A Practical Introduction to Computer Graphics by Ian O. Angell (auth.)

By Ian O. Angell (auth.)

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6 In the routine to find the inverse of a matrix we had to calculate the determinant of the matrix, DET. The matrix in the last example is in a very special form, and so we recalculate DET DET =Pt (Ptq2 2 - P2qtq2 + Ptq/ - P3qtq3) +P2(P2q/ -P3q2q3 +P2qt 2 -ptQ2qd + P3(P3Qt 2 - PtQ3Qt + P3Q/ - P2Q3Q2) = Pt 2 (Q2 2 +Q/) + P2 2 (Q/ +Q:! 2) + P3 2 (Qt 2 + Q2 2) - 2 L PiPjQiQj i

B =(1,2, 3),d = (1,0,1) - (l, 2, 3) = (0, -2, -2),n =(2,1,2) n •b = (2 x n . d = (2 x 1+1x 2 +2 °+ 1 x x 3) = 10 -2 + 2 x -2) = -6 hence the point of intersection is (l, 2, 3) + (5 - 10) -6 (0, -2, -2) = (l, 1/3,4/3) and the distance ofthe plane from the origin = 5/1 nl = 5/3. 2). Here vectors are stored as one-dimensional arrays whose indices lie between 1 and 3, corresponding to the x, y and z-coordinates respectively. The program reads in the plane information K and N(3), and the line information, base vector B(3) and directional vector D(3).

X = KUj ; 1=1,2 ßR 3. ; , N , I ,3; ; • REAL N(3,3j ,"I(3,3j ,K(3j ,PT(3j REAO (5, '~j N, K CALL INV(N,ND C THE CßLUMN VECTßR PT IS THE PRßOUCT ßF THE INVERSE MATRIX NI C ANO THE CßLUMN VECTßR K. O Oß 1 J=1,3 PTI=PTI+NI

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