**Math 155 - Computer Graphics
U.C. San Diego - Winter 2001**

**Written Homework Assignments**

Written homework assignments will be made in class lectures and are usually due one week after the assignment is made, i.e., in the third class lecture after the assignment is given. Due dates are given below in parentheses.

*SEE BOTTOM OF PAGE FOR ASSIGNMENT DUE WED, MARCH 14.
ALSO, BEZIER ASSIGNMENT DUE FRIDAY, MARCH 16 WAS HANDED OUT IN CLASS.*

**1.** (due Friday, Jan. 19. If you scored a
"1/10" on this, you may resubmit a revised answer.) Give a proof of the
angle sum formulas for the *sin* and *cos* functions. I.e.,

*cos(a+b) = cos(a)cos(b) -
sin(a)sin(b)
sin(a+b) = sin(a)cos(b) +
cos(a)sin(b).
*Your proof should be based on the use of rotation matrices (see
hint given in class).

**2. **(due Monday, Jan 29). See the picture on the class handout.

**(a)** Is this a linear transformation?

**(b)** Is this an affine transformation?

**(c)** Give the 3x3 matrix representation of this
transformation.

**3.** (due Monday, Jan 29). Give the 3x3 matrix which represents
the inverse of the transformation from problem #2.

**4. **(due Monday, Jan 29). Consider a generalized rotation of 45
degrees around the the point (0,1). See the picture on the class handout.

**(a)** Give the 3x3 matrix representation of this
transformation.

**(b)** What are the xy-coordinates of the points **A**
and **B**. Here, **A** and **B** are the
images of (0,-1) and (1,1).

**5. **(due Monday, Jan 29) Give the 4x4 matrix representation of a
transformation, A, which is linear, rigid and orientation-preserving and maps the x-axis
into the center of the first octant. The latter condition is that same ask requiring
that A(<1,0,0>) = <1/sqrt(3), 1/sqrt(3), 1/sqrt(3)>.

**Another page of assignments (handwritten)** was distributed in class on
Friday, and is due Wednesday, February 14 in class.

**Homework on barycentric coordinates and bilinear interpolation**.
Due Wednesday March 14. Postscript format and PDF
format