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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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• 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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• 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 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• Sort rectangles in a grid based on a comparison of the center point of each

  - by Mrwolfy

  If I have a grid of rectangles and I move one of the rectangles, say above and to the left of another rectangle, how would I resort the rectangles? Note the rectangles are in an array, so each rectangle has an index and a matching tag. All I really need to do is set the proper index based on the rectangles new center point position within the rectangle, as compared with the center point position of the other rectangles in the grid. Here is what I am doing now in pseudo code (works somewhat, but not accurate): -(void)sortViews:myView { int newIndex; // myView is the view that was moved. [viewsArray removeObject:myView]; [viewsArray enumerate:obj*view]{ if (myView.center.x > view.center.x) { if (myView.center.y > view.center.y) { newIndex = view.tag -1; *stop = YES; } else { newIndex = view.tag +1; *stop = YES; } } else if (myView.center.x < view.center.x) { if (myView.center.y > view.center.y) { newIndex = view.tag -1; *stop = YES; } else { newIndex = view.tag +1; *stop = YES; } } }]; if (newIndex < 0) { newIndex = 0; } else if (newIndex > 5) { newIndex = 5; } [viewsArray insertObject:myView atIndex:newIndex]; [self arrangeGrid]; }

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• How do I build a matrix to translate one set of points to another?

  - by dotminic

  I've got 3 points in space that define a triangle. I've also got a vertex buffer made up of three vertices, that also represent a triangle that I will refer to as a "model". How can I can I find the matrix M that will transform vertex in my buffer to those 3 points in space ? For example, let's say my three points A, B, C are at locations: A.x = 10, A.y = 16, A.z = 8 B.x = 12, B.y = 11, B.z = 1 C.x = 19, C.y = 12, C.z = 3 given these coordinates how can I build a matrix that will translate and rotate my model such that both triangles have the exact same world space ? That is, I want the first vertex in my triangle model to have the same coordinates as A, the second to have the same coordinates as B, and same goes for C. nb: I'm using instanced rendering so I can't just give each vertex the same position as my 3 points. I have a set of three points defining a triangle, and only three vertices in my vertex buffer.

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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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• How do you blend multiple colors in HSV (polar) color-space?

  - by Toxikman

  In RGB color space, you can do a weighted multiple-color blend by just doing: Start with R = G = B = 0. Then we perform a blend at index i using a set of colors C, and a set of normalized weights w like so: R += w[i] * C[i].r G += w[i] * C[i].g B += w[i] * C[i].b But I'd like to interpolate the colors in the HSV color-space instead, so that saturation and brightness are uniform across the interpolation. I know I can blend saturation and brightness in the same way as above, but the HUE component is an angle around a continuous circle, since HSV is essentially a polar coordinate system. Blending only two HSV colors makes sense to me, you just find the shortest arc around the circle and interpolate between the two hues. But when you attempt to blend more than 2 colors, it becomes a bit of a puzzle. You have to handle anomalous cases, like 4 equally-weighted colors with a hue at 0, 90, 180, and 270 degrees. They basically cancel each other out, so any hue will do. Any ideas would be greatly appreciated.

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• Modular spaceship control

  - by SSS

  I am developing a physics based game with spaceships. A spaceship is constructed from circles connected by joints. Some of the circles have engines attached. Engines can rotate around the center of circle and create thrust. I want to be able to move the ship in a direction or rotate around a point by setting the rotation and thrust for each of the ship's engines. How can I find the rotation and thrust needed for each engine to achieve this?

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• Moving two objects proportionally

  - by SSL

  I'm trying to move two objects away from each other at a proportional distance, but on different scales. I'm not quite sure how to do this. Object A can go from position 0.1 to 1. Object B has no limits. If object B is decreasing, then Object A should be decreasing at rate R. Likewise, if Object B is increasing, then Object A increases at rate R. How can I tie these two Object positions together so that in an update loop, they automatically update their positions? I tried using: ObjA.Pos += 0.001f * ObjB.VelocityY; //0.001f is the rate This works but there's an error each time it runs. ObjA starts off at its max position 1 but then the next time it will stop at 0.97, 0.94, 0.91 etc.. This is due to the 0.001f rate I put in. Is there a way to control the rate, yet not end up with the rounding error?

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• setting the position in different resolution

  - by Moaz

  I have a normal game window which is 640*480, and everything is fine, but when I try to maximize the window, the objects translate to different positions on the screen, for example If I have a circle which is drawn at the center in the normal window, when I try to maximize it, it shifts away from the center of the screen. How do I adjust it so it draws at the center in both normal window and maximized window ?

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• How to determine which thrusters to turn on to rotate the ship?

  - by migimunz

  The configuration of the ship changes dynamically, so I have to determine which thruster to turn on when I want to rotate the ship clockwise or counter clockwise. The thrusters are always axis aligned with the ship (never at an angle) and are either on or off. Here's one of the possible setups: What I've tried so far is to visualize the firing vector and the direction vector to the center of mass of the ship: Unfortunately, I didn't get very far with that.

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• Get all triangles that are < N dist from you?

  - by CyanPrime

  Does anyone know of a way I could add a radius to this code for p? Like basically saying "this is true if the triangle is < N dist from the point" public boolean isPointInTriangle( Vector3f p, Vector3f a, Vector3f b, Vector3f c ) { return ( pointsAreOnSameSide(p, a, b, c) && pointsAreOnSameSide(p, b, a, c) && pointsAreOnSameSide(p, c, a, b) ); } public boolean pointsAreOnSameSide( Vector3f p1, Vector3f p2, Vector3f a, Vector3f b ) { Vector3f diffba = new Vector3f(0,0,0); Vector3f.sub( b, a, diffba ); Vector3f diffp1a = new Vector3f(0,0,0); Vector3f.sub( p1, a, diffp1a ); Vector3f diffp2a = new Vector3f(0,0,0); Vector3f.sub( p2, a, diffp2a ); Vector3f cross1 = Vector3f.cross(diffba, diffp1a); Vector3f cross2 = Vector3f.cross(diffba, diffp2a); return ( Vector3f.dot( cross1, cross2 ) >= 0 ); }

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• Should Equality be commutative within a Class Hierachy?

  - by vossad01

  It is easy to define the Equals operation in ways that are not commutative. When providing equality against other types, there are obviously situations (in most languages) were equality not being commutative is unavoidable. However, within one's own inheritance hierarchy where the root base class defines an equality member, a programmer has more control. Thus you can create situations where (A = B) ? (B = A), where A and B both derive from base class T Substituting the = with the appropriate variation for a given language. (.Equals(_), ==, etc.) That seems wrong to me, however, I recognize I may be biased by background in Mathematics. I have not been in programming long enough to know what is standard/accepted/preferred practice when programming. Do most programmers just accept .Equals(_)may not be commutative and code defensibly. Do they expect commutativity and get annoyed if it is not. In short, when working in a class hierarchy, should effort me made to ensure Equality is commutative?

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• Fastest way to check if two square 2D arrays are rotationally and reflectively distinct

  - by kustrle

  The best idea I have so far is to rotate first array by {0, 90, 180, 270} degrees and reflect it horizontally or/and vertically. We basically get 16 variations [1] of first array and compare them with second array. if none of them matches the two arrays are rotationally and reflectively distinct. I am wondering if there is more optimal solution than this brute-force approach? [1] 0deg, no reflection 0deg, reflect over x 0deg, reflect over y 0deg, reflect over x and y 90deg, no reflection ...

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