Three-dimensional quiver¶
Upward unit normals of the Julia field's surface, drawn as arrows from the nodes of a coarse grid over the surface itself.
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Source¶
The figure is built by the following code. Its data comes from the functions on the data helpers page.
use ironlab::prelude::*;
use crate::fields::*;
pub const TITLE: &str = "Three-dimensional quiver";
pub const DESCRIPTION: &str = "Upward unit normals of the Julia field's surface, drawn as arrows from the nodes of a \
coarse grid over the surface itself.";
pub fn figure() -> Figure {
let (x, y, z) = julia_grid(15);
let (nx, ny, nz) = surface_normals(&x, &y, &z);
// quiver3 takes the position of every arrow, so expand the grid vectors to the coordinates of every node; each
// arrow starts on the surface, at height z.
let (xx, yy) = meshgrid(&x, &y);
let mut fig = Figure::new()
.size_mm(160.0, 100.0)
.title(r"Normals of the surface of $\ln(1 + |z_3|)$")
.label("quiver")
.label("surface")
.label("gradient")
.label("overlay")
.parameter("dimensionality", "3D")
.parameter("artists", 2)
.parameter("data_points", 1605)
.parameter("has_legend", false);
let mut ax = fig.axes3(0, 0);
ax.surf(&x, &y, &z).edge_width(0.25);
ax.quiver3(
xx.values(),
yy.values(),
z.values(),
nx.values(),
ny.values(),
nz.values(),
)
.color(Color::BLACK)
.line_width(0.5)
.display_name(r"$\hat{n}$");
ax.xlabel("$x$")
.ylabel("$y$")
.zlabel(r"$\ln(1 + |z_3|)$")
.view(-30.0, 40.0);
fig
}