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  • 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.

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  • 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[3][0], mParent[3][1], mParent[3][2] ); 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[0][3], mParent[1][3], mParent[2][3] ); thanks!

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  • 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 ??

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  • 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.

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  • 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? :)

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  • Trouble with SAT style vector projection in C#/XNA

    - by ssb
    Simply put I'm having a hard time working out how to work with XNA's Vector2 types while maintaining spatial considerations. I'm working with separating axis theorem and trying to project vectors onto an arbitrary axis to check if those projections overlap, but the severe lack of XNA-specific help online combined with pseudo code everywhere that omits key parts of the algorithm, googling has left me little help. I'm aware of HOW to project a vector, but the way that I know of doing it involves the two vectors starting from the same point. Particularly here: http://www.metanetsoftware.com/technique/tutorialA.html So let's say I have a simple rectangle, and I store each of its corners in a list of Vector2s. How would I go about projecting that onto an arbitrary axis? The crux of my problem is that taking the dot product of say, a vector2 of (1, 0) and a vector2 of (50, 50) won't get me the dot product I'm looking for.. or will it? Because that (50, 50) won't be the vector of the polygon's vertex but from whatever XNA calculates. It's getting the calculation from the right starting point that's throwing me off. I'm sorry if this is unclear, but my brain is fried from trying to think about this. I need a better understanding of how XNA calculates Vector2s as actual vectors and not just as random points.

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  • 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?

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  • 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?

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  • 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)))))

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  • 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

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  • 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.

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  • 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.

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  • View matrix question (rotate by 180 degrees)

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

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  • 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[16]; 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

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  • 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..

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  • Faster method for Matrix vector product for large matrix in C or C++ for use in GMRES

    - by user35959
    I have a large, dense matrix A, and I aim to find the solution to the linear system Ax=b using an iterative method (in MATLAB was the plan using its built in GMRES). For more than 10,000 rows, this is too much for my computer to store in memory, but I know that the entries in A are constructed by two known vectors x and y of length N and the entries satisfy: A(i,j) = .5*(x[i]-x[j])^2+([y[i]-y[j])^2 * log(x[i]-x[j])^2+([y[i]-y[j]^2). MATLAB's GMRES command accepts as input a function call that can compute the matrix vector product A*x, which allows me to handle larger matrices than I can store in memory. To write the matrix-vecotr product function, I first tried this in matlab by going row by row and using some vectorization, but I avoid spawning the entire array A (since it would be too large). This was fairly slow unfortnately in my application for GMRES. My plan was to write a mex file for MATLAB to, which is in C, and ideally should be significantly faster than the matlab code. I'm rather new to C, so this went rather poorly and my naive attempt at writing the code in C was slower than my partially vectorized attempt in Matlab. #include <math.h> #include "mex.h" void Aproduct(double *x, double *ctrs_x, double *ctrs_y, double *b, mwSize n) { mwSize i; mwSize j; double val; for (i=0; i<n; i++) { for (j=0; j<i; j++) { val = pow(ctrs_x[i]-ctrs_x[j],2)+pow(ctrs_y[i]-ctrs_y[j],2); b[i] = b[i] + .5* val * log(val) * x[j]; } for (j=i+1; j<n; j++) { val = pow(ctrs_x[i]-ctrs_x[j],2)+pow(ctrs_y[i]-ctrs_y[j],2); b[i] = b[i] + .5* val * log(val) * x[j]; } } } The above is the computational portion of the code for the matlab mex file (which is slightly modified C, if I understand correctly). Please note that I skip the case i=j, since in that case the variable val will be a 0*log(0), which should be interpreted as 0 for me, so I just skip it. Is there a more efficient or faster way to write this? When I call this C function via the mex file in matlab, it is quite slow, slower even than the matlab method I used. This surprises me since I suspected that C code should be much faster than matlab. The alternative matlab method which is partially vectorized that I am comparing it with is function Ax = Aprod(x,ctrs) n = length(x); Ax = zeros(n,1); for j=1:(n-3) v = .5*((ctrs(j,1)-ctrs(:,1)).^2+(ctrs(j,2)-ctrs(:,2)).^2).*log((ctrs(j,1)-ctrs(:,1)).^2+(ctrs(j,2)-ctrs(:,2)).^2); v(j)=0; Ax(j) = dot(v,x(1:n-3); end (the n-3 is because there is actually 3 extra components, but they are dealt with separately,so I excluded that code). This is partly vectorized and only needs one for loop, so it makes some sense that it is faster. However, I was hoping I could go even faster with C+mex file. Any suggestions or help would be greatly appreciated! Thanks! EDIT: I should be more clear. I am open to any faster method that can help me use GMRES to invert this matrix that I am interested in, which requires a faster way of doing the matrix vector product without explicitly loading the array into memory. Thanks!

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  • View matrix in opengl

    - by user5584
    Hi! Sorry for my clumsy question. But I don't know where I am wrong at creating view matrix. I have the following code: createMatrix(vec4f(xAxis.x, xAxis.y, xAxis.z, dot(xAxis,eye)), vec4f( yAxis.x_, yAxis.y_, yAxis.z_, dot(yAxis,eye)), vec4f(-zAxis.x_, -zAxis.y_, -zAxis.z_, -dot(zAxis,eye)), vec4f(0, 0, 0, 1)); //column1, column2,... I have tried to transpose it, but with no success. I have also tried to use gluLookAt(...) with success. At the reference page, I watched the remarks about the to-be-created matrix, and it seems the same as mine. Where I am wrong?

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  • Matrix.CreateBillboard centre rotation problem

    - by Chris88
    I'm having an issue with Matrix.CreateBillboard and a textured Quad where the center axis seems to be positioned incorrectly to the quad object which is rotating around a center point: Using: BasicEffect quadEffect; Drawing the quad shape: Left = Vector3.Cross(Normal, Up); Vector3 uppercenter = (Up * height / 2) + origin; LowerLeft = uppercenter + (Left * width / 2); LowerRight = uppercenter - (Left * width / 2); UpperLeft = LowerLeft - (Up * height); UpperRight = LowerRight - (Up * height); Where height and width are float values passed in (it draws a square) Draw method: quadEffect.View = camera.view; quadEffect.Projection = camera.projection; quadEffect.World = Matrix.CreateBillboard(Origin, camera.cameraPosition, Vector3.Up, camera.cameraDirection); GraphicsDevice.BlendState = BlendState.Additive; foreach (EffectPass pass in quadEffect.CurrentTechnique.Passes) { pass.Apply(); GraphicsDevice.DrawUserIndexedPrimitives <VertexPositionNormalTexture>( PrimitiveType.TriangleList, Vertices, 0, 4, Indexes, 0, 2); } GraphicsDevice.BlendState = BlendState.Opaque; In the screenshots below i draw the image at Vector3(32f, 0f, 32f) The screenshots below show you the position of the quad in relation to the red cross. The red cross shows where it should be drawn http://i.imgur.com/YwRYj.jpg http://i.imgur.com/ZtoHL.jpg It rotates around the red cross position

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  • Building View Matrix in Direct3D11

    - by Balls
    Am I doing it right? I converted this. m_ViewMatrix = XMMatrixLookAtLH(XMLoadFloat3(&m_Position), lookAtVector, upVector); to this one. XMVECTOR vz = XMVector3Normalize( lookAtVector - XMLoadFloat3(&m_Position) ); XMVECTOR vx = XMVector3Normalize( XMVector3Cross( upVector, vz ) ); XMVECTOR vy = XMVector3Cross( vz, vx ); m_ViewMatrix.r[0] = vx; m_ViewMatrix.r[1] = vy; m_ViewMatrix.r[2] = vz; m_ViewMatrix.r[3] = XMLoadFloat3(&m_Position); m_ViewMatrix.r[0].m128_f32[3] = 0.0f; m_ViewMatrix.r[1].m128_f32[3] = 0.0f; m_ViewMatrix.r[2].m128_f32[3] = 0.0f; m_ViewMatrix.r[3].m128_f32[3] = 1.0f; m_ViewMatrix = XMMatrixInverse( &XMMatrixDeterminant(m_ViewMatrix), m_ViewMatrix ); Everything looks fine when I run it. Another question is, I saw on this site(http://webglfactory.blogspot.com/2011/06/how-to-create-view-matrix.html) that he subtracted lookat from position in his vector vz. I tried it but gave me wrong view matrix. Can anyone check my code. I'm studying linear algebra right now. Sucks my course doesn't have one. Thank you, Balls

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  • Simple 3x3 matrix inverse code (C++)

    - by batty
    What's the easiest way to compute a 3x3 matrix inverse? I'm just looking for a short code snippet that'll do the trick for non-singular matrices, possibly using Cramer's rule. It doesn't need to be highly optimized. I'd prefer simplicity over speed. I'd rather not link in additional libraries. Primarily I was hoping to have this on Stack Overflow so that I wouldn't have to hunt around for it or rewrite from scratch again next time.

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  • What is Chain Matrix Multiplication ?

    - by Hellnar
    Hello, I am trying to understand what is a chain matrix multiplication and how it is different from a regular multiplication. I have checked several sourcers yet all seem to be very academically explained for me to understand. I guess it is a form of dynamic programming algorithm to achieve the operation in an optimised way but I didn't go any further. Thanks

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  • Obtaining projection matrix

    - by rita
    I have calibrated stereo images. I want to get a projection matrix using rotation matrix ,translation vector, radial vector and a camera matrix. How can get the projection matrix?

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  • WebGL First Person Camera - Matrix issues

    - by Ryan Welsh
    I have been trying to make a WebGL FPS camera.I have all the inputs working correctly (I think) but when it comes to applying the position and rotation data to the view matrix I am a little lost. The results can be viewed here http://thistlestaffing.net/masters/camera/index.html and the code here var camera = { yaw: 0.0, pitch: 0.0, moveVelocity: 1.0, position: [0.0, 0.0, -70.0] }; var viewMatrix = mat4.create(); var rotSpeed = 0.1; camera.init = function(canvas){ var ratio = canvas.clientWidth / canvas.clientHeight; var left = -1; var right = 1; var bottom = -1.0; var top = 1.0; var near = 1.0; var far = 1000.0; mat4.frustum(projectionMatrix, left, right, bottom, top, near, far); viewMatrix = mat4.create(); mat4.rotateY(viewMatrix, viewMatrix, camera.yaw); mat4.rotateX(viewMatrix, viewMatrix, camera.pitch); mat4.translate(viewMatrix, viewMatrix, camera.position); } camera.update = function(){ viewMatrix = mat4.create(); mat4.rotateY(viewMatrix, viewMatrix, camera.yaw); mat4.rotateX(viewMatrix, viewMatrix, camera.pitch); mat4.translate(viewMatrix, viewMatrix, camera.position); } //prevent camera pitch from going above 90 and reset yaw when it goes over 360 camera.lockCamera = function(){ if(camera.pitch > 90.0){ camera.pitch = 90; } if(camera.pitch < -90){ camera.pitch = -90; } if(camera.yaw <0.0){ camera.yaw = camera.yaw + 360; } if(camera.yaw >360.0){ camera.yaw = camera.yaw - 0.0; } } camera.translateCamera = function(distance, direction){ //calculate where we are looking at in radians and add the direction we want to go in ie WASD keys var radian = glMatrix.toRadian(camera.yaw + direction); //console.log(camera.position[3], radian, distance, direction); //calc X coord camera.position[0] = camera.position[0] - Math.sin(radian) * distance; //calc Z coord camera.position[2] = camera.position [2] - Math.cos(radian) * distance; console.log(camera.position [2] - (Math.cos(radian) * distance)); } camera.rotateUp = function(distance, direction){ var radian = glMatrix.toRadian(camera.pitch + direction); //calc Y coord camera.position[1] = camera.position[1] + Math.sin(radian) * distance; } camera.moveForward = function(){ if(camera.pitch!=90 && camera.pitch!=-90){ camera.translateCamera(-camera.moveVelocity, 0.0); } camera.rotateUp(camera.moveVelocity, 0.0); } camera.moveBack = function(){ if(camera.pitch!=90 && camera.pitch!=-90){ camera.translateCamera(-camera.moveVelocity, 180.0); } camera.rotateUp(camera.moveVelocity, 180.0); } camera.moveLeft = function(){ camera.translateCamera(-camera.moveVelocity, 270.0); } camera.moveRight = function(){ camera.translateCamera(-camera.moveVelocity, 90.0); } camera.lookUp = function(){ camera.pitch = camera.pitch + rotSpeed; camera.lockCamera(); } camera.lookDown = function(){ camera.pitch = camera.pitch - rotSpeed; camera.lockCamera(); } camera.lookLeft = function(){ camera.yaw= camera.yaw - rotSpeed; camera.lockCamera(); } camera.lookRight = function(){ camera.yaw = camera.yaw + rotSpeed; camera.lockCamera(); } . If there is no problem with my camera then I am doing some matrix calculations within my draw function where a problem might be. //position cube 1 worldMatrix = mat4.create(); mvMatrix = mat4.create(); mat4.translate(worldMatrix, worldMatrix, [-20.0, 0.0, -30.0]); mat4.multiply(mvMatrix, worldMatrix, viewMatrix); setShaderMatrix(); gl.bindBuffer(gl.ARRAY_BUFFER, vertexBuffer); gl.vertexAttribPointer(shaderProgram.attPosition, 3, gl.FLOAT, false, 8*4,0); gl.vertexAttribPointer(shaderProgram.attTexCoord, 2, gl.FLOAT, false, 8*4, 3*4); gl.vertexAttribPointer(shaderProgram.attNormal, 3, gl.FLOAT, false, 8*4, 5*4); gl.activeTexture(gl.TEXTURE0); gl.bindTexture(gl.TEXTURE_2D, myTexture); gl.uniform1i(shaderProgram.uniSampler, 0); gl.useProgram(shaderProgram); gl.drawArrays(gl.TRIANGLES, 0, vertexBuffer.numItems); //position cube 2 worldMatrix = mat4.create(); mvMatrix = mat4.create(); mat4.multiply(mvMatrix, worldMatrix, viewMatrix); mat4.translate(worldMatrix, worldMatrix, [40.0, 0.0, -30.0]); setShaderMatrix(); gl.drawArrays(gl.TRIANGLES, 0, vertexBuffer.numItems); //position cube 3 worldMatrix = mat4.create(); mvMatrix = mat4.create(); mat4.multiply(mvMatrix, worldMatrix, viewMatrix); mat4.translate(worldMatrix, worldMatrix, [20.0, 0.0, -100.0]); setShaderMatrix(); gl.drawArrays(gl.TRIANGLES, 0, vertexBuffer.numItems); camera.update();

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