Recall from class the radiosity equation for n surface patches is (I ? F)x = E where I is the n n identity matrix, is diagonal matrix with giving the reflectivity of surface patch i, F is the form factor matrix, x is the unknown radiosities, and on the right hand side is the light emitted by patch i.

(a) Solve the radiosity equation (Using Matlab) for the following: F = [.00 .20 .20 .20 .10 .10 .10 .10; .20 .00 .20 .20 .10 .10 .10 .10; .20 .20 .00 .20 .10 .10 .10 .10; .20 .20 .20 .00 .10 .10 .10 .10; .20 .20 .20 .20 .00 .00 .11 .09; .20 .20 .20 .20 .00 .00 .09 .11; .20 .20 .20 .20 .11 .09 .00 .00; .20 .20 .20 .20 .09 .11 .00 .00], p = [.00 .42 .53 .82 .24 .77 .88 .10],

The p vector above gives the diagonal entries of the ? matrix (hint: Matlab has a diag() function for constructing diagonal matrices.) Also remember that the radiosity equation is usually solved for each of the red, green, and blue components. So rather than being a vector, the right hand side E is a matrix, whose first column is red components, second is green, and third is blue. So, for example, is the blue component being emitted by the fifth patch.

(b) Once you have solved the equation, answer the following questions about your part (a) answer. (i) Are all the components of the answer between 0.0 and 1.0? (ii) Which patch has radiosity with the largest red component? With the largest green? With the largest blue?

For this problem turn in a Matlab diary or script with the part (a) commands and output. For part (b) typewrite your answer and insert it into your Matlab file for Part B of this assignment.