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  • Qt drag & drop button; drop not detecting

    - by Thomas Verbeke
    I'm creating a 2D game in QT and i'm trying to implement a drag & drop into my program. For some reason the drop is not registered: qDebug should print a message on dropping but this doesn't happen. #include "dialog.h" #include "ui_dialog.h" #include "world.h" #include <vector> Dialog::Dialog(QWidget *parent) : QDialog(parent), ui(new Ui::Dialog) { ui->setupUi(this); scene = new QGraphicsScene(this); ui->graphicsView->setScene(scene); MySquare *item; QGraphicsRectItem *enemyItem; World *myWorld = new World(); std::vector<Tile*> tiles = myWorld->createWorld(":/texture.jpg"); int count = 0; foreach (Tile *tile, tiles){ count++; item = new MySquare(tile->getXPos()*4,tile->getYPos()*4,4,4); item->setBrush(QColor(tile->getValue()*255,tile->getValue()*255,tile->getValue()*255)); item->setAcceptDrops(true); scene->addItem(item); } player = new MySquare(10,20,10,10); player->setAcceptDrops(true); scene->addItem(player); //drag & drop part QPushButton *pushButton = new QPushButton("Click Me",this); connect(pushButton,SIGNAL(pressed()),this,SLOT(makeDrag())); setAcceptDrops(true); } void Dialog::makeDrag() { QDrag *dr = new QDrag(this); // The data to be transferred by the drag and drop operation is contained in a QMimeData object QMimeData *data = new QMimeData; data->setText("This is a test"); // Assign ownership of the QMimeData object to the QDrag object. dr->setMimeData(data); // Start the drag and drop operation dr->start(); } mysquare.cpp #include "mysquare.h" MySquare::MySquare(int _x,int _y, int _w, int _h) { isPlayer=false; Pressed=false; setFlag(ItemIsMovable); setFlag(ItemIsFocusable); setAcceptDrops(true); color=Qt::red; color_pressed = Qt::green; x = _x; y = _y; w = _w; h = _h; } QRectF MySquare::boundingRect() const { return QRectF(x,y,w,h); } void MySquare::paint(QPainter *painter, const QStyleOptionGraphicsItem *option, QWidget *widget) { QRectF rec = boundingRect(); QBrush brush(color); if (Pressed){ brush.setColor(color); } else { brush.setColor(color_pressed); } painter->fillRect(rec,brush); painter->drawRect(rec); } void MySquare::mousePressEvent(QGraphicsSceneMouseEvent *event) { Pressed=true; update(); QGraphicsItem::mousePressEvent(event); qDebug() << "mouse Pressed"; } void MySquare::mouseReleaseEvent(QGraphicsSceneMouseEvent *event) { Pressed=false; update(); QGraphicsItem::mousePressEvent(event); qDebug() << "mouse Released"; } void MySquare::keyPressEvent(QKeyEvent *event){ int x = pos().x(); int y = pos().y(); //key handling QGraphicsItem::keyPressEvent(event); } void MySquare::dropEvent(QDropEvent *event) { qDebug("dropEvent - square"); // Unpack dropped data and handle it the way you want qDebug("Contents: %s", event->mimeData()->text().toLatin1().data()); } void MySquare::dragMoveEvent(QDragMoveEvent *event){ qDebug("dragMoveEvent - square "); event->accept(); } void MySquare::dragEnterEvent(QDragEnterEvent *event){ event->setAccepted(true); qDebug("dragEnterEvent - square"); event->acceptProposedAction(); } void MySquare::setBrush(QColor _color){ color = _color; color_pressed = _color; update(); //repaint } edit; there is no problem with qDebug() i'm just using it to test them i'm inside the drag events..which i'm not

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  • Animation issue caused by C# parameters passed by reference rather than value, but where?

    - by Jordan Roher
    I'm having trouble with sprite animation in XNA that appears to be caused by a struct passed as a reference value. But I'm not using the ref keyword anywhere. I am, admittedly, a C# noob, so there may be some shallow bonehead error in here, but I can't see it. I'm creating 10 ants or bees and animating them as they move across the screen. I have an array of animation structs, and each time I create an ant or bee, I send it the animation array value it requires (just [0] or [1] at this time). Deep inside the animation struct is a timer that is used to change frames. The ant/bee class stores the animation struct as a private variable. What I'm seeing is that each ant or bee uses the same animation struct, the one I thought I was passing in and copying by value. So during Update(), when I advance the animation timer for each ant/bee, the next ant/bee has its animation timer advanced by that small amount. If there's 1 ant on screen, it animates properly. 2 ants, it runs twice as fast, and so on. Obviously, not what I want. Here's an abridged version of the code. How is BerryPicking's ActorAnimationGroupData[] getting shared between the BerryCreatures? class BerryPicking { private ActorAnimationGroupData[] animations; private BerryCreature[] creatures; private Dictionary<string, Texture2D> creatureTextures; private const int maxCreatures = 5; public BerryPickingExample() { this.creatures = new BerryCreature[maxCreatures]; this.creatureTextures = new Dictionary<string, Texture2D>(); } public void LoadContent() { // Returns data from an XML file Reader reader = new Reader(); animations = reader.LoadAnimations(); CreateCreatures(); } // This is called from another function I'm not including because it's not relevant to the problem. // In it, I remove any creature that passes outside the viewport by setting its creatures[] spot to null. // Hence the if(creatures[i] == null) test is used to recreate "dead" creatures. Inelegant, I know. private void CreateCreatures() { for (int i = 0; i < creatures.Length; i++) { if (creatures[i] == null) { // In reality, the name selection is randomized creatures[i] = new BerryCreature("ant"); // Load content and texture (which I create elsewhere) creatures[i].LoadContent( FindAnimation(creatures[i].Name), creatureTextures[creatures[i].Name]); } } } private ActorAnimationGroupData FindAnimation(string animationName) { int yourAnimation = -1; for (int i = 0; i < animations.Length; i++) { if (animations[i].name == animationName) { yourAnimation = i; break; } } return animations[yourAnimation]; } public void Update(GameTime gameTime) { for (int i = 0; i < creatures.Length; i++) { creatures[i].Update(gameTime); } } } class Reader { public ActorAnimationGroupData[] LoadAnimations() { ActorAnimationGroupData[] animationGroup; XmlReader file = new XmlTextReader(filename); // Do loading... // Then later file.Close(); return animationGroup; } } class BerryCreature { private ActorAnimation animation; private string name; public BerryCreature(string name) { this.name = name; } public void LoadContent(ActorAnimationGroupData animationData, Texture2D sprite) { animation = new ActorAnimation(animationData); animation.LoadContent(sprite); } public void Update(GameTime gameTime) { animation.Update(gameTime); } } class ActorAnimation { private ActorAnimationGroupData animation; public ActorAnimation(ActorAnimationGroupData animation) { this.animation = animation; } public void LoadContent(Texture2D sprite) { this.sprite = sprite; } public void Update(GameTime gameTime) { animation.Update(gameTime); } } struct ActorAnimationGroupData { // There are lots of other members of this struct, but the timer is the only one I'm worried about. // TimerData is another struct private TimerData timer; public ActorAnimationGroupData() { timer = new TimerData(2); } public void Update(GameTime gameTime) { timer.Update(gameTime); } } struct TimerData { public float currentTime; public float maxTime; public TimerData(float maxTime) { this.currentTime = 0; this.maxTime = maxTime; } public void Update(GameTime gameTime) { currentTime += (float)gameTime.ElapsedGameTime.TotalSeconds; if (currentTime >= maxTime) { currentTime = maxTime; } } }

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  • Image/"most resembling pixel" search optimization?

    - by SigTerm
    The situation: Let's say I have an image A, say, 512x512 pixels, and image B, 5x5 or 7x7 pixels. Both images are 24bit rgb, and B have 1bit alpha mask (so each pixel is either completely transparent or completely solid). I need to find within image A a pixel which (with its' neighbors) most closely resembles image B, OR the pixel that probably most closely resembles image B. Resemblance is calculated as "distance" which is sum of "distances" between non-transparent B's pixels and A's pixels divided by number of non-transparent B's pixels. Here is a sample SDL code for explanation: struct Pixel{ unsigned char b, g, r, a; }; void fillPixel(int x, int y, SDL_Surface* dst, SDL_Surface* src, int dstMaskX, int dstMaskY){ Pixel& dstPix = *((Pixel*)((char*)(dst->pixels) + sizeof(Pixel)*x + dst->pitch*y)); int xMin = x + texWidth - searchWidth; int xMax = xMin + searchWidth*2; int yMin = y + texHeight - searchHeight; int yMax = yMin + searchHeight*2; int numFilled = 0; for (int curY = yMin; curY < yMax; curY++) for (int curX = xMin; curX < xMax; curX++){ Pixel& cur = *((Pixel*)((char*)(dst->pixels) + sizeof(Pixel)*(curX & texMaskX) + dst->pitch*(curY & texMaskY))); if (cur.a != 0) numFilled++; } if (numFilled == 0){ int srcX = rand() % src->w; int srcY = rand() % src->h; dstPix = *((Pixel*)((char*)(src->pixels) + sizeof(Pixel)*srcX + src->pitch*srcY)); dstPix.a = 0xFF; return; } int storedSrcX = rand() % src->w; int storedSrcY = rand() % src->h; float lastDifference = 3.40282347e+37F; //unsigned char mask = for (int srcY = searchHeight; srcY < (src->h - searchHeight); srcY++) for (int srcX = searchWidth; srcX < (src->w - searchWidth); srcX++){ float curDifference = 0; int numPixels = 0; for (int tmpY = -searchHeight; tmpY < searchHeight; tmpY++) for(int tmpX = -searchWidth; tmpX < searchWidth; tmpX++){ Pixel& tmpSrc = *((Pixel*)((char*)(src->pixels) + sizeof(Pixel)*(srcX+tmpX) + src->pitch*(srcY+tmpY))); Pixel& tmpDst = *((Pixel*)((char*)(dst->pixels) + sizeof(Pixel)*((x + dst->w + tmpX) & dstMaskX) + dst->pitch*((y + dst->h + tmpY) & dstMaskY))); if (tmpDst.a){ numPixels++; int dr = tmpSrc.r - tmpDst.r; int dg = tmpSrc.g - tmpDst.g; int db = tmpSrc.g - tmpDst.g; curDifference += dr*dr + dg*dg + db*db; } } if (numPixels) curDifference /= (float)numPixels; if (curDifference < lastDifference){ lastDifference = curDifference; storedSrcX = srcX; storedSrcY = srcY; } } dstPix = *((Pixel*)((char*)(src->pixels) + sizeof(Pixel)*storedSrcX + src->pitch*storedSrcY)); dstPix.a = 0xFF; } This thing is supposed to be used for texture generation. Now, the question: The easiest way to do this is brute force search (which is used in example routine). But it is slow - even using GPU acceleration and dual core cpu won't make it much faster. It looks like I can't use modified binary search because of B's mask. So, how can I find desired pixel faster? Additional Info: It is allowed to use 2 cores, GPU acceleration, CUDA, and 1.5..2 gigabytes of RAM for the task. I would prefer to avoid some kind of lengthy preprocessing phase that will take 30 minutes to finish. Ideas?

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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  • XNA 4.0 SpriteBatch.Draw Out Of Memory Exception Thrown

    - by RustyGearGames
    Well, first of all, my guess is that I'm calling the spritebatch.draw() method to many times, but I need to (Or, it's the only way I can figure out how to) Draw my in-game windows. I'll just go ahead and dump my code; using System; using System.Text; using System.Collections.Generic; using System.Linq; using Microsoft.Xna.Framework; using Microsoft.Xna.Framework.Audio; using Microsoft.Xna.Framework.Content; using Microsoft.Xna.Framework.GamerServices; using Microsoft.Xna.Framework.Graphics; using Microsoft.Xna.Framework.Input; using Microsoft.Xna.Framework.Media; namespace System.Window { class Window { #region Variables public Texture2D importedTexture; public Texture2D WindowSkin; public RenderTarget2D currentWindow; public RenderTarget2D windowTexture; public Vector2 pos; public int prevWindowWidth; public int prevWindowHeight; public int windowWidth; public int windowHeight; public bool visible; public bool active; public bool drawNew; #region Rectangles public Rectangle clickRect; public Rectangle topLeftRect; public Rectangle topRightRect; public Rectangle buttonRect; public Rectangle botLeftRect; public Rectangle botRightRect; #endregion #endregion public Window() { } public void Initialize(GraphicsDevice g, Texture2D ws, Texture2D it, int w, int h, bool v, bool a) { WindowSkin = ws; importedTexture = it; windowWidth = w; prevWindowWidth = w; windowHeight = h; prevWindowHeight = h; windowTexture = new RenderTarget2D(g, windowWidth, windowHeight); currentWindow = windowTexture; visible = v; active = a; drawNew = true; topLeftRect = new Rectangle(0, 0, 32, 32); topRightRect = new Rectangle(32, 0, 32, 32); buttonRect = new Rectangle(64, 0, 32, 32); botLeftRect = new Rectangle(0, 64, 32, 32); botRightRect = new Rectangle(64, 64, 32, 32); } public void Update(GraphicsDevice g, Vector2 p, int width, int height) { prevWindowWidth = windowWidth; prevWindowHeight = windowHeight; pos = p; windowWidth = width; windowHeight = height; windowTexture = new RenderTarget2D(g, windowWidth+2, windowHeight+2); } public void Draw(SpriteBatch s, GraphicsDevice g) { s.Draw(currentWindow, pos, new Rectangle(0, 0, windowWidth, windowHeight), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); } public void DrawNewWindow(SpriteBatch s, GraphicsDevice g) { g.SetRenderTarget(windowTexture); g.Clear(Color.Transparent); s.Begin(); #region Draw Background for (int w = 3; w < (windowWidth); w += 32) { for (int h = 32; h < (windowHeight); h += 32) { s.Draw(WindowSkin, new Vector2(w, h), new Rectangle(32, 32, 32, 32), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); } } #endregion s.Draw(importedTexture, new Vector2(3, 32), new Rectangle(0, 0, importedTexture.Width, importedTexture.Height), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); #region Draw resizables for (int i = 32; i < (windowWidth - 64); i += 32) { s.Draw(WindowSkin, new Vector2(i, 0), new Rectangle(16, 0, 32, 32), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); } for (int i = 32; i < (windowWidth - 32); i += 32) { s.Draw(WindowSkin, new Vector2(i, windowHeight - 32), new Rectangle(32, 64, 32, 32), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); } for (int i = 64; i < (windowHeight - 32); i += 32) { s.Draw(WindowSkin, new Vector2(0, i), new Rectangle(0, 48, 32, 32), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); } for (int i = 64; i < (windowHeight - 32); i += 32) { s.Draw(WindowSkin, new Vector2(windowWidth - 32, i), new Rectangle(64, 48, 32, 32), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); } #endregion #region Draw Corners s.Draw(WindowSkin, new Vector2(0, 0), topLeftRect, Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); s.Draw(WindowSkin, new Vector2(0, 32), new Rectangle(0, 32, 32, 32), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); s.Draw(WindowSkin, new Vector2(windowWidth - 64, 0), topRightRect, Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); s.Draw(WindowSkin, new Vector2(windowWidth - 32, 32), new Rectangle(64, 32, 32, 32), Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); s.Draw(WindowSkin, new Vector2(windowWidth - 32, 0), buttonRect, Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); s.Draw(WindowSkin, new Vector2(0, windowHeight - 32), botLeftRect, Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); s.Draw(WindowSkin, new Vector2(windowWidth - 32, windowHeight - 32), botRightRect, Color.White, 0, Vector2.Zero, 1.0f, SpriteEffects.None, 0); #endregion s.End(); currentWindow = windowTexture; } } } It's all nice and configured for my little windowskin texture, and such. the only problem is that it will get a little laggy, and then completely crash on me about a minute into running it. It throws an Out Of Memory Exception, but I don't know and can't find any other topic or post on this relating to spritebatch. Does anybody have any suggestions on how I can get this working and not take up much memory? I would think this as an easy, cost effective way of drawing a window. I'm just not sure how cut down on my draw calls, or get any of that memory back.

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