Computer Animation - Christine Lauber



4378325123190Name _______________________________________ Hands On ActivityComputer Animation Goal: To learn how matrix multiplication is used in the computer animation industry.In this lesson, students will create their own image on graph paper. Using specific points of their image, they will explore the effects of several geometric transformations through the use of matrix multiplication. After learning how to specific matrices can affect their image, they will then create a series of pictures in which their original image becomes animated.Objectives:Given a matrix created by the student and several given matrices, the student will apply matrix multiplication skillsGiven matrices based on an object on graph paper, the student will explore connections between geometric transformations and matrix multiplicationNational Council of Teachers of Mathematics StandardsGeometry 9 – 12Apply transformations and use symmetry to analyze mathematical situations understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices;use various representations to help understand the effects of simple transformations and their compositions.Numbers and Operations 9 – 12Understand meanings of operations and how they relate to one another develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices;Compute fluently and make reasonable estimates develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.Materials Required:Quarter size sheets of graph paperGraphing calculatorComputer Animation Activity PacketPowerPoint presentation with examplesBased on the lesson from NCTM, Computer Animation.Russell, C (2012). Computer animation. National Council of Teachers of Mathematics; Illuminations. Retrieved April 10, 2012 from: Name _______________________________________ Date _____________438577735443Hands On ActivityComputer Animation Your first step as an animator is to create a character on graph paper that has 5-10 points and is NOT symmetrical. You will then turn your image into a matrix of the form 2xn. The x-coordinate is the top row, and the y-coordinate is the bottom row. Call this matrix M (for mine).Find the products for each of the following. Graph the shape on your graph paper. Explain what happens to each by using the geometric terms (translation, reflection, rotation, dilation.)-1001M=100-1M=35-454535M=0110M=2004M=Find a 2x2 transformation that will make your image shrink into a single dot. Do you think there is more than one matrix that might do this. What matrix will flatten your image into a flat line (horizontal or vertical)?Shrink to a single dot:Flatten to a line: What matrix will not change your image? Do you think there is more than one matrix that would have this effect?Represent your shape using a 3xn matrix by adding a third row of all 1’s. This will be used to look at other transformations.M2=Now, compute the products for each of the following below and describe what happens to your shapes. Use the row of 1’s in your calculations, but ignore it in your graph.102010001M2=10001-3001M2=10201-3001M2=012100001M2=Now, using the information you have gained, animate your picture on the graph paper. You must create at least four different movements. Be careful that your picture moves smoothly and does not jump across the page.You may put your animated picture on the computer. Use the PowerPoint program to compile your pictures as I have done in the example. If you use this method be watchful of the following:The graph picture should be imported from the graphing calculator.Turn off the axes on the calculator for a clearer picture.Be sure the dimensions of each consecutive picture are the same ................
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