Angle	cos	sin
0	1	0
30	√3/2	1/2
45	√2/2	√2/2
60	1/2	√3/2
90	0	1

Homework 2 CMPS160:

NAME:__________________

2. Adapted (yet changed) from Suresh Lodha

a) A cubical table is defined in its local coordinate frame centered around the origin and with sides of length 4. It is placed in the world so that it is resting on the xz-plane and centered at (1,2,2). What is the matrix that transforms the table points from local to world coordinates? Call it M1

b) A cylindrical vase of radius 1.0 is defined in its local coordinate system centered on the y-axis and extends from 0 to 2 in y. The vase is to be placed on top of the table at the table’s center top surface. What is the matrix that transforms the vase from local to the table coordinates? Call it M2

c) The vase is knocked over by a z-rotation of 90 degrees. (Do not worry that it sinks into the table). What is the matrix that describes this rotation? Call this M3

d) What are the matrices (list them in order) that describe the vase points in terms of the world frame?

e) What is the location of the center top of the vase as seen from the world coordinates? Show all work!