BEGIN {# conformal modulus    mod = 1    nx = 51;# maximal aspect ratio    a = 2.0;    PI = 3.14159265357989;# step by X (uniform)    dx = 1.0 / (nx - 1);# initial step by Y    dy0 = dx * mod;}{    y = 0.0;    for (j = 1; y <= 1.0; ++j) {	x = 0.0;	for (i = 1; i <= nx; ++i) {	    printf("%.10g %.10g\n", x, y);	    x += dx;	}	s = sin(PI * y);	dy = dy0 * (1.0 + (a - 1.0) * s * s);	y += dy;    }    printf("## %d x %d\n", nx, j - 1);}