Add interpolation grid generators
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@ -6,6 +6,7 @@ members = [
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"euler",
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"maxwell",
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"shallow_water",
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"gridgeneration",
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]
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default-members = ["sbp", "euler", "maxwell", "shallow_water"]
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@ -0,0 +1,14 @@
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[package]
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name = "gridgeneration"
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version = "0.1.0"
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authors = ["Magnus Ulimoen <magnus@ulimoen.dev>"]
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edition = "2018"
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[dependencies]
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ndarray = { version = "0.13.1", default-features = false }
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plotters = { version = "0.3.0", default-features = false, features = ["svg_backend", "line_series", "point_series"] }
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sbp = { path = "../sbp" }
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json5 = { version = "0.2.8", optional = true }
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[features]
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serde = ["sbp/serde1", "json5"]
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@ -0,0 +1,125 @@
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use ndarray::Array2;
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pub use sbp::{consts::*, grid::Grid, Float};
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pub fn unit(ny: usize, nx: usize) -> Grid {
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let x = Array2::from_shape_fn((ny, nx), |(_j, i)| i as Float / (nx - 1) as Float);
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let y = Array2::from_shape_fn((ny, nx), |(j, _i)| j as Float / (ny - 1) as Float);
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Grid::new(x, y).unwrap()
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}
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pub fn shell(ny: usize, nx: usize, mut inner: Float, mut outer: Float) -> Grid {
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let mut unit = unit(ny, nx);
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#[allow(unused)]
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enum Mode {
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Log,
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Exp,
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Normal,
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}
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let mode = Mode::Log;
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match mode {
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Mode::Exp => {
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inner = inner.exp();
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outer = outer.exp();
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}
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Mode::Log => {
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inner = inner.ln();
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outer = outer.ln();
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}
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_ => {}
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}
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let (mut gx, mut gy) = unit.components();
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gx.iter_mut().zip(gy.iter_mut()).for_each(|(x, y)| {
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let mut r = (*x) * (outer - inner) + inner;
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match mode {
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Mode::Exp => {
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r = r.ln();
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}
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Mode::Log => {
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r = r.exp();
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}
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_ => {}
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}
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let theta = *y * 2.0 * PI;
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*x = r * theta.cos();
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*y = r * theta.sin();
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});
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unit
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}
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pub fn vertical_interpolation(jlen: usize, north: &[Float], south: &[Float]) -> Grid {
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let ilen = north.len();
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assert_eq!(north.len(), south.len());
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let mut grid = unit(jlen, ilen);
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for j in 0..jlen {
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for i in 0..ilen {
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let y = grid.y()[(j, i)];
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grid.y_mut()[(j, i)] = (north[i] - south[i]) * y + south[i];
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}
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}
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grid
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}
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pub fn horizontal_interpolation(ilen: usize, east: &[Float], west: &[Float]) -> Grid {
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let jlen = east.len();
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assert_eq!(east.len(), west.len());
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let mut grid = unit(jlen, ilen);
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for j in 0..jlen {
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for i in 0..ilen {
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let x = grid.x()[(j, i)];
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grid.x_mut()[(j, i)] = (east[j] - west[j]) * x + west[j];
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}
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}
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grid
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}
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pub fn horizontal_interpolation_dual(
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ilen: usize,
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east: (&[Float], &[Float]),
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west: (&[Float], &[Float]),
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) -> Grid {
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let jlen = east.0.len();
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assert_eq!(east.0.len(), east.1.len());
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assert_eq!(east.0.len(), west.0.len());
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assert_eq!(east.0.len(), west.1.len());
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let mut grid = unit(jlen, ilen);
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for j in 0..jlen {
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for i in 0..ilen {
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let x = grid.x()[(j, i)];
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grid.x_mut()[(j, i)] = (east.1[j] - west.1[j]) * x + west.1[j];
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grid.y_mut()[(j, i)] = (east.0[j] - west.0[j]) * x + west.0[j];
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}
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}
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grid
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}
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/// [east] : fn([0, 1]) -> (y, x)
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/// [west] : fn([0, 1]) -> (y, x)
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pub fn horizontal_interpolation_dual2(
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ilen: usize,
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jlen: usize,
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east: impl Fn(Float) -> (Float, Float),
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west: impl Fn(Float) -> (Float, Float),
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) -> Grid {
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let mut grid = unit(jlen, ilen);
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for j in 0..jlen {
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for i in 0..ilen {
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let x = grid.x()[(j, i)];
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let y = grid.y()[(j, i)];
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let east = east(y);
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let west = west(y);
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grid.x_mut()[(j, i)] = (east.1 - west.1) * x + west.1;
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grid.y_mut()[(j, i)] = (east.0 - west.0) * x + west.0;
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}
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}
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grid
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}
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@ -0,0 +1,145 @@
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#![allow(unused)]
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use gridgeneration::*;
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use plotters::prelude::*;
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fn main() {
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// let grid = Grid::unit(10, 11);
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// let grid = shell(30, 21, 0.1, 3.1);
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let grid = {
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let ybot = (0..100)
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.map(|x| (x as Float / 30.0).sin())
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.collect::<Vec<_>>();
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let ytop = (0..100)
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.map(|x| 2.5 + (x as Float / 10.0).sin())
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.collect::<Vec<_>>();
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// vertical_interpolation(10, &ytop, &ybot)
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// horizontal_interpolation(10, &ytop, &ybot)
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/*
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horizontal_interpolation_dual(
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30,
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(&[0.0, 0.0, 1.0, 3.0], &[0.0, 2.0, 4.0, 6.0]),
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(&[3.0, 5.0, 6.0, 7.0], &[0.0, 2.0, 3.0, 10.0]),
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)
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*/
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/*
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horizontal_interpolation_dual2(
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30,
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40,
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move |t| ((t * 3.0).sin(), t + 0.2),
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move |t| ((5.0 * t).sin() + 2.5, t),
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)
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*/
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horizontal_interpolation_dual2(
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30,
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40,
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move |t| (2.0 * t * std::f64::consts::PI).sin_cos(),
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move |t| {
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let (y, x) = (2.0 * t * std::f64::consts::PI).sin_cos();
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(0.1 * y, 0.1 * x)
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},
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)
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};
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draw_grid(&grid, "grid.svg");
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let grid = horizontal_interpolation_dual2(
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200,
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200,
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move |t| {
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let ts = [0.05, 0.25, 0.75, 0.95];
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if t < ts[0] {
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let t = t / (ts[0] - 0.0);
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(t, 5.0)
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} else if t < ts[1] {
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let t = (t - ts[0]) / (ts[1] - ts[0]);
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(1.0, 5.0 - 5.0 * t)
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} else if t < ts[2] {
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let t = (t - ts[1]) / (ts[2] - ts[1]);
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(std::f64::consts::PI * (t + 0.5)).sin_cos()
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} else if t < ts[3] {
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let t = (t - ts[2]) / (ts[3] - ts[2]);
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(-1.0, 5.0 * t)
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} else {
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let t = (t - ts[3]) / (1.0 - ts[3]);
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(-1.0 + t, 5.0)
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}
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},
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move |t| {
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let (y, x) = (2.0 * t * std::f64::consts::PI).sin_cos();
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(0.2 * y, 0.2 * x)
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},
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);
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draw_grid(&grid, "ctype.svg");
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#[cfg(feature = "serde")]
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println!("{}", json5::to_string(&grid).unwrap());
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}
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fn linspace(range: std::ops::Range<Float>, steps: usize) -> Vec<Float> {
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let start = range.start;
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let end = range.end;
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let dx = (end - start) / (steps - 1) as Float;
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(0..steps).map(|i| i as Float * dx).collect()
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}
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fn draw_grid(grid: &Grid, name: &str) {
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let drawing_area = SVGBackend::new(name, (1000, 1000)).into_drawing_area();
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drawing_area.fill(&WHITE).unwrap();
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let x_minmax = grid
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.x()
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.iter()
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.fold((Float::INFINITY, -Float::INFINITY), |(min, max), &x| {
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(min.min(x), max.max(x))
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});
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let y_minmax = grid
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.y()
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.iter()
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.fold((Float::INFINITY, -Float::INFINITY), |(min, max), &y| {
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(min.min(y), max.max(y))
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});
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let mut chart = ChartBuilder::on(&drawing_area)
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.x_label_area_size(40)
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.y_label_area_size(40)
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.build_cartesian_2d(x_minmax.0..x_minmax.1, y_minmax.0..y_minmax.1)
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.unwrap();
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chart
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.configure_mesh()
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.x_desc("x")
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.y_desc("y")
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.disable_mesh()
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.draw()
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.unwrap();
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let style = &BLACK.stroke_width(1);
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for axes in &[ndarray::Axis(1), ndarray::Axis(0)] {
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for (linex, liney) in grid.x().axis_iter(*axes).zip(grid.y().axis_iter(*axes)) {
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chart
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.draw_series(LineSeries::new(
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linex.iter().zip(&liney).map(|(&x, &y)| (x, y)),
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style.clone(),
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))
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.unwrap();
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}
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}
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/*
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let coord = |idx| (grid.x()[idx], grid.y()[idx]);
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let zero = coord((0, 0));
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let up = coord((1, 0));
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let right = coord((0, 1));
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chart
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.draw_series(PointSeries::of_element(
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[zero].iter().copied(),
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5,
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ShapeStyle::from(&RED).filled(),
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&|coord, size, style| {
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EmptyElement::at(coord)
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+ Circle::new((0, 0), size, style)
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+ Text::new("η", (1, 1), ("arial", 10))
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},
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))
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.unwrap();
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*/
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}
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