@spatial/isolines
Version:
turf isolines module
565 lines (501 loc) • 20.9 kB
JavaScript
import bbox from '@spatial/bbox';
import { featureEach, coordEach } from '@spatial/meta';
import { collectionOf, getCoords } from '@spatial/invariant';
import { isObject, featureCollection, multiLineString } from '@spatial/helpers';
/**
* @license GNU Affero General Public License.
* Copyright (c) 2015, 2015 Ronny Lorenz <ronny@tbi.univie.ac.at>
* v. 1.2.0
* https://github.com/RaumZeit/MarchingSquares.js
*/
/**
* Compute the isocontour(s) of a scalar 2D field given
* a certain threshold by applying the Marching Squares
* Algorithm. The function returns a list of path coordinates
*/
var defaultSettings = {
successCallback: null,
verbose: false
};
var settings = {};
function isoContours(data, threshold, options) {
/* process options */
options = options ? options : {};
var optionKeys = Object.keys(defaultSettings);
for (var i = 0; i < optionKeys.length; i++) {
var key = optionKeys[i];
var val = options[key];
val = ((typeof val !== 'undefined') && (val !== null)) ? val : defaultSettings[key];
settings[key] = val;
}
if (settings.verbose)
console.log('MarchingSquaresJS-isoContours: computing isocontour for ' + threshold);
var ret = contourGrid2Paths(computeContourGrid(data, threshold));
if (typeof settings.successCallback === 'function')
settings.successCallback(ret);
return ret;
}
/*
Thats all for the public interface, below follows the actual
implementation
*/
/*
################################
Isocontour implementation below
################################
*/
/* assume that x1 == 1 && x0 == 0 */
function interpolateX(y, y0, y1) {
return (y - y0) / (y1 - y0);
}
/* compute the isocontour 4-bit grid */
function computeContourGrid(data, threshold) {
var rows = data.length - 1;
var cols = data[0].length - 1;
var ContourGrid = { rows: rows, cols: cols, cells: [] };
for (var j = 0; j < rows; ++j) {
ContourGrid.cells[j] = [];
for (var i = 0; i < cols; ++i) {
/* compose the 4-bit corner representation */
var cval = 0;
var tl = data[j + 1][i];
var tr = data[j + 1][i + 1];
var br = data[j][i + 1];
var bl = data[j][i];
if (isNaN(tl) || isNaN(tr) || isNaN(br) || isNaN(bl)) {
continue;
}
cval |= ((tl >= threshold) ? 8 : 0);
cval |= ((tr >= threshold) ? 4 : 0);
cval |= ((br >= threshold) ? 2 : 0);
cval |= ((bl >= threshold) ? 1 : 0);
/* resolve ambiguity for cval == 5 || 10 via averaging */
var flipped = false;
if (cval === 5 || cval === 10) {
var average = (tl + tr + br + bl) / 4;
if (cval === 5 && (average < threshold)) {
cval = 10;
flipped = true;
} else if (cval === 10 && (average < threshold)) {
cval = 5;
flipped = true;
}
}
/* add cell to ContourGrid if it contains edges */
if (cval !== 0 && cval !== 15) {
var top, bottom, left, right;
top = bottom = left = right = 0.5;
/* interpolate edges of cell */
if (cval === 1) {
left = 1 - interpolateX(threshold, tl, bl);
bottom = 1 - interpolateX(threshold, br, bl);
} else if (cval === 2) {
bottom = interpolateX(threshold, bl, br);
right = 1 - interpolateX(threshold, tr, br);
} else if (cval === 3) {
left = 1 - interpolateX(threshold, tl, bl);
right = 1 - interpolateX(threshold, tr, br);
} else if (cval === 4) {
top = interpolateX(threshold, tl, tr);
right = interpolateX(threshold, br, tr);
} else if (cval === 5) {
top = interpolateX(threshold, tl, tr);
right = interpolateX(threshold, br, tr);
bottom = 1 - interpolateX(threshold, br, bl);
left = 1 - interpolateX(threshold, tl, bl);
} else if (cval === 6) {
bottom = interpolateX(threshold, bl, br);
top = interpolateX(threshold, tl, tr);
} else if (cval === 7) {
left = 1 - interpolateX(threshold, tl, bl);
top = interpolateX(threshold, tl, tr);
} else if (cval === 8) {
left = interpolateX(threshold, bl, tl);
top = 1 - interpolateX(threshold, tr, tl);
} else if (cval === 9) {
bottom = 1 - interpolateX(threshold, br, bl);
top = 1 - interpolateX(threshold, tr, tl);
} else if (cval === 10) {
top = 1 - interpolateX(threshold, tr, tl);
right = 1 - interpolateX(threshold, tr, br);
bottom = interpolateX(threshold, bl, br);
left = interpolateX(threshold, bl, tl);
} else if (cval === 11) {
top = 1 - interpolateX(threshold, tr, tl);
right = 1 - interpolateX(threshold, tr, br);
} else if (cval === 12) {
left = interpolateX(threshold, bl, tl);
right = interpolateX(threshold, br, tr);
} else if (cval === 13) {
bottom = 1 - interpolateX(threshold, br, bl);
right = interpolateX(threshold, br, tr);
} else if (cval === 14) {
left = interpolateX(threshold, bl, tl);
bottom = interpolateX(threshold, bl, br);
} else {
console.log('MarchingSquaresJS-isoContours: Illegal cval detected: ' + cval);
}
ContourGrid.cells[j][i] = {
cval: cval,
flipped: flipped,
top: top,
right: right,
bottom: bottom,
left: left
};
}
}
}
return ContourGrid;
}
function isSaddle(cell) {
return cell.cval === 5 || cell.cval === 10;
}
function isTrivial(cell) {
return cell.cval === 0 || cell.cval === 15;
}
function clearCell(cell) {
if ((!isTrivial(cell)) && (cell.cval !== 5) && (cell.cval !== 10)) {
cell.cval = 15;
}
}
function getXY(cell, edge) {
if (edge === 'top') {
return [cell.top, 1.0];
} else if (edge === 'bottom') {
return [cell.bottom, 0.0];
} else if (edge === 'right') {
return [1.0, cell.right];
} else if (edge === 'left') {
return [0.0, cell.left];
}
}
function contourGrid2Paths(grid) {
var paths = [];
var path_idx = 0;
var rows = grid.rows;
var cols = grid.cols;
var epsilon = 1e-7;
grid.cells.forEach(function (g, j) {
g.forEach(function (gg, i) {
if ((typeof gg !== 'undefined') && (!isSaddle(gg)) && (!isTrivial(gg))) {
var p = tracePath(grid.cells, j, i);
var merged = false;
/* we may try to merge paths at this point */
if (p.info === 'mergeable') {
/*
search backwards through the path array to find an entry
that starts with where the current path ends...
*/
var x = p.path[p.path.length - 1][0],
y = p.path[p.path.length - 1][1];
for (var k = path_idx - 1; k >= 0; k--) {
if ((Math.abs(paths[k][0][0] - x) <= epsilon) && (Math.abs(paths[k][0][1] - y) <= epsilon)) {
for (var l = p.path.length - 2; l >= 0; --l) {
paths[k].unshift(p.path[l]);
}
merged = true;
break;
}
}
}
if (!merged)
paths[path_idx++] = p.path;
}
});
});
return paths;
}
/*
construct consecutive line segments from starting cell by
walking arround the enclosed area clock-wise
*/
function tracePath(grid, j, i) {
var maxj = grid.length;
var p = [];
var dxContour = [0, 0, 1, 1, 0, 0, 0, 0, -1, 0, 1, 1, -1, 0, -1, 0];
var dyContour = [0, -1, 0, 0, 1, 1, 1, 1, 0, -1, 0, 0, 0, -1, 0, 0];
var dx, dy;
var startEdge = ['none', 'left', 'bottom', 'left', 'right', 'none', 'bottom', 'left', 'top', 'top', 'none', 'top', 'right', 'right', 'bottom', 'none'];
var nextEdge = ['none', 'bottom', 'right', 'right', 'top', 'top', 'top', 'top', 'left', 'bottom', 'right', 'right', 'left', 'bottom', 'left', 'none'];
var edge;
var startCell = grid[j][i];
var currentCell = grid[j][i];
var cval = currentCell.cval;
var edge = startEdge[cval];
var pt = getXY(currentCell, edge);
/* push initial segment */
p.push([i + pt[0], j + pt[1]]);
edge = nextEdge[cval];
pt = getXY(currentCell, edge);
p.push([i + pt[0], j + pt[1]]);
clearCell(currentCell);
/* now walk arround the enclosed area in clockwise-direction */
var k = i + dxContour[cval];
var l = j + dyContour[cval];
var prev_cval = cval;
while ((k >= 0) && (l >= 0) && (l < maxj) && ((k != i) || (l != j))) {
currentCell = grid[l][k];
if (typeof currentCell === 'undefined') { /* path ends here */
//console.log(k + " " + l + " is undefined, stopping path!");
break;
}
cval = currentCell.cval;
if ((cval === 0) || (cval === 15)) {
return { path: p, info: 'mergeable' };
}
edge = nextEdge[cval];
dx = dxContour[cval];
dy = dyContour[cval];
if ((cval === 5) || (cval === 10)) {
/* select upper or lower band, depending on previous cells cval */
if (cval === 5) {
if (currentCell.flipped) { /* this is actually a flipped case 10 */
if (dyContour[prev_cval] === -1) {
edge = 'left';
dx = -1;
dy = 0;
} else {
edge = 'right';
dx = 1;
dy = 0;
}
} else { /* real case 5 */
if (dxContour[prev_cval] === -1) {
edge = 'bottom';
dx = 0;
dy = -1;
}
}
} else if (cval === 10) {
if (currentCell.flipped) { /* this is actually a flipped case 5 */
if (dxContour[prev_cval] === -1) {
edge = 'top';
dx = 0;
dy = 1;
} else {
edge = 'bottom';
dx = 0;
dy = -1;
}
} else { /* real case 10 */
if (dyContour[prev_cval] === 1) {
edge = 'left';
dx = -1;
dy = 0;
}
}
}
}
pt = getXY(currentCell, edge);
p.push([k + pt[0], l + pt[1]]);
clearCell(currentCell);
k += dx;
l += dy;
prev_cval = cval;
}
return { path: p, info: 'closed' };
}
/**
* Takes a {@link Point} grid and returns a correspondent matrix {Array<Array<number>>}
* of the 'property' values
*
* @name gridToMatrix
* @param {FeatureCollection<Point>} grid of points
* @param {Object} [options={}] Optional parameters
* @param {string} [options.zProperty='elevation'] the property name in `points` from which z-values will be pulled
* @param {boolean} [options.flip=false] returns the matrix upside-down
* @param {boolean} [options.flags=false] flags, adding a `matrixPosition` array field ([row, column]) to its properties,
* the grid points with coordinates on the matrix
* @returns {Array<Array<number>>} matrix of property values
* @example
* var extent = [-70.823364, -33.553984, -70.473175, -33.302986];
* var cellSize = 3;
* var grid = turf.pointGrid(extent, cellSize);
* // add a random property to each point between 0 and 60
* for (var i = 0; i < grid.features.length; i++) {
* grid.features[i].properties.elevation = (Math.random() * 60);
* }
* gridToMatrix(grid);
* //= [
* [ 1, 13, 10, 9, 10, 13, 18],
* [34, 8, 5, 4, 5, 8, 13],
* [10, 5, 2, 1, 2, 5, 4],
* [ 0, 4, 56, 19, 1, 4, 9],
* [10, 5, 2, 1, 2, 5, 10],
* [57, 8, 5, 4, 5, 0, 57],
* [ 3, 13, 10, 9, 5, 13, 18],
* [18, 13, 10, 9, 78, 13, 18]
* ]
*/
function gridToMatrix(grid, options) {
// Optional parameters
options = options || {};
if (!isObject(options)) throw new Error('options is invalid');
var zProperty = options.zProperty || 'elevation';
var flip = options.flip;
var flags = options.flags;
// validation
collectionOf(grid, 'Point', 'input must contain Points');
var pointsMatrix = sortPointsByLatLng(grid, flip);
var matrix = [];
// create property matrix from sorted points
// looping order matters here
for (var r = 0; r < pointsMatrix.length; r++) {
var pointRow = pointsMatrix[r];
var row = [];
for (var c = 0; c < pointRow.length; c++) {
var point = pointRow[c];
// Check if zProperty exist
if (point.properties[zProperty]) row.push(point.properties[zProperty]);
else row.push(0);
// add flags
if (flags === true) point.properties.matrixPosition = [r, c];
}
matrix.push(row);
}
return matrix;
}
/**
* Sorts points by latitude and longitude, creating a 2-dimensional array of points
*
* @private
* @param {FeatureCollection<Point>} points GeoJSON Point features
* @param {boolean} [flip=false] returns the matrix upside-down
* @returns {Array<Array<Point>>} points ordered by latitude and longitude
*/
function sortPointsByLatLng(points, flip) {
var pointsByLatitude = {};
// divide points by rows with the same latitude
featureEach(points, function (point) {
var lat = getCoords(point)[1];
if (!pointsByLatitude[lat]) pointsByLatitude[lat] = [];
pointsByLatitude[lat].push(point);
});
// sort points (with the same latitude) by longitude
var orderedRowsByLatitude = Object.keys(pointsByLatitude).map(function (lat) {
var row = pointsByLatitude[lat];
var rowOrderedByLongitude = row.sort(function (a, b) {
return getCoords(a)[0] - getCoords(b)[0];
});
return rowOrderedByLongitude;
});
// sort rows (of points with the same latitude) by latitude
var pointMatrix = orderedRowsByLatitude.sort(function (a, b) {
if (flip) return getCoords(a[0])[1] - getCoords(b[0])[1];
else return getCoords(b[0])[1] - getCoords(a[0])[1];
});
return pointMatrix;
}
/**
* Takes a grid {@link FeatureCollection} of {@link Point} features with z-values and an array of
* value breaks and generates [isolines](http://en.wikipedia.org/wiki/Isoline).
*
* @name isolines
* @param {FeatureCollection<Point>} pointGrid input points
* @param {Array<number>} breaks values of `zProperty` where to draw isolines
* @param {Object} [options={}] Optional parameters
* @param {string} [options.zProperty='elevation'] the property name in `points` from which z-values will be pulled
* @param {Object} [options.commonProperties={}] GeoJSON properties passed to ALL isolines
* @param {Array<Object>} [options.breaksProperties=[]] GeoJSON properties passed, in order, to the correspondent isoline;
* the breaks array will define the order in which the isolines are created
* @returns {FeatureCollection<MultiLineString>} a FeatureCollection of {@link MultiLineString} features representing isolines
* @example
* // create a grid of points with random z-values in their properties
* var extent = [0, 30, 20, 50];
* var cellWidth = 100;
* var pointGrid = turf.pointGrid(extent, cellWidth, {units: 'miles'});
*
* for (var i = 0; i < pointGrid.features.length; i++) {
* pointGrid.features[i].properties.temperature = Math.random() * 10;
* }
* var breaks = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
*
* var lines = turf.isolines(pointGrid, breaks, {zProperty: 'temperature'});
*
* //addToMap
* var addToMap = [lines];
*/
function isolines(pointGrid, breaks, options) {
// Optional parameters
options = options || {};
if (!isObject(options)) throw new Error('options is invalid');
const zProperty = options.zProperty || 'elevation';
const commonProperties = options.commonProperties || {};
const breaksProperties = options.breaksProperties || [];
// Input validation
collectionOf(pointGrid, 'Point', 'Input must contain Points');
if (!breaks) throw new Error('breaks is required');
if (!Array.isArray(breaks)) throw new Error('breaks must be an Array');
if (!isObject(commonProperties)) throw new Error('commonProperties must be an Object');
if (!Array.isArray(breaksProperties)) throw new Error('breaksProperties must be an Array');
// Isoline methods
const matrix = gridToMatrix(pointGrid, {zProperty, flip: true});
const createdIsoLines = createIsoLines(matrix, breaks, zProperty, commonProperties, breaksProperties);
const scaledIsolines = rescaleIsolines(createdIsoLines, matrix, pointGrid);
return featureCollection(scaledIsolines);
}
/**
* Creates the isolines lines (featuresCollection of MultiLineString features) from the 2D data grid
*
* Marchingsquares process the grid data as a 3D representation of a function on a 2D plane, therefore it
* assumes the points (x-y coordinates) are one 'unit' distance. The result of the isolines function needs to be
* rescaled, with turfjs, to the original area and proportions on the map
*
* @private
* @param {Array<Array<number>>} matrix Grid Data
* @param {Array<number>} breaks Breaks
* @param {string} zProperty name of the z-values property
* @param {Object} [commonProperties={}] GeoJSON properties passed to ALL isolines
* @param {Object} [breaksProperties=[]] GeoJSON properties passed to the correspondent isoline
* @returns {Array<MultiLineString>} isolines
*/
function createIsoLines(matrix, breaks, zProperty, commonProperties, breaksProperties) {
const results = [];
for (let i = 1; i < breaks.length; i++) {
const threshold = +breaks[i]; // make sure it's a number
const properties = Object.assign(
{},
commonProperties,
breaksProperties[i]
);
properties[zProperty] = threshold;
const isoline = multiLineString(isoContours(matrix, threshold), properties);
results.push(isoline);
}
return results;
}
/**
* Translates and scales isolines
*
* @private
* @param {Array<MultiLineString>} createdIsoLines to be rescaled
* @param {Array<Array<number>>} matrix Grid Data
* @param {Object} points Points by Latitude
* @returns {Array<MultiLineString>} isolines
*/
function rescaleIsolines(createdIsoLines, matrix, points) {
// get dimensions (on the map) of the original grid
const gridBbox = bbox(points); // [ minX, minY, maxX, maxY ]
const originalWidth = gridBbox[2] - gridBbox[0];
const originalHeigth = gridBbox[3] - gridBbox[1];
// get origin, which is the first point of the last row on the rectangular data on the map
const x0 = gridBbox[0];
const y0 = gridBbox[1];
// get number of cells per side
const matrixWidth = matrix[0].length - 1;
const matrixHeight = matrix.length - 1;
// calculate the scaling factor between matrix and rectangular grid on the map
const scaleX = originalWidth / matrixWidth;
const scaleY = originalHeigth / matrixHeight;
const resize = function (point) {
point[0] = point[0] * scaleX + x0;
point[1] = point[1] * scaleY + y0;
};
// resize and shift each point/line of the createdIsoLines
createdIsoLines.forEach(function (isoline) {
coordEach(isoline, resize);
});
return createdIsoLines;
}
export default isolines;