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// zoom_iterate.asy
settings.outformat="pdf";
cd("../../../asy"); import jh; cd(""); define_texpreamble();
import graph;
path f = GENERIC_FCN_PLOT; // Shorter to type
real c = 3.1;
string OUTPUT_FN = "zoom_iterate%03d";
for (int i=0; i<4; ++i) {
picture pic; // Generate a new picture
size(pic, 3cm, 0); // Will be 3cm wide, scaling units to make it so
// Zoomed-in window spans c minus delta to c plus delta
real delta = 1/2^(i);
real xmin = c-delta; real xmax = c+delta;
// Find f(c) on f, and get f'(c) as a pair
real c_time = times(f, c)[0];
pair c_point = point(f,c_time);
pair d = dir(f, c_time);
real t_line_fcn(real x) { return (d.y/d.x)*(x-c_point.x) + c_point.y; }
path t_line = graph(t_line_fcn, xmin, xmax);
// Limits of f to show
real left_time = times(f, xmin)[0];
real right_time = times(f, xmax)[0];
path f_shown = subpath(f, left_time, right_time);
// Draw f and tangent line
transform f_trans = shift(0, 0.5*delta)*shift(0, -1*c_point.y); // Shift f close to axis
draw(pic, f_trans*f_shown, BOLD_COLOR);
draw(pic, f_trans*t_line, HIGHLIGHT_COLOR);
dotfactor = 3;
dot(pic, f_trans*c_point, HIGHLIGHT_COLOR);
// Just the x axis
real[] T = {xmin, xmax};
xaxis(pic, xmin=xmin, xmax=xmax,
RightTicks("%", T, Size=2pt));
labelx(pic, format("$c-%03f$",delta), xmin);
labelx(pic, format("$c+%03f$",delta), xmax);
// Produce PDF output file
shipout(format(OUTPUT_FN,i), pic);
}
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