in linear time. Because the answer is always equal or larger than half of the size of the set, it is enough to check for values of m upto median of the set. Also I noticed it is necessary to check for only prime values of m. However if values in the set are large the algorithm is still rather slow. Does anyone have any ideas how to improve it?

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• Find possible variations of one item out of multiple baskets.

  - by tugberk

  I have three baskets of balls and each of them has 10 balls which have the following numbers: Basket 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Basket 2: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 Basket 3: 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 What would be the possible variations If I were to pick one ball from each basket? I guess this is called as Probability in Mathematics but not sure. How would you write this code in C# (or any other programming language) to get the correct results? Edit: Based on @Kilian Foth's comment, here is the solution in C#: class Program { static void Main(string[] args) { IEnumerable<string> basket1 = new List<string> { "1", "2", "3", "4", "5", "6", "7", "8", "9", "10" }; IEnumerable<string> basket2 = new List<string> { "11", "12", "13", "14", "15", "16", "17", "18", "19", "20" }; IEnumerable<string> basket3 = new List<string> { "21", "22", "23", "24", "25", "26", "27", "28", "29", "30" }; foreach (var item1 in basket1) foreach (var item2 in basket2) foreach (var item3 in basket3) { Console.WriteLine("{0}, {1}, {2}", item1, item2, item3); } Console.ReadLine(); } }

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• Getting Center and Radius of Irregural Object

  - by Moaz ELdeen

  I have drawn an asteroid object manually , and would like to get its center/radius by a specific equation. I think I can get them by calculated and hard-coded values. The code to draw the asteroid: void Asteroid::Draw() { float ratio = app::getWindowWidth()/app::getWindowHeight(); gl::pushMatrices(); gl::translate(m_Pos*ratio); gl::scale(3.5*ratio,3.5*ratio,3.5*ratio); gl::color(ci::Color(1,1,1)); gl::drawLine(Vec2f(-15,0),Vec2f(-10,-5)); gl::drawLine(Vec2f(-10,-5),Vec2f(-5,-5)); gl::drawLine(Vec2f(-5,-5),Vec2f(-5,-8)); gl::drawLine(Vec2f(-5,-8),Vec2f(5,-8)); gl::drawLine(Vec2f(5,-8),Vec2f(5,-5)); gl::drawLine(Vec2f(5,-5),Vec2f(10,-5)); gl::drawLine(Vec2f(10,-5),Vec2f(15,0)); gl::drawLine(Vec2f(15,0),Vec2f(10,5)); gl::drawLine(Vec2f(10,5),Vec2f(-10,5)); gl::drawLine(Vec2f(-10,5),Vec2f(-10,5)); gl::drawLine(Vec2f(-15,0),Vec2f(-10,5)); gl::popMatrices(); } According to the answer I have written that code to calculate the radius, is it correct or not ? cinder::Vec2f Asteroid::getCenter() { return ci::Vec2f(m_Pos.x, m_Pos.y); } double Asteroid::getRadius() { ci::Vec2f _vec = (getCenter()- Vec2f(15,5)); return _vec.length()*0.3f; }

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• Help with a formula for Google Adwords [closed]

  - by XaviEsteve

  Hi guys, This question is more about maths and algorythms in Google Adwords but guess it's the most appropriate community in SE to ask this. I am creating a spreadsheet to calculate Adword formulas and I am stuck in how to calculate the Monthly Net Income for each keyword. I have created a formula which calculates it but can't figure out how to limit the Monthly Budget. The formula I've created is this one: Monthly Net Income = ( DailyClicks x ConversionRate x SaleProfit) - ( CPC x DailyClicks ) There is an example of the formula in the file which is a Google Spreadsheet publicly available here: https://spreadsheets.google.com/ccc?key=0AnQMyM9XJ0EidDB6TUF0OTdaZ2dFb2ZGNmhQeE5lb0E&hl=en_GB#gid=2 (you can create your own copy going to File Make a copy...) I am releasing this set of tools as Public Domain so feel free to use it :) Any help is much appreciated!

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• Separating merged array of arithmetic and geometric series [closed]

  - by user1814037

  Possible Duplicate: Separating merged array of arithmetic and geometric series My friend asked me an interseting question. Given an array of positive integers in increasing order. Seperate them in two series, an arithmetic sequence and geometric sequence. The given array is such that a solution do exist. The union of numbers of the two sequence must be the given array. Both series can have common elements i.e. series need not to be disjoint. The ratio of the geometric series can be fractional. Example: Given series : 2,4,6,8,10,12,25 AP: 2,4,6,8,10,12 GP: 4,10,25 I tried taking few examples but could not reach a general way. Even tried some graph implementation by introducing edges if they follow a particular sequence but could not reach solution.

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• rotate opengl mesh relative to camera

  - by shuall

  I have a cube in opengl. It's position is determined by multiplying it's specific model matrix, the view matrix, and the projection matrix and then passing that to the shader as per this tutorial (http://www.opengl-tutorial.org/beginners-tutorials/tutorial-3-matrices/). I want to rotate it relative to the camera. The only way I can think of getting the correct axis is by multiplying the inverse of the model matrix (because that's where all the previous rotations and tranforms are stored) times the view matrix times the axis of rotation (x or y). I feel like there's got to be a better way to do this like use something other than model, view and projection matrices, or maybe I'm doing something wrong. That's what all the tutorials I've seen use. PS I'm also trying to keep with opengl 4 core stuff. edit: If quaternions would fix my problems, could someone point me to a good tutorial/example for switching from 4x4 matrices to quaternions. I'm a little daunted by the task.

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• Particles are not moving correctly [closed]

  - by cr33p

  I want to make a particle explosion, after something gets destroyed, but somehow only one line of mixed colors show up on the screen. Here's the header: http://pastebin.com/JW5bPLj2 Here's the source: http://pastebin.com/KHmFqytD I don't get what's wrong, as it's nearly the same as in "Programming Linux Games" Can somebody help me fix that? PS: "Uint32 delta" is needed to update the pixels based on time. PSS: Maybe I should add that it's programmed in C and includes SDL. EDIT: Found the problem. It was the "drawParticles" function. The problem was, that I passed a double to "offset" (as particles[i].x, etc are all doubles). So I ended up with values like ~MAX_INT because I didn't cast the doubles properly to ints.

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• Following a set of points?

  - by user1010005

  Lets assume that i have a set of path that an entity should follow : const int Paths = 2 Vector2D<float> Path[Paths] = { Vector2D(100,0),Vector2D(100,50) }; Now i define my entity's position in a 2D vector as follows : Vector2D<float> FollowerPosition(0,0); And now i would like to move the "follower" to the path at index 1 : int PathPosition = 0; //Start with path 1 Currently i do this : Vector2D<float>& Target = Path[PathPosition]; bool Changed = false; if (FollowerPosition.X < Target.X) FollowerPosition.X += Vel,Changed = true; if (FollowerPosition.X > Target.X) FollowerPosition.X -= Vel,Changed = true; if (FollowerPosition.Y < Target.Y) FollowerPosition.Y += Vel;,Changed = true; if (FollowerPosition.Y > Target.Y) FollowerPosition.Y -= Vel,Changed = true; if (!Changed) { PathPosition = PathPosition + 1; if (PathPosition > Paths) PathPosition = 0; } Which works except for one little detail : The movement is not smooth!! ...So i would like to ask if anyone sees anything wrong with my code. Thanks and sorry for my english.

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• How much does game development mathematics change over time?

  - by FlightOfGrey

  This question is mainly aimed at this book, Essential Mathematics for Games and Interactive Applications, Second Edition which I have seen highly recommended all around the internet, so I'm sure there are people on here who own a copy. What I want to know specifically is if any of the information would be out dated since the book was released on June 2, 2008? Also interested to see how the mathematics behind game development has changed over time.

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• Bitmap rotation jitter around pivot

  - by Manderin87

  I am working on a asteriods clone and I have the ship graphic loaded as a 96x96 bitmap. When the player rotates the ship I rotate the bitmap by degree (float). rotation function: if(m_Matrix == null) { m_Matrix = new Matrix(); } else { m_Matrix.reset(); } m_Matrix.setRotate(degree, m_BaseImage.getWidth() / 2, m_BaseImage.getHeight() / 2); m_RotatedImage = Bitmap.createBitmap(m_BaseImage, 0, 0, m_BaseImage.getWidth(), m_BaseImage.getHeight(), m_Matrix, true); draw function: m_Paint.setAntiAlias(true); m_Paint.setFilterBitmap(true); m_Paint.setDither(true); canvas.drawBitmap(m_RotatedImage, (int) posX - m_RotatedImage.getWidth() / 2, (int) posY - m_RotatedImage.getHeight() / 2, m_Paint); When the bitmap is drawn, the bitmap jitters slightly around the pivot. Can anyone fix or tell me why the bitmap is jittering around the pivot? It needs to be smooth.

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• Fiscal quarter vs calendar quarter

  - by Geotarget

  I'm building a Date/Time class with a "configurable quarter" system as follows. User specifies which month the quarter starts at (config) Set of functions to deal with quarters (next quarter, prev quarter, etc) All quarter functions respect the config Now this class is primarily to be used for fiscal quarter calculations. So assuming I have this class with a configurable "quarter" system, would I need another parallel set of functions for calendar quarters too? What are the applications for calendar quarters anyways? By calendar quarters I mean where Q1 is Jan-Mar, and Q4 is Oct-Dec. By fiscal quarters I mean whatever standard your Country uses (in India Q1 starts in April)

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• Determining if something is on the right or left side of an object?

  - by meds

  I have a character in a 3D world which is facing an arbitrary direction on a flat plane, the player can click on the left or right side of the character and based on which side is clicked on a different action happens. How can I determine which side the click occured on? Obviously for straight on ahead (0,0,1) I can simply use the x coordinate of the click point to determine if it's the left or right hand side, but what about other cases?

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• How to offset particles from point of origin

  - by Sun

  Hi I'm having troubles off setting particles from a point of origin. I want my particles to spread out after a certain radius from a the point of origin. For example, this is what I have right now: All particles emitted from a point of origin. What I want is this: Particles are offset from the point of origin by some amount, i.e after the circle. What is the best way to achieve this? At the moment, I have the point of origin, the position of each particle and its rotation angle. Sorry for the poor illustrations. Edit: I was mistaken, when a particle is created, I have only the point of origin. When the particle is created I am able to calculate the rotation of the particle in the update method after it has moved to a new location using atan2() method. This is how I create/manage particles: Created new particle at enemy ship death location, for every new particle which is added to the list, call Update and Draw to update its position, calculate new angle and draw it.

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• How to detect and collide two elastic line segments?

  - by Tautrimas

  There are 4 moving physical nodes in 3D space. They are paired with two elastic line segments / strings (1 <- 2; 3 <- 4). Part I: How to detect the collision of two segments? Part II: On the moment of collision, fifth node is created at the intersection point and here you have the force-based graph. 5-th node (bend point) can slide among the strings as in a real world. Given the new coordinates of 4 nodes, how to calculate the position of the 5-th node on the next frame? I assume string force on the nodes to be F = -k * x where x is the string length. All I came up to is that the force between 5 and 1 equals 5 and 2 (the same with 3 and 4). What are the other properties?.

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• Possible to map mouse coordinates to isometric tiles with this coordinate system?

  - by plukich

  I'm trying to implement mouse interaction in a 2d isometric game, but I'm not sure if it's possible given the coordinate system used for tile maps in the game. I've read some helpful articles like this one: How to convert mouse coordinates to isometric indexes? However, this game's coordinate system is "jagged" for lack of a better word, and looks like this: Is it even possible to map mouse coordinates to this successfully, since the y-axis can't be drawn on this tile-map as a straight line? I've thought about doing odd-y-value translations and even-y-value translations with two different matricies, but that only makes sense going from tile-screen.

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• Y Axis inverted on vertex output

  - by Yonathan Klijnsma

  I've got my project running and somehow it seems my vertex y components are inverted. 10 in the positive on Y goes down and 10 negative on the Y axis goes up. I can't find anything with the initialization and I am not doing any negative scaling in the view matrix. I've never had something like this happen before, does anyone have some tips or things to look for ? How I am sending verteces to the GPU ( Currently intermediate mode ) glVertex3f( x_pos_n, 10, z_pos ); I am using CG in the project but even without shaders the Y axis seems to be inverted.

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• Predictive firing (in a tile-based game)

  - by n00bster

  I have a (turn-based) tile-based game, in which you can shoot at entities. You can move around with mouse and keyboard, it's all tile-based, except that bullets move "freely". I've got it all working just fine except that when I move, and the creatures shoot towards the player, they shoot towards the previous tiles.. resulting in ugly looking "miss hits" or lag. I think I need to implement some kind of predictive firing based on the bullet speed and the distance, but I don't quite know how to implement such a thing... Here's a simplified snip of my firing code. class Weapon { public void fire(int x, int y) { ... ... ... Creature owner = getOwner(); Tile targetTile = Zone.getTileAt(x, y); float dist = Vector.distance(owner.getCenterPosition(), targetTile.getCenterPosition()); Bullet b = new Bullet(); b.setPosition(owner.getCenterPosition()); // Take dist into account in the duration to get constant speed regardless of distance float duration = dist / 600f; // Moves the bullet to the centre of the target tile in the given amount of time (in seconds) b.moveTo(targetTile.getCenterPosition(), duration); // This is what I'm after // Vector v = predict the position // b.moveTo(v, duration); Zone.add(bullet); // Now the bullet gets "ticked" and moveTo will be implemented } } Movement of creatures is as simple as setting the position variable. If you need more information, just ask.

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• Find the new coordinates using a starting point, a distance, and an angle

  - by dqhendricks

  Okay, say I have a point coordinate. var coordinate = { x: 10, y: 20 }; Now I also have a distance and an angle. var distance = 20; var angle = 72; The problem I am trying to solve is, if I want to travel 20 points in the direction of angle from the starting coordinate, how can I find what my new coordinates will be? I know the answer involves things like sin/cosin, because I used to know how to do this, but I have since forgotten the formula. Can anyone help?

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• What is the purpose of the canonical view volume?

  - by breadjesus

  I'm currently learning OpenGL and haven't been able to find an answer to this question. After the projection matrix is applied to the view space, the view space is "normalized" so that all the points lie within the range [-1, 1]. This is generally referred to as the "canonical view volume" or "normalized device coordinates". While I've found plenty of resources telling me about how this happens, I haven't seen anything about why it happens. What is the purpose of this step?

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• Is it possible to procedurally place objects in a non-gridded game?

  - by nickbadal

  I'd like to implement procedural world generation, but I don't want it to look gridded or blocky, where everything is obviously placed on an integer grid. I know that you can do this in gridded worlds by inputting a square's x and y into a noise function, or similar, but is it possible to generate a more natural looking object placement using procedural methods? This is in the context of an adventure game, if it matters. Edit: I guess I should have been a bit more clear in my original question, but I'm mostly wondering about the actual placement of objects in game, e.g. trees, buildings.

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• Why does DirectX use a left-handed coordinate system?

  - by greyfade

  I considered posting on Stack Overflow, but the question strikes me as being far too subjective since I can't think of a reasonable technical explanation for Microsoft's choice in this matter. But this question has bugged me for so long and the issue keeps coming up in one of my projects, and I have never actually seen an attempt at explaining this: OpenGL uses a right-handed coordinate system, where the +Z part of the world coordinate system extends toward the viewer. DirectX uses a left-handed system where the +Z part of the world coordinate extends into the screen, away from the viewer. I never used the Glide API, so I don't know how it worked, but from what I can gather, it uses a left-handed system as well. Is there a technical reason for this? And if not, is there some conceptual advantage to a particular handedness of a coordinate system? Why would one choose one over the other?

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• Algorithm to zoom a plotted function

  - by astinx

  I'm making a game in android and I need plot a function, my algorithm is this: @Override protected void onDraw(Canvas canvas) { float e = 0.5f; //from -x axis to +x evaluate f(x) for (float x = -z(canvas.getWidth()); x < z(canvas.getWidth()); x+=e) { float x1,y1; x1 = x; y1 = f(x); canvas.drawPoint((canvas.getWidth()/2)+x1, (canvas.getHeight()/2)-y1, paintWhite); } super.onDraw(canvas); } This is how it works. If my function is, for example f(x)=x^2, then z(x) is sqrt(x). I evaluate each point between -z(x) to z(x) and then I draw them. As you can see I use the half of the size of the screen to put the function in the middle of the screen. The problem isn't that the code isn't working, actually plots the function. But if the screen is of 320*480 then this function will be really tiny like in the image below. My question is: how can I change this algorithm to scale the function?. BTW what I'm really wanting to do is trace a route to later display an animated sprite, so actually scale this image doesnt gonna help me. I need change the algorithm in order to draw the same interval but in a larger space. Any tip helps, thanks! Current working result Desired result UPDATE: I will try explain more in detail what the problem is. Given this interval [-15...15] (-z(x) to z(x)) I need divide this points in a bigger interval [-320...320] (-x to x). For example, when you use some plotting software like this one. Although the div where is contain the function has 640 px of width, you dont see that the interval is from -320 to 320, you see that the interval is from -6 to 6. How can I achieve this?

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