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• Estimate angle to launch missile, maths question

  - by Jonathan

  I've been working on this for an hour or two now and my maths really isn't my strong suit which is definitely not a good thing for a game programmer but that shouldn't stop me enjoying a hobby surely? After a few failed attempts I was hoping someone else out there could help so here's the situation. I'm trying to implement a bit of faked intelligence when the A.I fires it's missiles at a target in a 2D game world. By predicting the likely position the target will be in given it's current velocity and the time it will take the missile to reach it's target. I created an image to demonstrate my thinking: http://i.imgur.com/SFmU3.png which also contains the logic I use for accelerating the missile after launch. The ship that fires the missile can fire within a total of 40 degree angle, 20 either side of itself, but this could likely become variable. My current attempt was to break the space between the two lines into segments which match the targets width. Then calculate the time it would take the missile to get to that location using the formula. So for each iteration of this we total up the values and that tells us the distance travelled, ad it would then just need compared to distance to the segment. startVelocity * ((startVelocity * acceleration)^(currentframe-1) So for example. If we start at a velocity of 1f/frame with an acceleration of 0.1f the formula, at frame 4, would be 1 * (1.1^3) = 1.331 But I quickly realized I was getting lost when trying to put this into practice. Does this seem like a correct starting point or am I going completely the wrong way about it? Any pointers would help me greatly. Maths really isn't my strong suit so I get easily lost in these matters and don't even really know a good phrase to search for with this. So I guess in summary my question is more about the correct way to approach this problem and any additional code samples on top of that would be great but I'm not averse to working out the complete code from helpful pointers.

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• Position Reconstruction from Depth by inverting Perspective Projection

  - by user1294203

  I had some trouble reconstructing position from depth sampled from the depth buffer. I use the equivalent of gluPerspective in GLM. The code in GLM is: template GLM_FUNC_QUALIFIER detail::tmat4x4 perspective ( valType const & fovy, valType const & aspect, valType const & zNear, valType const & zFar ) { valType range = tan(radians(fovy / valType(2))) * zNear; valType left = -range * aspect; valType right = range * aspect; valType bottom = -range; valType top = range; detail::tmat4x4 Result(valType(0)); Result[0][0] = (valType(2) * zNear) / (right - left); Result[1][2] = (valType(2) * zNear) / (top - bottom); Result[2][3] = - (zFar + zNear) / (zFar - zNear); Result[2][4] = - valType(1); Result[3][5] = - (valType(2) * zFar * zNear) / (zFar - zNear); return Result; } There doesn't seem to be any errors in the code. So I tried to invert the projection, the formula for the z and w coordinates after projection are: and dividing z' with w' gives the post-projective depth (which lies in the depth buffer), so I need to solve for z, which finally gives: Now, the problem is I don't get the correct position (I have compared the one reconstructed with a rendered position). I then tried using the respective formula I get by doing the same for this Matrix. The corresponding formula is: For some reason, using the above formula gives me the correct position. I really don't understand why this is the case. Have I done something wrong? Could someone enlighten me please?

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• I am looking to create realistic car movement using vectors

  - by bobthemac

  I have goggled how to do this and found this http://www.helixsoft.nl/articles/circle/sincos.htm I have had a go at it but most of the functions that were showed didn't work I just got errors because they didn't exist. I have looked at the cos and sin functions but don't understand how to use them or how to get the car movement working correctly using vectors. I have no code because I am not sure what to do sorry. Any help is appreciated. EDIT: I have restrictions that I must use the TL engine for my game, I am not allowed to add any sort of physics engine. It must be programmed in c++. Here is a sample of what i got from trying to follow what was done in the link I provided. if(myEngine->KeyHeld(Key_W)) { length += carSpeedIncrement; } if(myEngine->KeyHeld(Key_S)) { length -= carSpeedIncrement; } if(myEngine->KeyHeld(Key_A)) { angle -= carSpeedIncrement; } if(myEngine->KeyHeld(Key_D)) { angle += carSpeedIncrement; } carVolocityX = cos(angle); carVolocityZ = cos(angle); car->MoveX(carVolocityX * frameTime); car->MoveZ(carVolocityZ * frameTime);

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• Algorithm to shoot at a target in a 3d game

  - by Sebastian Bugiu

  For those of you remembering Descent Freespace it had a nice feature to help you aim at the enemy when shooting non-homing missiles or lasers: it showed a crosshair in front of the ship you chased telling you where to shoot in order to hit the moving target. I tried using the answer from http://stackoverflow.com/questions/4107403/ai-algorithm-to-shoot-at-a-target-in-a-2d-game?lq=1 but it's for 2D so I tried adapting it. I first decomposed the calculation to solve the intersection point for XoZ plane and saved the x and z coordinates and then solving the intersection point for XoY plane and adding the y coordinate to a final xyz that I then transformed to clipspace and put a texture at those coordinates. But of course it doesn't work as it should or else I wouldn't have posted the question. From what I notice the after finding x in XoZ plane and the in XoY the x is not the same so something must be wrong. float a = ENG_Math.sqr(targetVelocity.x) + ENG_Math.sqr(targetVelocity.y) - ENG_Math.sqr(projectileSpeed); float b = 2.0f * (targetVelocity.x * targetPos.x + targetVelocity.y * targetPos.y); float c = ENG_Math.sqr(targetPos.x) + ENG_Math.sqr(targetPos.y); ENG_Math.solveQuadraticEquation(a, b, c, collisionTime); First time targetVelocity.y is actually targetVelocity.z (the same for targetPos) and the second time it's actually targetVelocity.y. The final position after XoZ is crossPosition.set(minTime * finalEntityVelocity.x + finalTargetPos4D.x, 0.0f, minTime * finalEntityVelocity.z + finalTargetPos4D.z); and after XoY crossPosition.y = minTime * finalEntityVelocity.y + finalTargetPos4D.y; Is my approach of separating into 2 planes and calculating any good? Or for 3D there is a whole different approach? sqr() is square not sqrt - avoiding a confusion.

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• What's the normal way machine-learning algorithms are integrated into normal programs?

  - by Benjamin Pollack

  I'm currently taking a machine learning course for fun, and the course heavily focuses on Matlab/Octave to write the code. One thing mentioned in the course is that, while Matlab/Octave are great for prototyping, they're very rarely used for production algorithms. Instead, those algorithms are typically rewritten in C++/Python/etc., using appropriate libraries, before reaching customers. Fair enough; I get that. But here's my question: is that done for cultural reasons, for technical reasons, or because there is really no language that provides Matlab/Octave-like fluidity, but in a compiled form that can be linked from C/C++/$MainstreamLanguage? The game industry uses Lua for game logic because it's easy to embed, and vastly superior for expressing things like AI. Likewise, there are Prolog variants for rules-heavy applications, Scheme variants for compilers, and so on. If there's a matrix equivalent language, what is it? If there isn't, why is this field different?

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• Is it 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 things like this. 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 matrices, but that only makes sense going from tile to screen.

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• How do I draw a dotted or dashed line?

  - by Gagege

  I'm trying to draw a dashed or dotted line by placing individual segments(dashes) along a path and then separating them. The only algorithm I could come up with for this gave me a dash length that was variable based on the angle of the line. Like this: private function createDashedLine(fromX:Float, fromY:Float, toX:Float, toY:Float):Sprite { var line = new Sprite(); var currentX = fromX; var currentY = fromY; var addX = (toX - fromX) * 0.0075; var addY = (toY - fromY) * 0.0075; line.graphics.lineStyle(1, 0xFFFFFF); var count = 0; // while line is not complete while (!lineAtDestination(fromX, fromY, toX, toY, currentX, currentY)) { /// move line draw cursor to beginning of next dash line.graphics.moveTo(currentX, currentY); // if dash is even if (count % 2 == 0) { // draw the dash line.graphics.lineTo(currentX + addX, currentY + addY); } // add next dash's length to current cursor position currentX += addX; currentY += addY; count++; } return line; } This just happens to be written in Haxe, but the solution should be language neutral. What I would like is for the dash length to be the same no matter what angle the line is. As is, it's just adding 75 thousandths of the line length to the x and y, so if the line is and a 45 degree angle you get pretty much a solid line. If the line is at something shallow like 85 degrees then you get a nice looking dashed line. So, the dash length is variable, and I don't want that. How would I make a function that I can pass a "dash length" into and get that length of dash, no matter what the angle is? If you need to completely disregard my code, be my guest. I'm sure there's a better solution.

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• Using NumPy arrays as 2D mathematical vectors?

  - by CorundumGames

  Right now I'm using lists as position, velocity, and acceleration vectors in my game. Is that a better option than using NumPy's arrays (not the standard library's) as vectors (with float data types)? I'm frequently adding vectors and changing their values directly, then placing the values in these vectors into a Pygame Rect. The vector is used for position (because Rects can't hold floats, so we can't go "between" pixels), and the Rect is used for rendering (because Pygame will only take in Rects for rendering positions).

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• How is fundamental mathematics efficiently evaluated by programming languages?

  - by Korvin Szanto

  As I get more and more involved with the theory behind programming, I find myself fascinated and dumbfounded by seemingly simple things.. I realize that my understanding of the majority of fundamental processes is justified through circular logic Q: How does this work? A: Because it does! I hate this realization! I love knowledge, and on top of that I love learning, which leads me to my question (albeit it's a broad one). Question: How are fundamental mathematical operators assessed with programming languages? How have current methods been improved? Example var = 5 * 5; My interpretation: $num1 = 5; $num2 = 5; $num3 = 0; while ($num2 > 0) { $num3 = $num3 + $num1; $num2 = $num2 - 1; } echo $num3; This seems to be highly inefficient. With Higher factors, this method is very slow while the standard built in method is instantanious. How would you simulate multiplication without iterating addition? var = 5 / 5; How is this even done? I can't think of a way to literally split it 5 into 5 equal parts. var = 5 ^ 5; Iterations of iterations of addition? My interpretation: $base = 5; $mod = 5; $num1 = $base; while ($mod > 1) { $num2 = 5; $num3 = 0; while ($num2 > 0) { $num3 = $num3 + $num1; $num2 = $num2 - 1; } $num1 = $num3; $mod -=1; } echo $num3; Again, this is EXTREMELY inefficient, yet I can't think of another way to do this. This same question extends to all mathematical related functions that are handled automagically.

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• Changing coordinate system from Z-up to Y-up

  - by Jari Komppa

  Blender's coordinate system is different from what I'm used to, in that Z points upwards instead of Y. What would be the simplest way of converting all the world data (so that all animations, texture coordinates, etc still work) so that Y points upwards? Clarification: Object positions are defined as matrices, so just switching translation/rotation/scale information in matrices is not a trivial task.

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• Confusion about Rotation matrices from Euler Angles

  - by xEnOn

  I am trying to learn more about Euler Angles so as to help myself in understanding how I can control my camera better in the game. I came across the following formula that converts Euler Angles to rotation matrices: In the equation, I could see that the first matrix from the left is the rotation matrix about x-axis, the second is about y-axis and the third is about z-axis. From my understanding about ordinary matrix transformations, the later transformation is always applied to the right hand side. And if I'm right about this, then the above equation should have a rotation order starting from rotating about z-axis, y-axis, then finally x-axis. But, from the symbols it seems that the rotation order start rotating about x-axis, then y-axis, then finally z-axis. What should the actual order of the rotation be? Also, I am confuse about if the input vector, in this case, would be a row vector on the left, or a column vector on the right?

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• Optimizing hierarchical transform

  - by Geotarget

  I'm transforming objects in 3D space by transforming each vector with the object's 4x4 transform matrix. In order to achieve hierarchical transform, I transform the child by its own matrix, and then the child by the parent matrix. This becomes costly because objects deeper in the display tree have to be transformed by all the parent objects. This is what's happening, in summary: Root -- transform its verts by Root matrix Parent -- transform its verts by Parent, Root matrix Child -- transform its verts by Child, Parent, Root matrix Is there a faster way to transform vertices to achieve hierarchical transform? What If I first concatenated each transform matrix with the parent matrices, and then transform verts by that final resulting matrix, would that work and wouldn't that be faster? Root -- transform its verts by Root matrix Parent -- concat Parent, Root matrices, transform its verts by Concated matrix Child -- concat Child, Parent, Root matrices, transform its verts by Concated matrix

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• Checking for collisions on a 3D heightmap

  - by Piku

  I have a 3D heightmap drawn using OpenGL (which isn't important). It's represented by a 2D array of height data. To draw this I go through the array using each point as a vertex. Three vertices are wound together to form a triangle, two triangles to make a quad. To stop the whole mesh being tiny I scale this by a certain amount called 'gridsize'. This produces a fairly nice and lumpy, angular terrain kind of similar to something you'd see in old Atari/Amiga or DOS '3D' games (think Virus/Zarch on the Atari ST). I'm now trying to work out how to do collision with the terrain, testing to see if the player is about to collide with a piece of scenery sticking upwards or fall into a hole. At the moment I am simply dividing the player's co-ordinates by the gridsize to find which vertex the player is on top of and it works well when the player is exactly over the corner of a triangle piece of terrain. However... How can I make it more accurate for the bits between the vertices? I get confused since they don't exist in my heightmap data, they're a product of the GPU trying to draw a triangle between three points. I can calculate the height of the point closest to the player, but not the space between them. I.e if the player is hovering over the centre of one of these 'quads', rather than over the corner vertex of one, how do I work out the height of the terrain below them? Later on I may want the player to slide down the slopes in the terrain.

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• 2D Smooth Turning in a Tile-Based Game

  - by ApoorvaJ

  I am working on a 2D top-view grid-based game. A ball that rolls on the grid made up of different tiles. The tiles interact with the ball in a variety of ways. I am having difficulty cleanly implementing the turning tile. The image below represents a single tile in the grid, which turns the ball by a right angle. If the ball rolls in from the bottom, it smoothly changes direction and rolls to the right. If it rolls in from the right, it is turned smoothly to the bottom. If the ball rolls in from top or left, its trajectory remains unchanged by the tile. The tile shouldn't change the magnitude of the velocity of the ball - only change its direction. The ball has Velocity and Position vectors, and the tile has Position and Dimension vectors. I have already implemented this, but the code is messy and buggy. What is an elegant way to achieve this, preferably by modification of the ball's Velocity vector by a formula?

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• Is it possible to learn maths via programming, or you should learn maths for programming?

  - by SAFAD

  I am not the best in maths, not very horrid either, but lower than the average, I've always been thinking to improve my maths, but schools and books didn't do the job because I get bored too fast. The only thing I don't get bored with is coding and gaming, so I thought what if coding a program that solves mathematical problems will help me understand maths better, most of these problems are limits (calculus), functions, Differential calculus, and some other subjects (I already said am not that good) similar to the previous noted. My question is: Am I able to achieve a better knowledge in maths if I do some specific program coding, and if possible, is physics possible that way too? Or am I wrong and Maths should be learned before programming to help improve my coding? P.S : C++ is the preferred language.

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• Need the co-ordinates of innerPolygon

  - by user960567

  Let say I have this diagram, Given that i have all the co-ordinates of outer polygon and the distance between inner and outer polygon is d is also given. How to calculate the inner polygon co-ordinates? Edit: I was able to solved the issue by getting the mid-points of all lines. From these mid-points I can move d distance, So I can get three points. No I have 3 points and 3 slopes. From this, I can get three new equations. Simultaneously, solving the equation get the 3 points.

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• Normalizing the direction to check if able to move

  - by spartan2417

  i have a a room with 4 walls along the x and z axis respectively. My player who is in first person (therefore the camera) should have collision detection with these walls. I'm relatively new to this so please bare with me. I believe the way to do this is to calculate the direction and distance to the wall from the camera and then normalize the directions. However i can only get this far before i dont know what to do. I think you should work out the angle and direction your facing? where _dx and _dz is the small buffer in front of the camera. float CalcDirection(float Cam_x, float Cam_z, float Wall_x, float Wall_z) { //Calculate direction and distance to obstacle. float ob_dirx = Cam_x + _dx - Wall_x; float ob_dirz = Cam_z + _dz - Wall_z; float ob_dist = sqrt(ob_dirx*ob_dirx + ob_dirz*ob_dirz); //Normalise directions float ob_norm = sqrt(ob_dirx*ob_dirx + ob_dirz*ob_dirz); ob_dirx = (ob_dirx)/ob_norm; ob_dirz = (ob_dirz)/ob_norm; can anyone explain in laymen's terms how i work out the angle?

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• Explaining Asteroids Movement code

  - by Moaz ELdeen

  I'm writing an Asteroids Atari clone, and I want to figure out how the AI for the asteroids is done. I have came across that piece of code, but I can't get what it does 100% if ((float)rand()/(float)RAND_MAX < 0.5) { m_Pos.x = -app::getWindowWidth() / 2; if ((float)rand()/(float)RAND_MAX < 0.5) m_Pos.x = app::getWindowWidth() / 2; m_Pos.y = (int) ((float)rand()/(float)RAND_MAX * app::getWindowWidth()); } else { m_Pos.x = (int) ((float)rand()/(float)RAND_MAX * app::getWindowWidth()); m_Pos.y = -app::getWindowHeight() / 2; if (rand() < 0.5) m_Pos.y = app::getWindowHeight() / 2; } m_Vel.x = (float)rand()/(float)RAND_MAX * 2; if ((float)rand()/(float)RAND_MAX < 0.5) { m_Vel.x = -m_Vel.x; } m_Vel.y =(float)rand()/(float)RAND_MAX * 2; if ((float)rand()/(float)RAND_MAX < 0.5) m_Vel.y = -m_Vel.y;

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• Zooming to point of interest

  - by user1010005

  I have the following variables: Point of interest which is the position(x,y) in pixels of the place to focus. Screen width,height which are the dimensions of the window. Zoom level which sets the zoom level of the camera. And this is the code I have so far. void Zoom(int pointOfInterestX,int pointOfInterstY,int screenWidth, int screenHeight,int zoomLevel) { glTranslatef( (pointOfInterestX/2 - screenWidth/2), (pointOfInterestY/2 - screenHeight/2),0); glScalef(zoomLevel,zoomLevel,zoomLevel); } And I want to do zoom in/out but keep the point of interest in the middle of the screen. but so far all of my attempts have failed and I would like to ask for some help.

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• Is there a (family of) monotonically non-decreasing noise function(s)?

  - by Joe Wreschnig

  I'd like a function to animate an object moving from point A to point B over time, such that it reaches B at some fixed time, but its position at any time is randomly perturbed in a continuous fashion, but never goes backwards. The objects move along straight lines, so I only need one dimension. Mathematically, that means I'm looking for some continuous f(x), x ? [0,1], such that: f(0) = 0 f(1) = 1 x < y ? f(x) = f(y) At "most" points f(x + d) - f(x) bears no obvious relation to d. (The function is not uniformly increasing or otherwise predictable; I think that's also equivalent to saying no degree of derivative is a constant.) Ideally, I would actually like some way to have a family of these functions, providing some seed state. I'd need at least 4 bits of seed (16 possible functions), for my current use, but since that's not much feel free to provide even more. To avoid various issues with accumulation errors, I'd prefer the function not require any kind of internal state. That is, I want it to be a real function, not a programming "function".

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• Bending of track in a racing game

  - by caius

  I am trying to create a small racing game in which the track would be modeled using a BSpline curve for the path's center line and directional vectors to define the 'bending' of the track at each point. My problem is that I don't know how to calculate the correct bending / slope of the curve, in such a way that it would be optimal or at least visually nice for a car to 'bend in the corner'. My idea was to use the direction of the 2nd derivatives of the curve, however while this approach looks fine for most of the track, there are points in which the 2nd derivative makes sharp 'twists' / very quick 180 degree flips. I also read about 'knots' of bsplines, but I don't know if such 'twist' in 2nd derivatives is a knot or knots are something else. Can you tell me that using a BSpline: 1. How could I calculate a visually nice bending of a track for a racing game? 2. Is it possible to do this by using some simple calculations of centripertal force / gravity? 3. Is it possible to do this by using 1st, 2nd and 3rd derivatives of the BSpline curve? I am not looking for the 'physically correct' bending angle for the track, I would just like to create something which is visually pleasing in a simple game. I am using a framework which has a built-in class for BSpline, including support for 1st, 2nd and 3rd derivatives of the curve.

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• Separating merged array of arithmetic and geometric series

  - by user1814037

  Given an array of positive integers in increasing order. Separate 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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• How to get distance from point to line with distinction between side of line?

  - by tesselode

  I'm making a 2d racing game. I'm taking the nice standard approach of having a set of points defining the center of the track and detecting whether the car is off the track by detecting its distance from the nearest point. The nicest way I've found of doing this is using the formula: d = |Am + Bn + C| / sqrt(A^2 + B^2) Unfortunately, to have proper collision resolution, I need to know which side of the line the car is hitting, but I can't do that with this formula because it only returns positive numbers. So my question is: is there a formula that will give me positive or negative numbers based on which side of the line the point is on? Can I just get rid of the absolute value in the formula or do I need to do something else?

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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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• Premultiplying matrices with Perspective destroys them

  - by Shadows In Rain

  If I apply world_to_camera, perspective and camera_to_screen to my mesh, everything is okay. But if I premultiply given matrices (i.e. transform = world_to_camera * perpective * camera_to_screen) before applying, then it seems like only perspective has effect. If it is important... My 3d framework was written from scratch (test project for job interview). But it works flawlessly, or at least I think so. So, question. This is expected behaviour, or my implementation is wrong?

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