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computer s system clock. The system dock keeps track of the current time in seconds. The time ( > function defined in the header file <time. h> returns the current time as an unsigned integer. This then can be used as the seed for the rand ( > function.

EXAMPLE 3.22 Generating Pseudo-Random Numbers #include #include #include <iostream.h> <stdlib.h> <time.h>

Polyhedra A polyhedron is a solid bounded by plane (flat) surfaces only. Thus, the pyramid and cube are polyhedrons. The cone, cylinder, and sphere are not polyhedra, since each has a curved surface. The bounding surfaces of the polyhedron are its faces; the lines of intersection of the faces are its edges, and the points of intersection of its edges are its vertices. A diagonal of a polyhedron joins two vertices not in the same face. Thus, the polyhedron shown in Fig. 17-1 has six faces. Two of them are triangles (ABC and CFG), and the other four are quadrilaterals. Note AF is a diagonal of the polyhedron. The shaded polygon HJKL is a section of the polyhedron formed by the intersection of the solid and a plane passing through it.

main0 -t unsigned seed = time(NULL); tout << "seed = ' CC seed -CC endl; srand(seed); for (int i = 0; i < 8; i++) tout << rand() -CC endl;

Fig. 17-1

seed = ~808248257 1$7736%330 352899587 1443923328 , 1 8 5 7 4 2 3 2 8 9

Note: This problem can be solved more efficiently using arrays. (c)

The angle between any two intersecting faces is a dihedral angle. The angle between the covers of an open book is a dihedral angle. As the book is opened wider, the dihedral angle grows from one that is acute to one that is right, obtuse, and then straight. The dihedral angle can be measured by measuring the plane angle between two lines, one in each face, and in a plane perpendicular to the intersection between the faces.

On the first run, the time ( > function returns the integer 808,148,157 which is used to seed the random number generator. The second run is done 3 seconds later, so the time ( > function returns the integer 808,148,160 which generates a completely different sequence.

A prism (Fig. 17-2) is a polyhedron two of whose faces are parallel polygons, and whose remaining faces are parallelograms. The bases of a prism are its parallel polygons. These may have any number of sides. The lateral (sides) faces are the parallelograms. The distance between the two bases is h; it is measured along a line at right angles to both bases. A right prism is a prism whose lateral faces are rectangles. The distance h is the height of any of the lateral faces.

In many simulation programs, one needs to generate random integers that are uniformly distributed in a given range. The next example illustrates how to do that.

Fig. 17-2

EXAMPLE 3.23 Generating Pseudo-Random Numbers #include #include #include <iostream.h> <stdlib.h> <time.h>

main0 1 unsigned seed = time(NULL); tout << "seed = 'I CC seed -X endl; srand(seed); int min, max; tout << "Enter minimum and maximum: 'I; // lowest and highest numbers tin >> min >> max; // number of numbers in range int range = max - min + 1; for (int i = 0; i < 20; i++) { int r = rand()/lOO%range + min; tout c-c r << I II; > tout K-C endl; seed = 808237677 Enter minimum and maximum: 1 3.00 85 57 1 10 5 73 81 43 46 42 17 44 48 3 3 7 4 41 4 30 6 8 seed = 808238101 Enter minimum a& maximum: 22 66 63 29 56 22 53 57 341 56 43 36 6 2 30 $1 57 26.61

Fig. 17-3

5 9 26 28