Transformations [10 points]
A. Provide a transformation that can be used to transform from the letter g to the number 8. Please note that due to the symmetry factor of the number 8, there are multiple transformations that can be used to produce the new image.
B. Compute the combined transformation matrices. Show your work.
5. Transformation matrices [14]:
a. Write the 4x4 transformation matrix for a translation of 1 in the x direction, 2 in the y direction, and 3 in the z direction. Call this matrix T(1,2,3). [3]
b. Write the 4x4 transformation matrix for a scaling of 3 in the x direction, 2 in the y direction, and 1 in the z direction. Call this matrix S(3,2,1). [3]
c. Compute the 4x4 transformation matrix S(3,2,1)T(1,2,3). Call this matrix Q. [4]
d. Consider the 4x4 transformation matrix of the form T(x, y, z)S(3,2,1). What values of x, y, and z are necessary for this product to be equal to Q? Hint: You might want to compute T(1,2,3)S(3,2,1) to help you find the solution. [4]
6. Write the 2D rotation matrix that rotates by 90 degrees clockwise. Justify your response. [8]