# Search Results

• ### Matrix multiplication - Scene Graphs

##### - by bgarate
I wrote a MatrixStack class in C# to use in a SceneGraph. So, to get the world matrix for an object I am suposed to use: WorldMatrix = ParentWorld * LocalTransform But, in fact, it only works as expected when I do the other way: WorldMatrix = LocalTransform * ParentWorld Mi code is: public class MatrixStack { Stack<Matrix> stack = new Stack<Matrix>(); Matrix result = Matrix.Identity; public void PushMatrix(Matrix matrix) { stack.Push(matrix); result = matrix * result; } public Matrix PopMatrix() { result = Matrix.Invert(stack.Peek()) * result; return stack.Pop(); } public Matrix Result { get { return result; } } public void Clear() { stack.Clear(); result = Matrix.Identity; } } Why it works this way and not the other? Thanks!

• ### Find the "largest" dense sub matrix in a large sparse matrix

##### - by BCS
Given a large sparse matrix (say 10k+ by 1M+) I need to find a subset, not necessarily continuous, of the rows and columns that form a dense matrix (all non-zero elements). I want this sub matrix to be as large as possible (not the largest sum, but the largest number of elements) within some aspect ratio constraints. Are there any known exact or aproxamate solutions to this problem? A quick scan on Google seems to give a lot of close-but-not-exactly results. What terms should I be looking for? edit: Just to clarify; the sub matrix need not be continuous. In fact the row and column order is completely arbitrary so adjacency is completely irrelevant. A thought based on Chad Okere's idea Order the rows from largest count to smallest count (not necessary but might help perf) Select two rows that have a "large" overlap Add all other rows that won't reduce the overlap Record that set Add whatever row reduces the overlap by the least Repeat at #3 until the result gets to small Start over at #2 with a different starting pair Continue until you decide the result is good enough

• ### XNA matrix order problem

##### - by user1990950
I want a matrix that scales first and then rotates. I tried the code below, but it didn't work. zRotation, yRotation and xRotation are rotations that shouldn't be affected by the origin. allrot should be affected. xScale, yScale and zScale are the scaling variables. The code below works except that it rotates and then scales. Matrix worldMatrix = ( Matrix.CreateRotationZ(MathHelper.ToRadians(zRotation)) * Matrix.CreateRotationX(MathHelper.ToRadians(xRotation)) * Matrix.CreateRotationY(MathHelper.ToRadians(yRotation)) ) * ( Matrix.CreateTranslation(origin) * Matrix.CreateRotationY(MathHelper.ToRadians(allrot)) * Matrix.CreateScale(xScale, yScale, zScale) );

• ### Correct Rotation and Translation with a 4x4 matrix

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

• ### Faster Matrix Multiplication in C#

##### - by Kyle Lahnakoski
I have as small c# project that involves matrices. I am processing large amounts of data by splitting it into n-length chunks, treating the chucks as vectors, and multiplying by a Vandermonde** matrix. The problem is, depending on the conditions, the size of the chucks and corresponding Vandermonde** matrix can vary. I have a general solution which is easy to read, but way too slow: public byte[] addBlockRedundancy(byte[] data) { if (data.Length!=numGood) D.error("Expecting data to be just "+numGood+" bytes long"); aMatrix d=aMatrix.newColumnMatrix(this.mod, data); var r=vandermonde.multiplyBy(d); return r.ToByteArray(); }//method This can process about 1/4 megabytes per second on my i5 U470 @ 1.33GHz. I can make this faster by manually inlining the matrix multiplication: int o=0; int d=0; for (d=0; d<data.Length-numGood; d+=numGood) { for (int r=0; r<numGood+numRedundant; r++) { Byte value=0; for (int c=0; c<numGood; c++) { value=mod.Add(value, mod.Multiply(vandermonde.get(r, c), data[d+c])); }//for output[r][o]=value; }//for o++; }//for This can process about 1 meg a second. (Please note the "mod" is performing operations over GF(2^8) modulo my favorite irreducible polynomial.) I know this can get a lot faster: After all, the Vandermonde** matrix is mostly zeros. I should be able to make a routine, or find a routine, that can take my matrix and return a optimized method which will effectively multiply vectors by the given matrix, but faster. Then, when I give this routine a 5x5 Vandermonde matrix (the identity matrix), there is simply no arithmetic to perform, and the original data is just copied. ** Please note: What I use the term "Vandermonde", I actually mean an Identity matrix with some number of rows from the Vandermonde matrix appended (see comments). This matrix is wonderful because of all the zeros, and because if you remove enough rows (of your choosing) to make it square, it is an invertible matrix. And, of course, I would like to use this same routine to convert any one of those inverted matrices into an optimized series of instructions. How can I make this matrix multiplication faster? Thanks! (edited to correct my mistake with Vandermonde matrix)

• ### Repeated Squaring - Matrix Multiplication using NEWMAT

##### - by Dinakar Kulkarni
I'm trying to use the repeated squaring algorithm (using recursion) to perform matrix exponentiation. I've included header files from the NEWMAT library instead of using arrays. The original matrix has elements in the range (-5,5), all numbers being of type float. # include "C:\User\newmat10\newmat.h" # include "C:\User\newmat10\newmatio.h" # include "C:\User\newmat10\newmatap.h" # include <iostream> # include <time.h> # include <ctime> # include <cstdlib> # include <iomanip> using namespace std; Matrix repeated_squaring(Matrix A, int exponent, int n) //Recursive function { A(n,n); IdentityMatrix I(n); if (exponent == 0) //Matrix raised to zero returns an Identity Matrix return I; else { if ( exponent%2 == 1 ) // if exponent is odd return (A * repeated_squaring (A*A, (exponent-1)/2, n)); else //if exponent is even return (A * repeated_squaring( A*A, exponent/2, n)); } } Matrix direct_squaring(Matrix B, int k, int no) //Brute Force Multiplication { B(no,no); Matrix C = B; for (int i = 1; i <= k; i++) C = B*C; return C; } //----Creating a matrix with elements b/w (-5,5)---- float unifRandom() { int a = -5; int b = 5; float temp = (float)((b-a)*( rand()/RAND_MAX) + a); return temp; } Matrix initialize_mat(Matrix H, int ord) { H(ord,ord); for (int y = 1; y <= ord; y++) for(int z = 1; z<= ord; z++) H(y,z) = unifRandom(); return(H); } //--------------------------------------------------- void main() { int exponent, dimension; cout<<"Insert exponent:"<<endl; cin>>exponent; cout<< "Insert dimension:"<<endl; cin>>dimension; cout<<"The number of rows/columns in the square matrix is: "<<dimension<<endl; cout<<"The exponent is: "<<exponent<<endl; Matrix A(dimension,dimension),B(dimension,dimension); Matrix C(dimension,dimension),D(dimension,dimension); B= initialize_mat(A,dimension); cout<<"Initial Matrix: "<<endl; cout<<setw(5)<<setprecision(2)<<B<<endl; //----------------------------------------------------------------------------- cout<<"Repeated Squaring Result: "<<endl; clock_t time_before1 = clock(); C = repeated_squaring (B, exponent , dimension); cout<< setw(5) <<setprecision(2) <<C; clock_t time_after1 = clock(); float diff1 = ((float) time_after1 - (float) time_before1); cout << "It took " << diff1/CLOCKS_PER_SEC << " seconds to complete" << endl<<endl; //--------------------------------------------------------------------------------- cout<<"Direct Squaring Result:"<<endl; clock_t time_before2 = clock(); D = direct_squaring (B, exponent , dimension); cout<<setw(5)<<setprecision(2)<<D; clock_t time_after2 = clock(); float diff2 = ((float) time_after2 - (float) time_before2); cout << "It took " << diff2/CLOCKS_PER_SEC << " seconds to complete" << endl<<endl; } I face the following problems: The random number generator returns only "-5" as each element in the output. The Matrix multiplication yield different results with brute force multiplication and using the repeated squaring algorithm. I'm timing the execution time of my code to compare the times taken by brute force multiplication and by repeated squaring. Could someone please find out what's wrong with the recursion and with the matrix initialization? NOTE: While compiling this program, make sure you've imported the NEWMAT library. Thanks in advance!

• ### OpenGL - Calculating camera view matrix

##### - by Karle
Problem I am calculating the model, view and projection matrices independently to be used in my shader as follows: gl_Position = projection * view * model * vec4(in_Position, 1.0); When I try to calculate my camera's view matrix the Z axis is flipped and my camera seems like it is looking backwards. My program is written in C# using the OpenTK library. Translation (Working) I've created a test scene as follows: From my understanding of the OpenGL coordinate system they are positioned correctly. The model matrix is created using: Matrix4 translation = Matrix4.CreateTranslation(modelPosition); Matrix4 model = translation; The view matrix is created using: Matrix4 translation = Matrix4.CreateTranslation(-cameraPosition); Matrix4 view = translation; Rotation (Not-Working) I now want to create the camera's rotation matrix. To do this I use the camera's right, up and forward vectors: // Hard coded example orientation: // Normally calculated from up and forward // Similar to look-at camera. Vector3 r = Vector.UnitX; Vector3 u = Vector3.UnitY; Vector3 f = -Vector3.UnitZ; Matrix4 rot = new Matrix4( r.X, r.Y, r.Z, 0, u.X, u.Y, u.Z, 0, f.X, f.Y, f.Z, 0, 0.0f, 0.0f, 0.0f, 1.0f); This results in the following matrix being created: I know that multiplying by the identity matrix would produce no rotation. This is clearly not the identity matrix and therefore will apply some rotation. I thought that because this is aligned with the OpenGL coordinate system is should produce no rotation. Is this the wrong way to calculate the rotation matrix? I then create my view matrix as: // OpenTK is row-major so the order of operations is reversed: Matrix4 view = translation * rot; Rotation almost works now but the -Z/+Z axis has been flipped, with the green cube now appearing closer to the camera. It seems like the camera is looking backwards, especially if I move it around. My goal is to store the position and orientation of all objects (including the camera) as: Vector3 position; Vector3 up; Vector3 forward; Apologies for writing such a long question and thank you in advance. I've tried following tutorials/guides from many sites but I keep ending up with something wrong. Edit: Projection Matrix Set-up Matrix4 projection = Matrix4.CreatePerspectiveFieldOfView( (float)(0.5 * Math.PI), (float)display.Width / display.Height, 0.1f, 1000.0f);

• ### Xna Equivalent of Viewport.Unproject in a draw call as a matrix transformation

##### - by Nick Crowther
I am making a 2D sidescroller and I would like to draw my sprite to world space instead of client space so I do not have to lock it to the center of the screen and when the camera stops the sprite will walk off screen instead of being stuck at the center. In order to do this I wanted to make a transformation matrix that goes in my draw call. I have seen something like this: http://stackoverflow.com/questions/3570192/xna-viewport-projection-and-spritebatch I have seen Matrix.CreateOrthographic() used to go from Worldspace to client space but, how would I go about using it to go from clientspace to worldspace? I was going to try putting my returns from the viewport.unproject method I have into a scale matrix such as: blah = Matrix.CreateScale(unproject.X,unproject.Y,0); however, that doesn't seem to work correctly. Here is what I'm calling in my draw method(where X is the coordinate my camera should follow): Vector3 test = screentoworld(X, graphics); var clienttoworld = Matrix.CreateScale(test.X,test.Y, 0); animationPlayer.Draw(theSpriteBatch, new Vector2(X.X,X.Y),false,false,0,Color.White,new Vector2(1,1),clienttoworld); Here is my code in my unproject method: Vector3 screentoworld(Vector2 some, GraphicsDevice graphics): Vector2 Position =(some.X,some.Y); var project = Matrix.CreateOrthographic(5*graphicsdevice.Viewport.Width, graphicsdevice.Viewport.Height, 0, 1); var viewMatrix = Matrix.CreateLookAt( new Vector3(0, 0, -4.3f), new Vector3(X.X,X.Y,0), Vector3.Up); //I have also tried substituting (cam.Position.X,cam.Position.Y,0) in for the (0,0,-4.3f) Vector3 nearSource = new Vector3(Position, 0f); Vector3 nearPoint = graphicsdevice.Viewport.Unproject(nearSource, project, viewMatrix, Matrix.Identity); return nearPoint;

• ### Inverting matrix then decomposing gives different quaternion than decomposing then inverting the quat

##### - by Fraser
I'm getting different signs when I convert a matrix to quaternion and invert that, versus when I invert a matrix and then get the quaternion from it: Quaternion a = Quaternion.Invert(getRotation(m)); Quaternion b = getRotation(Matrix.Invert(m)); I would expect a and b to be identical (or inverses of each other). However, it looks like q1 = (x, y, -z, -w) while q2 = (-x, -y, w, z). In other words, the Z and W components have been switched for some reason. Note: getRotation() decomposes the transform matrix and returns just the rotation part of it (I've tried normalizing the result; it does nothing). The matrix m is a complete transform matrix and contains a translation (and possibly a scale) as well as a rotation. I'm using D3DXMatrixDecompose to do the actual decomposition.

• ### matrix 4x4 position data

##### - by freefallr
I understand that a 4x4 matrix holds rotation and position data. The rotation data is held in the 3x3 sub-matrix at the top left of the matrix. The position data is held in the last column of the matrix. e.g. glm::vec3 vParentPos( mParent, mParent, mParent ); My question is - am I accessing the parent matrix correctly in the example above? I know that opengl uses a different matrix ordering that directx, (row order instead of column order or something), so, should the mParent be accessed as follows instead? glm::vec3 vParentPos( mParent, mParent, mParent ); thanks!

• ### C++ templates - matrix class

##### - by lastOfMohicans
Hi I'm learning templates in C++ so I decied to write matrix class which would be a template class. In Matrix.h file I wrote #pragma once #include "stdafx.h" #include <vector> using namespace std; template<class T> class Matrix { public: Matrix(); ~Matrix(); GetDataVector(); SetDataVector(vector<vector<T>> dataVector); bool operator == (Matrix* matrix); bool operator < (Matrix* matrix); bool operator <= (Matrix* matrix); bool operator > (Matrix* matrix); bool operator >= (Matrix* matrix); Matrix* operator + (Matrix* matrix); Matrix* operator - (Matrix* matrix); Matrix* operator * (Matrix* matrix); private: vector<vector<T>> datavector; int columns,rows; }; In Matrix cpp Visual Stuio automaticlly generated code for default constructors #include "StdAfx.h" #include "Matrix.h" Matrix::Matrix() { } Matrix::~Matrix() { } However if I want to compile this I get an error 'Matrix' : use of class template requires template argument list The error are in file Matrix.cpp in default constructors What may be the problem ??

• ### Matrix rotation wrong orientation LibGDX

##### - by glz
I'm having a problem with matrix rotation in libgdx. I rotate it using the method matrix.rotate(Vector3 axis, float angle) but the rotation happens in the model orientation and I need it happens in the world orientation. For example: on create() method: matrix.rotate(new Vector3(0,0,1), 45); That is ok, but after: on render() method: matrix.rotate(new Vector3(0,1,0), 1); I need it rotate in world axis.

• ### Converting 3 axis vectors to a rotation matrix

##### - by user38858
I am trying to get a rotation matrix (in 3dsmax) from 3 vectors that form an axis (all 3 vectors are aligned by 90 degrees each other) Somewhere I read that I could build a rotation matrix just by inserting in every row one vector at a time (source: http://renderdan.blogspot.cz/2006/05/rotation-matrix-from-axis-vectors.html) So, I built a matrix with these example vectors x-axis : [-0.194624,-0.23715,-0.951778] y-axis : [-0.773012,0.634392,0] z-axis : [-0.6038,-0.735735,0.306788] But for some reason, if I try to convert this matrix to eulerangles, I receive this rotation: (eulerAngles 47.7284 6.12831 36.8263) ... which is totally wrong, and doesn't align to my 3 vectors at all. I know that rotation is quite difficult to understand, may someone shed some light? :)

• ### What is the best algorithm for solving a band-diagonal matrix?

##### - by Goose Bumper
I'm trying to figure out the best way to solve a pentadiagonal matrix. Is there something faster than gaussian elimination?

• ### In R, when using named rows, can a sparse matrix column be added to another sparse matrix?

##### - by ayman
I have two sparse matrices, m1 and m2: > m1 <- Matrix(data=0,nrow=2, ncol=1, sparse=TRUE, dimnames=list(c("b","d"),NULL)) > m2 <- Matrix(data=0,nrow=2, ncol=1, sparse=TRUE, dimnames=list(c("a","b"),NULL)) > m1["b",1]<- 4 > m2["a",1]<- 5 > m1 2 x 1 sparse Matrix of class "dgCMatrix" b 4 d . > m2 2 x 1 sparse Matrix of class "dgCMatrix" a 5 b . > and I want to cbind() them to make a sparse matrix like: [,1] [,2] a . 5 b 4 . d . . however cbind() ignores the named rows: > cbind(m1[,1],m2[,1]) [,1] [,2] b 4 5 d 0 0 is there some way to do this without a brute force loop?

• ### XNA Sprite Rotation Matrix - Moving Origin

##### - by Jon
I am currently grouping sprites together, then applying a rotation transformation on draw: private void UpdateMatrix(ref Vector2 origin, float radians) { Vector3 matrixorigin = new Vector3(origin, 0); _rotationMatrix = Matrix.CreateTranslation(-matrixorigin) * Matrix.CreateRotationZ(radians) * Matrix.CreateTranslation(matrixorigin); } Where the origin is the Centermost point of my group of sprites. I apply this transformation to each sprite in the group. My problem is that when I adjust the point of origin, my entire sprite group will re-position itself on screen. How could I differentiate the point of rotation used in the transformation, from the position of the sprite group? Is there a better way of creating this transformation matrix?

• ### 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; 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?

• ### Matrix addition in Scheme

##### - by user285012
I am trying to add a matrix and it is not working... (define (matrix-matrix-add a b) (map (lambda (row) (row-matrix-add row b)) a)) (define (row-matrix-add row matrix) (if (null? (car matrix)) '() (cons (add-m row (map car matrix)) (row-matrix-add row (map cdr matrix))))) (define (add-m row col) (if (null? col) 0 (+ (car row) (car col) (add-m (cdr row) (cdr col)))))

• ### Need to translate a Rotation Matrix to Rotation y, x, z OpenGL & Jitter for 3D Game

##### - by MineMan287
I am using the Jitter Physics engine which gives a rotation matrix: M11 M12 M13 M21 M22 M23 M21 M32 M33 And I need it so OpenGL can use it for rotation GL.Rotate(xr, 1, 0, 0) GL.Rotate(yr, 0, 1, 0) GL.Rotate(zr, 0, 0, 1) Initially I Tried xr = M11 yr = M22 zr = M33 [1 0 0] [0 1 0] [0 0 1] Which did not work, please help, I have been struggling on this for days :( Re-Edit The blocks are stored in text files with Euler angles so it needs to be converted or the rendering engine will simply fail. I am now using the matrix in the text files. Example Block 1,1,1 'Size 0,0,0 'Position 255,255,255 'Colour 0,0,0,0,0,0,0,0,0 'Rotation Matrix

• ### Is it possible to billboard a sprite using a transformation matrix?

##### - by Ross
None of the current topics on billboarding seemed to answer this question. But, given a sprite (or quad) that has it's own 4x4 transformation matrix a camera with a view matrix (a standard 4x4 transformation matrix) is it possible to compute a 4x4 transformation matrix such that when the quad's matrix is multiplied with this matrix it has an orientation of looking at the camera? Thank you in advance.

• ### Matrix rotation of a rectangle to "face" a given point in 2d

##### - by justin.m.chase
Suppose you have a rectangle centered at point (0, 0) and now I want to rotate it such that it is facing the point (100, 100), how would I do this purely with matrix math? To give some more specifics I am using javascript and canvas and I may have something like this: var position = {x : 0, y: 0 }; var destination = { x : 100, y: 100 }; var transform = Matrix.identity(); this.update = function(state) { // update transform to rotate to face destination }; this.draw = function(ctx) { ctx.save(); ctx.transform(transform); // a helper that just calls setTransform() ctx.beginPath(); ctx.rect(-5, -5, 10, 10); ctx.fillStyle = 'Blue'; ctx.fill(); ctx.lineWidth = 2; ctx.stroke(); ctx.restore(); } Feel free to assume any matrix function you need is available.

• ### View matrix question (rotate by 180 degrees)

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

• ### Getting the MODELVIEW matrix...

##### - by james.ingham
Hi, I've been pulling my hair out trying to get some matrix calculations working properly and started to wonder. If I have the following: glPushMatrix(); float m; glGetFloatv(GL_MODELVIEW_MATRIX, m); glPopMatrix(); What should I expect the values of m to equal? Currently I'm getting these values and I'm confused as to where they're coming from: -1, 0, 0, 0, 0, -0.6139, 0.7893522, 0, 0, 0.789352238, 0.61394, 0, 0, 0.0955992, -1.344529, 1, I'm assuming there is something which affects this, but I'm not sure what. Could anyone help? I've tried changing pretty much anything but everytime I push the matrix stack I always get this matrix straight away! I don't think this makes a difference but I'm using OpenGLES. Thanks

• ### Use a vector to index a matrix without linear index

##### - by David_G
G'day, I'm trying to find a way to use a vector of [x,y] points to index from a large matrix in MATLAB. Usually, I would convert the subscript points to the linear index of the matrix.(for eg. Use a vector as an index to a matrix in MATLab) However, the matrix is 4-dimensional, and I want to take all of the elements of the 3rd and 4th dimensions that have the same 1st and 2nd dimension. Let me hopefully demonstrate with an example: Matrix = nan(4,4,2,2); % where the dimensions are (x,y,depth,time) Matrix(1,2,:,:) = 999; % note that this value could change in depth (3rd dim) and time (4th time) Matrix(3,4,:,:) = 888; % note that this value could change in depth (3rd dim) and time (4th time) Matrix(4,4,:,:) = 124; Now, I want to be able to index with the subscripts (1,2) and (3,4), etc and return not only the 999 and 888 which exist in Matrix(:,:,1,1) but the contents which exist at Matrix(:,:,1,2),Matrix(:,:,2,1) and Matrix(:,:,2,2), and so on (IRL, the dimensions of Matrix might be more like size(Matrix) = (300 250 30 200) I don't want to use linear indices because I would like the results to be in a similar vector fashion. For example, I would like a result which is something like: ans(time=1) 999 888 124 999 888 124 ans(time=2) etc etc etc etc etc etc I'd also like to add that due to the size of the matrix I'm dealing with, speed is an issue here - thus why I'd like to use subscript indices to index to the data. I should also mention that (unlike this question: Accessing values using subscripts without using sub2ind) since I want all the information stored in the extra dimensions, 3 and 4, of the i and jth indices, I don't think that a slightly faster version of sub2ind still would not cut it..