By Ian O. Angell (auth.)
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Extra info for A Practical Introduction to Computer Graphics
A> C CALCULATE 2-D AXES SCALING MATRIX. A> C CALCULATE 2-D AXES ROTATION MATRIX A. 0 CßNTINUE A (3. 3 Of course we need a routine for multiplying matrices in order to combine the various transformations - sub routine MULT2. SUBRBUTINE MULT2(A,B,Ci C 3X3 MATRIX PRBDUCT. O DB 1 K=1,3 AB=AB+A (I. K) ":s (K, J) CßNTINUE C (! 1 can be solved by computer with the following statements calculating the required points. T<3,3) CALL TRAN2 (1. 0. 2). 2 The functional representation of this ellipse is very involved and so the problem looks extremely complicated.
Ifthe curve divides space into two parts then the functional representation tells whether a point (x, y) is on the curve or, if not, in which part it lies. The two parts of space are defmed by the sign of the functionf(x. y). For example, the circle fex, y) ==,2 _ x 2 _ y2 is such that if (l) (2) (3) fex, y) = 0 then (x, y) lies on the circumference of the circle; fex, y) > 0 then (x, y) lies inside the circle; fex, y) < 0 then (x, y) lies outside the circle. Points (x I, Y I) and (X2, Y2) are on the same side of the curve if and only if the non-zero sign of fex I, Y d is equal to the sign of f(x2, Y2).
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