By Ian O. Angell, G.H. Griffith

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Before introducing a second way of representing a line (which, as we shall see, is more useful in computer graphics) two operations on vectors, scalar multiple and addition, must be defmed along with the magnitude or modulus of a vector. Y1 +y2) by vector addition. The modulus of a vector p 1 is defined as the distance of the point (x 1, y 1) from the origin, denoted I p 1 I lp1l = y(x1 2 + Y1 2 ) To define a line we choose any two fixed points on the line which we again call p 1 = (x 1 , y 1) and p2 = (x2 , Y2 ).

The list data structure is a very powerful tool, and has wide ranging applications in computer science. For our needs, however, we will concentrate on a restricted form of a list called a stack of integers. The information part of elements in the list are limited to INTEGERs, and these can only be added to and deleted from the front of the list: respectively the so-called push and pop routines. One method of implementing a stack is to have an array ISTACK (say) holding integer information values for each link in the list and a variable IPOINT, initially the null pointer zero, which points to an element in the array: the top of the stack.

A path in a graph is a consecutive sequence of edges- for example, the path {i, j, k, 1} consists of the three edges {i, j}, {j, k}, {k, /}. A network is a graph that does not contain a cycle or loop - that is, there is no path, other than the trivial path {i, i}, starting and ending at the same node. 5 is therefore a network: if an extra edge {5, 2} (say) had been added then there would be cycles, such as {2, 5, 2} and {2, 4, 5, 2}, and the graph would no longer be a network. We implement a graph by defining an array LIST of integers.

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