Add an option to have approximate Gaussian points instead of solid points with a blur.

examples/heatmap/index.jade

@@ -31,6 +31,9 @@ block append mainContent
  .form-group(title="Radius of blur around points in pixels.")
  label(for="blurRadius") Blur Radius
  input#blurRadius(type="number" placeholder="15" min=0)
+ .form-group(title="Use either a Gaussian distribution or a solid circle with a blurred edge for each point. If a Guassian is used, the total radius is the sume of the radius and blur radius values.")
+ label(for="gaussian") Gaussian Points
+ input#gaussian(type="checkbox", placeholder="true", checked="checked")
  .form-group(title="Color Gradient. Entries with intensities of 0 and 1 are needed to form a valid color gradient.")
  label Color Gradient
  table.gradient

examples/heatmap/main.js

@@ -50,6 +50,10 @@ $(function () {
  case 'dataset':
  ctlvalue = value ? value : 'adderall';
  break;
+ case 'gaussian':
+ ctlvalue = value === 'true';
+ heatmapOptions.style[key] = value;
+ break;
  case 'gradient':
  var parts = value.split(',').map(parseFloat);
  if (parts.length >= 5) {
@@ -82,11 +86,6 @@ $(function () {
  points = ctlvalue = parseInt(value, 10);
  }
  break;
- case 'updateDelay':
- if (value.length) {
- heatmapOptions[key] = ctlvalue = parseInt(value, 10);
- }
- break;
  case 'radius': case 'blurRadius':
  if (value.length) {
  value = parseFloat(value);
@@ -95,6 +94,11 @@ $(function () {
  }
  }
  break;
+ case 'updateDelay':
+ if (value.length) {
+ heatmapOptions[key] = ctlvalue = parseInt(value, 10);
+ }
+ break;
  // add gaussian and binning when they are added as features
  }
  if (ctlvalue !== undefined) {
@@ -216,6 +220,11 @@ $(function () {
  case 'dataset':
  fetch_data();
  break;
+ case 'gaussian':
+ heatmapOptions.style[param] = processedValue;
+ heatmap.style(param, processedValue);
+ map.draw();
+ break;
  case 'gradient':
  var gradient = {};
  for (var idx = 1; idx <= 6; idx += 1) {

src/canvas/heatmapFeature.js

@@ -96,27 +96,58 @@ var canvas_heatmapFeature = function (arg) {
  */
  ////////////////////////////////////////////////////////////////////////////
  this._createCircle = function () {
- var circle, ctx, r, r2, blur;
+ var circle, ctx, r, r2, blur, gaussian;
  r = m_this.style('radius');
  blur = m_this.style('blurRadius');
- if (!m_this._circle || m_this._circle.radius !== r ||
- m_this._circle.blurRadius !== blur) {
+ gaussian = m_this.style('gaussian');
+ if (!m_this._circle || m_this._circle.gaussian !== gaussian ||
+ m_this._circle.radius !== r || m_this._circle.blurRadius !== blur) {
  circle = m_this._circle = document.createElement('canvas');
  ctx = circle.getContext('2d');
-
  r2 = blur + r;
-
  circle.width = circle.height = r2 * 2;
- ctx.shadowOffsetX = ctx.shadowOffsetY = r2 * 2;
- ctx.shadowBlur = blur;
- ctx.shadowColor = 'black';
-
- ctx.beginPath();
- ctx.arc(-r2, -r2, r, 0, Math.PI * 2, true);
- ctx.closePath();
- ctx.fill();
+ if (!gaussian) {
+ ctx.shadowOffsetX = ctx.shadowOffsetY = r2 * 2;
+ ctx.shadowBlur = blur;
+ ctx.shadowColor = 'black';
+ ctx.beginPath();
+ ctx.arc(-r2, -r2, r, 0, Math.PI * 2, true);
+ ctx.closePath();
+ ctx.fill();
+ } else {
+ /* This approximates a gaussian distribution by using a 10-step
+ * piecewise linear radial gradient. Strictly, it should not stop at
+ * the radius, but should be attenuated further. The scale has been
+ * selected such that the values at the radius are around 1/256th of
+ * the maximum, and therefore would not be visible using an 8-bit alpha
+ * channel for the summation. The values for opacity were generated by
+ * the python expression:
+ * from scipy.stats import norm
+ * for r in [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]:
+ * opacity = norm.pdf(r, scale=0.3) / norm.pdf(0, scale=0.3)
+ * Usng a 10-interval approximation is accurate to within 0.5% of the
+ * actual Gaussian magnitude. Switching to a 20-interval approximation
+ * would get within 0.1%, at which point there is more error from using
+ * a Gaussian truncated at the radius than from the approximation.
+ */
+ var grad = ctx.createRadialGradient(r2, r2, 0, r2, r2, r2);
+ grad.addColorStop(0.0, 'rgba(255,255,255,1)');
+ grad.addColorStop(0.1, 'rgba(255,255,255,0.946)');
+ grad.addColorStop(0.2, 'rgba(255,255,255,0.801)');
+ grad.addColorStop(0.3, 'rgba(255,255,255,0.607)');
+ grad.addColorStop(0.4, 'rgba(255,255,255,0.411)');
+ grad.addColorStop(0.5, 'rgba(255,255,255,0.249)');
+ grad.addColorStop(0.6, 'rgba(255,255,255,0.135)');
+ grad.addColorStop(0.7, 'rgba(255,255,255,0.066)');
+ grad.addColorStop(0.8, 'rgba(255,255,255,0.029)');
+ grad.addColorStop(0.9, 'rgba(255,255,255,0.011)');
+ grad.addColorStop(1.0, 'rgba(255,255,255,0)');
+ ctx.fillStyle = grad;
+ ctx.fillRect(0, 0, r2 * 2, r2 * 2);
+ }
  circle.radius = r;
  circle.blurRadius = blur;
+ circle.gaussian = gaussian;
  m_this._circle = circle;
  }
  return m_this;

src/heatmapFeature.js

@@ -10,13 +10,6 @@ var transform = require('./transform');
  * @class
  * @param {Object} arg Options object
  * @extends geo.feature
- * @param {Object|string|Function} [color] Color transfer function that.
- * will be used to evaluate color of each pixel using normalized intensity
- * as the look up value.
- * @param {Object|Function} [radius=10] Radius of a point in terms of number
- * of pixels.
- * @param {Object|Function} [blurRadius=10] Gaussian blur radius for each
- * point in terms of number of pixels.
  * @param {Object|Function} [position] Position of the data. Default is
  * (data). The position is an Object which specifies the location of the
  * data in geo-spatial context.
@@ -33,6 +26,18 @@ var transform = require('./transform');
  * be computed.
  * @param {number} [updateDelay=1000] Delay in milliseconds after a zoom,
  * rotate, or pan event before recomputing the heatmap.
+ * @param {Object|string|Function} [style.color] Color transfer function that.
+ * will be used to evaluate color of each pixel using normalized intensity
+ * as the look up value.
+ * @param {Object|Function} [style.radius=10] Radius of a point in terms of
+ * number of pixels.
+ * @param {Object|Function} [style.blurRadius=10] Blur radius for each point in
+ * terms of number of pixels.
+ * @param {boolean} [style.gaussian=true] If true, appoximate a gaussian
+ * distribution for each point using a multi-segment linear radial
+ * appoximation. The total weight of the gaussian area is approximately the
+ * 9/16 r^2. The sum of radius + blurRadius is used as the radius for the
+ * gaussian distribution.
  * @returns {geo.heatmapFeature}
  */
 //////////////////////////////////////////////////////////////////////////////
@@ -179,6 +184,7 @@ var heatmapFeature = function (arg) {
  {
  radius: 10,
  blurRadius: 10,
+ gaussian: true,
  color: {0: {r: 0, g: 0, b: 0.0, a: 0.0},
  0.25: {r: 0, g: 0, b: 1, a: 0.5},
  0.5: {r: 0, g: 1, b: 1, a: 0.6},

tests/cases/heatmap.js

@@ -36,7 +36,7 @@ describe('canvas heatmap feature', function () {
  map.resize(0, 0, width, height);
  });
 
- it('Add features to a layer', function () {
+ it('Add feature to a layer', function () {
  feature1 = layer.createFeature('heatmap')
  .data(testData)
  .intensity(function (d) {
@@ -55,7 +55,7 @@ describe('canvas heatmap feature', function () {
  map.draw();
  stepAnimationFrame(new Date().getTime());
  expect(layer.children().length).toBe(1);
- unmockAnimationFrame();
+ // leave animation frames mocked for later tests.
  });
 
  it('Validate selection API option', function () {
@@ -103,11 +103,36 @@ describe('canvas heatmap feature', function () {
  clock.tick(2000);
  expect(feature1.buildTime().getMTime()).toBe(buildTime);
  });
+ it('radius, blurRadius, and gaussian', function () {
+ // animation frames are already mocked
+ expect(feature1._circle.radius).toBe(5);
+ expect(feature1._circle.blurRadius).toBe(15);
+ expect(feature1._circle.gaussian).toBe(true);
+ expect(feature1._circle.width).toBe(40);
+ expect(feature1._circle.height).toBe(40);
+ feature1.style('gaussian', false);
+ map.draw();
+ stepAnimationFrame(new Date().getTime());
+ expect(feature1._circle.gaussian).toBe(false);
+ feature1.style('radius', 10);
+ expect(feature1._circle.radius).toBe(5);
+ map.draw();
+ stepAnimationFrame(new Date().getTime());
+ expect(feature1._circle.radius).toBe(10);
+ expect(feature1._circle.width).toBe(50);
+ expect(feature1._circle.height).toBe(50);
+ feature1.style('blurRadius', 0);
+ map.draw();
+ stepAnimationFrame(new Date().getTime());
+ expect(feature1._circle.blurRadius).toBe(0);
+ expect(feature1._circle.width).toBe(20);
+ expect(feature1._circle.height).toBe(20);
+ unmockAnimationFrame();
+ });
  it('Remove a feature from a layer', function () {
  layer.deleteFeature(feature1).draw();
  expect(layer.children().length).toBe(0);
  });
-
 });
 
 describe('core.heatmapFeature', function () {