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  • Calculate Matrix Rank using scipy

    - by Hooked
    I'd like to calculate the mathematical rank of a matrix using scipy. The most obvious function numpy.rank calculates the dimension of an array (ie. scalars have dimension 0, vectors 1, matrices 2, etc...). I am aware that the numpy.linalg.lstsq module has this capability, but I was wondering if such a fundamental operation is built into the matrix class somewhere. Here is an explicit example: from numpy import matrix, rank A = matrix([[1,3,7],[2,8,3],[7,8,1]]) print rank(A) This gives 2 the dimension, where I'm looking for an answer of 3.

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  • Octave: Multiple submatrices from a matrix

    - by fbrereto
    I have a large matrix from which I would like to gather a collection of submatrices. If my matrix is NxN and the submatrix size is MxM, I want to collect I=(N - M + 1)^2 submatrices. In other words I want one MxM submatrix for each element in the original matrix that can be in the top-left corner of such a matrix. Here's the code I have: for y = 1:I for x = 1:I index = (y - 1) * I + x; block_set(index) = big_mat(x:x+M-1, y:y+M-1) endfor endfor The output if a) wrong, and b) implying there is something in the big_mat(x:x+M-1, y:y+M-1) expression that can get me what I want without needing the two for loops. Any help would be much appreciated

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  • Math: How to sum each row of a matrix

    - by macek
    I have a 1x8 matrix of students where each student is a 4x1 matrix of scores. Something like: SCORES S [62, 91, 74, 14] T [59, 7 , 59, 21] U [44, 9 , 69, 6 ] D [4 , 32, 28, 53] E [78, 99, 53, 83] N [48, 86, 89, 60] T [56, 71, 15, 80] S [47, 67, 79, 40] Main question: Using sigma notation, or some other mathematical function, how can I get a 1x8 matrix where each student's scores are summed? # expected result TOTAL OF SCORES S [241] T [146] U [128] D [117] E [313] N [283] T [222] S [233] Sub question. To get the average, I will multiply the matrix by 1/4. Would there be a quicker way to get the final result? AVERAGE SCORE S [60.25] T [36.50] U [32.00] D [29.25] E [78.25] N [70.75] T [55.50] S [58.25] Note: I'm not looking for programming-related algorithms here. I want to know if it is possible to represent this with pure mathematical functions alone.

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  • how to displaying pivot in matrix reporting service?

    - by Chandradyani
    Dear All, I have problem relating to pivot query and matrix reporting. I don't know how to display it on matrix reporting service so it will dynamic column. Can any body help me to show how to configure the matrix table? or could you give the link where can I find the answer of my problem? I'm newbie in reporting service.

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  • Looking for actively maintained matrix math library for php

    - by Mnebuerquo
    Does anyone know where I might find a PHP matrix math library which is still actively maintained? I need to be able to do the basic matrix operations like reduce, transpose (including non-square matrices), invert, determinant, etc. This question was asked in the past, then closed with no answers. Now I need an answer to the same question. See these links to related questions: http://stackoverflow.com/questions/428473/matrix-artihmetic-in-php http://stackoverflow.com/questions/435074/matrix-arithmetic-in-php-again I was in the process of installing the pear Math_Matrix library when I saw these and realized it wouldn't help me. (Thanks Ben for putting that comment about transpose in your question.) I can code this stuff myself, but I would make me happier to see that there is a library for this somewhere.

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  • Reporting Services Matrix Order

    - by James Stewart
    I've got a reporting services report which display data in a matrix. The matrix rows are ordered by the report on a specific field's value. Trouble is I want a particular value to always appear last in the matrix even though it won't naturally be ordered there. Is there a way I can do this using an expression? Thanks.

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  • plot matrix missing points in different color using gnuplot

    - by kitt
    I have a file 'matrix.dat': 1 2 3 4 5 5 - 3 4 5 - 4 5 B - 1 B 2 B 3 - 3 2 - 3 I want to plot numbers using palette, '-' using white color and 'B' using black color. In gnuplot, I use this palette (blue - cyan - green - orange - red): set palette model HSV functions 0.666*(1-gray), 1, 1 And set '-' as missing data: set datafile missing "-" plot 'matrix.dat' matrix with image Now I can only plot numbers and '-' in correct colors.

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  • Sort a matrix with another matrix

    - by Jacob
    Suppose I have a matrix A and I sort the rows of this matrix. How do I replicate the same ordering on a matrix B (same size of course)? E.g. A = rand(3,4); [val ind] = sort(A,2); B = rand(3,4); %// Reorder the elements of B according the reordering of A This is the best I've come up with m = size(A,1); B = B(bsxfun(@plus,(ind-1)*m,(1:m)')); Out of curiosity, any alternatives?

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  • The bigger value in a matrix row

    - by marionmaiden
    How can I get the 2 biggers numbers of a matrix row? If the matrix have a bigger number in other row, it can't be shown. For example, let's suppose I have the following matrix int mat[][] ={{1,2,3}{4,5,6}{7,8,9}}; if I search the 2 biggers numbers from the row 0, it should return me 1 and 2.

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  • Matrix multiplication using pairs

    - by sc_ray
    Hi, I am looking into alternate ways to do a Matrix Multiplication. Instead of storing my matrix as a two-dimensional array, I am using a vector such as vector<pair<pair<int,int >,int > > to store my matrix. The pair within my pair (pair) stores my indices (i,j) and the other int stores the value for the given (i,j) pair. I thought I might have some luck implementing my sparse array this way. The problem is when I try to multiply this matrix with itself. If this was a 2-d array implementation, I would have multiplied the matrix as follows: for(i=0; i<row1; i++) { for(j=0; j<col1; j++) { C[i][j] = 0; for(k=0; k<col2; k++) C[i][j] += A[i][j] * A[j][k]; } } Can somebody point out a way to achieve the same result using my vector of 'pair of pairs'? Thanks

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  • iPhone Image Processing--matrix convolution

    - by James
    I am implementing a matrix convolution blur on the iPhone. The following code converts the UIImage supplied as an argument of the blur function into a CGImageRef, and then stores the RGBA values in a standard C char array. CGImageRef imageRef = imgRef.CGImage; int width = imgRef.size.width; int height = imgRef.size.height; CGColorSpaceRef colorSpace = CGColorSpaceCreateDeviceRGB(); unsigned char *pixels = malloc((height) * (width) * 4); NSUInteger bytesPerPixel = 4; NSUInteger bytesPerRow = bytesPerPixel * (width); NSUInteger bitsPerComponent = 8; CGContextRef context = CGBitmapContextCreate(pixels, width, height, bitsPerComponent, bytesPerRow, colorSpace, kCGImageAlphaPremultipliedLast | kCGBitmapByteOrder32Big); CGContextDrawImage(context, CGRectMake(0, 0, width, height), imageRef); CGContextRelease(context); Then the pixels values stored in the pixels array are convolved, and stored in another array. unsigned char *results = malloc((height) * (width) * 4); Finally, these augmented pixel values are changed back into a CGImageRef, converted to a UIImage, and the returned at the end of the function with the following code. context = CGBitmapContextCreate(results, width, height, bitsPerComponent, bytesPerRow, colorSpace, kCGImageAlphaPremultipliedLast | kCGBitmapByteOrder32Big); CGImageRef finalImage = CGBitmapContextCreateImage(context); UIImage *newImage = [UIImage imageWithCGImage:CGBitmapContextCreateImage(context)]; CGImageRelease(finalImage); NSLog(@"edges found"); free(results); free(pixels); CGColorSpaceRelease(colorSpace); return newImage; This works perfectly, once. Then, once the image is put through the filter again, very odd, unprecedented pixel values representing input pixel values that don't exist, are returned. Is there any reason why this should work the first time, but then not afterward? Beneath is the entirety of the function. -(UIImage*) blur:(UIImage*)imgRef { CGImageRef imageRef = imgRef.CGImage; int width = imgRef.size.width; int height = imgRef.size.height; CGColorSpaceRef colorSpace = CGColorSpaceCreateDeviceRGB(); unsigned char *pixels = malloc((height) * (width) * 4); NSUInteger bytesPerPixel = 4; NSUInteger bytesPerRow = bytesPerPixel * (width); NSUInteger bitsPerComponent = 8; CGContextRef context = CGBitmapContextCreate(pixels, width, height, bitsPerComponent, bytesPerRow, colorSpace, kCGImageAlphaPremultipliedLast | kCGBitmapByteOrder32Big); CGContextDrawImage(context, CGRectMake(0, 0, width, height), imageRef); CGContextRelease(context); height = imgRef.size.height; width = imgRef.size.width; float matrix[] = {0,0,0,0,1,0,0,0,0}; float divisor = 1; float shift = 0; unsigned char *results = malloc((height) * (width) * 4); for(int y = 1; y < height; y++){ for(int x = 1; x < width; x++){ float red = 0; float green = 0; float blue = 0; int multiplier=1; if(y>0 && x>0){ int index = (y-1)*width + x; red = matrix[0]*multiplier*(float)pixels[4*(index-1)] + matrix[1]*multiplier*(float)pixels[4*(index)] + matrix[2]*multiplier*(float)pixels[4*(index+1)]; green = matrix[0]*multiplier*(float)pixels[4*(index-1)+1] + matrix[1]*multiplier*(float)pixels[4*(index)+1] + matrix[2]*multiplier*(float)pixels[4*(index+1)+1]; blue = matrix[0]*multiplier*(float)pixels[4*(index-1)+2] + matrix[1]*multiplier*(float)pixels[4*(index)+2] + matrix[2]*multiplier*(float)pixels[4*(index+1)+2]; index = (y)*width + x; red = red+ matrix[3]*multiplier*(float)pixels[4*(index-1)] + matrix[4]*multiplier*(float)pixels[4*(index)] + matrix[5]*multiplier*(float)pixels[4*(index+1)]; green = green + matrix[3]*multiplier*(float)pixels[4*(index-1)+1] + matrix[4]*multiplier*(float)pixels[4*(index)+1] + matrix[5]*multiplier*(float)pixels[4*(index+1)+1]; blue = blue + matrix[3]*multiplier*(float)pixels[4*(index-1)+2] + matrix[4]*multiplier*(float)pixels[4*(index)+2] + matrix[5]*multiplier*(float)pixels[4*(index+1)+2]; index = (y+1)*width + x; red = red+ matrix[6]*multiplier*(float)pixels[4*(index-1)] + matrix[7]*multiplier*(float)pixels[4*(index)] + matrix[8]*multiplier*(float)pixels[4*(index+1)]; green = green + matrix[6]*multiplier*(float)pixels[4*(index-1)+1] + matrix[7]*multiplier*(float)pixels[4*(index)+1] + matrix[8]*multiplier*(float)pixels[4*(index+1)+1]; blue = blue + matrix[6]*multiplier*(float)pixels[4*(index-1)+2] + matrix[7]*multiplier*(float)pixels[4*(index)+2] + matrix[8]*multiplier*(float)pixels[4*(index+1)+2]; red = red/divisor+shift; green = green/divisor+shift; blue = blue/divisor+shift; if(red<0){ red=0; } if(green<0){ green=0; } if(blue<0){ blue=0; } if(red>255){ red=255; } if(green>255){ green=255; } if(blue>255){ blue=255; } int realPos = 4*(y*imgRef.size.width + x); results[realPos] = red; results[realPos + 1] = green; results[realPos + 2] = blue; results[realPos + 3] = 1; }else { int realPos = 4*((y)*(imgRef.size.width) + (x)); results[realPos] = 0; results[realPos + 1] = 0; results[realPos + 2] = 0; results[realPos + 3] = 1; } } } context = CGBitmapContextCreate(results, width, height, bitsPerComponent, bytesPerRow, colorSpace, kCGImageAlphaPremultipliedLast | kCGBitmapByteOrder32Big); CGImageRef finalImage = CGBitmapContextCreateImage(context); UIImage *newImage = [UIImage imageWithCGImage:CGBitmapContextCreateImage(context)]; CGImageRelease(finalImage); free(results); free(pixels); CGColorSpaceRelease(colorSpace); return newImage;} THANKS!!!

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  • Camera for 2.5D Game

    - by me--
    I'm hoping someone can explain this to me like I'm 5, because I've been struggling with this for hours and simply cannot understand what I'm doing wrong. I've written a Camera class for my 2.5D game. The intention is to support world and screen spaces like this: The camera is the black thing on the right. The +Z axis is upwards in that image, with -Z heading downwards. As you can see, both world space and screen space have (0, 0) at their top-left. I started writing some unit tests to prove that my camera was working as expected, and that's where things started getting...strange. My tests plot coordinates in world, view, and screen spaces. Eventually I will use image comparison to assert that they are correct, but for now my test just displays the result. The render logic uses Camera.ViewMatrix to transform world space to view space, and Camera.WorldPointToScreen to transform world space to screen space. Here is an example test: [Fact] public void foo() { var camera = new Camera(new Viewport(0, 0, 250, 100)); DrawingVisual worldRender; DrawingVisual viewRender; DrawingVisual screenRender; this.Render(camera, out worldRender, out viewRender, out screenRender, new Vector3(30, 0, 0), new Vector3(30, 40, 0)); this.ShowRenders(camera, worldRender, viewRender, screenRender); } And here's what pops up when I run this test: World space looks OK, although I suspect the z axis is going into the screen instead of towards the viewer. View space has me completely baffled. I was expecting the camera to be sitting above (0, 0) and looking towards the center of the scene. Instead, the z axis seems to be the wrong way around, and the camera is positioned in the opposite corner to what I expect! I suspect screen space will be another thing altogether, but can anyone explain what I'm doing wrong in my Camera class? UPDATE I made some progress in terms of getting things to look visually as I expect, but only through intuition: not an actual understanding of what I'm doing. Any enlightenment would be greatly appreciated. I realized that my view space was flipped both vertically and horizontally compared to what I expected, so I changed my view matrix to scale accordingly: this.viewMatrix = Matrix.CreateLookAt(this.location, this.target, this.up) * Matrix.CreateScale(this.zoom, this.zoom, 1) * Matrix.CreateScale(-1, -1, 1); I could combine the two CreateScale calls, but have left them separate for clarity. Again, I have no idea why this is necessary, but it fixed my view space: But now my screen space needs to be flipped vertically, so I modified my projection matrix accordingly: this.projectionMatrix = Matrix.CreatePerspectiveFieldOfView(0.7853982f, viewport.AspectRatio, 1, 2) * Matrix.CreateScale(1, -1, 1); And this results in what I was expecting from my first attempt: I have also just tried using Camera to render sprites via a SpriteBatch to make sure everything works there too, and it does. But the question remains: why do I need to do all this flipping of axes to get the space coordinates the way I expect? UPDATE 2 I've since improved my rendering logic in my test suite so that it supports geometries and so that lines get lighter the further away they are from the camera. I wanted to do this to avoid optical illusions and to further prove to myself that I'm looking at what I think I am. Here is an example: In this case, I have 3 geometries: a cube, a sphere, and a polyline on the top face of the cube. Notice how the darkening and lightening of the lines correctly identifies those portions of the geometries closer to the camera. If I remove the negative scaling I had to put in, I see: So you can see I'm still in the same boat - I still need those vertical and horizontal flips in my matrices to get things to appear correctly. In the interests of giving people a repro to play with, here is the complete code needed to generate the above. If you want to run via the test harness, just install the xunit package: Camera.cs: using Microsoft.Xna.Framework; using Microsoft.Xna.Framework.Graphics; using System.Diagnostics; public sealed class Camera { private readonly Viewport viewport; private readonly Matrix projectionMatrix; private Matrix? viewMatrix; private Vector3 location; private Vector3 target; private Vector3 up; private float zoom; public Camera(Viewport viewport) { this.viewport = viewport; // for an explanation of the negative scaling, see: http://gamedev.stackexchange.com/questions/63409/ this.projectionMatrix = Matrix.CreatePerspectiveFieldOfView(0.7853982f, viewport.AspectRatio, 1, 2) * Matrix.CreateScale(1, -1, 1); // defaults this.location = new Vector3(this.viewport.Width / 2, this.viewport.Height, 100); this.target = new Vector3(this.viewport.Width / 2, this.viewport.Height / 2, 0); this.up = new Vector3(0, 0, 1); this.zoom = 1; } public Viewport Viewport { get { return this.viewport; } } public Vector3 Location { get { return this.location; } set { this.location = value; this.viewMatrix = null; } } public Vector3 Target { get { return this.target; } set { this.target = value; this.viewMatrix = null; } } public Vector3 Up { get { return this.up; } set { this.up = value; this.viewMatrix = null; } } public float Zoom { get { return this.zoom; } set { this.zoom = value; this.viewMatrix = null; } } public Matrix ProjectionMatrix { get { return this.projectionMatrix; } } public Matrix ViewMatrix { get { if (this.viewMatrix == null) { // for an explanation of the negative scaling, see: http://gamedev.stackexchange.com/questions/63409/ this.viewMatrix = Matrix.CreateLookAt(this.location, this.target, this.up) * Matrix.CreateScale(this.zoom) * Matrix.CreateScale(-1, -1, 1); } return this.viewMatrix.Value; } } public Vector2 WorldPointToScreen(Vector3 point) { var result = viewport.Project(point, this.ProjectionMatrix, this.ViewMatrix, Matrix.Identity); return new Vector2(result.X, result.Y); } public void WorldPointsToScreen(Vector3[] points, Vector2[] destination) { Debug.Assert(points != null); Debug.Assert(destination != null); Debug.Assert(points.Length == destination.Length); for (var i = 0; i < points.Length; ++i) { destination[i] = this.WorldPointToScreen(points[i]); } } } CameraFixture.cs: using Microsoft.Xna.Framework.Graphics; using System; using System.Collections.Generic; using System.Linq; using System.Windows; using System.Windows.Controls; using System.Windows.Media; using Xunit; using XNA = Microsoft.Xna.Framework; public sealed class CameraFixture { [Fact] public void foo() { var camera = new Camera(new Viewport(0, 0, 250, 100)); DrawingVisual worldRender; DrawingVisual viewRender; DrawingVisual screenRender; this.Render( camera, out worldRender, out viewRender, out screenRender, new Sphere(30, 15) { WorldMatrix = XNA.Matrix.CreateTranslation(155, 50, 0) }, new Cube(30) { WorldMatrix = XNA.Matrix.CreateTranslation(75, 60, 15) }, new PolyLine(new XNA.Vector3(0, 0, 0), new XNA.Vector3(10, 10, 0), new XNA.Vector3(20, 0, 0), new XNA.Vector3(0, 0, 0)) { WorldMatrix = XNA.Matrix.CreateTranslation(65, 55, 30) }); this.ShowRenders(worldRender, viewRender, screenRender); } #region Supporting Fields private static readonly Pen xAxisPen = new Pen(Brushes.Red, 2); private static readonly Pen yAxisPen = new Pen(Brushes.Green, 2); private static readonly Pen zAxisPen = new Pen(Brushes.Blue, 2); private static readonly Pen viewportPen = new Pen(Brushes.Gray, 1); private static readonly Pen nonScreenSpacePen = new Pen(Brushes.Black, 0.5); private static readonly Color geometryBaseColor = Colors.Black; #endregion #region Supporting Methods private void Render(Camera camera, out DrawingVisual worldRender, out DrawingVisual viewRender, out DrawingVisual screenRender, params Geometry[] geometries) { var worldDrawingVisual = new DrawingVisual(); var viewDrawingVisual = new DrawingVisual(); var screenDrawingVisual = new DrawingVisual(); const int axisLength = 15; using (var worldDrawingContext = worldDrawingVisual.RenderOpen()) using (var viewDrawingContext = viewDrawingVisual.RenderOpen()) using (var screenDrawingContext = screenDrawingVisual.RenderOpen()) { // draw lines around the camera's viewport var viewportBounds = camera.Viewport.Bounds; var viewportLines = new Tuple<int, int, int, int>[] { Tuple.Create(viewportBounds.Left, viewportBounds.Bottom, viewportBounds.Left, viewportBounds.Top), Tuple.Create(viewportBounds.Left, viewportBounds.Top, viewportBounds.Right, viewportBounds.Top), Tuple.Create(viewportBounds.Right, viewportBounds.Top, viewportBounds.Right, viewportBounds.Bottom), Tuple.Create(viewportBounds.Right, viewportBounds.Bottom, viewportBounds.Left, viewportBounds.Bottom) }; foreach (var viewportLine in viewportLines) { var viewStart = XNA.Vector3.Transform(new XNA.Vector3(viewportLine.Item1, viewportLine.Item2, 0), camera.ViewMatrix); var viewEnd = XNA.Vector3.Transform(new XNA.Vector3(viewportLine.Item3, viewportLine.Item4, 0), camera.ViewMatrix); var screenStart = camera.WorldPointToScreen(new XNA.Vector3(viewportLine.Item1, viewportLine.Item2, 0)); var screenEnd = camera.WorldPointToScreen(new XNA.Vector3(viewportLine.Item3, viewportLine.Item4, 0)); worldDrawingContext.DrawLine(viewportPen, new Point(viewportLine.Item1, viewportLine.Item2), new Point(viewportLine.Item3, viewportLine.Item4)); viewDrawingContext.DrawLine(viewportPen, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y)); screenDrawingContext.DrawLine(viewportPen, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y)); } // draw axes var axisLines = new Tuple<int, int, int, int, int, int, Pen>[] { Tuple.Create(0, 0, 0, axisLength, 0, 0, xAxisPen), Tuple.Create(0, 0, 0, 0, axisLength, 0, yAxisPen), Tuple.Create(0, 0, 0, 0, 0, axisLength, zAxisPen) }; foreach (var axisLine in axisLines) { var viewStart = XNA.Vector3.Transform(new XNA.Vector3(axisLine.Item1, axisLine.Item2, axisLine.Item3), camera.ViewMatrix); var viewEnd = XNA.Vector3.Transform(new XNA.Vector3(axisLine.Item4, axisLine.Item5, axisLine.Item6), camera.ViewMatrix); var screenStart = camera.WorldPointToScreen(new XNA.Vector3(axisLine.Item1, axisLine.Item2, axisLine.Item3)); var screenEnd = camera.WorldPointToScreen(new XNA.Vector3(axisLine.Item4, axisLine.Item5, axisLine.Item6)); worldDrawingContext.DrawLine(axisLine.Item7, new Point(axisLine.Item1, axisLine.Item2), new Point(axisLine.Item4, axisLine.Item5)); viewDrawingContext.DrawLine(axisLine.Item7, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y)); screenDrawingContext.DrawLine(axisLine.Item7, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y)); } // for all points in all geometries to be rendered, find the closest and furthest away from the camera so we can lighten lines that are further away var distancesToAllGeometrySections = from geometry in geometries let geometryViewMatrix = geometry.WorldMatrix * camera.ViewMatrix from section in geometry.Sections from point in new XNA.Vector3[] { section.Item1, section.Item2 } let viewPoint = XNA.Vector3.Transform(point, geometryViewMatrix) select viewPoint.Length(); var furthestDistance = distancesToAllGeometrySections.Max(); var closestDistance = distancesToAllGeometrySections.Min(); var deltaDistance = Math.Max(0.000001f, furthestDistance - closestDistance); // draw each geometry for (var i = 0; i < geometries.Length; ++i) { var geometry = geometries[i]; // there's probably a more correct name for this, but basically this gets the geometry relative to the camera so we can check how far away each point is from the camera var geometryViewMatrix = geometry.WorldMatrix * camera.ViewMatrix; // we order roughly by those sections furthest from the camera to those closest, so that the closer ones "overwrite" the ones further away var orderedSections = from section in geometry.Sections let startPointRelativeToCamera = XNA.Vector3.Transform(section.Item1, geometryViewMatrix) let endPointRelativeToCamera = XNA.Vector3.Transform(section.Item2, geometryViewMatrix) let startPointDistance = startPointRelativeToCamera.Length() let endPointDistance = endPointRelativeToCamera.Length() orderby (startPointDistance + endPointDistance) descending select new { Section = section, DistanceToStart = startPointDistance, DistanceToEnd = endPointDistance }; foreach (var orderedSection in orderedSections) { var start = XNA.Vector3.Transform(orderedSection.Section.Item1, geometry.WorldMatrix); var end = XNA.Vector3.Transform(orderedSection.Section.Item2, geometry.WorldMatrix); var viewStart = XNA.Vector3.Transform(start, camera.ViewMatrix); var viewEnd = XNA.Vector3.Transform(end, camera.ViewMatrix); worldDrawingContext.DrawLine(nonScreenSpacePen, new Point(start.X, start.Y), new Point(end.X, end.Y)); viewDrawingContext.DrawLine(nonScreenSpacePen, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y)); // screen rendering is more complicated purely because I wanted geometry to fade the further away it is from the camera // otherwise, it's very hard to tell whether the rendering is actually correct or not var startDistanceRatio = (orderedSection.DistanceToStart - closestDistance) / deltaDistance; var endDistanceRatio = (orderedSection.DistanceToEnd - closestDistance) / deltaDistance; // lerp towards white based on distance from camera, but only to a maximum of 90% var startColor = Lerp(geometryBaseColor, Colors.White, startDistanceRatio * 0.9f); var endColor = Lerp(geometryBaseColor, Colors.White, endDistanceRatio * 0.9f); var screenStart = camera.WorldPointToScreen(start); var screenEnd = camera.WorldPointToScreen(end); var brush = new LinearGradientBrush { StartPoint = new Point(screenStart.X, screenStart.Y), EndPoint = new Point(screenEnd.X, screenEnd.Y), MappingMode = BrushMappingMode.Absolute }; brush.GradientStops.Add(new GradientStop(startColor, 0)); brush.GradientStops.Add(new GradientStop(endColor, 1)); var pen = new Pen(brush, 1); brush.Freeze(); pen.Freeze(); screenDrawingContext.DrawLine(pen, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y)); } } } worldRender = worldDrawingVisual; viewRender = viewDrawingVisual; screenRender = screenDrawingVisual; } private static float Lerp(float start, float end, float amount) { var difference = end - start; var adjusted = difference * amount; return start + adjusted; } private static Color Lerp(Color color, Color to, float amount) { var sr = color.R; var sg = color.G; var sb = color.B; var er = to.R; var eg = to.G; var eb = to.B; var r = (byte)Lerp(sr, er, amount); var g = (byte)Lerp(sg, eg, amount); var b = (byte)Lerp(sb, eb, amount); return Color.FromArgb(255, r, g, b); } private void ShowRenders(DrawingVisual worldRender, DrawingVisual viewRender, DrawingVisual screenRender) { var itemsControl = new ItemsControl(); itemsControl.Items.Add(new HeaderedContentControl { Header = "World", Content = new DrawingVisualHost(worldRender)}); itemsControl.Items.Add(new HeaderedContentControl { Header = "View", Content = new DrawingVisualHost(viewRender) }); itemsControl.Items.Add(new HeaderedContentControl { Header = "Screen", Content = new DrawingVisualHost(screenRender) }); var window = new Window { Title = "Renders", Content = itemsControl, ShowInTaskbar = true, SizeToContent = SizeToContent.WidthAndHeight }; window.ShowDialog(); } #endregion #region Supporting Types // stupidly simple 3D geometry class, consisting of a series of sections that will be connected by lines private abstract class Geometry { public abstract IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get; } public XNA.Matrix WorldMatrix { get; set; } } private sealed class Line : Geometry { private readonly XNA.Vector3 magnitude; public Line(XNA.Vector3 magnitude) { this.magnitude = magnitude; } public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get { yield return Tuple.Create(XNA.Vector3.Zero, this.magnitude); } } } private sealed class PolyLine : Geometry { private readonly XNA.Vector3[] points; public PolyLine(params XNA.Vector3[] points) { this.points = points; } public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get { if (this.points.Length < 2) { yield break; } var end = this.points[0]; for (var i = 1; i < this.points.Length; ++i) { var start = end; end = this.points[i]; yield return Tuple.Create(start, end); } } } } private sealed class Cube : Geometry { private readonly float size; public Cube(float size) { this.size = size; } public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get { var halfSize = this.size / 2; var frontBottomLeft = new XNA.Vector3(-halfSize, halfSize, -halfSize); var frontBottomRight = new XNA.Vector3(halfSize, halfSize, -halfSize); var frontTopLeft = new XNA.Vector3(-halfSize, halfSize, halfSize); var frontTopRight = new XNA.Vector3(halfSize, halfSize, halfSize); var backBottomLeft = new XNA.Vector3(-halfSize, -halfSize, -halfSize); var backBottomRight = new XNA.Vector3(halfSize, -halfSize, -halfSize); var backTopLeft = new XNA.Vector3(-halfSize, -halfSize, halfSize); var backTopRight = new XNA.Vector3(halfSize, -halfSize, halfSize); // front face yield return Tuple.Create(frontBottomLeft, frontBottomRight); yield return Tuple.Create(frontBottomLeft, frontTopLeft); yield return Tuple.Create(frontTopLeft, frontTopRight); yield return Tuple.Create(frontTopRight, frontBottomRight); // left face yield return Tuple.Create(frontTopLeft, backTopLeft); yield return Tuple.Create(backTopLeft, backBottomLeft); yield return Tuple.Create(backBottomLeft, frontBottomLeft); // right face yield return Tuple.Create(frontTopRight, backTopRight); yield return Tuple.Create(backTopRight, backBottomRight); yield return Tuple.Create(backBottomRight, frontBottomRight); // back face yield return Tuple.Create(backBottomLeft, backBottomRight); yield return Tuple.Create(backTopLeft, backTopRight); } } } private sealed class Sphere : Geometry { private readonly float radius; private readonly int subsections; public Sphere(float radius, int subsections) { this.radius = radius; this.subsections = subsections; } public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections { get { var latitudeLines = this.subsections; var longitudeLines = this.subsections; // see http://stackoverflow.com/a/4082020/5380 var results = from latitudeLine in Enumerable.Range(0, latitudeLines) from longitudeLine in Enumerable.Range(0, longitudeLines) let latitudeRatio = latitudeLine / (float)latitudeLines let longitudeRatio = longitudeLine / (float)longitudeLines let nextLatitudeRatio = (latitudeLine + 1) / (float)latitudeLines let nextLongitudeRatio = (longitudeLine + 1) / (float)longitudeLines let z1 = Math.Cos(Math.PI * latitudeRatio) let z2 = Math.Cos(Math.PI * nextLatitudeRatio) let x1 = Math.Sin(Math.PI * latitudeRatio) * Math.Cos(Math.PI * 2 * longitudeRatio) let y1 = Math.Sin(Math.PI * latitudeRatio) * Math.Sin(Math.PI * 2 * longitudeRatio) let x2 = Math.Sin(Math.PI * nextLatitudeRatio) * Math.Cos(Math.PI * 2 * longitudeRatio) let y2 = Math.Sin(Math.PI * nextLatitudeRatio) * Math.Sin(Math.PI * 2 * longitudeRatio) let x3 = Math.Sin(Math.PI * latitudeRatio) * Math.Cos(Math.PI * 2 * nextLongitudeRatio) let y3 = Math.Sin(Math.PI * latitudeRatio) * Math.Sin(Math.PI * 2 * nextLongitudeRatio) let start = new XNA.Vector3((float)x1 * radius, (float)y1 * radius, (float)z1 * radius) let firstEnd = new XNA.Vector3((float)x2 * radius, (float)y2 * radius, (float)z2 * radius) let secondEnd = new XNA.Vector3((float)x3 * radius, (float)y3 * radius, (float)z1 * radius) select new { First = Tuple.Create(start, firstEnd), Second = Tuple.Create(start, secondEnd) }; foreach (var result in results) { yield return result.First; yield return result.Second; } } } } #endregion }

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  • Recover Intel Matrix Raid Configuration

    - by Catalin DICU
    Hello, I had 2 HDDs in Intel Matrix Raid configuration on a motherboard with intel ICH9R. I had some RAID 0 partitions and one RAID 1 partition. Somehow when replacing my videocard I partially unpulugged the power connector from one of the HDD. I booted and only one disk was showing. So I turned off the PC and correctly plugged the power connector and how both HDDs are showing as "Non-Raid Disk" Is there a way to restore the raid configuration from before ? In fact I don't really remember how my partitions where configured, I had 2x100Gb + 1x296Gb in RAID 0 and one 50Gb in RAID 1 (using 2x320Gb HDDs) but I'm not sure how many volumes and how the partitions where allocated on the volumes. Is there a tool to find that ? Thanks

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  • Retrieving model position after applying modeltransforms in XNA

    - by Glen Dekker
    For this method that the goingBeyond XNA tutorial provides, it would be really convenient if I could retrieve the new position of the model after I apply all the transforms to the mesh. I have edited the method a little for what I need. Does anyone know a way I can do this? public void DrawModel( Camera camera ) { Matrix scaleY = Matrix.CreateScale(new Vector3(1, 2, 1)); Matrix temp = Matrix.CreateScale(100f) * scaleY * rotationMatrix * translationMatrix * Matrix.CreateRotationY(MathHelper.Pi / 6) * translationMatrix2; Matrix[] modelTransforms = new Matrix[model.Bones.Count]; model.CopyAbsoluteBoneTransformsTo(modelTransforms); if (camera.getDistanceFromPlayer(position+position1) > 3000) return; foreach (ModelMesh mesh in model.Meshes) { foreach (BasicEffect effect in mesh.Effects) { effect.EnableDefaultLighting(); effect.World = modelTransforms[mesh.ParentBone.Index] * temp * worldMatrix; effect.View = camera.viewMatrix; effect.Projection = camera.projectionMatrix; } mesh.Draw(); } }

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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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  • How do I build a matrix to translate one set of points to another?

    - by dotminic
    I've got 3 points in space that define a triangle. I've also got a vertex buffer made up of three vertices, that also represent a triangle that I will refer to as a "model". How can I can I find the matrix M that will transform vertex in my buffer to those 3 points in space ? For example, let's say my three points A, B, C are at locations: A.x = 10, A.y = 16, A.z = 8 B.x = 12, B.y = 11, B.z = 1 C.x = 19, C.y = 12, C.z = 3 given these coordinates how can I build a matrix that will translate and rotate my model such that both triangles have the exact same world space ? That is, I want the first vertex in my triangle model to have the same coordinates as A, the second to have the same coordinates as B, and same goes for C. nb: I'm using instanced rendering so I can't just give each vertex the same position as my 3 points. I have a set of three points defining a triangle, and only three vertices in my vertex buffer.

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  • How to fill in Different String Values in Different Cells in Excel 2007 VBA marcos

    - by user325160
    Hello everyone, So I am trying to fill in Values "A-Z, 0-9" in a 2007 excel macro in four different locations (I am trying to put A-Z and 0-9 in cells: a1 to d9, e1 to h9, a10 to d18, and e10 to h18). So far I have the code: Sub TwoDArrays() Dim Matrix(9, 4) As Variant Dim Matrix2(9, 4) As Variant Dim Matrix3(9, 4) As Variant Dim Matrix4(9, 4) As Variant Matrix(1, 1) = "A" Matrix(1, 2) = "B" Matrix(1, 3) = "C" Matrix(1, 4) = "D" Matrix(2, 1) = "E" Matrix(2, 2) = "F" Matrix(2, 3) = "G" Matrix(2, 4) = "H" Matrix(3, 1) = "I" Matrix(3, 2) = "J" Matrix(3, 3) = "K" Matrix(3, 4) = "L" Matrix(4, 1) = "M" Matrix(4, 2) = "N" Matrix(4, 3) = "O" Matrix(4, 4) = "P" Matrix(5, 1) = "Q" Matrix(5, 2) = "R" Matrix(5, 3) = "S" Matrix(5, 4) = "T" Matrix(6, 1) = "U" Matrix(6, 2) = "V" Matrix(6, 3) = "W" Matrix(6, 4) = "X" Matrix(7, 1) = "Y" Matrix(7, 2) = "Z" Matrix(7, 3) = "0" Matrix(7, 4) = "1" Matrix(8, 1) = "2" Matrix(8, 2) = "3" Matrix(8, 3) = "4" Matrix(8, 4) = "5" Matrix(9, 1) = "6" Matrix(9, 2) = "7" Matrix(9, 3) = "8" Matrix(9, 4) = "9" Matrix2(1, 1) = "A" Matrix2(1, 2) = "B" Matrix2(1, 3) = "C" Matrix2(1, 4) = "D" Matrix2(2, 1) = "E" Matrix2(2, 2) = "F" Matrix2(2, 3) = "G" Matrix2(2, 4) = "H" Matrix2(3, 1) = "I" Matrix2(3, 2) = "J" Matrix2(3, 3) = "K" Matrix2(3, 4) = "L" Matrix2(4, 1) = "M" Matrix2(4, 2) = "N" Matrix2(4, 3) = "O" Matrix2(4, 4) = "P" Matrix2(5, 1) = "Q" Matrix2(5, 2) = "R" Matrix2(5, 3) = "S" Matrix2(5, 4) = "T" Matrix2(6, 1) = "U" Matrix2(6, 2) = "V" Matrix2(6, 3) = "W" Matrix2(6, 4) = "X" Matrix2(7, 1) = "Y" Matrix2(7, 2) = "Z" Matrix2(7, 3) = "0" Matrix2(7, 4) = "1" Matrix2(8, 1) = "2" Matrix2(8, 2) = "3" Matrix2(8, 3) = "4" Matrix2(8, 4) = "5" Matrix2(9, 1) = "6" Matrix2(9, 2) = "7" Matrix2(9, 3) = "8" Matrix2(9, 4) = "9" Matrix3(1, 1) = "A" Matrix3(1, 2) = "B" Matrix3(1, 3) = "C" Matrix3(1, 4) = "D" Matrix3(2, 1) = "E" Matrix3(2, 2) = "F" Matrix3(2, 3) = "G" Matrix3(2, 4) = "H" Matrix3(3, 1) = "I" Matrix3(3, 2) = "J" Matrix3(3, 3) = "K" Matrix3(3, 4) = "L" Matrix3(4, 1) = "M" Matrix3(4, 2) = "N" Matrix3(4, 3) = "O" Matrix3(4, 4) = "P" Matrix3(5, 1) = "Q" Matrix3(5, 2) = "R" Matrix3(5, 3) = "S" Matrix3(5, 4) = "T" Matrix3(6, 1) = "U" Matrix3(6, 2) = "V" Matrix3(6, 3) = "W" Matrix3(6, 4) = "X" Matrix3(7, 1) = "Y" Matrix3(7, 2) = "Z" Matrix3(7, 3) = "0" Matrix3(7, 4) = "1" Matrix3(8, 1) = "2" Matrix3(8, 2) = "3" Matrix3(8, 3) = "4" Matrix3(8, 4) = "5" Matrix3(9, 1) = "6" Matrix3(9, 2) = "7" Matrix3(9, 3) = "8" Matrix3(9, 4) = "9" Matrix4(1, 1) = "A" Matrix4(1, 2) = "B" Matrix4(1, 3) = "C" Matrix4(1, 4) = "D" Matrix4(2, 1) = "E" Matrix4(2, 2) = "F" Matrix4(2, 3) = "G" Matrix4(2, 4) = "H" Matrix4(3, 1) = "I" Matrix4(3, 2) = "J" Matrix4(3, 3) = "K" Matrix4(3, 4) = "L" Matrix4(4, 1) = "M" Matrix4(4, 2) = "N" Matrix4(4, 3) = "O" Matrix4(4, 4) = "P" Matrix4(5, 1) = "Q" Matrix4(5, 2) = "R" Matrix4(5, 3) = "S" Matrix4(5, 4) = "T" Matrix4(6, 1) = "U" Matrix4(6, 2) = "V" Matrix4(6, 3) = "W" Matrix4(6, 4) = "X" Matrix4(7, 1) = "Y" Matrix4(7, 2) = "Z" Matrix4(7, 3) = "0" Matrix4(7, 4) = "1" Matrix4(8, 1) = "2" Matrix4(8, 2) = "3" Matrix4(8, 3) = "4" Matrix4(8, 4) = "5" Matrix4(9, 1) = "6" Matrix4(9, 2) = "7" Matrix4(9, 3) = "8" Matrix4(9, 4) = "9" For i = 1 To 9 For j = 1 To 4 Cells(i, j) = Matrix(i, j) Next j Next i 'For i = 1 To 9 'For j = 1 To 4 ' Range("a1:d1", "a1:a10").Value = Matrix(i, j) 'Application.WorksheetFunction.Transpose (Matrix) 'Next j 'Next i End Sub However, at the top for loop where it does not use the Range function with the cells, I can only do this for cells a1:d9 (a1 to d9) and if I use the second for loop with the range, get the value 9 appearing in every cell from a1 to d9. So is there a way to make it so that I can get the values A-Z and 0-9 in the other cells I specified above? Thank you.

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  • Windows 2008 Terminal Services "Easy Print" and Matrix Printers

    - by Cesar87
    Server: Windows 2008 Server Standard SP2 with "Terminal Services" role Clients: Windows XP SP3 + .NET 3.5 Framework SP1 + Remote Desktop Client 7.0 We are using "Easy Print" feature which allows programs running on server to "see" printers installed on client machines. Everything works fine, EXCEPT when we send a text-only output to a dot-matrix printer. In this case, the printer only outputs a blank page. At first, we had problems with the error "Windows Presentation Foundation Terminal Server Print W has encountered a problem and needs to close." but this was fixed by replacing TsWpfWrp.exe with the one from Vista SP1 as suggested here. But now, we only get a blank page! Every other (graphical) document we sent to printer works 100%. We also tried to use the "Generic text-only" driver, but the result is same. Now we are trying to change parameters like print processor on "advanced" tab from printer driver to see if something happen. But this is just guessing and we really don't know what to try anymore. The problem appears to be on Easy Print driver, but we found almost no resources about it. Any tips are welcome.

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  • XNA 4.0: 2D Camera Y and X are going in wrong direction

    - by Setheron
    I asked this question on stackoverflow but assumed this might be a better area to ask it as well for a more informed answer. My problem is that I am trying to create a camera class and have it so that my camera follows the proper RHS, however the Y axis seems to be inverted since on the screen the 0 starts at the top. Here is my Camera2D Class: class Camera2D { private Vector2 _position; private float _zoom; private float _rotation; private float _cameraSpeed; private Viewport _viewport; private Matrix _viewMatrix; private Matrix _viewMatrixIverse; public static float MinZoom = float.Epsilon; public static float MaxZoom = float.MaxValue; public Camera2D(Viewport viewport) { _viewMatrix = Matrix.Identity; _viewport = viewport; _cameraSpeed = 4.0f; _zoom = 1.0f; _rotation = 0.0f; _position = Vector2.Zero; } public void Move(Vector2 amount) { _position += amount; } public void Zoom(float amount) { _zoom += amount; _zoom = MathHelper.Clamp(_zoom, MaxZoom, MinZoom); UpdateViewTransform(); } public Vector2 Position { get { return _position; } set { _position = value; UpdateViewTransform(); } } public Matrix ViewMatrix { get { return _viewMatrix; } } private void UpdateViewTransform() { Matrix proj = Matrix.CreateTranslation(new Vector3(_viewport.Width * 0.5f, _viewport.Height * 0.5f, 0)) * Matrix.CreateScale(new Vector3(1f, 1f, 1f)); _viewMatrix = Matrix.CreateRotationZ(_rotation) * Matrix.CreateScale(new Vector3(_zoom, _zoom, 1.0f)) * Matrix.CreateTranslation(_position.X, _position.Y, 0.0f); _viewMatrix = proj * _viewMatrix; } } I test it using SpriteBatch in the following way: protected override void Draw(GameTime gameTime) { GraphicsDevice.Clear(Color.CornflowerBlue); Vector2 position = new Vector2(0, 0); // TODO: Add your drawing code here spriteBatch.Begin(SpriteSortMode.Immediate, BlendState.AlphaBlend, null, null, null, null, camera.ViewMatrix); Texture2D circle = CreateCircle(100); spriteBatch.Draw(circle, position, Color.Red); spriteBatch.End(); base.Draw(gameTime); }

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  • How can I transform a Point2f with a matrix on Android?

    - by Vivendi
    I'm developing for Android and I'm using the android.renderscript.Matrix3f class to do some calculations. What I need to do now is to now is to do something like mat.tranform(pointIn, pointOut); So I need to transform a matrix by a given Point class. In awt I would simply do this: AffineTransform t = new AffineTransform(); Point2D.Float p = new Point2D.Float(); t.transform( p, p ); But in Android I now have this: Matrix3f t = new Matrix3f(); PointF p = new PointF(); // Now I need to tranform it somehow.. But the Matrix3f class in Android doesn't have a Matrix.transform(Point2D ptSrc, Point2D ptDst) method. So I guess I have to do the transformation manually. But I'm not really sure how that works. From what I've seen it's something like a translate and then a rotate? Could anyone please tell me how to do this in code?

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  • Performance of Java matrix math libraries?

    - by dfrankow
    We are computing something whose runtime is bound by matrix operations. (Some details below if interested.) This experience prompted the following question: Do folk have experience with the performance of Java libraries for matrix math (e.g., multiply, inverse, etc.)? For example: JAMA: http://math.nist.gov/javanumerics/jama/ COLT: http://acs.lbl.gov/~hoschek/colt/ Apache commons math: http://commons.apache.org/math/ I searched and found nothing. Details of our speed comparison: We are using Intel FORTRAN (ifort (IFORT) 10.1 20070913). We have reimplemented it in Java (1.6) using Apache commons math 1.2 matrix ops, and it agrees to all of its digits of accuracy. (We have reasons for wanting it in Java.) (Java doubles, Fortran real*8). Fortran: 6 minutes, Java 33 minutes, same machine. jvisualm profiling shows much time spent in RealMatrixImpl.{getEntry,isValidCoordinate} (which appear to be gone in unreleased Apache commons math 2.0, but 2.0 is no faster). Fortran is using Atlas BLAS routines (dpotrf, etc.). Obviously this could depend on our code in each language, but we believe most of the time is in equivalent matrix operations. In several other computations that do not involve libraries, Java has not been much slower, and sometimes much faster.

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  • reformatting a matrix in matlab with nan values

    - by Kate
    This post follows a previous question regarding the restructuring of a matrix: re-formatting a matrix in matlab An additional problem I face is demonstrated by the following example: depth = [0:1:20]'; data = rand(1,length(depth))'; d = [depth,data]; d = [d;d(1:20,:);d]; Here I would like to alter this matrix so that each column represents a specific depth and each row represents time, so eventually I will have 3 rows (i.e. days) and 21 columns (i.e. measurement at each depth). However, we cannot reshape this because the number of measurements for a given day are not the same i.e. some are missing. This is known by: dd = sortrows(d,1); for i = 1:length(depth); e(i) = length(dd(dd(:,1)==depth(i),:)); end From 'e' we find that the number of depth is different for different days. How could I insert a nan into the matrix so that each day has the same depth values? I could find the unique depths first by: unique(d(:,1)) From this, if a depth (from unique) is missing for a given day I would like to insert the depth to the correct position and insert a nan into the respective location in the column of data. How can this be achieved?

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  • How is the gimbal locked problem solved using accumulative matrix transformations

    - by Luke San Antonio
    I am reading the online "Learning Modern 3D Graphics Programming" book by Jason L. McKesson As of now, I am up to the gimbal lock problem and how to solve it using quaternions. However right here, at the Quaternions page. Part of the problem is that we are trying to store an orientation as a series of 3 accumulated axial rotations. Orientations are orientations, not rotations. And orientations are certainly not a series of rotations. So we need to treat the orientation of the ship as an orientation, as a specific quantity. I guess this is the first spot I start to get confused, the reason is because I don't see the dramatic difference between orientations and rotations. I also don't understand why an orientation cannot be represented by a series of rotations... Also: The first thought towards this end would be to keep the orientation as a matrix. When the time comes to modify the orientation, we simply apply a transformation to this matrix, storing the result as the new current orientation. This means that every yaw, pitch, and roll applied to the current orientation will be relative to that current orientation. Which is precisely what we need. If the user applies a positive yaw, you want that yaw to rotate them relative to where they are current pointing, not relative to some fixed coordinate system. The concept, I understand, however I don't understand how if accumulating matrix transformations is a solution to this problem, how the code given in the previous page isn't just that. Here's the code: void display() { glClearColor(0.0f, 0.0f, 0.0f, 0.0f); glClearDepth(1.0f); glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glutil::MatrixStack currMatrix; currMatrix.Translate(glm::vec3(0.0f, 0.0f, -200.0f)); currMatrix.RotateX(g_angles.fAngleX); DrawGimbal(currMatrix, GIMBAL_X_AXIS, glm::vec4(0.4f, 0.4f, 1.0f, 1.0f)); currMatrix.RotateY(g_angles.fAngleY); DrawGimbal(currMatrix, GIMBAL_Y_AXIS, glm::vec4(0.0f, 1.0f, 0.0f, 1.0f)); currMatrix.RotateZ(g_angles.fAngleZ); DrawGimbal(currMatrix, GIMBAL_Z_AXIS, glm::vec4(1.0f, 0.3f, 0.3f, 1.0f)); glUseProgram(theProgram); currMatrix.Scale(3.0, 3.0, 3.0); currMatrix.RotateX(-90); //Set the base color for this object. glUniform4f(baseColorUnif, 1.0, 1.0, 1.0, 1.0); glUniformMatrix4fv(modelToCameraMatrixUnif, 1, GL_FALSE, glm::value_ptr(currMatrix.Top())); g_pObject->Render("tint"); glUseProgram(0); glutSwapBuffers(); } To my understanding, isn't what he is doing (modifying a matrix on a stack) considered accumulating matrices, since the author combined all the individual rotation transformations into one matrix which is being stored on the top of the stack. My understanding of a matrix is that they are used to take a point which is relative to an origin (let's say... the model), and make it relative to another origin (the camera). I'm pretty sure this is a safe definition, however I feel like there is something missing which is blocking me from understanding this gimbal lock problem. One thing that doesn't make sense to me is: If a matrix determines the difference relative between two "spaces," how come a rotation around the Y axis for, let's say, roll, doesn't put the point in "roll space" which can then be transformed once again in relation to this roll... In other words shouldn't any further transformations to this point be in relation to this new "roll space" and therefore not have the rotation be relative to the previous "model space" which is causing the gimbal lock. That's why gimbal lock occurs right? It's because we are rotating the object around set X, Y, and Z axes rather than rotating the object around it's own, relative axes. Or am I wrong? Since apparently this code I linked in isn't an accumulation of matrix transformations can you please give an example of a solution using this method. So in summary: What is the difference between a rotation and an orientation? Why is the code linked in not an example of accumulation of matrix transformations? What is the real, specific purpose of a matrix, if I had it wrong? How could a solution to the gimbal lock problem be implemented using accumulation of matrix transformations? Also, as a bonus: Why are the transformations after the rotation still relative to "model space?" Another bonus: Am I wrong in the assumption that after a transformation, further transformations will occur relative to the current? Also, if it wasn't implied, I am using OpenGL, GLSL, C++, and GLM, so examples and explanations in terms of these are greatly appreciated, if not necessary. The more the detail the better! Thanks in advance...

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  • best way to get a vector from sparse matrix

    - by niko
    Hi, I have a m x n matrix where each row consists of zeros and same values for each row. an example would be: M = -0.6 1.8 -2.3 0 0 0; 0 0 0 3.4 -3.8 -4.3; -0.6 0 0 3.4 0 0 In this example the first column consists of 0s and -0.6, second 0 and 1.8, third -2.3 and so on. In such case I would like to reduce m to 1 (get a vector from a given matrix) so in this example a vector would be (-0.6 1.8 -2.3 3.4 -3.8 -4.3) Does anyone know what is the best way to get a vector from such matrix? Thank you!

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