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
Sep 23, 2022
Importers
1 star
Illustrations for the proof of Green's theoremGreen's theorem and polygonal areaChampionship probabiltiesCorrelationA Taylor series about π/4\pi/4π/4Classification of 2D linear systems via trace and determinantDisks for a solid of revolutionTracing a path on a sphereFunctions of two variablesPartial derivativesDijkstra's algorithm on an RGGGradient ascentTangent plane to a level surfaceA strange discontinuityHills and valleysThe definition of ⇒Polar CoordinatesParametric region generatorParametric Plot 2DContour plotsThe Kings Problem
Level surfaces
show_x3d([
create_level_surface(
(x, y, z) => x ** 2 + y ** 2 + z ** 2 - 4,
[
[-2, 2],
[-2, 2],
[-2, 2]
]
)
])
show_x3d([
// A scarlet hyperboloid
create_level_surface(
(x, y, z) => x ** 2 - y ** 2 + z ** 2 - 1,
[
[-2, 2],
[-2, 2],
[-2, 2]
],
{ color: d3.color("red").darker(2) }
),
// A gray sphere
create_level_surface(
(x, y, z) => x ** 2 + y ** 2 + z ** 2 - 2,
[
[-1.5, 1.5],
[-1.5, 1.5],
[-1.5, 1.5]
],
{ color: "gray" }
)
])
show_x3d([
create_level_surface(
(x, y, z) => x ** 6 + y ** 6 + z ** 6 - 1,
[
[-1, 1],
[-1, 1],
[-1, 1]
],
{ show_surface_mesh: true }
)
])
// (x, y, z) => (x ** 4 - x ** 2 + y ** 2) ** 2 + z ** 2 - 1 / 25
show_x3d(
[
create_level_surface(
(x, y, z) => (x ** 4 - x ** 2 + y ** 2) ** 2 + z ** 2 - 1 / 25,
[
[-1.2, 1.2],
[-0.7, 0.7],
[-0.2, 0.2]
],
{ show_surface_mesh: true, Nx: 32, Ny: 16, Nz: 8 }
)
],
{
viewpoint: {
position: "2.411474665489146 1.379943295458121 2.0661348794365195",
orientation:
"0.2632114701336716 0.419218026686788 0.8688935309293689,2.272917153903575"
}
}
)
function create_level_surface(f, domain, opts = {}) {
let {
Nx = 30,
Ny = 30,
Nz = 30,
color = "#40bfbf",
transparency = 0,
show_surface_mesh = false
} = opts;
// The following use of surfaceNets was entirely inspired by Ricky Reusser's notebook:
// https://observablehq.com/@rreusser/mathematical-easter-egg-coloring
let resolution = [Nx, Ny, Nz];
let b = domain.map((b, i) => [b[0], (b[1] - b[0]) / (resolution[i] - 1)]);
let gridValues = ndarrayProxy(resolution, (i, j, k) =>
f(b[0][0] + i * b[0][1], b[1][0] + j * b[1][1], b[2][0] + k * b[2][1])
);
let mesh = surfaceNets(gridValues);
for (var i = 0; i < mesh.positions.length; i++) {
const p = mesh.positions[i];
p[0] = b[0][0] + b[0][1] * p[0];
p[1] = b[1][0] + b[1][1] * p[1];
p[2] = b[2][0] + b[2][1] * p[2];
}
let container = d3.create("transform");
if (opts.id) {
container.attr("id", opts.id);
}
if (opts.class) {
container.attr("class", opts.class);
}
mesh.cells.forEach((pt) => pt.push(pt[0]));
let face_index_string = mesh.cells.join(" -1 ").toString();
let coord_string = mesh.positions.toString();
let shape = container.append("shape");
let appearance = shape.append("appearance");
if (opts.sortKey || opts.sortKey === 0) {
appearance.attr("sortKey", opts.sortKey);
}
let material = appearance.append("material");
material.attr("diffuseColor", color);
if (opts.transparency) {
material.attr("transparency", opts.transparency);
}
let indexedFaceSet = shape
.append("indexedFaceset")
.attr("solid", false)
.attr("coordIndex", face_index_string)
.attr("creaseAngle", 3.14);
indexedFaceSet.append("coordinate").attr("point", coord_string);
if (show_surface_mesh) {
let surface_mesh = container.append("shape");
surface_mesh
.append("appearance")
.append("material")
.attr("transparency", 0.4);
surface_mesh
.append("IndexedLineSet")
.attr("coordIndex", face_index_string)
.append("Coordinate")
.attr("point", coord_string);
}
let xs = mesh.positions.map((pt) => pt[0]);
let xmin = d3.min(xs);
let xmax = d3.max(xs);
let ys = mesh.positions.map((pt) => pt[1]);
let ymin = d3.min(ys);
let ymax = d3.max(ys);
let zs = mesh.positions.map((pt) => pt[2]);
let zmin = d3.min(zs);
let zmax = d3.max(zs);
let node = container.node();
node.extent = { xmin, xmax, ymin, ymax, zmin, zmax };
return node;
}
surfaceNets = require("https://bundle.run/surface-nets@1.0.2")
ndarrayProxy = require("https://bundle.run/ndarray-proxy@1.0.0")
import { show_x3d, style } from "@mcmcclur/plotx3d"
import {
rotation_vector,
normalize,
path_list_to_indexString,
path_list_to_coordString
} from '@mcmcclur/x3dom-utilities'
style
Purpose-built for displays of data
Observable is your go-to platform for exploring data and creating expressive data visualizations. Use reactive JavaScript notebooks for prototyping and a collaborative canvas for visual data exploration and dashboard creation.
