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• Working with vectors and transformations

  - by user29163

  I am going to write an graphical 2D application that allows user to create polygons and transform them through transformation such as rotation an so on. I was hoping someone can give pro and cons arguments for the different choices I got in my mind. (Its all in Java btw!) a). Represent vectors by filling matrices with 'real' numbers. This means making a matrix datas tructure that supports multiplication, transposing etc b). Make a own vector class, such that I can make a matrix class that support those vectors.

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• Do I need the 'w' component in my Vector class?

  - by bobobobo

  Assume you're writing matrix code that handles rotation, translation etc for 3d space. Now the transformation matrices have to be 4x4 to fit the translation component in. However, you don't actually need to store a w component in the vector do you? Even in perspective division, you can simply compute and store w outside of the vector, and perspective divide before returning from the method. For example: // post multiply vec2=matrix*vector Vector operator*( const Matrix & a, const Vector& v ) { Vector r ; // do matrix mult r.x = a._11*v.x + a._12*v.y ... real w = a._41*v.x + a._42*v.y ... // perspective divide r /= w ; return r ; } Is there a point in storing w in the Vector class?

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• Random Vector within a cone

  - by Paul

  I'm looking to create a random vector within a cone given the radius (base). It feels like I've been traversing through many pages on the internet and still I'm no further forward to getting an answer. I was thinking I could get a point within the base of the cone and have it point towards the apex (then just use the inverse of that for my animation) but this seems like an incredibly long winded approach.

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• Effective and simple matching for 2 unequal small-scale point sets

  - by Pavlo Dyban

  I need to match two sets of 3D points, however the number of points in each set can be different. It seems that most algorithms are designed to align images and trimmed to work with hundreds of thousands of points. My case are 50 to 150 points in each of the two sets. So far I have acquainted myself with Iterative Closest Point and Procrustes Matching algorithms. Implementing Procrustes algorithms seems like a total overkill for this small quantity. ICP has many implementations, but I haven't found any readily implemented version accounting for the so-called "outliers" - points without a matching pair. Besides the implementation expense, algorithms like Fractional and Sparse ICP use some statistics information to cancel points that are considered outliers. For series with 50 to 150 points statistic measures are often biased or statistic significance criteria are not met. I know of Assignment Problem in linear optimization, but it is not suitable for cases with unequal sets of points. Are there other, small-scale algorithms that solve the problem of matching 2 point sets? I am looking for algorithm names, scientific papers or C++ implementations. I need some hints to know where to start my search.

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• Java chunk negative number problem

  - by user1990950

  I've got a tile based map, which is divided in chunks. I got a method, which puts tiles in this map and with positive numbers it's working. But when using negative numbers it wont work. This is my setTile method: public static void setTile(int x, int y, Tile tile) { int chunkX = x / Chunk.CHUNK_SIZE, chunkY = y / Chunk.CHUNK_SIZE; IntPair intPair = new IntPair(chunkX, chunkY); world.put(intPair, new Chunk(chunkX, chunkY)); world.get(intPair).setTile(x - chunkX * Chunk.CHUNK_SIZE, y - chunkY * Chunk.CHUNK_SIZE, tile); } This is the setTile method in the chunk class (CHUNK_SIZE is a constant with the value 64): public void setTile(int x, int y, Tile t) { if (x >= 0 && x < CHUNK_SIZE && y >= 0 && y < CHUNK_SIZE) tiles[x][y] = t; } What's wrong with my code?

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• how to calculate intersection time and place of multiple moving arcs

  - by user20733

  I have rocks orbiting moons, moons orbiting planets, planets orbiting suns, and suns orbiting black holes, and the current system could have many many layers of orbitage. the position of any object is a function of time and relative to the object it orbits. (so far so good). now I want to know for a given 2 objects(A,B), a start time and a speed, how can I work out the when and where to go. I can work out where A and B is given a time. so i just need. 1: direction to travel in from A to B(remember B is moving(not in a straight line)) 2: Time to get to b in a straight line. travel must be in a straight line with the shortest possible distance. as an extension to this question, how will i know if its better to wait, EG is it faster to stay on object A and wait for a hour when the objects may be closer, than to set off from A to B at the start. Cheers, it hurt my brain.

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• How can I get a 2D texture to rotate like a compass in XNA?

  - by IronGiraffe

  I'm working on a small maze puzzle game and I'm trying to add a compass to make it somewhat easier for the player to find their way around the maze. The problem is: I'm using XNA's draw method to rotate the arrow and I don't really know how to get it to rotate properly. What I need it to do is point towards the exit from the player's position, but I'm not sure how I can do that. So does anyone know how I can do this? Is there a better way to do it?

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• Accounting for waves when doing planar reflections

  - by CloseReflector

  I've been studying Nvidia's examples from the SDK, in particular the Island11 project and I've found something curious about a piece of HLSL code which corrects the reflections up and down depending on the state of the wave's height. Naturally, after examining the brief paragraph of code: // calculating correction that shifts reflection up/down according to water wave Y position float4 projected_waveheight = mul(float4(input.positionWS.x,input.positionWS.y,input.positionWS.z,1),g_ModelViewProjectionMatrix); float waveheight_correction=-0.5*projected_waveheight.y/projected_waveheight.w; projected_waveheight = mul(float4(input.positionWS.x,-0.8,input.positionWS.z,1),g_ModelViewProjectionMatrix); waveheight_correction+=0.5*projected_waveheight.y/projected_waveheight.w; reflection_disturbance.y=max(-0.15,waveheight_correction+reflection_disturbance.y); My first guess was that it compensates for the planar reflection when it is subjected to vertical perturbation (the waves), shifting the reflected geometry to a point where is nothing and the water is just rendered as if there is nothing there or just the sky: Now, that's the sky reflecting where we should see the terrain's green/grey/yellowish reflection lerped with the water's baseline. My problem is now that I cannot really pinpoint what is the logic behind it. Projecting the actual world space position of a point of the wave/water geometry and then multiplying by -.5f, only to take another projection of the same point, this time with its y coordinate changed to -0.8 (why -0.8?). Clues in the code seem to indicate it was derived with trial and error because there is redundancy. For example, the author takes the negative half of the projected y coordinate (after the w divide): float waveheight_correction=-0.5*projected_waveheight.y/projected_waveheight.w; And then does the same for the second point (only positive, to get a difference of some sort, I presume) and combines them: waveheight_correction+=0.5*projected_waveheight.y/projected_waveheight.w; By removing the divide by 2, I see no difference in quality improvement (if someone cares to correct me, please do). The crux of it seems to be the difference in the projected y, why is that? This redundancy and the seemingly arbitrary selection of -.8f and -0.15f lead me to conclude that this might be a combination of heuristics/guess work. Is there a logical underpinning to this or is it just a desperate hack? Here is an exaggeration of the initial problem which the code fragment fixes, observe on the lowest tessellation level. Hopefully, it might spark an idea I'm missing. The -.8f might be a reference height from which to deduce how much to disturb the texture coordinate sampling the planarly reflected geometry render and -.15f might be the lower bound, a security measure.

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• Smoothing rotation

  - by Lewis

  I've spent the last three days trying to work out how to rotate a sprite smoothly depending on the velocity.x value of the sprite. I'm using this: float Proportion = 9.5; float maxDiff = 200; float rotation = fmaxf(fminf(playerVelocity.x * Proportion, maxDiff), -maxDiff); player.rotation = rotation; The behaviour is what I required but if the velocity changes rapidly then it will look like the sprite will jump to face left or jump to face right. I'll go into the behaviour in a little more detail: 0 velocity = sprite faces forwards negative velocity = sprite faces left depending on value. positive velocity = sprite faces right (higher velocity the more it faces right) same as above. I've read about using interpolation rather than an absolute angle to rotate it to but I don't know how to implement that. I have a physics engine available. There is one other way to get around this: to use += on the rotation angle. The thing is that I would then have to change the equation to produce positive and negative values then to make sure the sprite faces 0 once it reaches 0 velocity again. If I add that in now, it keeps the previous angle even after the velocity has dropped / is dropping. Any ideas/code snippets would be greatly appreciated.

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• Camera placement sphere for an always fully visible object

  - by BengtR

  Given an object: With the bounds [x, y, z, width, height, depth] And an orthographic projection [left, right, bottom, top, near, far] I want to determine the radius of a sphere which allows me to randomly place my camera on so that: The object is fully visible from all positions on this sphere The sphere radius is the smallest possible value while still satisfying 1. Assume the object is centered around the origin. How can I find this radius? I'm currently using sqrt(width^2 + height^2 + depth^2) but I'm not sure that's the correct value, as it doesn't take the camera into account. Thanks for any advice. I'm sorry for confusing a few things here. My comments below should clarify what I'm trying to do actually.

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• How do I create weapon attachments?

  - by Tron86

  My question is; I am developing a game for XNA and I am trying to create a weapon attachment for my player model. My player model loads the .md3 format and reads tags for attachment points. I am able to get the tag of my model's hand. And I am also able to get the tag of my weapon's handle. Each tag I am able to get the rotation and position of and this is how I am calculating it: Model.worldMatrix = Matrix.CreateScale(Model.scale) * Matrix.CreateRotationX(-MathHelper.PiOver2) * Matrix.CreateRotationY(MathHelper.PiOver2); Pretty simple, the player model has a scale and its orientation(it loads on its side so I just use a 90 degree X axis rotation, and a Y axis rotation to face away from the camera). I then calculate the torso tag on the lower body, which gives me a local coordinate at the waist. Then I take that matrix and calculate the tag_weapon in the upper body. This gives me the hand position in local space. I also get the rotation matrix from that tag that I store for later use. All this seems to work fine. Now I move onto my weapon: Matrix weaponWorld = Matrix.CreateScale(CurrentWeapon.scale) * Matrix.CreateRotationX(-MathHelper.PiOver2) * TagRotationMatrix * Matrix.CreateTranslation(HandTag.Position) * Matrix.CreateRotationY(PlayerRotation) * Matrix.CreateTranslation(CollisionBody.Position) * You may notice the weapon matrix gets rotated by 90 degress on the X axis as well. This is because they load in on their sides. Once again this seems pretty simple and follows the SRT order I keep reading about. My TagRotation matrix is the hand's rotation. HandTag.Position is its position in local space. CreateRotationY(PlayerRotation) is the player's rotation in world space, and the CollisionBody.Position is the player's world location. Everything seems to be in order, and almost works in game. However when the gun spawns and follows the player's hand it seems to be flipped on an axis every couple frames. Almost like the X or Y axis is being inversed then put right back. Its hard to explain and I am totally stumped. Even removing all my X axis fixes does nothing to solve the problem. Hopefully I explained everything enough as I am a bit new to this! Thanks!

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• Best way to calculate unit deaths in browser game combat?

  - by MikeCruz13

  My browser game's combat system is written and mechanically functioning well. It's written in PHP and uses a SQL database. I'm happy with the unit balance in relation to one another. I am, however, a little worried about how I'm calculating unit deaths when one player attacks another because the deaths seem to pile up a little fast for my taste. For this system, a battle doesn't just trigger, calculate winner, and end. Instead, it is allowed to go for several rounds (say one round every 15 mins.) until one side passes a threshold of being too strong for the other player and allows players to send reinforcements between rounds. Each round, units pair up and attack each other. Essentially what I do is calculate the damage: AP = Attack Points HP = Hit Points Units AP * Quantity * Random Factors * other factors (such as attrition) I take that and divide by the defending unit's HP to find the number of casualties of defending units. So, for example (simplified to take out some factors), if I have: 500 attackers with 50 AP vs 1000 defenders with 100 HP = 250 deaths. I wonder if that last step could be handled better to reduce the deaths piling up. Some ideas: I just change all the units with more HP? I make sure to set the Attacking unit's AP to be a max of the defender's HP to make sure they only kill 1 unit. (is that fair if I have less huge units vs many small units?) I spread the damage around more by including the defending unit's quantity more? i.e. in that scenario some are dead and some are 50% damage. (How would I track this every round?) Other better mathematical approaches?

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• Why use other number bases when programming

  - by JMD

  My coworkers and I have been bending our minds to figuring out why anyone would go out of their way to program numbers in a base other than base 10. I suggested that perhaps you could optimize longer equations by putting the variables in the correct base you are working with (for instance, if you have only sets of 5 of something with no remainders you could use base 5), but I'm not sure if that's true. Any thoughts?

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• When to use Euler vs Axis angles vs Quaternions?

  - by manning18

  I understand the theory behind each but I was wondering if people could share their experiences in when one would use one over the other For instance, if you were implementing a chase camera, a FPS-style mouse look or writing some kinematic routine, what would be the factors you consider to go with one type over the other and when might you need to convert from one form of representation to the other? Are there certain things that only one system can do that the others can't? (eg smooth interpolation with quaternions)

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• Portal View/Projection Matrix near plane

  - by melak47

  For RenderToTexture/Camera based portal rendering, the basics seems simple enough. However, with a free camera, most of the time it is going to be looking at such portals at an angle: Now a regular near clipping plane will not always work here, it will either intersect with the wall the portal is sitting on, or possibly with objects in front of the wall. The desired near clipping plane would be aligned like the portal, producing a view volume more like this: or this in 3D: So here is my question: How does one construct or "truncate" a view/projection matrix to achieve such an off-camera-normal (near) clipping plane?

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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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• 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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• 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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