Advanced Programming Guide

6.6 Vector Field Plots • 263> makevectors := proc( F, r1, r2 )> local v1, v2;>> # Generate the numerical grid> # of components of the vectors.> v1 := convert( F[1], ’gridpoints’, r1, r2,> args[4 .. nargs] );> v2 := convert( F[2], ’gridpoints’, r1, r2,> args[4 .. nargs] );>> # The domain information is contained in first> # two operands of v1. The function values in> # the 3rd components of v1 and v2.> [ v1[1], v1[2], v1[3], v2[3] ]> end proc:Here is the new version of vectorfieldplot.> vectorfieldplot := proc(F, r1, r2)> local R1, R2, m, n, a, b, v1, v2, dx, dy, v;>> v := makevectors( F, r1, r2, args[4..nargs] );> R1 := v[1]; R2 := v[2]; v1 := v[3]; v2 := v[4];>> n := nops(v1); m := nops(v1[1]);> a,b,dx,dy := domaininfo(R1, R2, m, n);>> generateplot(v1, v2, m, n, a, b, dx, dy);> end proc:Test this procedure.> p := (x,y) -> cos(x*y):> q := (x,y) -> sin(x*y):> vectorfieldplot( [p, q], 0..Pi, 0..Pi,> grid=[3, 4] );32.521.510.500.5 1 1.5 2 2.5 3 3.5All the versions of vectorfieldplot so far have scaled each arrowso that each vector fits into a single grid box. No overlapping of arrowsoccurs. However, the arrows still vary in length. Often this results in