Quiver¶

use ironlab::prelude::*;

use crate::fields::*;

pub const TITLE: &str = "Quiver";
pub const DESCRIPTION: &str = "Arrows showing the gradient of the Julia field on a coarse grid, drawn over isolines \
     of the field on a fine grid. The arrows point uphill and cross the isolines at right angles.";

pub fn figure() -> Figure {
    // A fine grid gives smooth isolines; a coarse grid keeps the arrows far enough apart to read.
    let (x_fine, y_fine, z_fine) = julia_grid(121);
    let (x, y, z) = julia_grid(21);
    let (dzdx, dzdy) = gradient(&x, &y, &z);
    // quiver takes the position of every arrow, so expand the grid vectors to the coordinates of every node.
    let (xx, yy) = meshgrid(&x, &y);

    let mut fig = Figure::new()
        .size_mm(120.0, 100.0)
        .title(r"Gradient of $\ln(1 + |z_3|)$");
    let mut ax = fig.axes(0, 0);
    ax.contour(&x_fine, &y_fine, &z_fine).levels(12);
    ax.quiver(xx.values(), yy.values(), dzdx.values(), dzdy.values())
        .color(Color::BLACK)
        .line_width(0.5)
        .display_name(r"$\nabla f$");
    ax.xlabel("$x$").ylabel("$y$");
    fig
}