| license: apache2.0 | |
| height: 673 | |
| border: no |
http://bl.ocks.org/jackielii/d3523c9116e5d3b45ec3d8aa76fb1f57
Sparse data contouring with d3-contour
Data from http://www.bgs.ac.uk/products/geophysics/aeromagneticRegional.html
Steps:
| [[417244,398355,487], | |
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| ] |
| <!DOCTYPE html> | |
| <h1>Original Points</h1> | |
| <svg id="originalpoints" width="960" height="673" stroke="#fff" stroke-width="0.5"></svg> | |
| <h1>Step 1: delaunay triagulation: find the smallest triangle of the closest 3 points</h1> | |
| <canvas id="s3" width="960" height="673"></canvas> | |
| <h1>Step 2: pick a regular grid and interpolate the grid point</h1> | |
| <p>grid point is interpolated from the triangle that contains the point using "Berycentric Interpolation" algorithm</p> | |
| <svg id="grid" width="960" height="673" stroke="#fff" stroke-width="0.5"></svg> | |
| <h1>Step 3: Contour plot using "marching squares" algorithm</h1> | |
| <svg id="contourplot" width="960" height="673" stroke="#fff" stroke-width="0.5"></svg> | |
| <script src="https://d3js.org/d3.v4.min.js"></script> | |
| <script src="https://d3js.org/d3-hsv.v0.1.min.js"></script> | |
| <script src="https://d3js.org/d3-contour.v1.min.js"></script> | |
| <script src="https://unpkg.com/faster-delaunay@1.0.0/delaunay.js"></script> | |
| <script src="https://unpkg.com/lodash/lodash.min.js"></script> | |
| <script> | |
| // grided points | |
| d3.json("ca55.json", function (error, aero) { | |
| if (error) throw error; | |
| var i0 = d3.interpolateHsvLong(d3.hsv(120, 1, 0.65), d3.hsv(60, 1, 0.90)), | |
| i1 = d3.interpolateHsvLong(d3.hsv(60, 1, 0.90), d3.hsv(0, 0, 0.95)), | |
| interpolateTerrain = function (t) { return t < 0.5 ? i0(t * 2) : i1((t - 0.5) * 2); }; | |
| let triangles; | |
| const xmin = _.minBy(aero, getx)[0]; | |
| const ymin = _.minBy(aero, gety)[1]; | |
| const zmin = _.minBy(aero, getz)[2]; | |
| const xmax = _.maxBy(aero, getx)[0]; | |
| const ymax = _.maxBy(aero, gety)[1]; | |
| const zmax = _.maxBy(aero, getz)[2]; | |
| // contour | |
| (function () { | |
| const svg = d3.select("#contourplot"), | |
| width = +svg.attr("width"), | |
| height = +svg.attr("height"); | |
| const x = d3.scaleLinear().range([0, width]).domain([xmin, xmax]), | |
| y = d3.scaleLinear().range([0, height]).domain([ymin, ymax]), | |
| color = d3.scaleSequential(interpolateTerrain).domain([zmin, zmax]); | |
| const gridCellSize = 15 // unit: pixel | |
| const levels = 10; // number of contour levels | |
| const ib = Math.trunc(width / gridCellSize); | |
| const jb = Math.trunc(height / gridCellSize); | |
| triangles = new Delaunay(aero).triangulate(); | |
| console.time("generateData"); | |
| // generate a regular grid | |
| const data = new Float64Array(ib * jb); | |
| const gridData = []; | |
| for (let i = 0; i < ib; i++) { | |
| for (let j = 0; j < jb; j++) { | |
| const p = [x.invert((i + 0.5) * gridCellSize), y.invert((j + 0.5) * gridCellSize)]; | |
| let value; | |
| for (let i = 0; i < triangles.length; i += 3) { | |
| const param = contains(triangles[i], triangles[i + 1], triangles[i + 2], p); | |
| if (param) { | |
| const [u, v] = param | |
| value = (1 - u - v) * triangles[i][2] + u * triangles[i][2] + v * triangles[i][2] | |
| break; | |
| } | |
| } | |
| if (value == null) { | |
| // FIXME: should try to find the closest point? | |
| value = zmin | |
| } | |
| data[j * ib + i] = value; | |
| gridData[j * ib + i] = p.concat(value); | |
| } | |
| } | |
| console.timeEnd("generateData"); | |
| console.log("data size", data.length); | |
| svg.selectAll("path") | |
| .data(d3.contours() | |
| .size([ib, jb]) | |
| .thresholds(d3.range(zmin, zmax, (zmax - zmin) / levels)) | |
| (data)) | |
| .enter().append("path") | |
| .attr("d", d3.geoPath(d3.geoIdentity().scale(width / ib))) | |
| .attr("fill", function (d) { return color(d.value); }); | |
| const svgGridPoints = d3.select("#grid"); | |
| svgGridPoints.selectAll("circle") | |
| .data(gridData) | |
| .enter().append("circle") | |
| .attr('cx', function (d) { return x(d[0]) }) | |
| .attr('cy', function (d) { return y(d[1]) }) | |
| .attr('r', 2) | |
| .attr('fill', function (d) { return color(d[2]) }); | |
| }()); | |
| // original points | |
| (function () { | |
| let svg = d3.select("#originalpoints"), | |
| width = +svg.attr("width"), | |
| height = +svg.attr("height"); | |
| const xmin = _.minBy(aero, getx)[0]; | |
| const ymin = _.minBy(aero, gety)[1]; | |
| const zmin = _.minBy(aero, getz)[2]; | |
| const xmax = _.maxBy(aero, getx)[0]; | |
| const ymax = _.maxBy(aero, gety)[1]; | |
| const zmax = _.maxBy(aero, getz)[2]; | |
| let x = d3.scaleLinear().range([0, width]).domain([xmin, xmax]), | |
| y = d3.scaleLinear().range([0, height]).domain([ymin, ymax]), | |
| color = d3.scaleSequential(interpolateTerrain).domain([zmin, zmax]); | |
| svg.selectAll("circle") | |
| .data(aero) | |
| .enter().append("circle") | |
| .attr('cx', function (d) { return x(d[0]) }) | |
| .attr('cy', function (d) { return y(d[1]) }) | |
| .attr('r', 2) | |
| .attr('fill', function (d) { return color(d[2]) }); | |
| }()); | |
| // triagulation | |
| (function () { | |
| var canvas = document.getElementById("s3"), | |
| ctx = canvas.getContext("2d"); | |
| const x = d3.scaleLinear().range([0, 960]).domain([xmin, xmax]), | |
| y = d3.scaleLinear().range([0, 673]).domain([ymin, ymax]); | |
| for (i = triangles.length; i;) { | |
| ctx.beginPath(); | |
| --i; ctx.moveTo(x(triangles[i][0]), y(triangles[i][1])); | |
| --i; ctx.lineTo(x(triangles[i][0]), y(triangles[i][1])); | |
| --i; ctx.lineTo(x(triangles[i][0]), y(triangles[i][1])); | |
| ctx.closePath(); | |
| ctx.stroke(); | |
| } | |
| }()) | |
| }) | |
| // https://github.com/ironwallaby/delaunay/blob/2c60fbd36662ae970b1e8402b18285317a60d0b6/delaunay.js#L203 | |
| const contains = function (p0, p1, p2, p) { | |
| /* Bounding box test first, for quick rejections. */ | |
| if ((p[0] < p0[0] && p[0] < p1[0] && p[0] < p2[0]) || | |
| (p[0] > p0[0] && p[0] > p1[0] && p[0] > p2[0]) || | |
| (p[1] < p0[1] && p[1] < p1[1] && p[1] < p2[1]) || | |
| (p[1] > p0[1] && p[1] > p1[1] && p[1] > p2[1])) | |
| return null; | |
| var a = p1[0] - p0[0], | |
| b = p2[0] - p0[0], | |
| c = p1[1] - p0[1], | |
| d = p2[1] - p0[1], | |
| i = a * d - b * c; | |
| /* Degenerate tri. */ | |
| if (i === 0.0) | |
| return null; | |
| var u = (d * (p[0] - p0[0]) - b * (p[1] - p0[1])) / i, | |
| v = (a * (p[1] - p0[1]) - c * (p[0] - p0[0])) / i; | |
| /* If we're outside the tri, fail. */ | |
| if (u <= 0.0 || v <= 0.0 || (u + v) >= 1.0) | |
| return null; | |
| return [u, v]; | |
| } | |
| // berycentric interpolate | |
| // http://answers.unity3d.com/questions/383804/calculate-uv-coordinates-of-3d-point-on-plane-of-m.html | |
| // https://math.stackexchange.com/questions/516219/finding-out-the-area-of-a-triangle-if-the-coordinates-of-the-three-vertices-are | |
| // p: [x,y,z?], tri: [p0,p1,p2] | |
| // turns out method "contains" already calculates this | |
| const interpolate = function (tri, p) { | |
| const A = (tri[1][0] - tri[0][0]) * (tri[2][1] - tri[0][1]) - (tri[2][0] - tri[0][0]) * (tri[1][1] - tri[0][1]) | |
| const A1 = (tri[1][0] - p[0]) * (tri[2][1] - p[1]) - (tri[2][0] - p[0]) * (tri[1][1] - p[1]) | |
| const A2 = (p[0] - tri[0][0]) * (tri[2][1] - tri[0][1]) - (tri[2][0] - tri[0][0]) * (p[1] - tri[0][1]) | |
| const A3 = (tri[1][0] - tri[0][0]) * (p[1] - tri[0][1]) - (p[0] - tri[0][0]) * (tri[1][1] - tri[0][1]) | |
| const u = A2 / A, v = A3 / A | |
| return (1 - u - v) * tri[0][2] + u * tri[1][2] + v * tri[2][2] | |
| } | |
| const getx = function (o) { return o[0]; } | |
| const gety = function (o) { return o[1]; } | |
| const getz = function (o) { return o[2]; } | |
| </script> |