MATLAB: Linear Transformations In this activity you will create a linear transformation matrix and apply it...

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MATLAB: Linear Transformations In this activity you will create a linear transformation matrix and apply it to a set of points, creating a plot of the original and rotated polygons. The following matrix represents a linear transformation from R² to R², rotating each point counterclockwise about the origin by an angle , in radians. [cos(0) -sin(0)] [sin(0) cos(0) A = The standard matrix A that rotates a point 45 degrees counterclockwise about the origin is given below. A = [cos(pi/4) -sin(pi/4); sin(pi/4) cos(pi/4)] %Create a matrix S containing the points of the unit square as the columns. Order the points as they %would be traversed when drawing the edges of the square, repeating the starting point so that the %drawing starts and ends there. S = [0 1 1 0 0; 0 0 1 1 0] Plot the unit square. plot (S(1,:), S (2,:)) %Perform matrix multiplication to transform each of the points in S. T1 = A*S *Plot the original unit square and the transformed unit square. plot (S(1,:), S(2,:), T1(1,:), T1(2,:)) For this activity, rotate the triangle formed by the points (0,0), (1,1), and (3,0) counterclockwise 60° about the origin. The order for drawing the triangle is to start at point (0,0), move to (1,1), then to (3,0), and finish at (0,0). %Do you run into any difficulties? Explain what is happening as a comment in your code. Script> Save C Reset MATLAB Documentation 1 %Creat the standard matrix A that rotates a point 60 degrees counterclockwise about the origin. 2 3%Create a matrix S containing the points of the triangle as the columns. 4 5 %Perform matrix multiplication to transform each of the points in S. Store this in T1. 6 7 %Plot the original triangle and the transformed triangle in a single graph. 8 9 %Do you run into any difficulties? Explain what is happening as a comment in your code. 10 ▶ Run Script MATLAB: Linear Transformations In this activity you will create a linear transformation matrix and apply it to a set of points, creating a plot of the original and rotated polygons. The following matrix represents a linear transformation from R² to R², rotating each point counterclockwise about the origin by an angle , in radians. [cos(0) -sin(0)] [sin(0) cos(0) A = The standard matrix A that rotates a point 45 degrees counterclockwise about the origin is given below. A = [cos(pi/4) -sin(pi/4); sin(pi/4) cos(pi/4)] %Create a matrix S containing the points of the unit square as the columns. Order the points as they %would be traversed when drawing the edges of the square, repeating the starting point so that the %drawing starts and ends there. S = [0 1 1 0 0; 0 0 1 1 0] Plot the unit square. plot (S(1,:), S (2,:)) %Perform matrix multiplication to transform each of the points in S. T1 = A*S *Plot the original unit square and the transformed unit square. plot (S(1,:), S(2,:), T1(1,:), T1(2,:)) For this activity, rotate the triangle formed by the points (0,0), (1,1), and (3,0) counterclockwise 60° about the origin. The order for drawing the triangle is to start at point (0,0), move to (1,1), then to (3,0), and finish at (0,0). %Do you run into any difficulties? Explain what is happening as a comment in your code. Script> Save C Reset MATLAB Documentation 1 %Creat the standard matrix A that rotates a point 60 degrees counterclockwise about the origin. 2 3%Create a matrix S containing the points of the triangle as the columns. 4 5 %Perform matrix multiplication to transform each of the points in S. Store this in T1. 6 7 %Plot the original triangle and the transformed triangle in a single graph. 8 9 %Do you run into any difficulties? Explain what is happening as a comment in your code. 10 ▶ Run Script