By Ian O. Angell, Brian J. Jones

ISBN-10: 1349067652

ISBN-13: 9781349067657

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46 Advanced Graphics with the Sinclair ZX Spectrum vector addition PI + P2 = (XI + X2 , YI +Y2) , add the x-coordinates together, and the j-coordinates together . absolute value Ipi 1= y(xi +yi) is the distance of the point PI from the origin (this is also called the length, and the amplitude of the vector) . To deflne a line we first arbitrarily choose any two points on the line , again we call them PI == (XI. YI) and P2 == (X2 , Y2)' A general point p(/l) == (x, y) is given by the combination of scalar multiples and vector addition (1 - /l)JI + /lP2 for some real value of /l that is, the vector «(1 - /l) x XI + /l X X2, (1 - /l) X YI + /l x Y2).

The ball can be a pixel or character block , and the bat (s) should be controlled from the keyboard like the worm in the above program . You will find it useful to tum some of the program sections from this chapter into subroutines. In this chapter we have restricted ourselves to using the screen as a fixed piece of PAPER for patterns and games. To step up from pixel graphics to drawing pictures of real objects , we need commands that will relate the real world to our PAPER. In the following chapters we shall explore and develop the techniques needed to draw these real graphics pictures .

We know that (2, 0) lies on the first line because we used the value /l = -1/2 : our answer is correct if it also lies on the second line ; it does with A= 1/2. 3 Write a program that reads in data about two straight lines (it can be either in the form of equations , or in the base/directional vector form) and then calculates their point of intersection (if any). Two-dimensional Coordinate Geometry 51 Clipping By now you will have realised that it is impossible to PLOT, or DRAW, to a pixel (x, y) outside the graphics area, and thus we are limited to 0 ~ x ~ 255 and 0 ~ y ~ 175 .