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

By Ian O. Angell (auth.)

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N33). These three equations can be replaced by the matrix equation ("""""" and so the solution for xis given by the column vector = ("" nll (yX) z n31 So any program requiring the intersection of three planes necessarily uses the inverse of a 3 x 3 matrix; we could use a computer package 10 salve this problem. but it is much simpler to write Dur own routine. Sub routine (NV uses the Adj oint method to fi nd NI, the inverse of the REAL 3 x 3 matrix N. X HI . THE INVERSE 131'" I'1"ITRJX N BY THE ADJßINT r-E rl-

P) CALL t1-'L T2 'P. Q. O) BY R. AND M(JvE TO THAT POINT PLOT HEAD UP ) . 031415926535 C FIND 200 PO INTS ON THE EL LIPSE . TRANSFORM THEM WITH R. AND JO Tri C THEM IN SEQUENCE. 3) of radius R, cent red at (XC, YC), where one axis of the figure makes an angle PHI with the positive x-axis. The parametric form of an astroid is {(R cos 3 0, R sin 3 0) I 0 :e;;; 0 :e;;; 21T} . -1 >< CIS I >. 3 CHANGE OF SPACE Instead of transforming the axes of a coordinate system we now consider what happens when the axes are fIXed and the whole fabric of space is changed about them.

Up to now the coordinate origin, axes and dimensions defmed for the two-dimensional space have been identified with the origin, axes and scale of the screen (the so-called observer coordinate system). This is not the general case, and so it is necessary to change from the old defined system to the observer coordinate system of the screen. There need only be three basic forms of coordinate-system change, that is, translation of origin, change of scale and rotation ofaxes; all other changes can be formulated in terms of these three types.

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