I'm a professor of mathematics at the University of North Carolina Asheville. I've also done a fair amount of consulting work over the years focusing on scientific and data visualization.
I'm happy to be part of the first Observable Ambassador's cohort.
Published
Edited
Nov 25, 2020
Importers
7 stars
function make_plot(input) {
let F, xp_parsed, xp, yp_parsed, yp;
d3.select(parse_warning).html('');
try {
try {
xp_parsed = math.compile(input.xp);
xp = (x, y) => xp_parsed.evaluate({ x: x, y: y });
yp_parsed = math.compile(input.yp);
yp = (x, y) => yp_parsed.evaluate({ x: x, y: y });
F = ([x, y]) => [xp(x, y), yp(x, y)];
} catch (e1) {
d3.select(parse_warning).html(
'<span style="color:red">Parse error</span>'
);
F = () => [0, 0];
}
F([1, 2]);
} catch (e2) {
F = () => [0, 0];
let message;
if (e2.toString().indexOf('not a function') != -1) {
message =
'Parse error, consider using explicit multiplication - for example, write y*(t+1), instead of y(t+1).';
} else {
message = e2;
}
d3.select(parse_warning).html(
`<span style="color:green">${message}</span>`
);
F = () => [0, 0];
}
let xmin = input.xmin;
let xmax = input.xmax;
let ymin = input.ymin;
let ymax = input.ymax;
let aspect = (ymax - ymin) / (xmax - xmin);
let w = 0.9 * width;
let h = aspect * w;
let pad = 35;
let xScale = d3
.scaleLinear()
.domain([xmin, xmax])
.range([pad, w - pad]);
let yScale = d3
.scaleLinear()
.domain([ymin, ymax])
.range([h - pad, pad]);
let pts_to_path = d3
.line()
.x(function(d) {
return xScale(d[0]);
})
.y(function(d) {
return yScale(d[1]);
});
let dx = (xmax - xmin) / 10;
let dy = dx;
let grid = d3
.range(ymin + dy, ymax, dy)
.map(y => d3.range(xmin + dx, xmax, dx).map(x => [x, y]));
grid = grid.reduce(function(accumulated, currentValue) {
return accumulated.concat(currentValue);
}, []);
let svg = d3
.create('svg')
.attr('width', w)
.attr('height', h)
.style('background-color', 'white');
let arrow_group = svg.append('g');
arrow_group // from http://thenewcode.com/1068/Making-Arrows-in-SVG
.append('svg:defs')
.append('marker')
.attr('id', 'arrowhead')
.attr("markerWidth", 10)
.attr("markerHeight", 7)
.attr("refX", 0)
.attr("refY", 3.5)
.attr("orient", "auto")
.append('polygon')
.attr('points', '0 0, 10 3.5, 0 7');
arrow_group
.selectAll('path')
.data(grid)
.join('path')
.attr('d', d => pts_to_path([d, add(d, mul(0.1, F(d)))]))
.style('stroke', 'black')
.style('stroke-width', 0.8)
.style('fill', 'none')
.attr("marker-end", function(d) {
let Fd = F(d);
let mag2 = Fd[0] ** 2 + Fd[1] ** 2;
if (mag2 > 0.01) {
return "url(#arrowhead)";
} else {
return null;
}
});
function draw_solution([x0, y0]) {
let pts = rk4(F, [x0, y0], 0, -10, 10, 500);
svg.selectAll('.solution').remove();
let solution_group = svg.append('g').attr('class', 'solution');
solution_group
.append('path')
.attr('class', 'solution')
.attr('d', pts_to_path(pts))
.style('stroke', '#1f77b4')
.style('stroke-width', 4)
.style('fill', 'none');
solution_group
.append('circle')
.attr('cx', xScale(x0))
.attr('cy', yScale(y0))
.attr('r', 5)
.attr('fill', '#2ca02c')
.attr('stroke', 'black');
}
// draw_solution();
let tracking = true;
svg
.on('mousemove', function(evt) {
if (tracking) {
let [i, j] = d3.pointer(evt);
let [x0, y0] = [xScale.invert(i), yScale.invert(j)];
draw_solution([x0, y0]);
}
})
.on('mouseleave', function() {
if (tracking) {
svg.selectAll('.solution').remove();
}
})
.on('click', function(evt) {
if (tracking) {
tracking = false;
} else {
tracking = true;
let [i, j] = d3.pointer(evt);
let [x0, y0] = [xScale.invert(i), yScale.invert(j)];
draw_solution([x0, y0]);
}
});
svg
.append('g')
.attr('transform', `translate(0, ${h - pad})`)
.call(d3.axisBottom(xScale));
svg
.append('g')
.attr('transform', `translate(${pad})`)
.call(d3.axisLeft(yScale));
return svg.node();
}
examples = {
let examples = new Map();
examples.set('identity', {
xp: 'x',
yp: 'y',
xmin: -2,
xmax: 2,
ymin: -2,
ymax: 2
});
examples.set('harmonic', {
xp: 'y',
yp: '-x',
xmin: -2,
xmax: 2,
ymin: -2,
ymax: 2
});
examples.set('spiral_in', {
xp: 'y-x/2',
yp: '-x-y/2',
xmin: -2,
xmax: 2,
ymin: -2,
ymax: 2
});
examples.set('damped_pendulum', {
xp: 'y',
yp: '-sin(x)-y',
xmin: -2,
xmax: 2,
ymin: -2,
ymax: 2
});
examples.set('lotka-volterra', {
xp: 'x-x*y',
yp: '-y+x*y',
xmin: -0.2,
xmax: 3,
ymin: -0.2,
ymax: 3
});
examples.set('circle_limit', {
xp: 'y+x*(1-x^2-y^2)',
yp: '-x+y*(1-x^2-y^2)',
xmin: -1.5,
xmax: 1.5,
ymin: -1.5,
ymax: 1.5
});
return examples;
}
import { rk4, add, mul } from '@mcmcclur/runge-kutta-for-systems-of-odes'
math = require('mathjs@7.6.0')
d3 = require('d3-selection@2', 'd3-scale@3', 'd3-shape@2', 'd3-axis@2', 'd3-array@2')
_ = require('lodash')
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