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

By Ian O. Angell (auth.)

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1 The Coordinate Geometry ofThree-dimensional Space 47 Since we are working with REAL numbers, with all their attendant rounding error problems, we cannot check whether the dot product is zero, instead we see whether its value is sufficiently small to be considered zero (and what is meant by sufficiently small is left to the programmer). X = K . B,D,N,X,PT ARE "ECTßR~. :I:D AND A PLANE REAL B (]) ,D (]) ,N (3) ,PT (]) ,K READ (5, :I:) K, N ,B ,D DßT 1 =DßT (N , D) C IF LINE AND PLANE ARE PARALLEL THEN STßP.

MENUS When the programmer has decided to draw, drag or delete, the required information has to be input. Of course it is always possible for the program to read the information from a keyboard; however, this tends to be tedious and error-prone, and so another method has been devised - the menu. A list of possible choices is drawn on the screen (or it may be a permanent fixture on a pad); each choice has its own box, which must be 'ticked' by moving the cursor (or pen sensor) into this area before the correct alteration can be made to the diagram.

If this is not the case, then the lines are not coplanar. If all three are similar, that is, each is a multiple of every other, then the lines are parallel. Hence the question reduces to one of finding two non-similar equations (if possible), solving them for /1 and A and then checking that this solution also satisfies the remaining equation. 6 give 1 + 3(-2/3) on the left-hand side and 1 + 1(1/3) on the right, which are obviously unequal ; thus the lines do not intersect. 1 Program this problem, remembering that we are working with REAL numbers, so when it is time to check the solution with the remaining equation, we cannot expect equality; check only that the difference between the left- and right-hand sides is sufficiently smalI.

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