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• Handling extremely large numbers in a language which can't?

  - by Mallow

  I'm trying to think about how I would go about doing calculations on extremely large numbers (to infinitum - intergers no floats) if the language construct is incapable of handling numbers larger than a certain value. I am sure I am not the first nor the last to ask this question but the search terms I am using aren't giving me an algorithm to handle those situations. Rather most suggestions offer a language change or variable change, or talk about things that seem irrelevant to my search. So I need a little guideance. I would sketch out an algorithm like this: Determine the max length of the integer variable for the language. If a number is more than half the length of the max length of the variable split it in an array. (give a little play room) Array order [0] = the numbers most to the right [n-max] = numbers most to the left Ex. Num: 29392023 Array[0]:23, Array[1]: 20, array[2]: 39, array[3]:29 Since I established half the length of the variable as the mark off point I can then calculate the ones, tenths, hundredths, etc. Place via the halfway mark so that if a variable max length was 10 digits from 0 to 9999999999 then I know that by halfing that to five digits give me some play room. So if I add or multiply I can have a variable checker function that see that the sixth digit (from the right) of array[0] is the same place as the first digit (from the right) of array[1]. Dividing and subtracting have their own issues which I haven't thought about yet. I would like to know about the best implementations of supporting larger numbers than the program can.

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• Calculating the position of an object with regards to current position using OpenGL like matrices

  - by spartan2417

  i have a 1st person camera that collides with walls, i also have a small sphere in front of my camera denoted by the camera position plus the distance ahead. I cannot get the postion of the sphere but i have the position of my camera. e.g. i need to find the position of the point or at the very least find away of calculating the position using the camera positions. code: static Float P_z = 0; P_z = -15; PushMatrix(); LoadMatrix(&Inv); Material(SCEGU_AMBIENT, 0x00000066); TranslateXYZ(0,0,P_z); ScaleXYZ(0.1f,0.1f,0.1f); pointer.Render(); PopMatrix(); where Inv is the camera positions (Inv.w.x,Inv.w.z), pointer is the sphere.

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• Constrained/penalized distance function

  - by sigma.z.1980

  Assume a character is located on a n by n grid and has to reach a certain entry on that grid. Its current position is (x1,y1). Also on the same grid is an enemy with coordinates (x2,y2). Each step algorithm randomly generates new candidate locations for the hero (if there are k candidates then there is a kx2 matrix of new potential locations. What I need is some distance objective function to compare the candidates. I'm currently using d1 - c * d2, where d1 is distance to the objective (measure in terms of number of pixels for each axis), d2 is distance to the enemy and c is some coefficient (this is very much like a set-up for Lagrangian). It's not working very well though. I'd be quite keen to learn how what constrained distance function are used for similar cases. Any suggestions are very much appreciated.

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• Are there studies on what programming languages does to the brain? [closed]

  - by Eduard Florinescu

  Are there studies on what effects have programming languages on the brain or for that matter any other artificial languages in general, like mathematics ? Speaking from my personal experience I feel very different every time I speak Italian, I feel like a virtuoso on a quest but at the other end when I coded in machine code in debug.exe I felt like the main charcter inp(Movie). Why do I bring this up because I am suspecting that languages affect your mind and popular legends back this up too often: are full of mathematicians that crossed the Rubicon.

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• Staggered Isometric Map: Calculate map coordinates for point on screen

  - by Chris

  I know there are already a lot of resources about this, but I haven't found one that matches my coordinate system and I'm having massive trouble adjusting any of those solutions to my needs. What I learned is that the best way to do this is to use a transformation matrix. Implementing that is no problem, but I don't know in which way I have to transform the coordinate space. Here's an image that shows my coordinate system: How do I transform a point on screen to this coordinate system?

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• 2D shader to draw representation of rotating sphere.

  - by TheBigO

  I want to display a 3D textured sphere, and then rotate it in one direction. The direction will never change, and the camera will never move. One way is to actually create a spherical mesh, map a texture to it, rotate the sphere, and render in 3D. My question is, is there a way to display a 2D circle, that looks like a rotating sphere, with just a 2D shader. In other words, can someone think of a trick, like mapping a texture to the circle in a particular way, to give the appearance of an in-place rotating sphere, that is always viewed from the side? I don't need exact shader code, I'm just looking for the right idea.

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• Regulating how much to draw based on how much was drawn last frame.

  - by Mike Howard

  I have a 3D game world on an iPhone (limited graphics speed), and I'm already regulating whether I draw each shape on the screen based on it's size and distance from the camera. Something like... if (how_big_it_looks_from_the_camera > constant) then draw What I want to do now is also take into account how many shapes are being drawn, so that in busier areas of the game world I can draw less than I otherwise would. I tried to do this by dividing how_big_it_looks by the number of shapes that were drawn last frame (well, the square root of this but I'm simplifying - the problem is the same). if (how_big_it_looks / shapes_drawn > constant2) then draw But the check happens at the level of objects which represent many drawn shapes, and if an object containing many shapes is switched on, it increases shapes_drawn lots and switches itself back off the next frame. It flickers on and off. I tried keeping a kind of weighted average of previous values, by each frame doing something like shapes_drawn_recently = 0.9 * shapes_drawn_recently + 0.1 * shapes_just_drawn, but of course it only slows the flickering down because of the nature of the feedback loop. Is there a good way of solving this? My project is in Objective-C, but a general algorithm or pseudo-code is good too. Thanks.

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• Adding 'swerve' to a direction

  - by Skoder

  Hey. I'm not much of a maths expert, so this is probably quite straight forward. I was playing a soccer flash game where you take free kicks. You provide Power, Swerve and Direction. I'm reading up on vectors and such so I can use the direction and power information to shoot the ball with the correct velocity. What I don't understand is how the 'Swerve' information is used. What formula connects the Swerve information with the Direction and Power? (This is all in 2D) Thanks for any advice.

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• How can calculus and linear algebra be useful to a system programmer?

  - by Victor

  I found a website saying that calculus and linear algebra are necessary for System Programming. System Programming, as far as I know, is about osdev, drivers, utilities and so on. I just can't figure out how calculus and linear algebra can be helpful on that. I know that calculus has several applications in science, but in this particular field of programming I just can't imagine how calculus can be so important. The information was on this site: http://www.wikihow.com/Become-a-Programmer Edit: Some answers here are explaining about algorithm complexity and optimization. When I made this question I was trying to be more specific about the area of System's Programming. Algorithm complexity and optimization can be applied to any area of programming not just System's Programming. That may be why I wasn't able to came up with such thinking at the time of the question.

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• Surface normal to screen angle

  - by Tannz0rz

  I've been struggling to get this working. I simply wish to take a surface normal and convert it to a screen angle. As an example, assuming we're working with the highlighted surface on the sphere below, where the arrow is the normal, the 2D angle would obviously be PI/4 radians. Here's one of the many things I've tried to no avail: float4 A = v.vertex; float4 B = v.vertex + float4(v.normal, 0.0); A = mul(VP, A); B = mul(VP, B); A.xy = (0.5 * (A.xy / A.w)) + 0.5; B.xy = (0.5 * (B.xy / B.w)) + 0.5; o.theta = atan2(B.y - A.y, B.x - A.x); I'm finally at my wit's end. Thanks for any and all help.

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• Make an object slide around an obstacle

  - by Isaiah

  I have path areas set up in a game I'm making for canvas/html5 and have got it working to keep the player within these areas. I have a function isOut(boundary, x, y) that returns true if the point is outside the boundary. What I do is check only the new position x/y separately with the corresponding old position x/y. Then if each one is out I assign them the past value from the frame before. The old positions are kept in a variable from a closure I made. like this: opos = [x,y];//old position npos = [x,y];//new position if(isOut(bound, npos[0], opos[1])){ npos[0] = opos[0]; //assign it the old x position } if(isOut(bound, opos[0], npos[1])){ npos[1] = opos[1]; //assign it the old y position } It looks nice and works good at certain angles, but if your boundary has diagonal regions it results in jittery motion. What's happening is the y pos exits the area while x doesn't and continues pushing the player to the side, once it has moved the player to the side a bit the player can move forward and then the y exits again and the whole process repeats. Anyone know how I may be able to achieve a smoother slide? I have access to the player's velocity vector, the angle, and the speed(when used with the angle). I can move the play with either angle/speed or x/yvelocities as I've built in backups to translate one to the other if either have been altered manually.

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• Comparing angles and working out the difference

  - by Thomas O

  I want to compare angles and get an idea of the distance between them. For this application, I'm working in degrees, but it would also work for radians and grads. The problem with angles is that they depend on modular arithmetic, i.e. 0-360 degrees. Say one angle is at 15 degrees and one is at 45. The difference is 30 degrees, and the 45 degree angle is greater than the 15 degree one. But, this breaks down when you have, say, 345 degrees and 30 degrees. Although they compare properly, the difference between them is 315 degrees instead of the correct 45 degrees. How can I solve this? I could write algorithmic code: if(angle1 > angle2) delta_theta = 360 - angle2 - angle1; else delta_theta = angle2 - angle1; But I'd prefer a solution that avoids compares/branches, and relies entirely on arithmetic.

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• Check if an object is facing another based on angles

  - by Isaiah

  I already have something that calculates the bearing angle to get one object to face another. You give it the positions and it returns the angle to get one to face the other. Now I need to figure out how tell if on object is facing toward another object within a specified field and I can't find any information about how to do this. The objects are obj1 and obj2. Their angles are at obj1.angle and obj2.angle. Their vectors are at obj1.pos and obj2.pos. It's in the format [x,y]. The angle to have one face directly at another is found with direction(obj1.pos,obj2.pos). I want to set the function up like this: isfacing(obj1,obj2,area){...} and return true/false depending if it's in the specified field area to the angle to directly see it. I've got a base like this: var isfacing = function (obj1,obj2,area){ var toface = direction(obj1.pos,obj2.pos); if(toface+area >= obj1.angle && ob1.angle >= toface-area){ return true; } return false; } But my problem is that the angles are in 360 degrees, never above 360 and never below 0. How can I account for that in this? If the first object's angle is say at 0 and say I subtract a field area of 20 or so. It'll check if it's less than -20! If I fix the -20 it becomes 340 but x < 340 isn't what I want, I'd have to x 340 in that case. Is there someone out there with more sleep than I that can help a new dev pulling an all-nighter just to get enemies to know if they're attacking in the right direction? I hope I'm making this harder than it seems. I'd just make them always face the main char if the producer didn't want attacks from behind to work while blocking. In which case I'll need the function above anyways. I've tried to give as much info as I can think would help. Also this is in 2d.

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• Automatically zoom out the camera to show all players (XNA)

  - by user36159

  I am building a game in XNA that takes place in a rectangular arena. The game is multiplayer and each player may go where they like within the arena. The camera is a persepective camera that looks directly downwards. The camera should be automatically repositioned based on the game state. Currently, the xy position is a weighted sum of the xy positions of important entities. I would like the camera's z position to be calculated from the xy coordinates so that it zooms out to the point where all important entities are visible. My current approach is to: hw = the greatest x distance from the camera to an important entity hh = the greatest y distance from the camera to an important entity Calculate z = max(hw / tan(FoVx), hh / tan(FoVy)) My code seems to almost work as it should, but the resulting z values are always too low by a factor of about 4. Any ideas?

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• Building View Matrix in Direct3D11

  - by Balls

  Am I doing it right? I converted this. m_ViewMatrix = XMMatrixLookAtLH(XMLoadFloat3(&m_Position), lookAtVector, upVector); to this one. XMVECTOR vz = XMVector3Normalize( lookAtVector - XMLoadFloat3(&m_Position) ); XMVECTOR vx = XMVector3Normalize( XMVector3Cross( upVector, vz ) ); XMVECTOR vy = XMVector3Cross( vz, vx ); m_ViewMatrix.r[0] = vx; m_ViewMatrix.r[1] = vy; m_ViewMatrix.r[2] = vz; m_ViewMatrix.r[3] = XMLoadFloat3(&m_Position); m_ViewMatrix.r[0].m128_f32[3] = 0.0f; m_ViewMatrix.r[1].m128_f32[3] = 0.0f; m_ViewMatrix.r[2].m128_f32[3] = 0.0f; m_ViewMatrix.r[3].m128_f32[3] = 1.0f; m_ViewMatrix = XMMatrixInverse( &XMMatrixDeterminant(m_ViewMatrix), m_ViewMatrix ); Everything looks fine when I run it. Another question is, I saw on this site(http://webglfactory.blogspot.com/2011/06/how-to-create-view-matrix.html) that he subtracted lookat from position in his vector vz. I tried it but gave me wrong view matrix. Can anyone check my code. I'm studying linear algebra right now. Sucks my course doesn't have one. Thank you, Balls

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• How to transform mesh components?

  - by Lea Hayes

  I am attempting to transform the components of a mesh directly using a 4x4 matrix. This is working for the vertex positions, but it is not working for the normals (and probably not the tangents either). Here is what I have: // Transform vertex positions - Works like a charm! vertices = mesh.vertices; for (int i = 0; i < vertices.Length; ++i) vertices[i] = transform.MultiplyPoint(vertices[i]); // Does not work, lighting is messed up on mesh normals = mesh.normals; for (int i = 0; i < normals.Length; ++i) normals[i] = transform.MultiplyVector(normals[i]); Note: The input matrix converts from local to world space and is needed to combine multiple meshes together.

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• Optimized algorithm for line-sphere intersection in GLSL

  - by fernacolo

  Well, hello then! I need to find intersection between line and sphere in GLSL. Right now my solution is based on Paul Bourke's page and was ported to GLSL this way: // The line passes through p1 and p2: vec3 p1 = (...); vec3 p2 = (...); // Sphere center is p3, radius is r: vec3 p3 = (...); float r = ...; float x1 = p1.x; float y1 = p1.y; float z1 = p1.z; float x2 = p2.x; float y2 = p2.y; float z2 = p2.z; float x3 = p3.x; float y3 = p3.y; float z3 = p3.z; float dx = x2 - x1; float dy = y2 - y1; float dz = z2 - z1; float a = dx*dx + dy*dy + dz*dz; float b = 2.0 * (dx * (x1 - x3) + dy * (y1 - y3) + dz * (z1 - z3)); float c = x3*x3 + y3*y3 + z3*z3 + x1*x1 + y1*y1 + z1*z1 - 2.0 * (x3*x1 + y3*y1 + z3*z1) - r*r; float test = b*b - 4.0*a*c; if (test >= 0.0) { // Hit (according to Treebeard, "a fine hit"). float u = (-b - sqrt(test)) / (2.0 * a); vec3 hitp = p1 + u * (p2 - p1); // Now use hitp. } It works perfectly! But it seems slow... I'm new at GLSL. You can answer this questions in two ways: Tell me there is no solution, showing some proof or strong evidence. Tell me about GLSL features (vector APIs, primitive operations) that makes the above algorithm faster, showing some example. Thanks a lot!

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• Finding closest object to a location within a specific perpendicular distance to direction vector

  - by Sniper

  I have a location and a direction vector indicating facing, I want to find the closest object to that location that is within some tolerance distance (perpendicular distance) to the ray formed by the location and direction vector. Basically I want to get the object that is being aimed at. I have thought about finding all objects within a box and then finding the closest object to my vector from them results, but I am sure that there is a more efficient way. The Z axis is optional, the objects are most likely within a few meters of the search vector.

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• Directional and orientation problem

  - by Ahmed Saleh

  I have drawn 5 tentacles which are shown in red. I have drew those tentacles on a 2D Circle, and positioned them on 5 vertices of the that circle. BTW, The circle is never be drawn, I have used it to simplify the problem. Now I wanted to attached that circle with tentacles underneath the jellyfish. There is a problem with the current code but I don't know what is it. You can see that the circle is parallel to the base of the jelly fish. I want it to be shifted so that it be inside the jelly fish. but I don't know how. I tried to multiply the direction vector to extend it but that didn't work. // One tentacle is constructed from nodes // Get the direction of the first tentacle's node 0 to node 39 of that tentacle; Vec3f dir = m_tentacle[0]->geNodesPos()[0] - m_tentacle[0]->geNodesPos()[39]; // Draw the circle with tentacles on it Vec3f pos = m_SpherePos; drawCircle(pos,dir,30,m_tentacle.size()); for (int i=0; i<m_tentacle.size(); i++) { m_tentacle[i]->Draw(); } // Draw the jelly fish, and orient it on the 2D Circle gl::pushMatrices(); Quatf q; // assign quaternion to rotate the jelly fish around the tentacles q.set(Vec3f(0,-1,0),Vec3f(dir.x,dir.y,dir.z)); // tanslate it to the position of the whole creature per every frame gl::translate(m_SpherePos.x,m_SpherePos.y,m_SpherePos.z); gl::rotate(q); // draw the jelly fish at center 0,0,0 drawHemiSphere(Vec3f(0,0,0),m_iRadius,90); gl::popMatrices();

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• Hydraulics in game

  - by Mungoid

  I'm not completely sure if this would be better in the Physics site or not as this question is more about how hydraulics should work in game as opposed to how they really work (although that is taken into account) - So I apologize if this is in the wrong place. A project we are on, we have a machine with hydraulics that are powered (They don't just look like they move something, they are the only thing moving/turning/lifting something) - However, the hydraulic extends the same speed no matter what it is pushing. So, say there is a 10 ton object attached to one end of the hydraulic and the other end is attached to a plate on the ground. In real life it takes a few seconds to build up pressure depending on how heavy the object is, but in our project the hydraulics don't care about that. It will lift a 100 ton object the same speed as a 10 ton object. We have a way to fake the hydraulic pressurizing by reducing the 'drive amount' (how fast or slow the hydraulic extends) when we sense that it is touching the ground and that does a relatively decent job but we would like to be able to take other things into account like engine speed, ratios, loads, etc. but we aren't too sure what we need to think about. I'm kinda wondering if anyone here has any experience with this and could offer some suggestions on what to take into account?

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• Quaternion LookAt for camera

  - by Homar

  I am using the following code to rotate entities to look at points. glm::vec3 forwardVector = glm::normalize(point - position); float dot = glm::dot(glm::vec3(0.0f, 0.0f, 1.0f), forwardVector); float rotationAngle = (float)acos(dot); glm::vec3 rotationAxis = glm::normalize(glm::cross(glm::vec3(0.0f, 0.0f, 1.0f), forwardVector)); rotation = glm::normalize(glm::quat(rotationAxis * rotationAngle)); This works fine for my usual entities. However, when I use this on my Camera entity, I get a black screen. If I flip the subtraction in the first line, so that I take the forward vector to be the direction from the point to my camera's position, then my camera works but naturally my entities rotate to look in the opposite direction of the point. I compute the transformation matrix for the camera and then take the inverse to be the View Matrix, which I pass to my OpenGL shaders: glm::mat4 viewMatrix = glm::inverse( cameraTransform->GetTransformationMatrix() ); The orthographic projection matrix is created using glm::ortho. What's going wrong?

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• Circle-Line Collision Detection Problem

  - by jazzdawg

  I am currently developing a breakout clone and I have hit a roadblock in getting collision detection between a ball (circle) and a brick (convex polygon) working correctly. I am using a Circle-Line collision detection test where each line represents and edge on the convex polygon brick. For the majority of the time the Circle-Line test works properly and the points of collision are resolved correctly. Collision detection working correctly. However, occasionally my collision detection code returns false due to a negative discriminant when the ball is actually intersecting the brick. Collision detection failing. I am aware of the inefficiency with this method and I am using axis aligned bounding boxes to cut down on the number of bricks tested. My main concern is if there are any mathematical bugs in my code below. /* * from and to are points at the start and end of the convex polygons edge. * This function is called for every edge in the convex polygon until a * collision is detected. */ bool circleLineCollision(Vec2f from, Vec2f to) { Vec2f lFrom, lTo, lLine; Vec2f line, normal; Vec2f intersectPt1, intersectPt2; float a, b, c, disc, sqrt_disc, u, v, nn, vn; bool one = false, two = false; // set line vectors lFrom = from - ball.circle.centre; // localised lTo = to - ball.circle.centre; // localised lLine = lFrom - lTo; // localised line = from - to; // calculate a, b & c values a = lLine.dot(lLine); b = 2 * (lLine.dot(lFrom)); c = (lFrom.dot(lFrom)) - (ball.circle.radius * ball.circle.radius); // discriminant disc = (b * b) - (4 * a * c); if (disc < 0.0f) { // no intersections return false; } else if (disc == 0.0f) { // one intersection u = -b / (2 * a); intersectPt1 = from + (lLine.scale(u)); one = pointOnLine(intersectPt1, from, to); if (!one) return false; return true; } else { // two intersections sqrt_disc = sqrt(disc); u = (-b + sqrt_disc) / (2 * a); v = (-b - sqrt_disc) / (2 * a); intersectPt1 = from + (lLine.scale(u)); intersectPt2 = from + (lLine.scale(v)); one = pointOnLine(intersectPt1, from, to); two = pointOnLine(intersectPt2, from, to); if (!one && !two) return false; return true; } } bool pointOnLine(Vec2f p, Vec2f from, Vec2f to) { if (p.x >= min(from.x, to.x) && p.x <= max(from.x, to.x) && p.y >= min(from.y, to.y) && p.y <= max(from.y, to.y)) return true; return false; }

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• Render 3d object to 2d surface (embedded system)

  - by Martin Berger

  i am working on an embedded system of a sort, and in some free time i would like to test its drawing capabilities. System in question is ARM Cortex M3 microcontroller attached to EasyMX Stellaris board. And i have a small 320x240 TFT screen :) Now, i have some free time each day and i want to create rotating cube. Micro C PRO for ARM doesnt have 3d drawing capabilities, which means it must be done in software. From the book Introduction to 3D Game Programming with DirectX 10 i know matrix algebra for transformations but that is cool when you have DirectX to set camera right. I gues i could make 2d object to rotate, but how would i go with 3d one? Any ideas and examples are welcome. Although i would prefer advices. I'd like to understand this.

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• Layout of mathematical views (iOS)

  - by William Jockusch

  I am trying to figure out the right way to encapsulate graphical information about mathematical objects. It is not simple. For example, a matrix can include square brackets around its entries, or not. Some things carry down to sub-objects -- for example, a matrix might track the font size to be used by its entries. Similarly, the font color and the background color would carry down to the entries. Other things do not carry down. For example, the entries of the matrix do not need to know whether or not the matrix has those square brackets. Based on all of the above, I need to calculate sizes for everything, then frames. All of this can depend on the properties stored above. The size of a matrix depends on the sizes of its entries, and also on whether or not it has those brackets. What I am having a hard time with is not the individual ways to calculate sensible frames for this or that. It is the overall organizational structure of the whole thing. How can I keep track of it all without going crazy. One particular obstacle is worth mentioning -- for reasons I don't want to go into here, I need to calculate the sizes and frames for everything before I instantiate any actual views. So, for example, if I have a Matrix object, I need to calculate its size before I make a MatrixView. If I have an equation, I need to calculate the size of the view for the equation before I create the actual view. So I clearly need separate objects for those calculations. But I can't figure out a sensible class structure for those objects. If I put them all into a single class, I get some advantages because copying then becomes easy. But I also end up with a bloated class that contains info that is irrelevant for some objects -- such as whether or not to include those brackets around the matrix. But if I use a lot of different classes, copying properties becomes a real pain. If it matters, this is all in Objective C, for an iOS environment. Any pointers would be greatly appreciated.

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• Automatically zoom out the camera to show all players

  - by user36159

  I am building a game in XNA that takes place in a rectangular arena. The game is multiplayer and each player may go where they like within the arena. The camera is a perspective camera that looks directly downwards. The camera should be automatically repositioned based on the game state. Currently, the xy position is a weighted sum of the xy positions of important entities. I would like the camera's z position to be calculated from the xy coordinates so that it zooms out to the point where all important entities are visible. My current approach is to: hw = the greatest x distance from the camera to an important entity hh = the greatest y distance from the camera to an important entity Calculate z = max(hw / tan(FoVx), hh / tan(FoVy)) My code seems to almost work as it should, but the resulting z values are always too low by a factor of about 4. Any ideas?

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