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  • How can I move a polygon edge 1 unit away from the center?

    - by Stephen
    Let's say I have a polygon class that is represented by a list of vector classes as vertices, like so: var Vector = function(x, y) { this.x = x; this.y = y; }, Polygon = function(vectors) { this.vertices = vectors; }; Now I make a polygon (in this case, a square) like so: var poly = new Polygon([ new Vector(2, 2), new Vector(5, 2), new Vector(5, 5), new Vector(2, 5) ]); So, the top edge would be [poly.vertices[0], poly.vertices[1]]. I need to stretch this polygon by moving each edge away from the center of the polygon by one unit, along that edge's normal. The following example shows the first edge, the top, moved one unit up: The final polygon should look like this new one: var finalPoly = new Polygon([ new Vector(1, 1), new Vector(6, 1), new Vector(6, 6), new Vector(1, 6) ]); It is important that I iterate, moving one edge at a time, because I will be doing some collision tests after moving each edge. Here is what I tried so far (simplified for clarity), which fails triumphantly: for(var i = 0; i < vertices.length; i++) { var a = vertices[i], b = vertices[i + 1] || vertices[0]; // in case of final vertex var ax = a.x, ay = a.y, bx = b.x, by = b.y; // get some new perpendicular vectors var a2 = new Vector(-ay, ax), b2 = new Vector(-by, bx); // make into unit vectors a2.convertToUnitVector(); b2.convertToUnitVector(); // add the new vectors to the original ones a.add(a2); b.add(b2); // the rest of the code, collision tests, etc. } This makes my polygon start slowly rotating and sliding to the left, instead of what I need. Finally, the example shows a square, but the polygons in question could be anything. They will always be convex, and always with vertices in clockwise order.

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  • Implementing Circle Physics in Java

    - by Shijima
    I am working on a simple physics based game where 2 balls bounce off each other. I am following a tutorial, 2-Dimensional Elastic Collisions Without Trigonometry, for the collision reactions. I am using Vector2 from the LIBGDX library to handle vectors. I am a bit confused on how to implement step 6 in Java from the tutorial. Below is my current code, please note that the code strictly follows the tutorial and there are redundant pieces of code which I plan to refactor later. Note: refrences to this refer to ball 1, and ball refers to ball 2. /* * Step 1 * * Find the Normal, Unit Normal and Unit Tangential vectors */ Vector2 n = new Vector2(this.position[0] - ball.position[0], this.position[1] - ball.position[1]); Vector2 un = n.normalize(); Vector2 ut = new Vector2(-un.y, un.x); /* * Step 2 * * Create the initial (before collision) velocity vectors */ Vector2 v1 = this.velocity; Vector2 v2 = ball.velocity; /* * Step 3 * * Resolve the velocity vectors into normal and tangential components */ float v1n = un.dot(v1); float v1t = ut.dot(v1); float v2n = un.dot(v2); float v2t = ut.dot(v2); /* * Step 4 * * Find the new tangential Velocities after collision */ float v1tPrime = v1t; float v2tPrime = v2t; /* * Step 5 * * Find the new normal velocities */ float v1nPrime = v1n * (this.mass - ball.mass) + (2 * ball.mass * v2n) / (this.mass + ball.mass); float v2nPrime = v2n * (ball.mass - this.mass) + (2 * this.mass * v1n) / (this.mass + ball.mass); /* * Step 6 * * Convert the scalar normal and tangential velocities into vectors??? */

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  • What is the most efficient way to handle points / small vectors in JavaScript?

    - by Chris
    Currently I'm creating an web based (= JavaScript) application thata is using a lot of "points" (= small, fixed size vectors). There are basically two obvious ways of representing them: var pointA = [ xValue, yValue ]; and var pointB = { x: xValue, y: yValue }; So translating my point a bit would look like: var pointAtrans = [ pointA[0] + 3, pointA[1] + 4 ]; var pointBtrans = { x: pointB.x + 3, pointB.y + 4 }; Both are easy to handle from a programmer point of view (the object variant is a bit more readable, especially as I'm mostly dealing with 2D data, seldom with 3D and hardly with 4D - but never more. It'll allways fit into x,y,z and w) But my question is now: What is the most efficient way from the language perspective - theoretically and in real implementations? What are the memory requirements? What are the setup costs of an array vs. an object? ... My target browsers are FireFox and the Webkit based ones (Chromium, Safari), but it wouldn't hurt to have a great (= fast) experience under IE and Opera as well...

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  • How can I use Font Awesome vectors in Illustrator?

    - by david.joyce13
    I'm stumped. As directed, I printed the Font Awesome Cheatsheet to PDF. When I open it with Acrobat Reader, it looks fine. However, when I try to open it with Illustrator, I get this warning: The font MuseoSlab-500 is missing. Affected text will be displayed using a substitute font. The font OTS-derived-font is missing. Affected text will be displayed using a substitute font. The font ProximaNova-Regular is missing. Affected text will be displayed using a substitute font. How can I 'fix' the PDF, so that I can see and use the icons in Illustrator?

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  • Angle between two 2d vectors, diff between two methods?

    - by Sean Ochoa
    Hey all. I've got this code snippet, and I'm wondering why the results of the first method differ from the results of the second method, given the same input? public double AngleBetween_1(vector a, vector b) { var dotProd = a.Dot(b); var lenProd = a.Len*b.Len; var divOperation = dotProd/lenProd; return Math.Acos(divOperation) * (180.0 / Math.PI); } public double AngleBetween_2(vector a, vector b) { var dotProd = a.Dot(b); var lenProd = a.Len*b.Len; var divOperation = dotProd/lenProd; return (1/Math.Cos(divOperation)) * (180.0 / Math.PI); }

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  • C# - Angle between two 2d vectors, diff between two methods?

    - by Sean Ochoa
    Hey all. I've got this code snippet, and I'm wondering why the results of the first method differ from the results of the second method, given the same input? public double AngleBetween_1(vector a, vector b) { var dotProd = a.Dot(b); var lenProd = Len*b.Len; var divOperation = dotProd/lenProd; return Math.Acos(divOperation) * (180.0 / Math.PI); } public double AngleBetween_2(vector a, vector b) { var dotProd = a.Dot(b); var lenProd = Len*b.Len; var divOperation = dotProd/lenProd; return (1/Math.Cos(divOperation)) * (180.0 / Math.PI); }

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  • GIS: When and why to use ArcObjects over GDAL programming to work with ArcGIS rasters and vectors?

    - by anotherobject
    Im just starting off with GDAL + python to support operations that cannot be done with ArcGIS python geoprocessing scripting. Mainly I am doing spatial modeling/analysis/editing of raster and vector data. I am a bit confused when ArcObject development is required versus when GDAL can be used? Is there functionality of ArcObjects that GDAL does not do? Is the opposite true too? I am assuming that ArcObjects are more useful in developing online tools versus Desktop analysis and modeling where the difference is more to do with preference? In my case i prefer GDAL because of python support, which I believe ArcObjects lack. thanks!

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  • C++: is it safe to work with std::vectors as if they were arrays?

    - by peoro
    I need to have a fixed-size array of elements and to call on them functions that require to know about how they're placed in memory, in particular: functions like glVertexPointer, that needs to know where the vertices are, how distant they are one from the other and so on. In my case vertices would be members of the elements to store. to get the index of an element within this array, I'd prefer to avoid having an index field within my elements, but would rather play with pointers arithmetic (ie: index of Element *x will be x - & array[0]) -- btw, this sounds dirty to me: is it good practice or should I do something else? Is it safe to use std::vector for this? Something makes me think that an std::array would be more appropriate but: Constructor and destructor for my structure will be rarely called: I don't mind about such overhead. I'm going to set the std::vector capacity to size I need (the size that would use for an std::array, thus won't take any overhead due to sporadic reallocation. I don't mind a little space overhead for std::vector's internal structure. I could use the ability to resize the vector (or better: to have a size chosen during setup), and I think there's no way to do this with std::array, since its size is a template parameter (that's too bad: I could do that even with an old C-like array, just dynamically allocating it on the heap). If std::vector is fine for my purpose I'd like to know into details if it will have some runtime overhead with respect to std::array (or to a plain C array): I know that it'll call the default constructor for any element once I increase its size (but I guess this won't cost anything if my data has got an empty default constructor?), same for destructor. Anything else?

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  • Find consecutive sub-vectors of length k out of a numeric vector which satisfy a given condition

    - by user3559153
    I have a numeric vector in R, say v= c(2,3,5,6,7,6,3,2,3,4,5,7,8,9,6,1,1,2,5,6,7,11,2,3,4). Now, I have to find all the consecutive sub-vector of size 4 out of it with the condition that each element of the sub-vector must be greater than 2 and all sub-vector must be disjoint in the sense that non of the two sub-vector can contain same index element. So my output will be: (3,5,6,7),(3,4,5,7),(5,6,7,11). [Explanation: c(2,3,5,6,7,6,3,2,3,4,5,7,8,9,6,1,3,2,5,6,7,11,2,3,4) ]

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  • Is there a simple isometric graphical game engine (using vectors?) that could be used for a (multiplayer) crafting/farming game? [closed]

    - by Renier Wijnen
    Possible Duplicate: Good, free isometric game engine? With little game development experience (albeit having graphical skills and some programming knowledge) a group currently working on a game used to explain permaculture through interaction would like to create a simple concept game. Is there a specific engine or set of tools we could used to achieve this? Being able to make it an (online) multiplayer game would be much preferred. Thank you in advance for your input.

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  • 2D OBB collision detection, resolving collisions?

    - by Milo
    I currently use OBBs and I have a vehicle that is a rigid body and some buildings. Here is my update() private void update() { camera.setPosition((vehicle.getPosition().x * camera.getScale()) - ((getWidth() ) / 2.0f), (vehicle.getPosition().y * camera.getScale()) - ((getHeight() ) / 2.0f)); //camera.move(input.getAnalogStick().getStickValueX() * 15.0f, input.getAnalogStick().getStickValueY() * 15.0f); if(input.isPressed(ControlButton.BUTTON_GAS)) { vehicle.setThrottle(1.0f, false); } if(input.isPressed(ControlButton.BUTTON_BRAKE)) { vehicle.setBrakes(1.0f); } vehicle.setSteering(input.getAnalogStick().getStickValueX()); vehicle.update(16.6666f / 1000.0f); ArrayList<Building> buildings = city.getBuildings(); for(Building b : buildings) { if(vehicle.getRect().overlaps(b.getRect())) { vehicle.update(-17.0f / 1000.0f); break; } } } The collision detection works well. What doesn't is how they are dealt with. My goal is simple. If the vehicle hits a building, it should stop, and never go into the building. When I apply negative torque to reverse the car should not feel buggy and move away from the building. I don't want this to look buggy. This is my rigid body class: class RigidBody extends Entity { //linear private Vector2D velocity = new Vector2D(); private Vector2D forces = new Vector2D(); private float mass; //angular private float angularVelocity; private float torque; private float inertia; //graphical private Vector2D halfSize = new Vector2D(); private Bitmap image; public RigidBody() { //set these defaults so we don't get divide by zeros mass = 1.0f; inertia = 1.0f; } //intialize out parameters public void initialize(Vector2D halfSize, float mass, Bitmap bitmap) { //store physical parameters this.halfSize = halfSize; this.mass = mass; image = bitmap; inertia = (1.0f / 20.0f) * (halfSize.x * halfSize.x) * (halfSize.y * halfSize.y) * mass; RectF rect = new RectF(); float scalar = 10.0f; rect.left = (int)-halfSize.x * scalar; rect.top = (int)-halfSize.y * scalar; rect.right = rect.left + (int)(halfSize.x * 2.0f * scalar); rect.bottom = rect.top + (int)(halfSize.y * 2.0f * scalar); setRect(rect); } public void setLocation(Vector2D position, float angle) { getRect().set(position, getWidth(), getHeight(), angle); } public Vector2D getPosition() { return getRect().getCenter(); } @Override public void update(float timeStep) { //integrate physics //linear Vector2D acceleration = Vector2D.scalarDivide(forces, mass); velocity = Vector2D.add(velocity, Vector2D.scalarMultiply(acceleration, timeStep)); Vector2D c = getRect().getCenter(); c = Vector2D.add(getRect().getCenter(), Vector2D.scalarMultiply(velocity , timeStep)); setCenter(c.x, c.y); forces = new Vector2D(0,0); //clear forces //angular float angAcc = torque / inertia; angularVelocity += angAcc * timeStep; setAngle(getAngle() + angularVelocity * timeStep); torque = 0; //clear torque } //take a relative Vector2D and make it a world Vector2D public Vector2D relativeToWorld(Vector2D relative) { Matrix mat = new Matrix(); float[] Vector2Ds = new float[2]; Vector2Ds[0] = relative.x; Vector2Ds[1] = relative.y; mat.postRotate(JMath.radToDeg(getAngle())); mat.mapVectors(Vector2Ds); return new Vector2D(Vector2Ds[0], Vector2Ds[1]); } //take a world Vector2D and make it a relative Vector2D public Vector2D worldToRelative(Vector2D world) { Matrix mat = new Matrix(); float[] Vectors = new float[2]; Vectors[0] = world.x; Vectors[1] = world.y; mat.postRotate(JMath.radToDeg(-getAngle())); mat.mapVectors(Vectors); return new Vector2D(Vectors[0], Vectors[1]); } //velocity of a point on body public Vector2D pointVelocity(Vector2D worldOffset) { Vector2D tangent = new Vector2D(-worldOffset.y, worldOffset.x); return Vector2D.add( Vector2D.scalarMultiply(tangent, angularVelocity) , velocity); } public void applyForce(Vector2D worldForce, Vector2D worldOffset) { //add linear force forces = Vector2D.add(forces ,worldForce); //add associated torque torque += Vector2D.cross(worldOffset, worldForce); } @Override public void draw( GraphicsContext c) { c.drawRotatedScaledBitmap(image, getPosition().x, getPosition().y, getWidth(), getHeight(), getAngle()); } } Essentially, when any rigid body hits a building it should exhibit the same behavior. How is collision solving usually done? Thanks

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  • For normal mapping, why can we not simply add the tangent normal to the surface normal?

    - by sebf
    I am looking at implementing bump mapping (which in all implementations I have seen is really normal mapping), and so far all I have read says that to do this, we create a matrix to convert from world-space to tangent-space, in order to transform the lights and eye direction vectors into tangent space, so that the vectors from the normal map may be used directly in place of those passed through from the vertex shader. What I do not understand though, is why we cannot just use the normalised sum of the sampled-normal vector, and the surface-normal? (assuming we already transform and pass through the surface normal for the existing lighting functions) Take the diagram below; the normal is simply the deviation from the 'reference normal' for any given coordinate system, correct? And transforming the surface normal of a mapped surface from world space to tangent space makes it equivalent to the tangent space 'reference normal', no? If so, why do we transform all lighting vectors into tangent space, instead of simply transforming the sampled tangent once in the pixel shader?

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  • Loading Wavefront Data into VAO and Render It

    - by Jordan LaPrise
    I have successfully loaded a triangulated wavefront(.obj) into 6 vectors, the first 3 vectors contain the locations for vertices, uv coords, and normals. The last three have the indices stored for each of the faces. I have been looking into using VAO's and VBO's to render, and I'm not quite sure how to load and render the data. One of my biggest concerns is the fact that indexed rendering only allows you to have one array of indices, meaning I somehow have to make all of the first three vectors the same size, the only way I thought of doing this, is to make 3 new vertex's of equal size, and load in the data for each face, but that would completely defeat the purpose of indexing. Any help would be appreciated. Thanks in advance, Jordan

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  • When to use an Array vs When to use a Vector, when dealing with GameObjects?

    - by user32465
    I understand that from other answers, Arrays and Vectors are the best choices. Many on SE claim that Linked Lists and Maps are bad for video game programming. I understand that for the most part, I can use Arrays. However, I don't really understand exactly when to use Vectors over Arrays. Why even use Vectors? Wouldn't it be best if I simply always used an Array, that way I know how much memory my game needs? Specifically my game would only ever load a single "Map" area of tiles, such as Map[100][100], so I could very easily have an array of GameObjectContainer GameObjects[100][100], which would reserve an entire map's worth of possible gameobjects, correct? So why use a Vector instead? Memory is quite large on modern hardware.

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  • Making only the outer vector in vector<vector<int>> fixed

    - by Dennis Ritchie
    I want to create a vector<vector<int>> where the outer vector is fixed (always containing the same vectors), but the inner vectors can be changed. For example: int n = 2; //decided at runtime assert(n>0); vector<vector<int>> outer(n); //outer vector contains n empty vectors outer.push_back(vector<int>()); //modifying outer vector - this should be error auto outer_it = outer.begin(); (*outer_it).push_back(3); //modifying inner vector. should work (which it does). I tried doing simply const vector<vector<int>>, but that makes even the inner vectors const. Is my only option to create my own custom FixedVectors class, or are there better ways out there to do this?

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  • How to perform spatial partitioning in n-dimensions?

    - by kevin42
    I'm trying to design an implementation of Vector Quantization as a c++ template class that can handle different types and dimensions of vectors (e.g. 16 dimension vectors of bytes, or 4d vectors of doubles, etc). I've been reading up on the algorithms, and I understand most of it: here and here I want to implement the Linde-Buzo-Gray (LBG) Algorithm, but I'm having difficulty figuring out the general algorithm for partitioning the clusters. I think I need to define a plane (hyperplane?) that splits the vectors in a cluster so there is an equal number on each side of the plane. [edit to add more info] This is an iterative process, but I think I start by finding the centroid of all the vectors, then use that centroid to define the splitting plane, get the centroid of each of the sides of the plane, continuing until I have the number of clusters needed for the VQ algorithm (iterating to optimize for less distortion along the way). The animation in the first link above shows it nicely. My questions are: What is an algorithm to find the plane once I have the centroid? How can I test a vector to see if it is on either side of that plane?

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  • The fastest way to iterate through a collection of objects

    - by Trev
    Hello all, First to give you some background: I have some research code which performs a Monte Carlo simulation, essential what happens is I iterate through a collection of objects, compute a number of vectors from their surface then for each vector I iterate through the collection of objects again to see if the vector hits another object (similar to ray tracing). The pseudo code would look something like this for each object { for a number of vectors { do some computations for each object { check if vector intersects } } } As the number of objects can be quite large and the amount of rays is even larger I thought it would be wise to optimise how I iterate through the collection of objects. I created some test code which tests arrays, lists and vectors and for my first test cases found that vectors iterators were around twice as fast as arrays however when I implemented a vector in my code in was somewhat slower than the array I was using before. So I went back to the test code and increased the complexity of the object function each loop was calling (a dummy function equivalent to 'check if vector intersects') and I found that when the complexity of the function increases the execution time gap between arrays and vectors reduces until eventually the array was quicker. Does anyone know why this occurs? It seems strange that execution time inside the loop should effect the outer loop run time.

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  • Distance between numpy arrays, columnwise

    - by Jaapsneep
    I have 2 arrays in 2D, where the column vectors are feature vectors. One array is of size F x A, the other of F x B, where A << B. As an example, for A = 2 and F = 3 (B can be anything): arr1 = np.array( [[1, 4], [2, 5], [3, 6]] ) arr2 = np.array( [[1, 4, 7, 10, ..], [2, 5, 8, 11, ..], [3, 6, 9, 12, ..]] ) I want to calculate the distance between arr1 and a fragment of arr2 that is of equal size (in this case, 3x2), for each possible fragment of arr2. The column vectors are independent of each other, so I believe I should calculate the distance between each column vector in arr1 and a collection of column vectors ranging from i to i + A from arr2 and take the sum of these distances (not sure though). Does numpy offer an efficient way of doing this, or will I have to take slices from the second array and, using another loop, calculate the distance between each column vector in arr1 and the corresponding column vector in the slice?

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  • small string optimization for vector?

    - by BuschnicK
    I know several (all?) STL implementations implement a "small string" optimization where instead of storing the usual 3 pointers for begin, end and capacity a string will store the actual character data in the memory used for the pointers if sizeof(characters) <= sizeof(pointers). I am in a situation where I have lots of small vectors with an element size <= sizeof(pointer). I cannot use fixed size arrays, since the vectors need to be able to resize dynamically and may potentially grow quite large. However, the median (not mean) size of the vectors will only be 4-12 bytes. So a "small string" optimization adapted to vectors would be quite useful to me. Does such a thing exist? I'm thinking about rolling my own by simply brute force converting a vector to a string, i.e. providing a vector interface to a string. Good idea?

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  • Very fast document similarity

    - by peyton
    Hello, I am trying to determine document similarity between a single document and each of a large number of documents (n ~= 1 million) as quickly as possible. More specifically, the documents I'm comparing are e-mails; they are grouped (i.e., there are folders or tags) and I'd like to determine which group is most appropriate for a new e-mail. Fast performance is critical. My a priori assumption is that the cosine similarity between term vectors is appropriate for this application; please comment on whether this is a good measure to use or not! I have already taken into account the following possibilities for speeding up performance: Pre-normalize all the term vectors Calculate a term vector for each group (n ~= 10,000) rather than each e-mail (n ~= 1,000,000); this would probably be acceptable for my application, but if you can think of a reason not to do it, let me know! I have a few questions: If a new e-mail has a new term never before seen in any of the previous e-mails, does that mean I need to re-compute all of my term vectors? This seems expensive. Is there some clever way to only consider vectors which are likely to be close to the query document? Is there some way to be more frugal about the amount of memory I'm using for all these vectors? Thanks!

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