Colourbar shared by a row¶

use ironlab::prelude::*;

pub const TITLE: &str = "Colourbar shared by a row";
pub const DESCRIPTION: &str = "The temperature of a thin aluminium plate at three times after a laser pulse heats a \
     spot 2 mm wide at its centre by 400 K. Heat diffuses outward with the diffusivity of aluminium, so the spot \
     widens and its peak falls as the energy spreads over a larger area. The three images name one colour scale, \
     fixed from 20 to 100 °C, and one horizontal colourbar in a panel spanning the row beneath them shows it; the \
     bar and its key together are half as long as the row of three plot boxes, centred beneath it, and the title of \
     the scale lies along the bar, below its labels. The first frame is hotter than the top of \
     the scale at its centre, so values above 100 °C are drawn in cyan rather than clipped to the last colour, and \
     the key beside the bar says so.";

/// The thermal diffusivity of aluminium, in mm²/s.
const DIFFUSIVITY_MM2_PER_S: f64 = 97.0;

/// The standard deviation of the Gaussian spot that the pulse heats, in millimetres.
const SPOT_MM: f64 = 2.0;

/// The temperature rise at the centre of the spot just after the pulse, in kelvin.
const PEAK_RISE_K: f64 = 400.0;

/// The temperature of the plate before the pulse, in degrees Celsius.
const AMBIENT_C: f64 = 20.0;

/// The number of samples along each side of the field.
const SAMPLES: usize = 121;

/// The times after the pulse at which the plate is shown, in seconds.
const TIMES_S: [f64; 3] = [0.05, 0.2, 0.5];

/// Returns the temperature, in degrees Celsius, at a distance `r` from the centre of the spot, in millimetres, a
/// time `t` after the pulse, in seconds.
///
/// A Gaussian spot in a thin plate whose faces lose no heat stays Gaussian under diffusion: its variance grows by
/// 2αt and, because the energy is conserved, its peak falls by the same factor.
fn temperature(r: f64, t: f64) -> f64 {
    let variance = SPOT_MM * SPOT_MM + 2.0 * DIFFUSIVITY_MM2_PER_S * t;
    AMBIENT_C
        + PEAK_RISE_K * SPOT_MM * SPOT_MM / variance * (-r * r / (2.0 * variance)).exp()
}

pub fn figure() -> Figure {
    let x = linspace(-20.0, 20.0, SAMPLES);

    let mut fig = Figure::new()
        .size_mm(160.0, 84.0)
        .tiles(2, 3)
        .fit_row(1)
        .title("Temperature of an aluminium plate after a laser pulse")
        .tag("image")
        .tag("subplots")
        .tag("color-scale")
        .tag("colorbar")
        .tag("out-of-range")
        .tag("aspect")
        .tag("physics")
        .parameter("dimensionality", "2D")
        .parameter("artists", 3)
        .parameter("data_points", 43_923)
        .parameter("has_legend", false);
    // One scale for the three times, so a colour means one temperature in every frame.
    let shared = fig
        .color_scale()
        .colormap(Colormap::Inferno)
        .limits(AMBIENT_C, 100.0)
        .above(Color::rgb(0.3, 0.85, 0.95))
        .show_key(ColorScaleKey::Above)
        .title("Temperature (°C)")
        .id();

    for (col, t) in TIMES_S.into_iter().enumerate() {
        let field = Matrix::from_fn(SAMPLES, SAMPLES, |row, col| {
            temperature(x[col].hypot(x[row]), t)
        });
        let mut ax = fig.axes(0, col as u32);
        ax.scalar_image(&field)
            .pixel_columns(x[0], x[SAMPLES - 1])
            .pixel_rows(x[0], x[SAMPLES - 1])
            .color_scale(shared);
        ax.title(format!("$t = {t}$ s"))
            .xlabel("$x$ (mm)")
            .aspect(Aspect::Equal);
        if col == 0 {
            ax.ylabel("$y$ (mm)");
        }
    }
    // The bar lies along a panel spanning the row beneath the images, whose height fits the bar, its ticks and its
    // title.
    fig.panel_span(1, 0, 1, 3)
        .colorbar(shared)
        .orientation(ColorbarOrientation::Horizontal);
    fig
}