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  • Obtaining a world point from a screen point with an orthographic projection

    - by vargonian
    I assumed this was a straightforward problem but it has been plaguing me for days. I am creating a 2D game with an orthographic camera. I am using a 3D camera rather than just hacking it because I want to support rotating, panning, and zooming. Unfortunately the math overwhelms me when I'm trying to figure out how to determine if a clicked point intersects a bounds (let's say rectangular) in the game. I was under the impression that I could simply transform the screen point (the clicked point) by the inverse of the camera's View * Projection matrix to obtain the world coordinates of the clicked point. Unfortunately this is not the case at all; I get some point that seems to be in some completely different coordinate system. So then as a sanity check I tried taking an arbitrary world point and transforming it by the camera's View*Projection matrices. Surely this should get me the corresponding screen point, but even that didn't work, and it is quickly shattering any illusion I had that I understood 3D coordinate systems and the math involved. So, if I could form this into a question: How would I use my camera's state information (view and projection matrices, for instance) to transform a world point to a screen point, and vice versa? I hope the problem will be simpler since I'm using an orthographic camera and can make several assumptions from that. I very much appreciate any help. If it makes a difference, I'm using XNA Game Studio.

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  • How can I generate a view or projection matrix for OpenGL 3.+

    - by Ken
    I'm transitioning from OpenGL 2 to OpenGL 3.+ and to GLSL 1.5. I'm trying to avoid using the deprecated features. My question how do we now generate the view or projection matrix. I was using the matrix stack to calculate the projection matrix for me; GLfloat ptr[16]; gluPerspective(...); glGetFloatv(GL_MODELVIEW_MATRIX, ptr); //then pass ptr via a uniform to the shader But obviously the matrix stack is deprecated. So this approach is not the best an option going forward. I have the 'Red Book', 7th ed, which covers 3.0 & 3.1 and it still uses the deprecated matrix functions in it's examples. I could write some utility-code myself to generate the matrices. But I don't want to re-invent this particular wheel, especially when this functionality is required for every 3D graphics program. What is the accepted way to generate world,view & projection matrices for OpenGL? Is there an emerging 'standard' library for this? Or is there some other hidden (to me) functionality in OpenGL/GLSL which I have overlooked?

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  • If a library doesn't provide all my needs, how should I proceed?

    - by 9a3eedi
    I'm developing an application involving math and physics models, and I'd like to use a Math library for things like Matrices. I'm using C#, and so I was looking for some libraries and found Math.NET. I'm under the impression, from past experience, that for math, using a robust and industry-approved third party library is much better than writing your own code. It seems good for many purposes, but it does not provide support for Quaternions, which I need to use as a type. Also, I need some functions in Vector and Matrix that also aren't provided, such as rotation matrices and vector rotation functions, and calculating cross products. At the same time, it provides a lot of functions/classes that I simply do not need, which might mean a lot of unnecessary bloat and complexity. At this rate, should I even bother using the library? Should I write my own math library? Or is it a better idea to stick to the third party library and somehow wrap around it? Perhaps I should make a subclass of the Matrix and Vector type of the library? But isn't that considered bad style? I've also tried looking for other libraries but unfortunately I couldn't find anything suitable.

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  • Managing constant buffers without FX interface

    - by xcrypt
    I am aware that there is a sample on working without FX in the samplebrowser, and I already checked that one. However, some questions arise: In the sample: D3DXMATRIXA16 mWorldViewProj; D3DXMATRIXA16 mWorld; D3DXMATRIXA16 mView; D3DXMATRIXA16 mProj; mWorld = g_World; mView = g_View; mProj = g_Projection; mWorldViewProj = mWorld * mView * mProj; VS_CONSTANT_BUFFER* pConstData; g_pConstantBuffer10->Map( D3D10_MAP_WRITE_DISCARD, NULL, ( void** )&pConstData ); pConstData->mWorldViewProj = mWorldViewProj; pConstData->fTime = fBoundedTime; g_pConstantBuffer10->Unmap(); They are copying their D3DXMATRIX'es to D3DXMATRIXA16. Checked on msdn, these new matrices are 16 byte aligned and optimised for intel pentium 4. So as my first question: 1) Is it necessary to copy matrices to D3DXMATRIXA16 before sending them to the constant buffer? And if no, why don't we just use D3DXMATRIXA16 all the time? I have another question about managing multiple constant buffers within one shader. Suppose that, within your shader, you have multiple constant buffers that need to be updated at different times: cbuffer cbNeverChanges { matrix View; }; cbuffer cbChangeOnResize { matrix Projection; }; cbuffer cbChangesEveryFrame { matrix World; float4 vMeshColor; }; Then how would I set these buffers all at different times? g_pd3dDevice->VSSetConstantBuffers( 0, 1, &g_pConstantBuffer10 ); gives me the possibility to set multiple buffers, but that is within one call. 2) Is that okay even if my constant buffers are updated at different times? And do I suppose I have to make sure the constantbuffers are in the same position in the array as the order they appear in the shader?

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  • MATLAB: What is an appropriate Data Structure for a Matrix with Random Variable Entries?

    - by user12707
    I'm working in an area that is related to simulation and trying to design a data structure that can include random variables within matrices. I am currently coding in MATLAB. To motivate this let me say I have the following matrix: [a b; c d] I want to find a data structure that will allow for a, b, c, d to be either real numbers or random variables. As an example, let's say that a = 1, b = -1, c = 2 but let d be a normally distributed random variable with mean 20 and SD 40. The data structure that I have in mind will give no value to d. However, I also want to be able to design a function that can take in the structure, simulate an uniform(0,1), obtain a value for d using an inverse CDF and then spit out an actual matrix. I have several ideas to do this (all related to the MATLAB icdf function) but would like to know how more experienced programmers would do it. In this application, it's important that the structure is as "lean" as possible since I will be working with very very large matrices and memory will be an issue.

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  • How to use onSensorChanged sensor data in combination with OpenGL

    - by Sponge
    I have written a TestSuite to find out how to calculate the rotation angles from the data you get in SensorEventListener.onSensorChanged(). I really hope you can complete my solution to help people who will have the same problems like me. Here is the code, i think you will understand it after reading it. Feel free to change it, the main idea was to implement several methods to send the orientation angles to the opengl view or any other target which would need it. method 1 to 4 are working, they are directly sending the rotationMatrix to the OpenGl view. all other methods are not working or buggy and i hope someone knows to get them working. i think the best method would be method 5 if it would work, because it would be the easiest to understand but i'm not sure how efficient it is. the complete code isn't optimized so i recommend to not use it as it is in your project. here it is: import java.nio.ByteBuffer; import java.nio.ByteOrder; import java.nio.FloatBuffer; import javax.microedition.khronos.egl.EGL10; import javax.microedition.khronos.egl.EGLConfig; import javax.microedition.khronos.opengles.GL10; import static javax.microedition.khronos.opengles.GL10.*; import android.app.Activity; import android.content.Context; import android.content.pm.ActivityInfo; import android.hardware.Sensor; import android.hardware.SensorEvent; import android.hardware.SensorEventListener; import android.hardware.SensorManager; import android.opengl.GLSurfaceView; import android.opengl.GLSurfaceView.Renderer; import android.os.Bundle; import android.util.Log; import android.view.WindowManager; /** * This class provides a basic demonstration of how to use the * {@link android.hardware.SensorManager SensorManager} API to draw a 3D * compass. */ public class SensorToOpenGlTests extends Activity implements Renderer, SensorEventListener { private static final boolean TRY_TRANSPOSED_VERSION = false; /* * MODUS overview: * * 1 - unbufferd data directly transfaired from the rotation matrix to the * modelview matrix * * 2 - buffered version of 1 where both acceleration and magnetometer are * buffered * * 3 - buffered version of 1 where only magnetometer is buffered * * 4 - buffered version of 1 where only acceleration is buffered * * 5 - uses the orientation sensor and sets the angles how to rotate the * camera with glrotate() * * 6 - uses the rotation matrix to calculate the angles * * 7 to 12 - every possibility how the rotationMatrix could be constructed * in SensorManager.getRotationMatrix (see * http://www.songho.ca/opengl/gl_anglestoaxes.html#anglestoaxes for all * possibilities) */ private static int MODUS = 2; private GLSurfaceView openglView; private FloatBuffer vertexBuffer; private ByteBuffer indexBuffer; private FloatBuffer colorBuffer; private SensorManager mSensorManager; private float[] rotationMatrix = new float[16]; private float[] accelGData = new float[3]; private float[] bufferedAccelGData = new float[3]; private float[] magnetData = new float[3]; private float[] bufferedMagnetData = new float[3]; private float[] orientationData = new float[3]; // private float[] mI = new float[16]; private float[] resultingAngles = new float[3]; private int mCount; final static float rad2deg = (float) (180.0f / Math.PI); private boolean mirrorOnBlueAxis = false; private boolean landscape; public SensorToOpenGlTests() { } /** Called with the activity is first created. */ @Override public void onCreate(Bundle savedInstanceState) { super.onCreate(savedInstanceState); mSensorManager = (SensorManager) getSystemService(Context.SENSOR_SERVICE); openglView = new GLSurfaceView(this); openglView.setRenderer(this); setContentView(openglView); } @Override protected void onResume() { // Ideally a game should implement onResume() and onPause() // to take appropriate action when the activity looses focus super.onResume(); openglView.onResume(); if (((WindowManager) getSystemService(WINDOW_SERVICE)) .getDefaultDisplay().getOrientation() == 1) { landscape = true; } else { landscape = false; } mSensorManager.registerListener(this, mSensorManager .getDefaultSensor(Sensor.TYPE_ACCELEROMETER), SensorManager.SENSOR_DELAY_GAME); mSensorManager.registerListener(this, mSensorManager .getDefaultSensor(Sensor.TYPE_MAGNETIC_FIELD), SensorManager.SENSOR_DELAY_GAME); mSensorManager.registerListener(this, mSensorManager .getDefaultSensor(Sensor.TYPE_ORIENTATION), SensorManager.SENSOR_DELAY_GAME); } @Override protected void onPause() { // Ideally a game should implement onResume() and onPause() // to take appropriate action when the activity looses focus super.onPause(); openglView.onPause(); mSensorManager.unregisterListener(this); } public int[] getConfigSpec() { // We want a depth buffer, don't care about the // details of the color buffer. int[] configSpec = { EGL10.EGL_DEPTH_SIZE, 16, EGL10.EGL_NONE }; return configSpec; } public void onDrawFrame(GL10 gl) { // clear screen and color buffer: gl.glClear(GL10.GL_COLOR_BUFFER_BIT | GL10.GL_DEPTH_BUFFER_BIT); // set target matrix to modelview matrix: gl.glMatrixMode(GL10.GL_MODELVIEW); // init modelview matrix: gl.glLoadIdentity(); // move camera away a little bit: if ((MODUS == 1) || (MODUS == 2) || (MODUS == 3) || (MODUS == 4)) { if (landscape) { // in landscape mode first remap the rotationMatrix before using // it with glMultMatrixf: float[] result = new float[16]; SensorManager.remapCoordinateSystem(rotationMatrix, SensorManager.AXIS_Y, SensorManager.AXIS_MINUS_X, result); gl.glMultMatrixf(result, 0); } else { gl.glMultMatrixf(rotationMatrix, 0); } } else { //in all other modes do the rotation by hand: gl.glRotatef(resultingAngles[1], 1, 0, 0); gl.glRotatef(resultingAngles[2], 0, 1, 0); gl.glRotatef(resultingAngles[0], 0, 0, 1); if (mirrorOnBlueAxis) { //this is needed for mode 6 to work gl.glScalef(1, 1, -1); } } //move the axis to simulate augmented behaviour: gl.glTranslatef(0, 2, 0); // draw the 3 axis on the screen: gl.glVertexPointer(3, GL_FLOAT, 0, vertexBuffer); gl.glColorPointer(4, GL_FLOAT, 0, colorBuffer); gl.glDrawElements(GL_LINES, 6, GL_UNSIGNED_BYTE, indexBuffer); } public void onSurfaceChanged(GL10 gl, int width, int height) { gl.glViewport(0, 0, width, height); float r = (float) width / height; gl.glMatrixMode(GL10.GL_PROJECTION); gl.glLoadIdentity(); gl.glFrustumf(-r, r, -1, 1, 1, 10); } public void onSurfaceCreated(GL10 gl, EGLConfig config) { gl.glDisable(GL10.GL_DITHER); gl.glClearColor(1, 1, 1, 1); gl.glEnable(GL10.GL_CULL_FACE); gl.glShadeModel(GL10.GL_SMOOTH); gl.glEnable(GL10.GL_DEPTH_TEST); gl.glEnableClientState(GL10.GL_VERTEX_ARRAY); gl.glEnableClientState(GL10.GL_COLOR_ARRAY); // load the 3 axis and there colors: float vertices[] = { 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 }; float colors[] = { 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1 }; byte indices[] = { 0, 1, 0, 2, 0, 3 }; ByteBuffer vbb; vbb = ByteBuffer.allocateDirect(vertices.length * 4); vbb.order(ByteOrder.nativeOrder()); vertexBuffer = vbb.asFloatBuffer(); vertexBuffer.put(vertices); vertexBuffer.position(0); vbb = ByteBuffer.allocateDirect(colors.length * 4); vbb.order(ByteOrder.nativeOrder()); colorBuffer = vbb.asFloatBuffer(); colorBuffer.put(colors); colorBuffer.position(0); indexBuffer = ByteBuffer.allocateDirect(indices.length); indexBuffer.put(indices); indexBuffer.position(0); } public void onAccuracyChanged(Sensor sensor, int accuracy) { } public void onSensorChanged(SensorEvent event) { // load the new values: loadNewSensorData(event); if (MODUS == 1) { SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, magnetData); } if (MODUS == 2) { rootMeanSquareBuffer(bufferedAccelGData, accelGData); rootMeanSquareBuffer(bufferedMagnetData, magnetData); SensorManager.getRotationMatrix(rotationMatrix, null, bufferedAccelGData, bufferedMagnetData); } if (MODUS == 3) { rootMeanSquareBuffer(bufferedMagnetData, magnetData); SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, bufferedMagnetData); } if (MODUS == 4) { rootMeanSquareBuffer(bufferedAccelGData, accelGData); SensorManager.getRotationMatrix(rotationMatrix, null, bufferedAccelGData, magnetData); } if (MODUS == 5) { // this mode uses the sensor data recieved from the orientation // sensor resultingAngles = orientationData.clone(); if ((-90 > resultingAngles[1]) || (resultingAngles[1] > 90)) { resultingAngles[1] = orientationData[0]; resultingAngles[2] = orientationData[1]; resultingAngles[0] = orientationData[2]; } } if (MODUS == 6) { SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, magnetData); final float[] anglesInRadians = new float[3]; SensorManager.getOrientation(rotationMatrix, anglesInRadians); if ((-90 < anglesInRadians[2] * rad2deg) && (anglesInRadians[2] * rad2deg < 90)) { // device camera is looking on the floor // this hemisphere is working fine mirrorOnBlueAxis = false; resultingAngles[0] = anglesInRadians[0] * rad2deg; resultingAngles[1] = anglesInRadians[1] * rad2deg; resultingAngles[2] = anglesInRadians[2] * -rad2deg; } else { mirrorOnBlueAxis = true; // device camera is looking in the sky // this hemisphere is mirrored at the blue axis resultingAngles[0] = (anglesInRadians[0] * rad2deg); resultingAngles[1] = (anglesInRadians[1] * rad2deg); resultingAngles[2] = (anglesInRadians[2] * rad2deg); } } if (MODUS == 7) { SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, magnetData); rotationMatrix = transpose(rotationMatrix); /* * this assumes that the rotation matrices are multiplied in x y z * order Rx*Ry*Rz */ resultingAngles[2] = (float) (Math.asin(rotationMatrix[2])); final float cosB = (float) Math.cos(resultingAngles[2]); resultingAngles[2] = resultingAngles[2] * rad2deg; resultingAngles[0] = -(float) (Math.acos(rotationMatrix[0] / cosB)) * rad2deg; resultingAngles[1] = (float) (Math.acos(rotationMatrix[10] / cosB)) * rad2deg; } if (MODUS == 8) { SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, magnetData); rotationMatrix = transpose(rotationMatrix); /* * this assumes that the rotation matrices are multiplied in z y x */ resultingAngles[2] = (float) (Math.asin(-rotationMatrix[8])); final float cosB = (float) Math.cos(resultingAngles[2]); resultingAngles[2] = resultingAngles[2] * rad2deg; resultingAngles[1] = (float) (Math.acos(rotationMatrix[9] / cosB)) * rad2deg; resultingAngles[0] = (float) (Math.asin(rotationMatrix[4] / cosB)) * rad2deg; } if (MODUS == 9) { SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, magnetData); rotationMatrix = transpose(rotationMatrix); /* * this assumes that the rotation matrices are multiplied in z x y * * note z axis looks good at this one */ resultingAngles[1] = (float) (Math.asin(rotationMatrix[9])); final float minusCosA = -(float) Math.cos(resultingAngles[1]); resultingAngles[1] = resultingAngles[1] * rad2deg; resultingAngles[2] = (float) (Math.asin(rotationMatrix[8] / minusCosA)) * rad2deg; resultingAngles[0] = (float) (Math.asin(rotationMatrix[1] / minusCosA)) * rad2deg; } if (MODUS == 10) { SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, magnetData); rotationMatrix = transpose(rotationMatrix); /* * this assumes that the rotation matrices are multiplied in y x z */ resultingAngles[1] = (float) (Math.asin(-rotationMatrix[6])); final float cosA = (float) Math.cos(resultingAngles[1]); resultingAngles[1] = resultingAngles[1] * rad2deg; resultingAngles[2] = (float) (Math.asin(rotationMatrix[2] / cosA)) * rad2deg; resultingAngles[0] = (float) (Math.acos(rotationMatrix[5] / cosA)) * rad2deg; } if (MODUS == 11) { SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, magnetData); rotationMatrix = transpose(rotationMatrix); /* * this assumes that the rotation matrices are multiplied in y z x */ resultingAngles[0] = (float) (Math.asin(rotationMatrix[4])); final float cosC = (float) Math.cos(resultingAngles[0]); resultingAngles[0] = resultingAngles[0] * rad2deg; resultingAngles[2] = (float) (Math.acos(rotationMatrix[0] / cosC)) * rad2deg; resultingAngles[1] = (float) (Math.acos(rotationMatrix[5] / cosC)) * rad2deg; } if (MODUS == 12) { SensorManager.getRotationMatrix(rotationMatrix, null, accelGData, magnetData); rotationMatrix = transpose(rotationMatrix); /* * this assumes that the rotation matrices are multiplied in x z y */ resultingAngles[0] = (float) (Math.asin(-rotationMatrix[1])); final float cosC = (float) Math.cos(resultingAngles[0]); resultingAngles[0] = resultingAngles[0] * rad2deg; resultingAngles[2] = (float) (Math.acos(rotationMatrix[0] / cosC)) * rad2deg; resultingAngles[1] = (float) (Math.acos(rotationMatrix[5] / cosC)) * rad2deg; } logOutput(); } /** * transposes the matrix because it was transposted (inverted, but here its * the same, because its a rotation matrix) to be used for opengl * * @param source * @return */ private float[] transpose(float[] source) { final float[] result = source.clone(); if (TRY_TRANSPOSED_VERSION) { result[1] = source[4]; result[2] = source[8]; result[4] = source[1]; result[6] = source[9]; result[8] = source[2]; result[9] = source[6]; } // the other values in the matrix are not relevant for rotations return result; } private void rootMeanSquareBuffer(float[] target, float[] values) { final float amplification = 200.0f; float buffer = 20.0f; target[0] += amplification; target[1] += amplification; target[2] += amplification; values[0] += amplification; values[1] += amplification; values[2] += amplification; target[0] = (float) (Math .sqrt((target[0] * target[0] * buffer + values[0] * values[0]) / (1 + buffer))); target[1] = (float) (Math .sqrt((target[1] * target[1] * buffer + values[1] * values[1]) / (1 + buffer))); target[2] = (float) (Math .sqrt((target[2] * target[2] * buffer + values[2] * values[2]) / (1 + buffer))); target[0] -= amplification; target[1] -= amplification; target[2] -= amplification; values[0] -= amplification; values[1] -= amplification; values[2] -= amplification; } private void loadNewSensorData(SensorEvent event) { final int type = event.sensor.getType(); if (type == Sensor.TYPE_ACCELEROMETER) { accelGData = event.values.clone(); } if (type == Sensor.TYPE_MAGNETIC_FIELD) { magnetData = event.values.clone(); } if (type == Sensor.TYPE_ORIENTATION) { orientationData = event.values.clone(); } } private void logOutput() { if (mCount++ > 30) { mCount = 0; Log.d("Compass", "yaw0: " + (int) (resultingAngles[0]) + " pitch1: " + (int) (resultingAngles[1]) + " roll2: " + (int) (resultingAngles[2])); } } }

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  • NET Math Libraries

    - by JoshReuben
    NET Mathematical Libraries   .NET Builder for Matlab The MathWorks Inc. - http://www.mathworks.com/products/netbuilder/ MATLAB Builder NE generates MATLAB based .NET and COM components royalty-free deployment creates the components by encrypting MATLAB functions and generating either a .NET or COM wrapper around them. .NET/Link for Mathematica www.wolfram.com a product that 2-way integrates Mathematica and Microsoft's .NET platform call .NET from Mathematica - use arbitrary .NET types directly from the Mathematica language. use and control the Mathematica kernel from a .NET program. turns Mathematica into a scripting shell to leverage the computational services of Mathematica. write custom front ends for Mathematica or use Mathematica as a computational engine for another program comes with full source code. Leverages MathLink - a Wolfram Research's protocol for sending data and commands back and forth between Mathematica and other programs. .NET/Link abstracts the low-level details of the MathLink C API. Extreme Optimization http://www.extremeoptimization.com/ a collection of general-purpose mathematical and statistical classes built for the.NET framework. It combines a math library, a vector and matrix library, and a statistics library in one package. download the trial of version 4.0 to try it out. Multi-core ready - Full support for Task Parallel Library features including cancellation. Broad base of algorithms covering a wide range of numerical techniques, including: linear algebra (BLAS and LAPACK routines), numerical analysis (integration and differentiation), equation solvers. Mathematics leverages parallelism using .NET 4.0's Task Parallel Library. Basic math: Complex numbers, 'special functions' like Gamma and Bessel functions, numerical differentiation. Solving equations: Solve equations in one variable, or solve systems of linear or nonlinear equations. Curve fitting: Linear and nonlinear curve fitting, cubic splines, polynomials, orthogonal polynomials. Optimization: find the minimum or maximum of a function in one or more variables, linear programming and mixed integer programming. Numerical integration: Compute integrals over finite or infinite intervals, over 2D and higher dimensional regions. Integrate systems of ordinary differential equations (ODE's). Fast Fourier Transforms: 1D and 2D FFT's using managed or fast native code (32 and 64 bit) BigInteger, BigRational, and BigFloat: Perform operations with arbitrary precision. Vector and Matrix Library Real and complex vectors and matrices. Single and double precision for elements. Structured matrix types: including triangular, symmetrical and band matrices. Sparse matrices. Matrix factorizations: LU decomposition, QR decomposition, singular value decomposition, Cholesky decomposition, eigenvalue decomposition. Portability and performance: Calculations can be done in 100% managed code, or in hand-optimized processor-specific native code (32 and 64 bit). Statistics Data manipulation: Sort and filter data, process missing values, remove outliers, etc. Supports .NET data binding. Statistical Models: Simple, multiple, nonlinear, logistic, Poisson regression. Generalized Linear Models. One and two-way ANOVA. Hypothesis Tests: 12 14 hypothesis tests, including the z-test, t-test, F-test, runs test, and more advanced tests, such as the Anderson-Darling test for normality, one and two-sample Kolmogorov-Smirnov test, and Levene's test for homogeneity of variances. Multivariate Statistics: K-means cluster analysis, hierarchical cluster analysis, principal component analysis (PCA), multivariate probability distributions. Statistical Distributions: 25 29 continuous and discrete statistical distributions, including uniform, Poisson, normal, lognormal, Weibull and Gumbel (extreme value) distributions. Random numbers: Random variates from any distribution, 4 high-quality random number generators, low discrepancy sequences, shufflers. New in version 4.0 (November, 2010) Support for .NET Framework Version 4.0 and Visual Studio 2010 TPL Parallellized – multicore ready sparse linear program solver - can solve problems with more than 1 million variables. Mixed integer linear programming using a branch and bound algorithm. special functions: hypergeometric, Riemann zeta, elliptic integrals, Frensel functions, Dawson's integral. Full set of window functions for FFT's. Product  Price Update subscription Single Developer License $999  $399  Team License (3 developers) $1999  $799  Department License (8 developers) $3999  $1599  Site License (Unlimited developers in one physical location) $7999  $3199    NMath http://www.centerspace.net .NET math and statistics libraries matrix and vector classes random number generators Fast Fourier Transforms (FFTs) numerical integration linear programming linear regression curve and surface fitting optimization hypothesis tests analysis of variance (ANOVA) probability distributions principal component analysis cluster analysis built on the Intel Math Kernel Library (MKL), which contains highly-optimized, extensively-threaded versions of BLAS (Basic Linear Algebra Subroutines) and LAPACK (Linear Algebra PACKage). Product  Price Update subscription Single Developer License $1295 $388 Team License (5 developers) $5180 $1554   DotNumerics http://www.dotnumerics.com/NumericalLibraries/Default.aspx free DotNumerics is a website dedicated to numerical computing for .NET that includes a C# Numerical Library for .NET containing algorithms for Linear Algebra, Differential Equations and Optimization problems. The Linear Algebra library includes CSLapack, CSBlas and CSEispack, ports from Fortran to C# of LAPACK, BLAS and EISPACK, respectively. Linear Algebra (CSLapack, CSBlas and CSEispack). Systems of linear equations, eigenvalue problems, least-squares solutions of linear systems and singular value problems. Differential Equations. Initial-value problem for nonstiff and stiff ordinary differential equations ODEs (explicit Runge-Kutta, implicit Runge-Kutta, Gear's BDF and Adams-Moulton). Optimization. Unconstrained and bounded constrained optimization of multivariate functions (L-BFGS-B, Truncated Newton and Simplex methods).   Math.NET Numerics http://numerics.mathdotnet.com/ free an open source numerical library - includes special functions, linear algebra, probability models, random numbers, interpolation, integral transforms. A merger of dnAnalytics with Math.NET Iridium in addition to a purely managed implementation will also support native hardware optimization. constants & special functions complex type support real and complex, dense and sparse linear algebra (with LU, QR, eigenvalues, ... decompositions) non-uniform probability distributions, multivariate distributions, sample generation alternative uniform random number generators descriptive statistics, including order statistics various interpolation methods, including barycentric approaches and splines numerical function integration (quadrature) routines integral transforms, like fourier transform (FFT) with arbitrary lengths support, and hartley spectral-space aware sequence manipulation (signal processing) combinatorics, polynomials, quaternions, basic number theory. parallelized where appropriate, to leverage multi-core and multi-processor systems fully managed or (if available) using native libraries (Intel MKL, ACMS, CUDA, FFTW) provides a native facade for F# developers

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  • 2D Inverse Kinematics Implementation

    - by Vic
    Hi I am trying to implement Inverse Kinematics on a 2D arm(made up of three sticks with joints). I am able to rotate the lowest arm to the desired position. Now, I have some questions: How can I make the upper arm move alongwith the third so the end point of the arm reaches the desired point. Do I need to use the rotation matrices for both and if yes can someone give me some example or an help and is there any other possibl;e way to do this without rotation matrices??? The lowest arm only moves in one direction. I tried google it, they are saying that cross product of two vectors give the direction for the arm but this is for 3D. I am using 2D and cross product of two 2D vectors give a scalar. So, how can I determine its direction??? Plz guys any help would be appreciated.... Thanks in advance Vikram

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  • Fast 4x4 matrix multiplication in Java with NIO float buffers

    - by kayahr
    I know there are LOT of questions like that but I can't find one specific to my situation. I have 4x4 matrices implemented as NIO float buffers (These matrices are used for OpenGL). Now I want to implement a multiply method which multiplies Matrix A with Matrix B and stores the result in Matrix C. So the code may look like this: class Matrix4f { private FloatBuffer buffer = FloatBuffer.allocate(16); public Matrix4f multiply(Matrix4f matrix2, Matrix4f result) { {{{result = this * matrix2}}} <-- I need this code return result; } } What is the fastest possible code to do this multiplication? Some OpenGL implementations (Like the OpenGL ES stuff in Android) provide native code for this but others doesn't. So I want to provide a generic multiplication method for these implementations.

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  • C# huge size 2-dim arrays

    - by 4eburek
    I need to declare square matrices in C# WinForms with more than 20000 items in a row. I read about 2GB .Net object size limit in 32bit and also the same case in 64bit OS. So as I understood the single answer - is using unsafe code or separate library built withing C++ compiler. The problem for me is worth because ushort[20000,20000] is smaller then 2GB but actually I cannot allocate even 700MB of memory. My limit is 650MB and I don't understand why - I have 32bit WinXP with 3GB of memory. I tried to use Marshal.AllocHGlobal(700<<20) but it throws OutOfMemoryException, GC.GetTotalMemory returns 4.5MB before trying to allocate memory. I found only that many people say use unsafe code but I cannot find example of how to declare 2-dim array in heap (any stack can't keep so huge amount of data) and how to work with it using pointers. Is it pure C++ code inside of unsafe{} brackets? Could you please provide a small example of working with matrices using pointers in unsafe code.

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  • matrix image processing in OpenGL CE

    - by iHorse
    im trying to create an image filter in OpenGL CE. currently I am trying to create a series of 4x4 matrices and multiply them together. then use glColorMask and glColor4f to adjust the image accordingly. I've been able to integrate hue rotation, saturation, and brightness. but i am having trouble adding contrast. thus far google hasn't been to helpful. I've found a few matrices but they don't seem to work. do you guys have any ideas?

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  • Averaging corrupted images to eliminate the noise

    - by Mertie Pertie
    Hi all As you can get it from the title, I want to average some .jpg images which are corrupted by zero-mean Gaussian additive. After searching over internet, I figured out to add image matrices and divide the sum by the # of matrices. However the resultant image is totally black. Normally when the number of image increases then the resultant image gets better. But When I use more images it gets darker. I am using 800x600 black and white images with .jpg ext Here is the script I used; image1 = imread ('PIC1.jpg'); image2 = imread ('PIC2.jpg'); image3 = imread ('PIC3.jpg'); image4 = imread ('PIC4.jpg'); sum = image1 + image2 + image3 + image4; av = sum / 4; imshow(av); Thanks in advance

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  • Problem with averaging corrupted images to eliminate the noise in MATLAB

    - by Mertie Pertie
    I want to average some .jpg images which are corrupted by zero-mean Gaussian additive noise. After searching around, I figured out to add the image matrices and divide the sum by the number of matrices. However, the resultant image is totally black. Normally when the number of image increases then the resultant image gets better. But when I use more images it gets darker. I am using 800x600 black and white .jpg images. Here is the script I used: image1 = imread ('PIC1.jpg'); image2 = imread ('PIC2.jpg'); image3 = imread ('PIC3.jpg'); image4 = imread ('PIC4.jpg'); sum = image1 + image2 + image3 + image4; av = sum / 4; imshow(av);

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  • Averaging corrupted images to eliminate the noise in Matlab

    - by Mertie Pertie
    Hi all As you can get it from the title, I want to average some .jpg images which are corrupted by zero-mean Gaussian additive. After searching over internet, I figured out to add image matrices and divide the sum by the # of matrices. However the resultant image is totally black. Normally when the number of image increases then the resultant image gets better. But When I use more images it gets darker. I am using 800x600 black and white images with .jpg ext Here is the script I used; image1 = imread ('PIC1.jpg'); image2 = imread ('PIC2.jpg'); image3 = imread ('PIC3.jpg'); image4 = imread ('PIC4.jpg'); sum = image1 + image2 + image3 + image4; av = sum / 4; imshow(av); Thanks in advance

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  • Grab triangles within a lower triangle

    - by Tyler Rinker
    I have the need to grab all the thee element triangles that make up the lower triangle of a symmetric matrix. I can not think of how to grab all these pieces in the order of far left column working down and then next column to the right and so on. I know that the numbe rof mini triangles inside of the lower triangle is: n = x(x - 1)/2 where: x = nrow(mats[[i]]) Here I've created three matrices with letters (it's easier for me to conceptualize this way) and the elements in the order I'm looking for: FUN <- function(n) { matrix(LETTERS[1:(n*n)], n) } mats <- lapply(3:5, FUN) So this is the output I'd like to get (I put it in code rather than output format) for each of the matrices created above: list(c("B", "C", "F")) list(c("B", "C", "G"), c("C", "D", "H"), c("G", "H", "L")) list(c("B", "C", "H"), c("C", "D", "I"), c("D", "E", "J"), c("H", "I", "N"), c("I", "J", "O"), c("N", "O", "T")) How can I do this task in the fastest manner possible while staying in base R? Not sure if this visual of what I'm after is helpful but it may be:

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  • QR Factorization Discrepancy

    - by KyleSum
    I'm trying to get a feel for the Intel MKL library with a simple back-solve (A*x = b) using a QR factorization and comparing my MKL answer to the answer of a known working solution. When my answers didn't come up correct I printed a diff between the Q and R matrices of the known working and the MKL test code. I know MKL/lapack uses "elementary reflectors" to store the values of both the Q and R matrices. So, I'm wondering if these differences (mostly +/-) are by design or the result of some bug. I'm using DGEQRF, DORMQR, and DTRSM routines to solve the system and DORGQR (for debugging) to get the Q matrix shown in the diff. diff with 6x6 matrix (top known, bottom mkl): http://pastebin.com/4uwcME0J

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  • divide the image into 3*3 blocks

    - by Jayanth Silesh
    I have a matrix that does not happen to have dimensions that are multiples of 3 or it might. How can we divide the entire image into blocks of 3*3 matrices. (Can ignore the last ones which does not come under the 3*3 multiples. Also, the 3*3 matrices can be be saved in arrays. a=3; b=3; %window size x=size(f,1)/a; y=size(f,2)/b; %f is the original image m=a*ones(1,x); n=b*ones(1,y); I=mat2cell(f,m,n);

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  • Proper use of use of "cor" function in R

    - by order
    I am interested to know what a proper x (vector matrix or data frame) input looks like. I am currently using the function in two different sorts of matrices. However, I am not sure how R would interpret my data the way I intend. I will explain the types of matrix by example. Type 1 Gene1 Gene2 Gene3 sample1 sample2 Type 2 Sample1 Sample2 Sample3 gene 1 gene 2 gene 3 Are either of these formats valid x parameters? I input both of types of matrices and get some results, but without knowing whether or not this a proper use the function, these are just random numbers. Thank you for your time. I apologize that this isn't more interesting.

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  • find lowest neighbor matlab

    - by user1812719
    I am trying to write a function [offset,coffset]=findLowNhbr(map) that for each pixel in a map finds the eight neighbors to the pixel, and returns two matrices with both the row and column offsets to the lowest neighbor (uses the numbers -1, 0 and 1). Border pixels are given 0 offsets for both the row and column, since they do not have neighbors. Here is what I think the general plan for this function should be: For each point, find the eight nearest neighbors. If the neighbor is lower than the point, return -1 If the neighbor is at the same elevation as the point, return 0 If the neighbor is higher than the point, return +1 Store these offsets in two matrices. I am at a complete loss as to where to start, so any advice or questions are welcome!

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  • Paper on Linux memory access techniques sought

    - by James
    Over on stackoverflow someone posted a link to a paper written by a Linux kernel engineer about how to use computers and RAM. He started off by explaining how RAM works (right down to the flip-flops) and then went on to discuss performance problems associated with operations on matrices (column vs row accesses), offered solutions and then dealt with some stuff MMX instructions can do. Sorry it's a bit vague but I can't find it anywhere. I think the guy had a Scandinavian name, possibly Anders

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  • Looking for Application Framework Features Lists, Comparisons and Guides [closed]

    - by Blah McBlah
    I am looking for lists of the things that application frameworks can do and for websites that have matrices, marketing content, blog articles and whatnot for comparing application frameworks to each other or just selling a framework. I'm talking generally, so regardless of coded language or operating system or client device. I want it all. I've found a few online, and would appreciate whatever sources I can glean from this site too.

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  • Question about BoundingSpheres and Ray intersections

    - by NDraskovic
    I'm working on a XNA project (not really a game) and I'm having some trouble with picking algorithm. I have a few types of 3D models that I draw to the screen, and one of them is a switch. So I'm trying to make a picking algorithm that would enable the user to click on the switch and that would trigger some other function. The problem is that the BoundingSphere.Intersect() method always returns null as result. This is the code I'm using: In the declaration section: ` //Basic matrices private Matrix world = Matrix.CreateTranslation(new Vector3(0, 0, 0)); private Matrix view = Matrix.CreateLookAt(new Vector3(10, 10, 10), new Vector3(0, 0, 0), Vector3.UnitY); private Matrix projection = Matrix.CreatePerspectiveFieldOfView(MathHelper.ToRadians(45), 800f / 600f, 0.01f, 100f); //Collision detection variables Viewport mainViewport; List<BoundingSphere> spheres = new List<BoundingSphere>(); Ray ControlRay; Vector3 nearPoint, farPoint, nearPlane, farPlane, direction; ` And then in the Update method: ` nearPlane = new Vector3((float)Mouse.GetState().X, (float)Mouse.GetState().Y, 0.0f); farPlane = new Vector3((float)Mouse.GetState().X, (float)Mouse.GetState().Y, 10.0f); nearPoint = GraphicsDevice.Viewport.Unproject(nearPlane, projection, view, world); farPoint = GraphicsDevice.Viewport.Unproject(farPlane, projection, view, world); direction = farPoint - nearPoint; direction.Normalize(); ControlRay = new Ray(nearPoint, direction); if (spheres.Count != 0) { for (int i = 0; i < spheres.Count; i++) { if (spheres[i].Intersects(ControlRay) != null) { Window.Title = spheres[i].Center.ToString(); } else { Window.Title = "Empty"; } } ` The "spheres" list gets filled when the 3D object data gets loaded (I read it from a .txt file). For every object marked as switch (I use simple numbers to determine which object is to be drawn), a BoundingSphere is created (center is on the coordinates of the 3D object, and the diameter is always the same), and added to the list. The objects are drawn normally (and spheres.Count is not 0), I can see them on the screen, but the Window title always says "Empty" (of course this is just for testing purposes, I will add the real function when I get positive results) meaning that there is no intersection between the ControlRay and any of the bounding spheres. I think that my basic matrices (world, view and projection) are making some problems, but I cant figure out what. Please help.

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  • 2D camera perspective projection from 3D coordinates -- HOW?

    - by Jack
    I am developing a camera for a 2D game with a top-down view that has depth. It's almost a 3D camera. Basically, every object has a Z even though it is in 2D, and similarly to parallax layers their position, scale and rotation speed vary based on their Z. I guess this would be a perspective projection. But I am having trouble converting the objects' 3D coordinates into the 2D space of the screen so that everything has correct perspective and scale. I never learned matrices though I did dig the topic a bit today. I tried without using matrices thanks to this article but every attempt gave awkward results. I'm using ActionScript 3 and Flash 11+ (Starling), where the screen coordinates work like this: Left-handed coordinates system illustration I can explain further what I did if you want to help me sort out what's wrong, or you can directly tell me how you would do it properly. In case you prefer the former, read on. These are images showing the formulas I used: upload.wikimedia.org/math/1/c/8/1c89722619b756d05adb4ea38ee6f62b.png upload.wikimedia.org/math/d/4/0/d4069770c68cb8f1aa4b5cfc57e81bc3.png (Sorry new users can't post images, but both are from the wikipedia article linked above, section "Perspective projection". That's where you'll find what all variables mean, too) The long formula is greatly simplified because I believe a normal top-down 2D camera has no X/Y/Z rotation values (correct ?). Then it becomes d = a - c. Still, I can't get it to work. Maybe you could explain what numbers I should put in a(xyz), c(xyz), theta(xyz), and particularly, e(xyz) ? I don't quite get how e is different than c in my case. c.z is also an issue to me. If the Z of the camera's target object is 0, should the camera's Z be something like -600 ? ( = focal length of 600) Whatever I do, it's wrong. I only got it to work when I used arbitrary calculations that "looked" right, like most cameras with parallax layers seem to do, but that's fake! ;) If I want objects to travel between Z layers I might as well do it right. :) Thanks a lot for your help!

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  • Ray Picking Problems

    - by A Name I Haven't Decided On
    I've read so many answers on here about how to do Ray Picking, that I thought I had the idea of it down. But when I try to implement it in my game, I get garbage. I'm working with LWJGL. Here's the code: public static Ray getPick(int mouseX, int mouseY){ glPushMatrix(); //Setting up the Mouse Clip Vector4f mouseClip = new Vector4f((float)mouseX * 2 / 960f - 1, 1 - (float)mouseY * 2 / 640f ,0 ,1); //Loading Matrices FloatBuffer modMatrix = BufferUtils.createFloatBuffer(16); FloatBuffer projMatrix = BufferUtils.createFloatBuffer(16); glGetFloat(GL_MODELVIEW_MATRIX, modMatrix); glGetFloat(GL_PROJECTION_MATRIX, projMatrix); //Assigning Matrices Matrix4f proj = new Matrix4f(); Matrix4f model = new Matrix4f(); model.load(modMatrix); proj.load(projMatrix); //Multiplying the Projection Matrix by the Model View Matrix Matrix4f tempView = new Matrix4f(); Matrix4f.mul(proj, model, tempView); tempView.invert(); //Getting the Camera Position in World Space. The 4th Column of the Model View Matrix. model.invert(); Point cameraPos = new Point(model.m30, model.m31, model.m32); //Theoretically getting the vector the Picking Ray goes Vector4f rayVector = new Vector4f(); Matrix4f.transform(tempView, mouseClip, rayVector); rayVector.translate((float)-cameraPos.getX(),(float) -cameraPos.getY(),(float) -cameraPos.getZ(), 0f); rayVector.normalise(); glPopMatrix(); //This Basically Spits out a value that changes as the Camera moves. //When the Mouse moves, the values change around 0.001 points from screen edge to edge. System.out.format("Vector: %f %f %f%n", rayVector.x, rayVector.y, rayVector.z); //return new Ray(cameraPos, rayVector); return null; } I don't really know why this isn't working. I was hoping some more experienced eyes might be able to help me out. I can get the camera position like a champ, it's the vector the rays going in that I can't seem to get right. Thanks.

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  • October patch links

    - by THE
    Along the lines of patching... While it is not 100% in our LOB, it might still be interesting for some of our readers: The Oracle critical patch update Advisory for October 2012 You will find a very detailed List with links to patches and matrices on that overview page for products ranging from Database via E-Business Suite to MySQL. Of course you can find patches for Identity Management, SOA and Weblogic also via the "Master Note on Fusion Middleware Proactive Patching - Patch Set Updates (PSUs) and Bundle Patches (BPs) [ID 1494151.1]"

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