Question

Find a 2D transformation matrix M that will perform rotation by 90 degrees about the point p=(0,1) in homogeneous coordinates. Hint - to compute M translate the point p to the origin, perform the rotation, then translate back. Compute the sum of the elements of the matrix M you computed and use this sum as the answer. Note that the matrix M is a 3×3 matrix.

Answer 1

To find the 2D transformation matrix M that will perform rotation by 90 degrees about the point p=(0,1) in homogeneous coordinates, you can follow the hint given. First, translate the point p to the origin, then perform the rotation, and finally translate back.

Step-by-step explanation:

To find the 2D transformation matrix M that will perform rotation by 90 degrees about the point p=(0,1) in homogeneous coordinates, we can follow the hint given. First, we translate the point p to the origin. This can be done by subtracting the coordinates of p from all points. Then, we perform the rotation by using the rotation formulas x' = x*cos(q) + y*sin(q) and y' = -x*sin(q) + y*cos(q), where q is the angle of rotation (in this case, 90 degrees). Finally, we translate back by adding the coordinates of p to all points. The resulting matrix M will be a 3x3 matrix.