By Ian O. Angell, Brian J. Jones
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Extra resources for Advanced Graphics with the Sinclair ZX Spectrum
160 INPUT "TYPE N "; N 170 LET XPT 1: LET YPT Ill: GO SUB moveto 180 LET XPT = -1 : LET YPT = 0: GO SUB Lineto 190 LET XPT = 0: LET YPT = 1: GO SUB Lineto 200 LET XPT 0: LET YPT -1: GO SUB l;~eto 208 REM produce N sets each of four po;nt s, one on each axis. 209 REM join the points of each se t in order. 7 Generalise this routine so that there is a variable number of arms, M, stretching out from the origin and dividing the plane into equal segments. 8; the routine will have an integer parameter N.
1, which shows a line segment between points (-3, -1) == p(O) and (3, 2)==p(1) : the point (1,1) lies on the line asp(2/3) . Note that (3, 2) is a distance 3y5 from (-3, -1), whereas (1, 1) is a distance 2Y5 . From now on we omit the (/l) from the point vector. 1. At first sight it looks complicated, but on closer inspection it is seen to be simply a square, outside a square, outside a square, etc. The squares are getting successively smaller and they are rotating through a constant angle. In order to draw the diagram we need a technique that, when given a general square, draws a smaller internal square rotated through this fixed angle.
FOR I 1 TO NO LET ALPHA ALPHA + ADIF LET BETA = ALPHA*ACB RAB*COS ALPHA + D*COS BETA LET XPT LET YPT = RAB*SIN ALPHA - D*SIN BEH GO SUB l i re to NEXT I RETURN = = = = = = = = = = = It is evident from this example that drawing patterns is not so straightforward as it appears. 8 requires the mathematical backup of Euclid. Progressing through computer graphics, we shall discover more and more that it is essential to have at least an elementary knowledge of not only coordinate geometry but also calculus, algebra, Euclidean geometry and number theory.
Advanced Graphics with the Sinclair ZX Spectrum by Ian O. Angell, Brian J. Jones