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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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  • Creating matrix of maximum values indices in MATLAB

    - by Gacek
    Using MATLAB, I have an array of values of size 8 rows x N columns. I need to create a matrix of the same size, that counts maximum values in each column and puts 1 in the cell that contains maximum value, and 0 elsewhere. A little example. Lets assume we have an array of values D: D = 0.0088358 0.0040346 0.40276 0.0053221 0.017503 0.011966 0.015095 0.017383 0.14337 0.38608 0.16509 0.15763 0.27546 0.25433 0.2764 0.28442 0.01629 0.0060465 0.0082339 0.0099775 0.034521 0.01196 0.016289 0.021012 0.12632 0.13339 0.11113 0.10288 0.3777 0.19219 0.005005 0.40137 Then, the output matrix for such matrix D would be: 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 Is there a way to do it without catching vector of indices from max function and then putting ones in the right place using for loop?

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  • dojo.gfx matrix transformation

    - by Linus
    Matrix transformations has got my head spinning. I've got a dojox.gfx.group which I want to be draggable with Mover and then be able to rotate it around a certain point on the surface. My basic code looks like this: this.m = dojox.gfx.matrix, . . . updateMatrix: function(){ var mtx = this.group._getRealMatrix(); var trans_m = this.m.translate(mtx.dx, mtx.dy); this.group.setTransform([this.m.rotateAt(this.rotation, 0, 0), trans_m]); } The rotation point is at (0,0) just to keep things simple. I don't seem to understand how the group is being rotated. Any reference to simplistic tutorial on matrix transformations would also help. The ones I've checked out haven't help too much.

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  • How to write a XSLT for this XML?

    - by atrueguy
    <?xml version="1.0" encoding="utf-8"?> <!-- Generator: Adobe Illustrator 14.0.0, SVG Export Plug-In . SVG Version: 6.00 Build 43363) --> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"> <svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" width="612px" height="792px" viewBox="0 0 612 792" enable-background="new 0 0 612 792" xml:space="preserve"> <g id="Original_Text"> <line x1="92.676" y1="500.913" x2="92.676" y2="500.262"/> <line x1="15.208" y1="500.913" x2="15.208" y2="500.262"/> <line x1="92.676" y1="500.262" x2="92.676" y2="500.913"/> <line x1="15.208" y1="510.329" x2="15.208" y2="509.678"/> <line x1="92.676" y1="500.913" x2="92.676" y2="500.262"/> <rect x="15.208" y="574.678" display="none" width="77.468" height="0.651"/> <text transform="matrix(1 0 0 1 258.6782 28.9111)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="8.4629">Bartlet</tspan><tspan x="24.459" y="0" font-family="'ArialMT'" font-size="8.4629">t</tspan><tspan x="26.895" y="0" font-family="'ArialMT'" font-size="8.4629"> </tspan><tspan x="29.035" y="0" font-family="'ArialMT'" font-size="8.4629">Managemen</tspan><tspan x="76.081" y="0" font-family="'ArialMT'" font-size="8.4629">t</tspan><tspan x="78.601" y="0" font-family="'ArialMT'" font-size="8.4629"> </tspan><tspan x="80.741" y="0" font-family="'ArialMT'" font-size="8.4629">Services</tspan></text> <text transform="matrix(1 0 0 1 522.9805 39.562)"><tspan x="0" y="0" fill="#0000FF" font-family="'ArialMT'" font-size="7.1609">Report</tspan><tspan x="21.493" y="0" fill="#0000FF" font-family="'ArialMT'" font-size="7.1609">s</tspan><tspan x="25.382" y="0" fill="#0000FF" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="27.343" y="0" fill="#0000FF" font-family="'ArialMT'" font-size="7.1609">Home</tspan></text> <line fill="none" stroke="#0000FF" stroke-width="0.651" stroke-miterlimit="10" x1="522.98" y1="40.213" x2="569.852" y2="40.213"/> <text transform="matrix(1 0 0 1 261.2822 39.3267)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Consolidate</tspan><tspan x="37.818" y="0" font-family="'ArialMT'" font-size="7.1609">d</tspan><tspan x="41.901" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="44.105" y="0" font-family="'ArialMT'" font-size="7.1609">Weekl</tspan><tspan x="64.001" y="0" font-family="'ArialMT'" font-size="7.1609">y</tspan><tspan x="67.975" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="70.18" y="0" font-family="'ArialMT'" font-size="7.1609">Sales</tspan><tspan x="88.092" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="90.297" y="0" font-family="'ArialMT'" font-size="7.1609">Report</tspan></text> <text transform="matrix(1 0 0 1 522.9775 49.3267)"><tspan x="0" y="0" fill="#0000FF" font-family="'ArialMT'" font-size="7.1609">Stor</tspan><tspan x="13.133" y="0" fill="#0000FF" font-family="'ArialMT'" font-size="7.1609">e</tspan><tspan x="17.566" y="0" fill="#0000FF" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="19.527" y="0" fill="#0000FF" font-family="'ArialMT'" font-size="7.1609">Finder</tspan></text> <line fill="none" stroke="#0000FF" stroke-width="0.651" stroke-miterlimit="10" x1="521.98" y1="49.978" x2="562.341" y2="49.978"/> <text transform="matrix(1 0 0 1 282.7881 49.9775)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">P</tspan><tspan x="4.776" y="0" font-family="'ArialMT'" font-size="7.1609">D</tspan><tspan x="10.27" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="12.475" y="0" font-family="'ArialMT'" font-size="7.1609"> / </tspan></text> <text transform="matrix(1 0 0 1 123.5044 60.8589)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Wee</tspan><tspan x="14.724" y="0" font-family="'ArialMT'" font-size="7.1609">k</tspan><tspan x="18.949" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="21.153" y="0" font-family="'ArialMT'" font-size="7.1609">1</tspan></text> <text transform="matrix(1 0 0 1 190.1138 60.8589)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Wee</tspan><tspan x="14.724" y="0" font-family="'ArialMT'" font-size="7.1609">k</tspan><tspan x="18.949" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="21.153" y="0" font-family="'ArialMT'" font-size="7.1609">2</tspan></text> <text transform="matrix(1 0 0 1 261.6782 60.8589)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Wee</tspan><tspan x="14.724" y="0" font-family="'ArialMT'" font-size="7.1609">k</tspan><tspan x="18.949" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="21.153" y="0" font-family="'ArialMT'" font-size="7.1609">3</tspan></text> <text transform="matrix(1 0 0 1 331.377 60.8589)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Wee</tspan><tspan x="14.724" y="0" font-family="'ArialMT'" font-size="7.1609">k</tspan><tspan x="18.949" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="21.153" y="0" font-family="'ArialMT'" font-size="7.1609">4</tspan></text> <text transform="matrix(1 0 0 1 400.3164 60.8589)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Wee</tspan><tspan x="14.724" y="0" font-family="'ArialMT'" font-size="7.1609">k</tspan><tspan x="18.949" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="21.153" y="0" font-family="'ArialMT'" font-size="7.1609">5</tspan></text> <text transform="matrix(1 0 0 1 461.751 60.9487)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">P</tspan><tspan x="4.805" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="7.404" y="0" font-family="'ArialMT'" font-size="7.1609">T</tspan><tspan x="11.808" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="14.406" y="0" font-family="'ArialMT'" font-size="7.1609">D</tspan><tspan x="19.864" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="22.068" y="0" font-family="'ArialMT'" font-size="7.1609">Total</tspan></text> <text transform="matrix(1 0 0 1 527.6309 60.8589)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Yea</tspan><tspan x="12.741" y="0" font-family="'ArialMT'" font-size="7.1609">r</tspan><tspan x="15.699" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="18.298" y="0" font-family="'ArialMT'" font-size="7.1609">T</tspan><tspan x="22.673" y="0" font-family="'ArialMT'" font-size="7.1609">o</tspan><tspan x="27.12" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="29.72" y="0" font-family="'ArialMT'" font-size="7.1609">Dat</tspan><tspan x="40.863" y="0" font-family="'ArialMT'" font-size="7.1609">e</tspan><tspan x="45.419" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="47.623" y="0" font-family="'ArialMT'" font-size="7.1609">Total</tspan></text> <text transform="matrix(1 0 0 1 112.853 72.6265)" font-family="'ArialMT'" font-size="7.1609">$</text> <text transform="matrix(1 0 0 1 148.0059 72.6265)" font-family="'ArialMT'" font-size="7.1609">%</text> <text transform="matrix(1 0 0 1 184.4619 72.6265)" font-family="'ArialMT'" font-size="7.1609">$</text> <text transform="matrix(1 0 0 1 218.9629 72.6265)" font-family="'ArialMT'" font-size="7.1609">%</text> <text transform="matrix(1 0 0 1 255.4194 72.6265)" font-family="'ArialMT'" font-size="7.1609">$</text> <text transform="matrix(1 0 0 1 289.9204 72.6265)" font-family="'ArialMT'" font-size="7.1609">%</text> <text transform="matrix(1 0 0 1 326.377 72.6265)" font-family="'ArialMT'" font-size="7.1609">$</text> <text transform="matrix(1 0 0 1 360.8779 72.6265)" font-family="'ArialMT'" font-size="7.1609">%</text> <text transform="matrix(1 0 0 1 397.334 72.6265)" font-family="'ArialMT'" font-size="7.1609">$</text> <text transform="matrix(1 0 0 1 431.835 72.6265)" font-family="'ArialMT'" font-size="7.1609">%</text> <text transform="matrix(1 0 0 1 470.2461 72.6265)" font-family="'ArialMT'" font-size="7.1609">$</text> <text transform="matrix(1 0 0 1 506.0508 72.6265)" font-family="'ArialMT'" font-size="7.1609">%</text> <text transform="matrix(1 0 0 1 546.4092 72.6265)" font-family="'ArialMT'" font-size="7.1609">$</text> <text transform="matrix(1 0 0 1 584.1689 72.6265)" font-family="'ArialMT'" font-size="7.1609">%</text> <text transform="matrix(1 0 0 1 15.1997 83.394)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Ne</tspan><tspan x="9.154" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="11.716" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="13.677" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="16.277" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.237" y="0" font-family="'ArialMT'" font-size="7.1609">KFC</tspan></text> <text transform="matrix(1 0 0 1 15.1997 94.1616)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Ne</tspan><tspan x="9.154" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="11.716" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="13.677" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="16.277" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.237" y="0" font-family="'ArialMT'" font-size="7.1609">A&amp;W</tspan></text> <text transform="matrix(1 0 0 1 15.1997 104.9287)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Ne</tspan><tspan x="9.154" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="11.716" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="13.677" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="16.277" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.237" y="0" font-family="'ArialMT'" font-size="7.1609">LJS</tspan></text> <text transform="matrix(1 0 0 1 15.1924 115.6963)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Ne</tspan><tspan x="9.154" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="11.716" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="13.677" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="16.277" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.237" y="0" font-family="'ArialMT'" font-size="7.1609">TB</tspan></text> <text transform="matrix(1 0 0 1 15.1924 126.9639)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Tota</tspan><tspan x="14.329" y="0" font-family="'ArialMT'" font-size="7.1609">l</tspan><tspan x="16.457" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.661" y="0" font-family="'ArialMT'" font-size="7.1609">Net</tspan></text> <text transform="matrix(1 0 0 1 15.1851 149.2949)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Las</tspan><tspan x="11.545" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="13.671" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="15.632" y="0" font-family="'ArialMT'" font-size="7.1609">Yea</tspan><tspan x="28.374" y="0" font-family="'ArialMT'" font-size="7.1609">r</tspan><tspan x="31.252" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="33.213" y="0" font-family="'ArialMT'" font-size="7.1609">Sales</tspan></text> <text transform="matrix(1 0 0 1 15.1855 161.0625)" font-family="'ArialMT'" font-size="7.1609">Increase</text> <text transform="matrix(1 0 0 1 15.2065 171.8296)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Las</tspan><tspan x="11.545" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="13.671" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="15.632" y="0" font-family="'ArialMT'" font-size="7.1609">yea</tspan><tspan x="27.178" y="0" font-family="'ArialMT'" font-size="7.1609">r</tspan><tspan x="29.949" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="31.91" y="0" font-family="'ArialMT'" font-size="7.1609">Nex</tspan><tspan x="44.644" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="46.884" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="48.845" y="0" font-family="'ArialMT'" font-size="7.1609">Week</tspan></text> <text transform="matrix(1 0 0 1 15.2065 193.3574)" font-family="'ArialMT'" font-size="7.1609">Chicken</text> <text transform="matrix(1 0 0 1 15.1997 205.125)" font-family="'ArialMT'" font-size="7.1609">Filets</text> <text transform="matrix(1 0 0 1 15.1997 215.8926)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Popcor</tspan><tspan x="22.689" y="0" font-family="'ArialMT'" font-size="7.1609">n</tspan><tspan x="26.686" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="28.646" y="0" font-family="'ArialMT'" font-size="7.1609">Chicken</tspan></text> <text transform="matrix(1 0 0 1 15.1997 226.6602)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Crisp</tspan><tspan x="16.71" y="0" font-family="'ArialMT'" font-size="7.1609">y</tspan><tspan x="20.828" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="22.788" y="0" font-family="'ArialMT'" font-size="7.1609">Strips</tspan></text> <text transform="matrix(1 0 0 1 15.1997 237.4272)" font-family="'ArialMT'" font-size="7.1609">Special</text> <text transform="matrix(1 0 0 1 15.1924 248.1948)" font-family="'ArialMT'" font-size="7.1609">Wings</text> <text transform="matrix(1 0 0 1 15.1924 257.9624)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Subtota</tspan><tspan x="24.686" y="0" font-family="'ArialMT'" font-size="7.1609">l</tspan><tspan x="26.448" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="28.652" y="0" font-family="'ArialMT'" font-size="7.1609">Chicken</tspan></text> <text transform="matrix(1 0 0 1 15.1851 280.2935)" font-family="'ArialMT'" font-size="7.1609">Shortening</text> <text transform="matrix(1 0 0 1 15.1851 291.5605)" font-family="'ArialMT'" font-size="7.1609">Flour</text> <text transform="matrix(1 0 0 1 15.1851 302.3281)" font-family="'ArialMT'" font-size="7.1609">Biscuits</text> <text transform="matrix(1 0 0 1 15.1851 313.0957)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Frie</tspan><tspan x="12.332" y="0" font-family="'ArialMT'" font-size="7.1609">s</tspan><tspan x="16.278" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.239" y="0" font-family="'ArialMT'" font-size="7.1609">/</tspan><tspan x="20.844" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="22.805" y="0" font-family="'ArialMT'" font-size="7.1609">Onio</tspan><tspan x="37.931" y="0" font-family="'ArialMT'" font-size="7.1609">n</tspan><tspan x="42.329" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="44.29" y="0" font-family="'ArialMT'" font-size="7.1609">Rings</tspan></text> <text transform="matrix(1 0 0 1 15.1851 323.9385)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Potatoe</tspan><tspan x="24.686" y="0" font-family="'ArialMT'" font-size="7.1609">s</tspan><tspan x="28.646" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="30.606" y="0" font-family="'ArialMT'" font-size="7.1609">-</tspan><tspan x="33.206" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="35.167" y="0" font-family="'ArialMT'" font-size="7.1609">Mashed</tspan></text> <text transform="matrix(1 0 0 1 15.1851 334.6309)" font-family="'ArialMT'" font-size="7.1609">Desserts</text> <text transform="matrix(1 0 0 1 15.1851 345.3979)" font-family="'ArialMT'" font-size="7.1609">Drinks</text> <text transform="matrix(1 0 0 1 15.1851 357.1655)" font-family="'ArialMT'" font-size="7.1609">Corn</text> <text transform="matrix(1 0 0 1 15.1851 367.4331)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Ms</tspan><tspan x="9.545" y="0" font-family="'ArialMT'" font-size="7.1609">c</tspan><tspan x="13.663" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="15.624" y="0" font-family="'ArialMT'" font-size="7.1609">Entrees</tspan></text> <text transform="matrix(1 0 0 1 15.1846 378.2002)" font-family="'ArialMT'" font-size="7.1609">Salads</text> <text transform="matrix(1 0 0 1 15.1846 388.9678)" font-family="'ArialMT'" font-size="7.1609">Condiments</text> <text transform="matrix(1 0 0 1 15.1846 400.2354)" font-family="'ArialMT'" font-size="7.1609">Paper</text> <text transform="matrix(1 0 0 1 15.2012 410.9385)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">A&amp;</tspan><tspan x="9.553" y="0" font-family="'ArialMT'" font-size="7.1609">W</tspan><tspan x="16.927" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.888" y="0" font-family="'ArialMT'" font-size="7.1609">Sandwiches</tspan></text> <text transform="matrix(1 0 0 1 15.1943 421.2051)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">LJ</tspan><tspan x="7.563" y="0" 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x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Hourl</tspan><tspan x="17.112" y="0" font-family="'ArialMT'" font-size="7.1609">y</tspan><tspan x="20.829" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="22.79" y="0" font-family="'ArialMT'" font-size="7.1609">Labor</tspan></text> <text transform="matrix(1 0 0 1 15.1797 474.8389)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Mgm</tspan><tspan x="15.913" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="18.225" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="20.186" y="0" font-family="'ArialMT'" font-size="7.1609">Labor</tspan></text> <text transform="matrix(1 0 0 1 15.1724 486.6064)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Tota</tspan><tspan x="14.329" y="0" font-family="'ArialMT'" font-size="7.1609">l</tspan><tspan x="16.457" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.661" y="0" font-family="'ArialMT'" font-size="7.1609">Labor</tspan></text> <text transform="matrix(1 0 0 1 15.1655 507.7412)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Tota</tspan><tspan x="14.329" y="0" font-family="'ArialMT'" font-size="7.1609">l</tspan><tspan x="16.457" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.661" y="0" font-family="'ArialMT'" font-size="7.1609">Controllable</tspan></text> <text transform="matrix(1 0 0 1 15.1655 530.2686)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Charg</tspan><tspan x="19.503" y="0" font-family="'ArialMT'" font-size="7.1609">e</tspan><tspan x="24.088" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="26.048" y="0" font-family="'ArialMT'" font-size="7.1609">Count</tspan></text> <text transform="matrix(1 0 0 1 15.1729 542.0361)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Charg</tspan><tspan x="19.503" y="0" font-family="'ArialMT'" font-size="7.1609">e</tspan><tspan x="24.088" 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font-size="7.1609"> </tspan><tspan x="27.346" y="0" font-family="'ArialMT'" font-size="7.1609">$</tspan></text> <text transform="matrix(1 0 0 1 15.1582 595.8594)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Ticke</tspan><tspan x="17.108" y="0" font-family="'ArialMT'" font-size="7.1609">t</tspan><tspan x="19.528" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="21.489" y="0" font-family="'ArialMT'" font-size="7.1609">Average</tspan></text> <text transform="matrix(1 0 0 1 15.1582 617.3867)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Hea</tspan><tspan x="13.136" y="0" font-family="'ArialMT'" font-size="7.1609">d</tspan><tspan x="17.57" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="19.531" y="0" font-family="'ArialMT'" font-size="7.1609">Average</tspan></text> <text transform="matrix(1 0 0 1 15.1582 628.1543)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Piece</tspan><tspan x="17.913" y="0" font-family="'ArialMT'" font-size="7.1609">s</tspan><tspan x="22.138" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="24.099" y="0" font-family="'ArialMT'" font-size="7.1609">Scrapped</tspan></text> <text transform="matrix(1 0 0 1 15.1514 639.4219)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Piece</tspan><tspan x="17.913" y="0" font-family="'ArialMT'" font-size="7.1609">s</tspan><tspan x="22.138" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="24.099" y="0" font-family="'ArialMT'" font-size="7.1609">Unacc</tspan><tspan x="44.396" y="0" font-family="'ArialMT'" font-size="7.1609">.</tspan><tspan x="46.887" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="48.848" y="0" font-family="'ArialMT'" font-size="7.1609">For</tspan></text> <text transform="matrix(1 0 0 1 15.1514 650.6895)" font-family="'ArialMT'" font-size="7.1609">Efficiency</text> <text transform="matrix(1 0 0 1 15.1514 671.2168)"><tspan x="0" y="0" font-family="'ArialMT'" font-size="7.1609">Cas</tspan><tspan x="12.734" y="0" font-family="'ArialMT'" font-size="7.1609">h</tspan><tspan x="16.925" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="18.885" y="0" font-family="'ArialMT'" font-size="7.1609">ove</tspan><tspan x="30.431" y="0" font-family="'ArialMT'" font-size="7.1609">r</tspan><tspan x="33.202" y="0" font-family="'ArialMT'" font-size="7.1609"> </tspan><tspan x="35.163" y="0" font-family="'ArialMT'" font-size="7.1609">/(short)</tspan></text> <path stroke="#000000" d="M10,488.932"/> </g> <g id="Pieces_Unaccounted"> <g id="l_x5F_u_x5F_pieces_x5F_unaccounted"> <line id="UnaccountedFor_1_" fill="none" stroke="#000000" stroke-width="0.5" x1="10" y1="640" x2="599.5" y2="640"/> </g> </g> <g id="Total_Labor"> <g id="Double_Lines"> <line id="Btm_Line" stroke="#000000" stroke-width="0.5" x1="11" y1="490.932" x2="600.5" y2="490.932"/> <line id="Top_Line" stroke="#000000" stroke-width="0.5" x1="11" y1="488.932" x2="600.5" y2="488.932"/> </g> <line id="Line_Above" stroke="#000000" stroke-width="0.5" x1="10.5" y1="477.5" x2="600" y2="477.5"/> </g> <g id="Total_Cos"> <g id="Double_Line_3_"> <line id="Btm_Line_3_" stroke="#000000" stroke-width="0.5" x1="11" y1="444.932" x2="600.5" y2="444.932"/> <line id="Top_Line_3_" stroke="#000000" stroke-width="0.5" x1="11" y1="442.932" x2="600.5" y2="442.932"/> </g> <line id="Line_Above_6_" stroke="#000000" stroke-width="0.5" x1="10.34" y1="433.097" x2="599.84" y2="433.097"/> </g> <g id="SubTotal_Chicken"> <g id="Double_Line_2_"> <line id="Btm_Line_1_" stroke="#000000" stroke-width="0.5" x1="7" y1="261.932" x2="596.5" y2="261.932"/> <line id="Top_Line_1_" stroke="#000000" stroke-width="0.5" x1="7" y1="259.932" x2="596.5" y2="259.932"/> </g> <line id="Line_Above_1_" stroke="#000000" stroke-width="0.5" x1="7" y1="250.097" x2="596.5" y2="250.097"/> </g> <g id="total_Net"> <g id="Double_Line_1_"> <line id="Btm_Line_2_" stroke="#000000" stroke-width="0.5" x1="7" y1="130.932" x2="596.5" y2="130.932"/> <line id="Top_Line_2_" stroke="#000000" stroke-width="0.5" x1="7" y1="128.932" x2="596.5" y2="128.932"/> </g> <line id="Line_Above_3_" stroke="#000000" stroke-width="0.5" x1="7" y1="119.097" x2="596.5" y2="119.097"/> </g> <g id="Header_Underline"> <line id="Line_Above_4_" stroke="#000000" stroke-width="0.5" x1="8.34" y1="74.5" x2="597.84" y2="74.5"/> </g> <g id="Total_Controllable"> <line id="Line_Above_2_" stroke="#000000" x1="7" y1="498.066" x2="600.5" y2="498.066"/> <line id="Line_Under" stroke="#000000" x1="7" y1="509.329" x2="600.5" y2="509.329"/> </g> </svg> The above code is generated xml file, and i need to write a xslt transformation to get the fo file, for the PDF generation, how do I do it?? 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  • dximagetransform.matrix, absolutely position child elements not rotating in IE 8 standards mode

    - by davydka
    I've looked all over for more information on this, and would like to know why it happens. Here's the code: <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html> <head> </head> <body> <div style="position:absolute; top:200px; left:200px; height:200px; width:200px; border:1px solid black; filter: progid:DXImageTransform.Microsoft.Matrix(sizingMethod='auto expand', M11=0.9886188373396114, M12=-0.15044199698646263, M21=0.15044199698646263, M22=0.9886188373396114);"> <div style="position:absolute; top:10px; left:10px; border:1px solid darkblue;"> I do not rotate in IE 8. </div> </div> </body> </html> The problem is that absolutely or relatively positioned elements within a div that has been rotated using MS's dximagetransform.matrix do not inherit the transformation in IE 8. IE 6 & 7 render correctly, and I can solve the IE8 problem by triggering compatibility mode, but I'd rather not do that. Does anyone have any experience with this? I'm using css3 transform on other browsers and using dximagetransform.matrix to achieve this effect in IE. EDIT: Added the opening html tag. Problem still exists. http://i45.tinypic.com/nf4gmq.png

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  • Functional way to get a matrix from text

    - by Elazar Leibovich
    I'm trying to solve some Google Code Jam problems, where an input matrix is typically given in this form: 2 3 #matrix dimensions 1 2 3 4 5 6 7 8 9 # all 3 elements in the first row 2 3 4 5 6 7 8 9 0 # each element is composed of three integers where each element of the matrix is composed of, say, three integers. So this example should be converted to #!scala Array( Array(A(1,2,3),A(4,5,6),A(7,8,9), Array(A(2,3,4),A(5,6,7),A(8,9,0), ) An imperative solution would be of the form #!python input = """2 3 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 0 """ lines = input.split('\n') print lines[0] m,n = (int(x) for x in lines[0].split()) array = [] row = [] A = [] for line in lines[1:]: for elt in line.split(): A.append(elt) if len(A)== 3: row.append(A) A = [] array.append(row) row = [] from pprint import pprint pprint(array) A functional solution I've thought of is #!scala def splitList[A](l:List[A],i:Int):List[List[A]] = { if (l.isEmpty) return List[List[A]]() val (head,tail) = l.splitAt(i) return head :: splitList(tail,i) } def readMatrix(src:Iterator[String]):Array[Array[TrafficLight]] = { val Array(x,y) = src.next.split(" +").map(_.trim.toInt) val mat = src.take(x).toList.map(_.split(" "). map(_.trim.toInt)). map(a => splitList(a.toList,3). map(b => TrafficLight(b(0),b(1),b(2)) ).toArray ).toArray return mat } But I really feel it's the wrong way to go because: I'm using the functional List structure for each line, and then convert it to an array. The whole code seems much less efficeint I find it longer less elegant and much less readable than the python solution. It is harder to which of the map functions operates on what, as they all use the same semantics. What is the right functional way to do that?

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  • Optimization of a c++ matrix/bitmap class

    - by Andrew
    I am searching a 2D matrix (or bitmap) class which is flexible but also fast element access. The contents A flexible class should allow you to choose dimensions during runtime, and would look something like this (simplified): class Matrix { public: Matrix(int w, int h) : data(new int[x*y]), width(w) {} void SetElement(int x, int y, int val) { data[x+y*width] = val; } // ... private: // symbols int width; int* data; }; A faster often proposed solution using templates is (simplified): template <int W, int H> class TMatrix { TMatrix() data(new int[W*H]) {} void SetElement(int x, int y, int val) { data[x+y*W] = val; } private: int* data; }; This is faster as the width can be "inlined" in the code. The first solution does not do this. However this is not very flexible anymore, as you can't change the size anymore at runtime. So my question is: Is there a possibility to tell the compiler to generate faster code (like when using the template solution), when the size in the code is fixed and generate flexible code when its runtime dependend? I tried to achieve this by writing "const" where ever possible. I tried it with gcc and VS2005, but no success. This kind of optimization would be useful for many other similar cases.

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  • tile_static, tile_barrier, and tiled matrix multiplication with C++ AMP

    - by Daniel Moth
    We ended the previous post with a mechanical transformation of the C++ AMP matrix multiplication example to the tiled model and in the process introduced tiled_index and tiled_grid. This is part 2. tile_static memory You all know that in regular CPU code, static variables have the same value regardless of which thread accesses the static variable. This is in contrast with non-static local variables, where each thread has its own copy. Back to C++ AMP, the same rules apply and each thread has its own value for local variables in your lambda, whereas all threads see the same global memory, which is the data they have access to via the array and array_view. In addition, on an accelerator like the GPU, there is a programmable cache, a third kind of memory type if you'd like to think of it that way (some call it shared memory, others call it scratchpad memory). Variables stored in that memory share the same value for every thread in the same tile. So, when you use the tiled model, you can have variables where each thread in the same tile sees the same value for that variable, that threads from other tiles do not. The new storage class for local variables introduced for this purpose is called tile_static. You can only use tile_static in restrict(direct3d) functions, and only when explicitly using the tiled model. What this looks like in code should be no surprise, but here is a snippet to confirm your mental image, using a good old regular C array // each tile of threads has its own copy of locA, // shared among the threads of the tile tile_static float locA[16][16]; Note that tile_static variables are scoped and have the lifetime of the tile, and they cannot have constructors or destructors. tile_barrier In amp.h one of the types introduced is tile_barrier. You cannot construct this object yourself (although if you had one, you could use a copy constructor to create another one). So how do you get one of these? You get it, from a tiled_index object. Beyond the 4 properties returning index objects, tiled_index has another property, barrier, that returns a tile_barrier object. The tile_barrier class exposes a single member, the method wait. 15: // Given a tiled_index object named t_idx 16: t_idx.barrier.wait(); 17: // more code …in the code above, all threads in the tile will reach line 16 before a single one progresses to line 17. Note that all threads must be able to reach the barrier, i.e. if you had branchy code in such a way which meant that there is a chance that not all threads could reach line 16, then the code above would be illegal. Tiled Matrix Multiplication Example – part 2 So now that we added to our understanding the concepts of tile_static and tile_barrier, let me obfuscate rewrite the matrix multiplication code so that it takes advantage of tiling. Before you start reading this, I suggest you get a cup of your favorite non-alcoholic beverage to enjoy while you try to fully understand the code. 01: void MatrixMultiplyTiled(vector<float>& vC, const vector<float>& vA, const vector<float>& vB, int M, int N, int W) 02: { 03: static const int TS = 16; 04: array_view<const float,2> a(M, W, vA); 05: array_view<const float,2> b(W, N, vB); 06: array_view<writeonly<float>,2> c(M,N,vC); 07: parallel_for_each(c.grid.tile< TS, TS >(), 08: [=] (tiled_index< TS, TS> t_idx) restrict(direct3d) 09: { 10: int row = t_idx.local[0]; int col = t_idx.local[1]; 11: float sum = 0.0f; 12: for (int i = 0; i < W; i += TS) { 13: tile_static float locA[TS][TS], locB[TS][TS]; 14: locA[row][col] = a(t_idx.global[0], col + i); 15: locB[row][col] = b(row + i, t_idx.global[1]); 16: t_idx.barrier.wait(); 17: for (int k = 0; k < TS; k++) 18: sum += locA[row][k] * locB[k][col]; 19: t_idx.barrier.wait(); 20: } 21: c[t_idx.global] = sum; 22: }); 23: } Notice that all the code up to line 9 is the same as per the changes we made in part 1 of tiling introduction. If you squint, the body of the lambda itself preserves the original algorithm on lines 10, 11, and 17, 18, and 21. The difference being that those lines use new indexing and the tile_static arrays; the tile_static arrays are declared and initialized on the brand new lines 13-15. On those lines we copy from the global memory represented by the array_view objects (a and b), to the tile_static vanilla arrays (locA and locB) – we are copying enough to fit a tile. Because in the code that follows on line 18 we expect the data for this tile to be in the tile_static storage, we need to synchronize the threads within each tile with a barrier, which we do on line 16 (to avoid accessing uninitialized memory on line 18). We also need to synchronize the threads within a tile on line 19, again to avoid the race between lines 14, 15 (retrieving the next set of data for each tile and overwriting the previous set) and line 18 (not being done processing the previous set of data). Luckily, as part of the awesome C++ AMP debugger in Visual Studio there is an option that helps you find such races, but that is a story for another blog post another time. May I suggest reading the next section, and then coming back to re-read and walk through this code with pen and paper to really grok what is going on, if you haven't already? Cool. Why would I introduce this tiling complexity into my code? Funny you should ask that, I was just about to tell you. There is only one reason we tiled our extent, had to deal with finding a good tile size, ensure the number of threads we schedule are correctly divisible with the tile size, had to use a tiled_index instead of a normal index, and had to understand tile_barrier and to figure out where we need to use it, and double the size of our lambda in terms of lines of code: the reason is to be able to use tile_static memory. Why do we want to use tile_static memory? Because accessing tile_static memory is around 10 times faster than accessing the global memory on an accelerator like the GPU, e.g. in the code above, if you can get 150GB/second accessing data from the array_view a, you can get 1500GB/second accessing the tile_static array locA. And since by definition you are dealing with really large data sets, the savings really pay off. We have seen tiled implementations being twice as fast as their non-tiled counterparts. Now, some algorithms will not have performance benefits from tiling (and in fact may deteriorate), e.g. algorithms that require you to go only once to global memory will not benefit from tiling, since with tiling you already have to fetch the data once from global memory! Other algorithms may benefit, but you may decide that you are happy with your code being 150 times faster than the serial-version you had, and you do not need to invest to make it 250 times faster. Also algorithms with more than 3 dimensions, which C++ AMP supports in the non-tiled model, cannot be tiled. Also note that in future releases, we may invest in making the non-tiled model, which already uses tiling under the covers, go the extra step and use tile_static memory on your behalf, but it is obviously way to early to commit to anything like that, and we certainly don't do any of that today. Comments about this post by Daniel Moth welcome at the original blog.

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  • Matlab matrix replacement assignment gives error

    - by Gulcan
    Hello, when i tried to update some part of a matrix, i got the following error message: ??? Assignment has fewer non-singleton rhs dimensions than non-singleton subscripts My code tries to update some values of a matrix that represent a binary image. My code is as follows: outImage(3:5,2:4,1) = max(imBinary(3:5,2:4,1)); When I delete last parameter (1), this time I get the same error. I guess there is a mismatch between dimensions but I could not get it. outImage is a new object that is created at that time (I tried to create it before, but nothing changed). What may be wrong? Thanks in advance, Gulcan

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  • MATLAB matrix replacement assignment gives error

    - by Gulcan
    I tried to update some part of a matrix, I got the following error message: ??? Assignment has fewer non-singleton rhs dimensions than non-singleton subscripts My code tries to update some values of a matrix that represent a binary image. My code is as follows: outImage(3:5,2:4,1) = max(imBinary(3:5,2:4,1)); When I delete last parameter (1), this time I get the same error. I guess there is a mismatch between dimensions but I could not get it. outImage is a new object that is created at that time (I tried to create it before, but nothing changed). What may be wrong?

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  • Problem sub-total Matrix with rdlc report in vb.NET

    - by Keven
    Hi everyone, I have a matrix and I need to add the money earned this year and past years. However, I must remove the money spent in past years. I must have the separate amount per year and the total of these amounts. This is what gives my matrix: Year = Fields!Year.value =formatnumber((sum(Fields!Results.Value))-(sum(iif( Fields!Year.value & Parameters!choosedYear.Value, Fields!Moneyspent.value,0))), 2) & "$" However, the subtotal gives me an error. What should I do? P.S.: I already found that the subtotal gives me an error because it's not in the scope of the rowgroup1, but is there a way to get the scope in the subtotal? or can anybody find another way to do it?

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  • Efficient 4x4 matrix inverse (affine transform)

    - by Budric
    Hi, I was hoping someone can point out an efficient formula for 4x4 affine matrix transform. Currently my code uses cofactor expansion and it allocates a temporary array for each cofactor. It's easy to read, but it's slower than it should be. Note, this isn't homework and I know how to work it out manually using 4x4 co-factor expansion, it's just a pain and not really an interesting problem for me. Also I've googled and came up with a few sites that give you the formula already (http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm). However this one could probably be optimized further by pre-computing some of the products. I'm sure someone came up with the "best" formula for this at one point or another? Thanks.

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  • Rotation Matrix calculates by column not by row

    - by pinnacler
    I have a class called forest and a property called fixedPositions that stores 100 points (x,y) and they are stored 250x2 (rows x columns) in MatLab. When I select 'fixedPositions', I can click scatter and it will plot the points. Now, I want to rotate the plotted points and I have a rotation matrix that will allow me to do that. The below code should work: theta = obj.heading * pi/180; apparent = [cos(theta) -sin(theta) ; sin(theta) cos(theta)] * obj.fixedPositions; But it wont. I get this error. ??? Error using == mtimes Inner matrix dimensions must agree. Error in == landmarkslandmarks.get.apparentPositions at 22 apparent = [cos(theta) -sin(theta) ; sin(theta) cos(theta)] * obj.fixedPositions; When I alter forest.fixedPositions to store the variables 2x250 instead of 250x2, the above code will work, but it wont plot. I'm going to be plotting fixedPositions constantly in a simulation, so I'd prefer to leave it as it, and make the rotation work instead. Any ideas? Also, fixed positions, is the position of the xy points as if you were looking straight ahead. i.e. heading = 0. heading is set to 45, meaning I want to rotate points clockwise 45 degrees. Here is my code: classdef landmarks properties fixedPositions %# positions in a fixed coordinate system. [x, y] heading = 45; %# direction in which the robot is facing end properties (Dependent) apparentPositions end methods function obj = landmarks(numberOfTrees) %# randomly generates numberOfTrees amount of x,y coordinates and set %the array or matrix (not sure which) to fixedPositions obj.fixedPositions = 100 * rand([numberOfTrees,2]) .* sign(rand([numberOfTrees,2]) - 0.5); end function obj = set.apparentPositions(obj,~) theta = obj.heading * pi/180; [cos(theta) -sin(theta) ; sin(theta) cos(theta)] * obj.fixedPositions; end function apparent = get.apparentPositions(obj) %# rotate obj.positions using obj.facing to generate the output theta = obj.heading * pi/180; apparent = [cos(theta) -sin(theta) ; sin(theta) cos(theta)] * obj.fixedPositions; end end end P.S. If you change one line to this: obj.fixedPositions = 100 * rand([2,numberOfTrees]) .* sign(rand([2,numberOfTrees]) - 0.5); Everything will work fine... it just wont plot.

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