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  • Simple C++ program on multidimensional arrays - Getting C2143 error among others. Not sure why?

    - by noobzilla
    Here is my simple multidimensional array program. The first error occurs where I declare the function addmatrices and then a second one where it is implemented. I am also getting an undefined variable error for bsize. What am I doing incorrectly? #include <iostream> #include <fstream> #include <string> #include <iomanip> using namespace std; //Function declarations void constmultiply (double matrixA[][4], int asize, double matrixC[][4], int bsize, double multiplier); //Pre: The address of the output file, the matrix to be multiplied by the constant, the matrix in which // the resultant values will be stored and the multiplier are passed in. //Post: The matrix is multiplied by the multiplier and the results are displayed on screen and written to the // output file. int addmatrices (double matrixA[][4], int asize, double matrixB[]4], int bsize, double matrixC[][4], int csize); //Pre: The addresses of three matrices are passed in //Post: The values in each of the two matrices are added together and put into a third matrix //Error Codes int INPUT_FILE_FAIL = 1; int UNEQUAL_MATRIX_SIZE = 2; //Constants const double multiplier = 2.5; const int rsize = 4; const int csize = 4; //Main Driver int main() { //Declare the two matrices double matrix1 [rsize][csize]; double matrix2 [rsize][csize]; double matrix3 [rsize][csize]; //Variables double temp; string filename; //Declare filestream object ifstream infile; //Ask the user for the name of the input file cout << "Please enter the name of the input file: "; cin >> filename; //Open the filestream object infile.open(filename.c_str()); //Verify that the input file opened correctly if (infile.fail()) { cout << "Input file failed to open" <<endl; exit(INPUT_FILE_FAIL); } //Begin reading in data from the first matrix for (int i = 0; i <= 3; i++)//i = row { for (int j = 0; j <= 3; j++)// j = column { infile >> temp; matrix1[i][j] = temp; } } //Begin reading in data from the second matrix for (int k = 0; k <= 3; k++)// k = row { for (int l = 0; l <= 3; l++)// l = column { infile >> temp; matrix2[k][l] = temp; } } //Notify user cout << "Input file open, reading matrices...Done!" << endl << "Read in 2 matrices..."<< endl; //Output the values read in for Matrix 1 for (int i = 0; i <= 3; i++) { for (int j = 0; j <= 3; j ++) { cout << setprecision(1) << matrix1[i][j] << setw(8); } cout << "\n"; } cout << setw(40)<< setfill('-') << "-" << endl ; //Output the values read in for Matrix 2 for (int i = 0; i <= 3; i++) { for (int j = 0; j <= 3; j ++) { cout << setfill(' ') << setprecision(2) << matrix2[i][j] << setw(8); } cout << "\n"; } cout << setw(40)<< setfill('-') << "-" << endl ; //Multiply matrix 1 by the multiplier value constmultiply (matrix1, rsize, matrix3, rsize, multiplier); //Output matrix 3 values to screen for (int i = 0; i <= 3; i++) { for (int j = 0; j <= 3; j ++) { cout << setfill(' ') << setprecision(2) << matrix3[i][j] << setw(8); } cout << "\n"; } cout << setw(40)<< setfill('-') << "-" << endl ; // //Add matrix1 and matrix2 // addmatrices (matrix1, 4, matrix2, 4, matrix3, 4); // //Finished adding. Now output matrix 3 values to screen // for (int i = 0; i <= 3; i++) // { //for (int j = 0; j <= 3; j ++) //{ // cout << setfill(' ') << setprecision(2) << matrix3[i][j] << setw(8); //} //cout << "\n"; // } // cout << setw(40)<< setfill('-') << "-" << endl ; //Close the input file infile.close(); return 0; } //Function implementation void constmultiply (double matrixA[][4], int asize, double matrixC[][4], int bsize, double multiplier) { //Loop through each row and multiply the value at that location with the multiplier for (int i = 0; i < asize; i++) { for (int j = 0; j < 4; j++) { matrixC[i][j] = matrixA[i][j] * multiplier; } } } int addmatrices (double matrixA[][4], int asize, double matrixB[]4], int bsize, double matrixC[][4], int csize) { //Remember that you can only add two matrices that have the same shape - i.e. They need to have an equal //number of rows and columns. Let's add some error checking for that: if(asize != bsize) { cout << "You are attempting to add two matrices that are not equal in shape. Program terminating!" << endl; return exit(UNEQUAL_MATRIX_SIZE); } //Confirmed that the matrices are of equal size, so begin adding elements for (int i = 0; i < asize; i++) { for (int j = 0; j < bsize; j++) { matrixC[i][j] = matrixA[i][j] + matrixB[i][j]; } } }

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  • JOGL hardware based shadow mapping - computing the texture matrix

    - by axel22
    I am implementing hardware shadow mapping as described here. I've rendered the scene successfully from the light POV, and loaded the depth buffer of the scene into a texture. This texture has correctly been loaded - I check this by rendering a small thumbnail, as you can see in the screenshot below, upper left corner. The depth of the scene appears to be correct - objects further away are darker, and that are closer to the light are lighter. However, I run into trouble while rendering the scene from the camera's point of view using the depth texture - the texture on the polygons in the scene is rendered in a weird, nondeterministic fashion, as shown in the screenshot. I believe I am making an error while computing the texture transformation matrix, but I am unsure where exactly. Since I have no matrix utilities in JOGL other then the gl[Load|Mult]Matrix procedures, I multiply the matrices using them, like this: void calcTextureMatrix() { glPushMatrix(); glLoadIdentity(); glLoadMatrixf(biasmatrix, 0); glMultMatrixf(lightprojmatrix, 0); glMultMatrixf(lightviewmatrix, 0); glGetFloatv(GL_MODELVIEW_MATRIX, shadowtexmatrix, 0); glPopMatrix(); } I obtained these matrices by using the glOrtho and gluLookAt procedures: glLoadIdentity() val wdt = width / 45 val hgt = height / 45 glOrtho(wdt, -wdt, -hgt, hgt, -45.0, 45.0) glGetFloatv(GL_MODELVIEW_MATRIX, lightprojmatrix, 0) glLoadIdentity() glu.gluLookAt( xlook + lightpos._1, ylook + lightpos._2, lightpos._3, xlook, ylook, 0.0f, 0.f, 0.f, 1.0f) glGetFloatv(GL_MODELVIEW_MATRIX, lightviewmatrix, 0) My bias matrix is: float[] biasmatrix = new float[16] { 0.5f, 0.f, 0.f, 0.f, 0.f, 0.5f, 0.f, 0.f, 0.f, 0.f, 0.5f, 0.f, 0.5f, 0.5f, 0.5f, 1.f } After applying the camera projection and view matrices, I do: glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_EYE_LINEAR) glTexGenfv(GL_S, GL_EYE_PLANE, shadowtexmatrix, 0) glEnable(GL_TEXTURE_GEN_S) for each component. Does anybody know why the texture is not being rendered correctly? Thank you.

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  • importing animations in Blender, weird rotations/locations

    - by user975135
    This is for the Blender 2.6 API. There are two problems: 1. When I import a single animation frame from my animation file to Blender, all bones look fine. But when I import multiple (all of the frames), just the first one looks right, seems like newer frames are affected by older ones, so you get slightly off positions/rotations. This is true when both assigning PoseBone.matrix and PoseBone.matrix_basis. bone_index = 0 # for each frame: for frame_index in range(frame_count): # for each pose bone: add a key for bone_name in bone_names: # "bone_names" - a list of bone names I got earlier pose.bones[bone_name].matrix = animation_matrices[frame_index][bone_index] # "animation_matrices" - a nested list of matrices generated from reading a file # create the 'keys' for the Action from the poses pose.bones[bone_name].keyframe_insert('location', frame = frame_index+1) pose.bones[bone_name].keyframe_insert('rotation_euler', frame = frame_index+1) pose.bones[bone_name].keyframe_insert('scale', frame = frame_index+1) bone_index += 1 bone_index = 0 Again, it seems like previous frames are affecting latter ones, because if I import a single frame from the middle of the animation, it looks fine. 2. I can't assign armature-space animation matrices read from a file to a skeleton with hierarchy (parenting). In Blender 2.4 you could just assign them to PoseBone.poseMatrix and bones would deform perfectly whether the bones had a hierarchy or none at all. In Blender 2.6, there's PoseBone.matrix_basis and PoseBone.matrix. While matrix_basis is relative to parent bone, matrix isn't, the API says it's in object space. So it should have worked, but doesn't. So I guess we need to calculate a local space matrix from our armature-space animation matrices from the files. So I tried multiplying it ( PoseBone.matrix ) with PoseBone.parent.matrix.inverted() in both possible orders with no luck, still weird deformations.

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  • How do I create a camera?

    - by Morphex
    I am trying to create a generic camera class for a game engine, which works for different types of cameras (Orbital, GDoF, FPS), but I have no idea how to go about it. I have read about quaternions and matrices, but I do not understand how to implement it. Particularly, it seems you need "Up", "Forward" and "Right" vectors, a Quaternion for rotations, and View and Projection matrices. For example, an FPS camera only rotates around the World Y and the Right Axis of the camera; the 6DoF rotates always around its own axis, and the orbital is just translating for a set distance and making it look always at a fixed target point. The concepts are there; implementing this is not trivial for me. SharpDX seems to have has already Matrices and Quaternions implemented, but I don't know how to use them to create a camera. Can anyone point me on what am I missing, what I got wrong? I would really enjoy if you could give a tutorial, some piece of code, or just plain explanation of the concepts.

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  • Problems with 3D transformation - (SharpDX)

    - by Morphex
    First of all , I have been trying to get this right for a couple of day already, I have read so much info and still fail miserably to understand this. So I am going to tell you that even though I have done fairly amount of research myself, I failed to implement it. I must say miserably I am trying to create a generic camera class for a game engine of sorts - for research purposes only - the thing is I have no idea how to go about it. I have read about quaternions and matrices, but when it comes to the actual implementation I suck at it. Sharpdx has already Matrices and QUaternions implemented. SO no big deal on the map behind it. How in the world would I go about creating a camera? I have seen so many camera examples and still can't make one that works as expected. I would like to implement diferent types too (Orbital, 6DoF, FPS). So what is need for a camera? UP, Forward and Right vectors I read they are needed, also a quaternion for rotations, and View and Projection matrices. I understand that a FPS camera for instance only rotates around the World Y and the Right Axis of the camera. the 6DoF rotates always around their own axis, and the orbital is just translating for set distance and making it look always at a fixed target point. The concepts are there, now implementing this is not trivial for me. Can anyone point me on what am I missing, what I got wrong? I would really enjoy if you could give a tutorial, some piece of code, or just plain explanation of the concepts. Thank you for readin, a frustrated coder.

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  • Iterative Reduction to Null Matrix

    - by user1459032
    Here's the problem: I'm given a matrix like Input: 1 1 1 1 1 1 1 1 1 At each step, I need to find a "second" matrix of 1's and 0's with no two 1's on the same row or column. Then, I'll subtract the second matrix from the original matrix. I will repeat the process until I get a matrix with all 0's. Furthermore, I need to take the least possible number of steps. I need to print all the "second" matrices in O(n) time. In the above example I can get to the null matrix in 3 steps by subtracting these three matrices in order: Expected output: 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 I have coded an attempt, in which I am finding the first maximum value and creating the second matrices based on the index of that value. But for the above input I am getting 4 output matrices, which is wrong: My output: 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 My solution works for most of the test cases but fails for the one given above. Can someone give me some pointers on how to proceed, or find an algorithm that guarantees optimality? Test case that works: Input: 0 2 1 0 0 0 3 0 0 Output 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0

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  • C# - can you name a matrix with the contents of a string

    - by RHodgett
    Basically I have x amount of matrices I need to establish of y by y size. I was hoping to name the matrices: matrixnumber1 matrixnumber2..matrixnumbern I cannot use an array as its matrices I have to form. Is it possible to use a string to name a string (or a matrix in this case)? Thank you in advance for any help on this! for (int i = 1; i <= numberofmatricesrequired; i++) { string number = Convert.ToString(i); Matrix (matrixnumber+number) = new Matrix(matrixsize, matrixsize); }

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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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  • How do I convert my matrix from OpenGL to Marmalade?

    - by King Snail
    I am using a third party rendering API, Marmalade, on top of OpenGL code and I cannot get my matrices correct. One of the API's authors states this: We're right handed by default, and we treat y as up by convention. Since IwGx's coordinate system has (0,0) as the top left, you typically need a 180 degree rotation around Z in your view matrix. I think the viewer does this by default. In my OpenGL app I have access to the view and projection matrices separately. How can I convert them to fit the criteria used by my third party rendering API? I don't understand what they mean to rotate 180 degrees around Z, is that in the view matrix itself or something in the camera before making the view matrix. Any code would be helpful, thanks.

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  • MD5 vertex skinning problem extending to multi-jointed skeleton (GPU Skinning)

    - by Soapy
    Currently I'm trying to implement GPU skinning in my project. So far I have achieved single joint translation and rotation, and multi-jointed translation. The problem arises when I try to rotate a multi-jointed skeleton. The image above shows the current progress. The left image shows how the model should deform. The middle image shows how it deforms in my project. The right shows a better deform (still not right) inverting a certain value, which I will explain below. The way I get my animation data is by exporting it to the MD5 format (MD5mesh for mesh data and MD5anim for animation data). When I come to parse the animation data, for each frame, I check if the bone has a parent, if not, the data is passed in as is from the MD5anim file. If it does have a parent, I transform the bones position by the parents orientation, and the add this with the parents translation. Then the parent and child orientations get concatenated. This is covered at this website. if (Parent < 0){ ... // Save this data without editing it } else { Math3::vec3 rpos; Math3::quat pq = Parent.Quaternion; Math3::quat pqi(pq); pqi.InvertUnitQuat(); pqi.Normalise(); Math3::quat::RotateVector3(rpos, pq, jv); Math3::vec3 npos(rpos + Parent.Pos); this->Translation = npos; Math3::quat nq = pq * jq; nq.Normalise(); this->Quaternion = nq; } And to achieve the image to the right, all I need to do is to change Math3::quat::RotateVector3(rpos, pq, jv); to Math3::quat::RotateVector3(rpos, pqi, jv);, why is that? And this is my skinning shader. SkinningShader.vert #version 330 core smooth out vec2 vVaryingTexCoords; smooth out vec3 vVaryingNormals; smooth out vec4 vWeightColor; uniform mat4 MV; uniform mat4 MVP; uniform mat4 Pallete[55]; uniform mat4 invBindPose[55]; layout(location = 0) in vec3 vPos; layout(location = 1) in vec2 vTexCoords; layout(location = 2) in vec3 vNormals; layout(location = 3) in int vSkeleton[4]; layout(location = 4) in vec3 vWeight; void main() { vec4 wpos = vec4(vPos, 1.0); vec4 norm = vec4(vNormals, 0.0); vec4 weight = vec4(vWeight, (1.0f-(vWeight[0] + vWeight[1] + vWeight[2]))); normalize(weight); mat4 BoneTransform; for(int i = 0; i < 4; i++) { if(vSkeleton[i] != -1) { if(i == 0) { // These are interchangable for some reason // BoneTransform = ((invBindPose[vSkeleton[i]] * Pallete[vSkeleton[i]]) * weight[i]); BoneTransform = ((Pallete[vSkeleton[i]] * invBindPose[vSkeleton[i]]) * weight[i]); } else { // These are interchangable for some reason // BoneTransform += ((invBindPose[vSkeleton[i]] * Pallete[vSkeleton[i]]) * weight[i]); BoneTransform += ((Pallete[vSkeleton[i]] * invBindPose[vSkeleton[i]]) * weight[i]); } } } wpos = BoneTransform * wpos; vWeightColor = weight; vVaryingTexCoords = vTexCoords; vVaryingNormals = normalize(vec3(vec4(vNormals, 0.0) * MV)); gl_Position = wpos * MVP; } The Pallete matrices are the matrices calculated using the above code (a rotation and translation matrix get created from the translation and quaternion). The invBindPose matrices are simply the inverted matrices created from the joints in the MD5mesh file. Update 1 I looked at GLM to compare the values I get with my own implementation. They turn out to be exactly the same. So now i'm checking if there's a problem with matrix creation... Update 2 Looked at GLM again to compare matrix creation using quaternions. Turns out that's not the problem either.

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  • Correct Rotation and Translation with a 4x4 matrix

    - by sFuller
    I am using a 4x4 matrix to transform verts in a shader. I multiply an identity matrix by a rotation matrix by a translation matrix. I am trying to first rotate the verts and then translate them, however in my result, it appears that the verts are being transformed and then rotated. My matrix looks something like this: m00 m01 m02 tx m10 m11 m12 ty m20 m21 m22 tz --- --- --- 1 I am not using OpenGL's fixed function pipeline, I am multiplying matrices on the client side, and uploading the matrix to a GLSL shader. If it helps, I am using my own matrix multiplication code, but I have recreated this problem using matrices on my graphing calculator, so I don't believe my matrix code has errors.. I'll include a visual aid if needed.

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  • Triangle Strips and Tangent Space Normal Mapping

    - by Koarl
    Short: Do triangle strips and Tangent Space Normal mapping go together? According to quite a lot of tutorials on bump mapping, it seems common practice to derive tangent space matrices in a vertex program and transform the light direction vector(s) to tangent space and then pass them on to a fragment program. However, if one was using triangle strips or index buffers, it is a given that the vertex buffer contains vertices that sit at border edges and would thus require more than one normal to derive tangent space matrices to interpolate between in fragment programs. Is there any reasonable way to not have duplicate vertices in your buffer and still use tangent space normal mapping? Which one do you think is better: Having normal and tangent encoded in the assets and just optimize the geometry handling to alleviate the cost of duplicate vertices or using triangle strips and computing normals/tangents completely at run time? Thinking about it, the more reasonable answer seems to be the first one, but why might my professor still be fussing about triangle strips when it seems so obvious?

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  • View matrix question (rotate by 180 degrees)

    - by King Snail
    I am using a third party rendering API on top of OpenGL code and I cannot get my matrices correct. The API states this: We're right handed by default, and we treat y as up by convention. Since IwGx's coordinate system has (0,0) as the top left, you typically need a 180 degree rotation around Z in your view matrix. I think the viewer does this by default. In my OpenGL app I have access to the view and projection matrices separately. How can I convert them to fit the criteria used by my third party rendering API? I don't understand what they mean to rotate 180 degrees around Z, is that in the view matrix itself or something in the camera before making the view matrix. Any code would be helpful, thanks.

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  • What Precalculus knowledge is required before learning Discrete Math Computer Science topics?

    - by Ein Doofus
    Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book. Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book. What Precalculus topics should one know before starting these Discrete Math Computer Science topics?: Discrete Mathematics CS Chapters 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 3.1 Algorithms 3.2 The Growths of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.8 Matrices 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.6 Generating Permutations and Combinations 6.1 An Introduction to Discrete Probability 6.4 Expected Value and Variance 7.1 Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.5 Inclusion-Exclusion 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.5 Equivalence Relations 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Ptahs 10.1 Introduction to Trees 10.2 Application of Trees 10.3 Tree Traversal 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits 12.1 Language and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines Precalculus Chapters R.1 The Real-Number System R.2 Integer Exponents, Scientific Notation, and Order of Operations R.3 Addition, Subtraction, and Multiplication of Polynomials R.4 Factoring R.5 Rational Expressions R.6 Radical Notation and Rational Exponents R.7 The Basics of Equation Solving 1.1 Functions, Graphs, Graphers 1.2 Linear Functions, Slope, and Applications 1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression 1.4 More on Functions 1.5 Symmetry and Transformations 1.6 Variation and Applications 1.7 Distance, Midpoints, and Circles 2.1 Zeros of Linear Functions and Models 2.2 The Complex Numbers 2.3 Zeros of Quadratic Functions and Models 2.4 Analyzing Graphs of Quadratic Functions 2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression 2.6 Zeros and More Equation Solving 2.7 Solving Inequalities 3.1 Polynomial Functions and Modeling 3.2 Polynomial Division; The Remainder and Factor Theorems 3.3 Theorems about Zeros of Polynomial Functions 3.4 Rational Functions 3.5 Polynomial and Rational Inequalities 4.1 Composite and Inverse Functions 4.2 Exponential Functions and Graphs 4.3 Logarithmic Functions and Graphs 4.4 Properties of Logarithmic Functions 4.5 Solving Exponential and Logarithmic Equations 4.6 Applications and Models: Growth and Decay 5.1 Systems of Equations in Two Variables 5.2 System of Equations in Three Variables 5.3 Matrices and Systems of Equations 5.4 Matrix Operations 5.5 Inverses of Matrices 5.6 System of Inequalities and Linear Programming 5.7 Partial Fractions 6.1 The Parabola 6.2 The Circle and Ellipse 6.3 The Hyperbola 6.4 Nonlinear Systems of Equations

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  • How to derive euler angles from matrix or quaternion?

    - by KlashnikovKid
    Currently working on steering behavior for my AI and just hit a little mathematical bump. I'm in the process of writing an align function, which basically tries to match the agent's orientation with a target orientation. I've got a good source material for implementing this behavior but it uses euler angles to calculate the rotational delta, acceleration, and so on. This is nice, however I store orientation as a quaternion and the math library I'm using doesn't provide any functionality for deriving the euler angles. But if it helps I also have rotational matrices at my disposal too. What would be the best way to decompose the quaternion or rotational matrix to get the euler information? I found one source for decomposing the matrix, but I'm not quite getting the correct results. I'm thinking it may be a difference of column/row ordering of my matrices but then again, math isn't my strong point. http://nghiaho.com/?page_id=846

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  • 5x5 matrix multiplication in C

    - by Rick
    I am stuck on this problem in my homework. I've made it this far and am sure the problem is in my three for loops. The question directly says to use 3 for loops so I know this is probably just a logic error. #include<stdio.h> void matMult(int A[][5],int B[][5],int C[][5]); int printMat_5x5(int A[5][5]); int main() { int A[5][5] = {{1,2,3,4,6}, {6,1,5,3,8}, {2,6,4,9,9}, {1,3,8,3,4}, {5,7,8,2,5}}; int B[5][5] = {{3,5,0,8,7}, {2,2,4,8,3}, {0,2,5,1,2}, {1,4,0,5,1}, {3,4,8,2,3}}; int C[5][5] = {0}; matMult(A,B,C); printMat_5x5(A); printf("\n"); printMat_5x5(B); printf("\n"); printMat_5x5(C); return 0; } void matMult(int A[][5], int B[][5], int C[][5]) { int i; int j; int k; for(i = 0; i <= 2; i++) { for(j = 0; j <= 4; j++) { for(k = 0; k <= 3; k++) { C[i][j] += A[i][k] * B[k][j]; } } } } int printMat_5x5(int A[5][5]){ int i; int j; for (i = 0;i < 5;i++) { for(j = 0;j < 5;j++) { printf("%2d",A[i][j]); } printf("\n"); } } EDIT: Here is the question, sorry for not posting it the first time. (2) Write a C function to multiply two five by five matrices. The prototype should read void matMult(int a[][5],int b[][5],int c[][5]); The resulting matrix product (a times b) is returned in the two dimensional array c (the third parameter of the function). Program your solution using three nested for loops (each generating the counter values 0, 1, 2, 3, 4) That is, DO NOT code specific formulas for the 5 by 5 case in the problem, but make your code general so it can be easily changed to compute the product of larger square matrices. Write a main program to test your function using the arrays a: 1 2 3 4 6 6 1 5 3 8 2 6 4 9 9 1 3 8 3 4 5 7 8 2 5 b: 3 5 0 8 7 2 2 4 8 3 0 2 5 1 2 1 4 0 5 1 3 4 8 2 3 Print your matrices in a neat format using a C function created for printing five by five matrices. Print all three matrices. Generate your test arrays in your main program using the C array initialization feature. enter code here

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  • Sparse constrained linear least-squares solver

    - by Jacob
    This great SO answer points to a good sparse solver, but I've got constraints on x (for Ax = b) such that each element in x is >=0 an <=N. The first thing which comes to mind is an QP solver for large sparse matrices. Also, A is huge (around 2e6x2e6) but very sparse with <=4 elements per row. Any ideas/recommendations? I'm looking for something like MATLAB's lsqlin but with huge sparse matrices.

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  • PyOpenGL - passing transformation matrix into shader

    - by M-V
    I am having trouble passing projection and modelview matrices into the GLSL shader from my PyOpenGL code. My understanding is that OpenGL matrices are column major, but when I pass in projection and modelview matrices as shown, I don't see anything. I tried the transpose of the matrices, and it worked for the modelview matrix, but the projection matrix doesn't work either way. Here is the code: import OpenGL from OpenGL.GL import * from OpenGL.GL.shaders import * from OpenGL.GLU import * from OpenGL.GLUT import * from OpenGL.GLUT.freeglut import * from OpenGL.arrays import vbo import numpy, math, sys strVS = """ attribute vec3 aVert; uniform mat4 uMVMatrix; uniform mat4 uPMatrix; uniform vec4 uColor; varying vec4 vCol; void main() { // option #1 - fails gl_Position = uPMatrix * uMVMatrix * vec4(aVert, 1.0); // option #2 - works gl_Position = vec4(aVert, 1.0); // set color vCol = vec4(uColor.rgb, 1.0); } """ strFS = """ varying vec4 vCol; void main() { // use vertex color gl_FragColor = vCol; } """ # particle system class class Scene: # initialization def __init__(self): # create shader self.program = compileProgram(compileShader(strVS, GL_VERTEX_SHADER), compileShader(strFS, GL_FRAGMENT_SHADER)) glUseProgram(self.program) self.pMatrixUniform = glGetUniformLocation(self.program, 'uPMatrix') self.mvMatrixUniform = glGetUniformLocation(self.program, "uMVMatrix") self.colorU = glGetUniformLocation(self.program, "uColor") # attributes self.vertIndex = glGetAttribLocation(self.program, "aVert") # color self.col0 = [1.0, 1.0, 0.0, 1.0] # define quad vertices s = 0.2 quadV = [ -s, s, 0.0, -s, -s, 0.0, s, s, 0.0, s, s, 0.0, -s, -s, 0.0, s, -s, 0.0 ] # vertices self.vertexBuffer = glGenBuffers(1) glBindBuffer(GL_ARRAY_BUFFER, self.vertexBuffer) vertexData = numpy.array(quadV, numpy.float32) glBufferData(GL_ARRAY_BUFFER, 4*len(vertexData), vertexData, GL_STATIC_DRAW) # render def render(self, pMatrix, mvMatrix): # use shader glUseProgram(self.program) # set proj matrix glUniformMatrix4fv(self.pMatrixUniform, 1, GL_FALSE, pMatrix) # set modelview matrix glUniformMatrix4fv(self.mvMatrixUniform, 1, GL_FALSE, mvMatrix) # set color glUniform4fv(self.colorU, 1, self.col0) #enable arrays glEnableVertexAttribArray(self.vertIndex) # set buffers glBindBuffer(GL_ARRAY_BUFFER, self.vertexBuffer) glVertexAttribPointer(self.vertIndex, 3, GL_FLOAT, GL_FALSE, 0, None) # draw glDrawArrays(GL_TRIANGLES, 0, 6) # disable arrays glDisableVertexAttribArray(self.vertIndex) class Renderer: def __init__(self): pass def reshape(self, width, height): self.width = width self.height = height self.aspect = width/float(height) glViewport(0, 0, self.width, self.height) glEnable(GL_DEPTH_TEST) glDisable(GL_CULL_FACE) glClearColor(0.8, 0.8, 0.8,1.0) glutPostRedisplay() def keyPressed(self, *args): sys.exit() def draw(self): glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT) # build projection matrix fov = math.radians(45.0) f = 1.0/math.tan(fov/2.0) zN, zF = (0.1, 100.0) a = self.aspect pMatrix = numpy.array([f/a, 0.0, 0.0, 0.0, 0.0, f, 0.0, 0.0, 0.0, 0.0, (zF+zN)/(zN-zF), -1.0, 0.0, 0.0, 2.0*zF*zN/(zN-zF), 0.0], numpy.float32) # modelview matrix mvMatrix = numpy.array([1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.5, 0.0, -5.0, 1.0], numpy.float32) # render self.scene.render(pMatrix, mvMatrix) # swap buffers glutSwapBuffers() def run(self): glutInitDisplayMode(GLUT_RGBA) glutInitWindowSize(400, 400) self.window = glutCreateWindow("Minimal") glutReshapeFunc(self.reshape) glutDisplayFunc(self.draw) glutKeyboardFunc(self.keyPressed) # Checks for key strokes self.scene = Scene() glutMainLoop() glutInit(sys.argv) prog = Renderer() prog.run() When I use option #2 in the shader without either matrix, I get the following output: What am I doing wrong?

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  • How can I save and read to XML the new C++ style matrix objects in OpenCV?

    - by neuviemeporte
    The old, C style cvMat matrices could be passed to the cvSave() function for easy writing to an XML file. The new C++ style cv::Mat and cv::Mat_ matrices are not accepted by this function. The OpenCV reference has a section on XML persistence, but the three classes (FileStorage, FileNode and FileNodeIterator) lack any description or example and I can't figure out how to use them from the interface. Thanks.

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  • Skewed: a rotating camera in a simple CPU-based voxel raycaster/raytracer

    - by voxelizr
    TL;DR -- in my first simple software voxel raycaster, I cannot get camera rotations to work, seemingly correct matrices notwithstanding. The result is skewed: like a flat rendering, correctly rotated, however distorted and without depth. (While axis-aligned ie. unrotated, depth and parallax are as expected.) I'm trying to write a simple voxel raycaster as a learning exercise. This is purely CPU based for now until I figure out how things work exactly -- fow now, OpenGL is just (ab)used to blit the generated bitmap to the screen as often as possible. Now I have gotten to the point where a perspective-projection camera can move through the world and I can render (mostly, minus some artifacts that need investigation) perspective-correct 3-dimensional views of the "world", which is basically empty but contains a voxel cube of the Stanford Bunny. So I have a camera that I can move up and down, strafe left and right and "walk forward/backward" -- all axis-aligned so far, no camera rotations. Herein lies my problem. Screenshot #1: correct depth when the camera is still strictly axis-aligned, ie. un-rotated. Now I have for a few days been trying to get rotation to work. The basic logic and theory behind matrices and 3D rotations, in theory, is very clear to me. Yet I have only ever achieved a "2.5 rendering" when the camera rotates... fish-eyey, bit like in Google Streetview: even though I have a volumetric world representation, it seems --no matter what I try-- like I would first create a rendering from the "front view", then rotate that flat rendering according to camera rotation. Needless to say, I'm by now aware that rotating rays is not particularly necessary and error-prone. Still, in my most recent setup, with the most simplified raycast ray-position-and-direction algorithm possible, my rotation still produces the same fish-eyey flat-render-rotated style looks: Screenshot #2: camera "rotated to the right by 39 degrees" -- note how the blue-shaded left-hand side of the cube from screen #2 is not visible in this rotation, yet by now "it really should"! Now of course I'm aware of this: in a simple axis-aligned-no-rotation-setup like I had in the beginning, the ray simply traverses in small steps the positive z-direction, diverging to the left or right and top or bottom only depending on pixel position and projection matrix. As I "rotate the camera to the right or left" -- ie I rotate it around the Y-axis -- those very steps should be simply transformed by the proper rotation matrix, right? So for forward-traversal the Z-step gets a bit smaller the more the cam rotates, offset by an "increase" in the X-step. Yet for the pixel-position-based horizontal+vertical-divergence, increasing fractions of the x-step need to be "added" to the z-step. Somehow, none of my many matrices that I experimented with, nor my experiments with matrix-less hardcoded verbose sin/cos calculations really get this part right. Here's my basic per-ray pre-traversal algorithm -- syntax in Go, but take it as pseudocode: fx and fy: pixel positions x and y rayPos: vec3 for the ray starting position in world-space (calculated as below) rayDir: vec3 for the xyz-steps to be added to rayPos in each step during ray traversal rayStep: a temporary vec3 camPos: vec3 for the camera position in world space camRad: vec3 for camera rotation in radians pmat: typical perspective projection matrix The algorithm / pseudocode: // 1: rayPos is for now "this pixel, as a vector on the view plane in 3d, at The Origin" rayPos.X, rayPos.Y, rayPos.Z = ((fx / width) - 0.5), ((fy / height) - 0.5), 0 // 2: rotate around Y axis depending on cam rotation. No prob since view plane still at Origin 0,0,0 rayPos.MultMat(num.NewDmat4RotationY(camRad.Y)) // 3: a temp vec3. planeDist is -0.15 or some such -- fov-based dist of view plane from eye and also the non-normalized, "in axis-aligned world" traversal step size "forward into the screen" rayStep.X, rayStep.Y, rayStep.Z = 0, 0, planeDist // 4: rotate this too -- 0,zstep should become some meaningful xzstep,xzstep rayStep.MultMat(num.NewDmat4RotationY(CamRad.Y)) // set up direction vector from still-origin-based-ray-position-off-rotated-view-plane plus rotated-zstep-vector rayDir.X, rayDir.Y, rayDir.Z = -rayPos.X - me.rayStep.X, -rayPos.Y, rayPos.Z + rayStep.Z // perspective projection rayDir.Normalize() rayDir.MultMat(pmat) // before traversal, the ray starting position has to be transformed from origin-relative to campos-relative rayPos.Add(camPos) I'm skipping the traversal and sampling parts -- as per screens #1 through #3, those are "basically mostly correct" (though not pretty) -- when axis-aligned / unrotated.

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  • HLSL 5 interpolation issues

    - by metredigm
    I'm having issues with the depth components of my shadowmapping shaders. The shadow map rendering shader is fine, and works very well. The world rendering shader is more problematic. The only value which seems to definitely be off is the pixel's position from the light's perspective, which I pass in parallel to the position. struct Pixel { float4 position : SV_Position; float4 light_pos : TEXCOORD2; float3 normal : NORMAL; float2 texcoord : TEXCOORD; }; The reason that I used the semantic 'TEXCOORD2' on the light's pixel position is because I believe that the problem lies with Direct3D's interpolation of values between shaders, and I started trying random semantics and also forcing linear and noperspective interpolations. In the world rendering shader, I observed in the pixel shader that the Z value of light_pos was always extremely close to, but less than the W value. This resulted in a depth result of 0.999 or similar for every pixel. Here is the vertex shader code : struct Vertex { float3 position : POSITION; float3 normal : NORMAL; float2 texcoord : TEXCOORD; }; struct Pixel { float4 position : SV_Position; float4 light_pos : TEXCOORD2; float3 normal : NORMAL; float2 texcoord : TEXCOORD; }; cbuffer Camera : register (b0) { matrix world; matrix view; matrix projection; }; cbuffer Light : register (b1) { matrix light_world; matrix light_view; matrix light_projection; }; Pixel RenderVertexShader(Vertex input) { Pixel output; output.position = mul(float4(input.position, 1.0f), world); output.position = mul(output.position, view); output.position = mul(output.position, projection); output.world_pos = mul(float4(input.position, 1.0f), world); output.world_pos = mul(output.world_pos, light_view); output.world_pos = mul(output.world_pos, light_projection); output.texcoord = input.texcoord; output.normal = input.normal; return output; } I suspect interpolation to be the culprit, as I used the camera matrices in place of the light matrices in the vertex shader, and had the same problem. The problem is evident as both of the same vectors were passed to a pixel from the VS, but only one of them showed a change in the PS. I have already thoroughly debugged the matrices' validity, the cbuffers' validity, and the multiplicative validity. I'm very stumped and have been trying to solve this for quite some time. Misc info : The light projection matrix and the camera projection matrix are the same, generated from D3DXMatrixPerspectiveFovLH(), with an FOV of 60.0f * 3.141f / 180.0f, a near clipping plane of 0.1f, and a far clipping plane of 1000.0f. Any ideas on what is happening? (This is a repost from my question on Stack Overflow)

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  • How do I make an on-screen HUD in libgdx?

    - by Devin Carless
    I'm new to libgdx, and I am finding I am getting stumped by the simplest of things. It seems to want me to do things a specific way, but the documentation won't tell me what that is. I want to make a very simple 2d game in which the player controls a spaceship. The mouse wheel will zoom in and out, and information and controls are displayed on the screen. But I can't seem to make the mouse wheel NOT zoom the UI. I've tried futzing with the projection matrices in between Here's my (current) code: public class PlayStage extends Stage { ... public void draw() { // tell the camera to update its matrices. camera.update(); // tell the SpriteBatch to render in the // coordinate system specified by the camera. spriteBatch.setProjectionMatrix(camera.combined); spriteBatch.begin(); aButton.draw(spriteBatch, 1F); playerShip.draw(spriteBatch, 1F); spriteBatch.end(); } } camera.zoom is set by scrolled(int amount). I've tried about a dozen variations on the theme of changing the camera's projection matrix after the button is drawn but before the ship is, but no matter what I do, the same things happen to both the button and the ship. So: What is the usual libgdx way of implementing an on-screen UI that isn't transformed by the camera's projection matrix/zoom?

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  • Converting to and from local and world 3D coordinate spaces?

    - by James Bedford
    Hey guys, I've been following a guide I found here (http://knol.google.com/k/matrices-for-3d-applications-view-transformation) on constructing a matrix that will allow me to 3D coordinates to an object's local coordinate space, and back again. I've tried to implement these two matrices using my object's look, side, up and location vectors and it seems to be working for the first three coordinates. I'm a little confused as to what I should expect for the w coordinate. Here are couple of examples from the print outs I've made of the matricies that are constructed. I'm passing a test vector of [9, 8, 14, 1] each time to see if I can convert both ways: Basic example: localize matrix: Matrix: 0.000000 -0.000000 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 5.237297 -45.530716 11.021271 1.000000 globalize matrix: Matrix: 0.000000 0.000000 1.000000 0.000000 -0.000000 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 -11.021271 -45.530716 -5.237297 1.000000 test: Vector4f(9.000000, 8.000000, 14.000000, 1.000000) localTest: Vector4f(14.000000, 8.000000, 9.000000, -161.812256) worldTest: Vector4f(9.000000, 8.000000, 14.000000, -727.491455) More complicated example: localize matrix: Matrix: 0.052504 -0.000689 -0.998258 0.000000 0.052431 0.998260 0.002068 0.000000 0.997241 -0.052486 0.052486 0.000000 58.806095 2.979346 -39.396252 1.000000 globalize matrix: Matrix: 0.052504 0.052431 0.997241 0.000000 -0.000689 0.998260 -0.052486 0.000000 -0.998258 0.002068 0.052486 0.000000 -42.413120 5.975957 -56.419727 1.000000 test: Vector4f(9.000000, 8.000000, 14.000000, 1.000000) localTest: Vector4f(-13.508600, 8.486917, 9.290090, 2.542114) worldTest: Vector4f(9.000190, 7.993863, 13.990230, 102.057129) As you can see in the more complicated example, the coordinates after converting both ways loose some precision, but this isn't a problem. I'm just wondering how I should deal with the last (w) coordinate? Should I just set it to 1 after performing the matrix multiplication, or does it look like I've done something wrong? Thanks in advance for your help!

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  • Servlet stops without giving any exception

    - by Fahim
    Hi, I have implemented a Servlet hosted on Tomcat 6 server on Mandriva Linux. I have been able to make the client communicate with the Servlet. In response to a request the Servlet tries to instantiate a another class (named KalmanFilter) located in the same directory. The KalmanFilter tries to create four Matrices (using Jama Matrix package). But at this point Servlet stops without giving any exception ! However, from another test code in the same directory I have been able to create instance of KalmanFilter class, and proceed without any error. The problem occurs only when my Servlet tries to instantiate the KalmanFilter class and create the matrices. Any idea? Below are the codes: MyServlet.java import javax.servlet.*; import javax.servlet.http.*; import java.io.*; import java.util.*; public class MyServlet extends HttpServlet { public void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException{ doGet(request, response); } public void doGet(HttpServletRequest request, HttpServletResponse response) throws ServletException{ PrintWriter out = null; //response.getWriter(); try{ System.out.println("creating new KalmanFilter"); KalmanFilter filter = new KalmanFilter(); out = response.getWriter(); out.print("filter created"); }catch(Exception ex){ ex.printStackTrace(); System.out.println("Exception in doGet(): " + ex.getMessage()); ex.printStackTrace(out); } } } KalmanFilter.java import Jama.Matrix; public class KalmanFilter { protected Matrix X, X0; protected Matrix F, Q; //protected Matrix F, B, U, Q; protected Matrix H, R; protected Matrix P, P0; private final double EPSILON = 0.001; public KalmanFilter(){ System.out.println("from constructor of KalmanFilter"); createInitialMatrices(); } private void createInitialMatrices(){ System.out.println("from KalmanFilter.createInitialMatrices()"); double[][] pVals = { {1.0, 0.0}, {0.0, 1.0} }; double[][] qVals = { {EPSILON, EPSILON}, {EPSILON, EPSILON} }; double[][] hVals = { {1.0, 0.0}, {0.0, 1.0}, {1.0, 0.0}, {0.0, 1.0} }; double[][] xVals = { {0.0}, {0.0}, }; System.out.println("creating P Q H X matrices in createInitialMatrices()"); try{ this.P = new Matrix(pVals); System.out.println("created P matrix in createInitialMatrices()"); this.Q = new Matrix(qVals); System.out.println("created Q matrix in createInitialMatrices()"); this.H = new Matrix(hVals); System.out.println("created H matrix in createInitialMatrices()"); this.X = new Matrix(xVals); System.out.println("created X matrix in createInitialMatrices()"); System.out.println("created P Q H X matrices in createInitialMatrices()"); }catch(Exception e){ System.out.println("Exception from createInitialMatrices()"+ e.getMessage()); e.printStackTrace(); } System.out.println("returning from createInitialMatrices()"); } }

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