From 36b9b025c414ba827959ef1bc9aa2d061c3b9820 Mon Sep 17 00:00:00 2001
From: hustcc <i@hust.cc>
Date: Wed, 31 May 2023 18:52:00 +0800
Subject: [PATCH] feat: add venn chart demo, tests (#5129)

* docs: add venn demo, tests

* chore: build success

* fix: sort data for occlusion
---
 .../snapshots/static/vennBasic.png            | Bin 0 -> 25418 bytes
 .../snapshots/static/vennHollow.png           | Bin 0 -> 37947 bytes
 __tests__/plots/static/index.ts               |   2 +
 __tests__/plots/static/venn-basic.ts          |  50 ++
 __tests__/plots/static/venn-hollow.ts         |  54 ++
 __tests__/unit/data/venn.spec.ts              |  24 +
 __tests__/unit/stdlib/index.spec.ts           |   2 +
 package.json                                  |   1 +
 site/examples/general/venn/demo/meta.json     |  24 +
 .../examples/general/venn/demo/venn-hollow.ts |  42 +
 site/examples/general/venn/demo/venn.ts       |  42 +
 site/examples/general/venn/index.en.md        |   4 +
 site/examples/general/venn/index.zh.md        |   4 +
 src/api/mark/index.ts                         |   3 +
 src/api/mark/mark.ts                          |  12 +
 src/data/index.ts                             |   2 +
 src/data/utils/venn/circleintersection.ts     | 235 ++++++
 src/data/utils/venn/diagram.ts                |  47 ++
 src/data/utils/venn/index.ts                  |   5 +
 src/data/utils/venn/layout.ts                 | 769 ++++++++++++++++++
 src/data/venn.ts                              |  58 ++
 src/shape/path/color.ts                       |  16 +-
 src/spec/dataTransform.ts                     |  25 +
 src/stdlib/index.ts                           |   2 +
 24 files changed, 1417 insertions(+), 6 deletions(-)
 create mode 100644 __tests__/integration/snapshots/static/vennBasic.png
 create mode 100644 __tests__/integration/snapshots/static/vennHollow.png
 create mode 100644 __tests__/plots/static/venn-basic.ts
 create mode 100644 __tests__/plots/static/venn-hollow.ts
 create mode 100644 __tests__/unit/data/venn.spec.ts
 create mode 100644 site/examples/general/venn/demo/meta.json
 create mode 100644 site/examples/general/venn/demo/venn-hollow.ts
 create mode 100644 site/examples/general/venn/demo/venn.ts
 create mode 100644 site/examples/general/venn/index.en.md
 create mode 100644 site/examples/general/venn/index.zh.md
 create mode 100644 src/data/utils/venn/circleintersection.ts
 create mode 100644 src/data/utils/venn/diagram.ts
 create mode 100644 src/data/utils/venn/index.ts
 create mode 100644 src/data/utils/venn/layout.ts
 create mode 100644 src/data/venn.ts

diff --git a/__tests__/integration/snapshots/static/vennBasic.png b/__tests__/integration/snapshots/static/vennBasic.png
new file mode 100644
index 0000000000000000000000000000000000000000..0c3673e24f4dbb70cfa0b3bb9529c52bc61ad0af
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HcmV?d00001

diff --git a/__tests__/plots/static/index.ts b/__tests__/plots/static/index.ts
index 140b2923a7..3421682fa5 100644
--- a/__tests__/plots/static/index.ts
+++ b/__tests__/plots/static/index.ts
@@ -236,3 +236,5 @@ export { HeatmapHeatmapBasic } from './heatmap-heatmap-basic';
 export { DiamondHeatmapDensity } from './diamond-heatmap-density';
 export { basicLineNullLabel } from './basic-line-null-label';
 export { alphabetIntervalViewStyle } from './alphabet-interval-view-style';
+export { vennBasic } from './venn-basic';
+export { vennHollow } from './venn-hollow';
diff --git a/__tests__/plots/static/venn-basic.ts b/__tests__/plots/static/venn-basic.ts
new file mode 100644
index 0000000000..7c68ad4702
--- /dev/null
+++ b/__tests__/plots/static/venn-basic.ts
@@ -0,0 +1,50 @@
+import { G2Spec } from '../../../src';
+
+export function vennBasic(): G2Spec {
+  return {
+    type: 'view',
+    width: 640,
+    height: 480,
+    children: [
+      {
+        type: 'path',
+        data: {
+          type: 'inline',
+          value: [
+            { sets: ['A'], value: 12, label: 'A' },
+            { sets: ['B'], value: 12, label: 'B' },
+            { sets: ['C'], value: 12, label: 'C' },
+            { sets: ['A', 'B'], value: 2, label: 'A&B' },
+            { sets: ['A', 'C'], value: 2, label: 'A&C' },
+            { sets: ['B', 'C'], value: 2, label: 'B&C' },
+            { sets: ['A', 'B', 'C'], value: 1 },
+          ],
+          transform: [
+            {
+              type: 'venn',
+              size: 'value',
+            },
+          ],
+        },
+        encode: {
+          d: 'path',
+          color: 'key',
+        },
+        style: {
+          fillOpacity: 0.8,
+        },
+        labels: [
+          {
+            text: 'key',
+            position: 'inside',
+            style: {
+              formatter: (_, datum) => `${datum.key}: ${datum.size}`,
+            },
+          },
+        ],
+      },
+    ],
+  };
+}
+
+vennBasic.maxError = 100;
diff --git a/__tests__/plots/static/venn-hollow.ts b/__tests__/plots/static/venn-hollow.ts
new file mode 100644
index 0000000000..3f400666d4
--- /dev/null
+++ b/__tests__/plots/static/venn-hollow.ts
@@ -0,0 +1,54 @@
+import { G2Spec } from '../../../src';
+
+export function vennHollow(): G2Spec {
+  return {
+    type: 'view',
+    width: 640,
+    height: 480,
+    children: [
+      {
+        type: 'path',
+        data: {
+          type: 'inline',
+          value: [
+            { sets: ['A'], value: 12, label: 'A' },
+            { sets: ['B'], value: 12, label: 'B' },
+            { sets: ['C'], value: 12, label: 'C' },
+            { sets: ['A', 'B'], value: 2, label: 'A&B' },
+            { sets: ['A', 'C'], value: 2, label: 'A&C' },
+            { sets: ['B', 'C'], value: 2, label: 'B&C' },
+            { sets: ['A', 'B', 'C'], value: 1 },
+          ],
+          transform: [
+            {
+              type: 'venn',
+              size: 'value',
+              padding: 10,
+            },
+          ],
+        },
+        encode: {
+          d: 'path',
+          color: 'key',
+          shape: 'hollow',
+        },
+        style: {
+          fillOpacity: 0.8,
+          lineWidth: 6,
+        },
+        labels: [
+          {
+            text: 'key',
+            position: 'inside',
+            style: {
+              formatter: (_, datum) => `${datum.key}: ${datum.size}`,
+              fill: '#000',
+            },
+          },
+        ],
+      },
+    ],
+  };
+}
+
+vennHollow.maxError = 100;
diff --git a/__tests__/unit/data/venn.spec.ts b/__tests__/unit/data/venn.spec.ts
new file mode 100644
index 0000000000..0c32988a4a
--- /dev/null
+++ b/__tests__/unit/data/venn.spec.ts
@@ -0,0 +1,24 @@
+import { Venn } from '../../../src/data/venn';
+
+describe('Venn', () => {
+  it('Venn({...}) returns function return layout venn data', async () => {
+    const data = [
+      { sets: ['A'], size: 102, label: 'A' },
+      { sets: ['B'], size: 12, label: 'B' },
+      { sets: ['C'], size: 12, label: 'C' },
+      { sets: ['A', 'B'], size: 2, label: 'A&B' },
+      { sets: ['A', 'C'], size: 2, label: 'A&C' },
+      { sets: ['B', 'C'], size: 2, label: 'B&C' },
+      { sets: ['A', 'B', 'C'], size: 1 },
+    ];
+    const v = Venn({
+      sets: 'sets',
+      size: 'size',
+      as: ['_key', '_path'],
+    });
+    const layout = await v(data);
+    expect(layout.length).toBe(7);
+    expect(layout[0]._path).toBeInstanceOf(Function);
+    expect(layout[6]._key).toBe('A&B&C');
+  });
+});
diff --git a/__tests__/unit/stdlib/index.spec.ts b/__tests__/unit/stdlib/index.spec.ts
index ca9e85d2e2..c419bd1e49 100644
--- a/__tests__/unit/stdlib/index.spec.ts
+++ b/__tests__/unit/stdlib/index.spec.ts
@@ -258,6 +258,7 @@ import {
   WordCloud,
   Join,
   KDE,
+  Venn,
 } from '../../../src/data';
 import {
   OverflowHide,
@@ -288,6 +289,7 @@ describe('stdlib', () => {
       'data.wordCloud': WordCloud,
       'data.join': Join,
       'data.kde': KDE,
+      'data.venn': Venn,
       'transform.maybeZeroY1': MaybeZeroY1,
       'transform.maybeZeroX': MaybeZeroX,
       'transform.maybeStackY': MaybeStackY,
diff --git a/package.json b/package.json
index 449acd46f5..436ee21a9f 100644
--- a/package.json
+++ b/package.json
@@ -66,6 +66,7 @@
     "d3-shape": "^3.1.0",
     "d3-voronoi": "^1.1.4",
     "flru": "^1.0.2",
+    "fmin": "^0.0.2",
     "pdfast": "^0.2.0"
   },
   "devDependencies": {
diff --git a/site/examples/general/venn/demo/meta.json b/site/examples/general/venn/demo/meta.json
new file mode 100644
index 0000000000..ec317e7e7f
--- /dev/null
+++ b/site/examples/general/venn/demo/meta.json
@@ -0,0 +1,24 @@
+{
+  "title": {
+    "zh": "中文分类",
+    "en": "Category"
+  },
+  "demos": [
+    {
+      "filename": "venn.ts",
+      "title": {
+        "zh": "韦恩图",
+        "en": "Venn Chart"
+      },
+      "screenshot": "https://mdn.alipayobjects.com/huamei_qa8qxu/afts/img/A*IZT9TJ3eVpwAAAAAAAAAAAAADmJ7AQ/original"
+    },
+    {
+      "filename": "venn-hollow.ts",
+      "title": {
+        "zh": "空心韦恩图",
+        "en": "Hollow Venn"
+      },
+      "screenshot": "https://mdn.alipayobjects.com/huamei_qa8qxu/afts/img/A*5XyrQppBM9YAAAAAAAAAAAAADmJ7AQ/original"
+    }
+  ]
+}
diff --git a/site/examples/general/venn/demo/venn-hollow.ts b/site/examples/general/venn/demo/venn-hollow.ts
new file mode 100644
index 0000000000..7776e4baa0
--- /dev/null
+++ b/site/examples/general/venn/demo/venn-hollow.ts
@@ -0,0 +1,42 @@
+import { Chart } from '@antv/g2';
+
+const chart = new Chart({
+  container: 'container',
+  theme: 'classic',
+  autoFit: true,
+});
+
+chart
+  .path()
+  .data({
+    type: 'inline',
+    value: [
+      { sets: ['A'], size: 15, label: 'A' },
+      { sets: ['B'], size: 12, label: 'B' },
+      { sets: ['C'], size: 10, label: 'C' },
+      { sets: ['A', 'B'], size: 2, label: 'A&B' },
+      { sets: ['A', 'C'], size: 2, label: 'A&C' },
+      { sets: ['B', 'C'], size: 1, label: 'B&C' },
+      { sets: ['A', 'B', 'C'], size: 1 },
+    ],
+    transform: [
+      {
+        type: 'venn',
+      },
+    ],
+  })
+  .encode('d', 'path')
+  .encode('color', 'key')
+  .encode('shape', 'hollow')
+  .label({
+    position: 'inside',
+    text: (d) => d.label || '',
+    style: {
+      fill: '#000',
+    },
+  })
+  .style('opacity', 0.6)
+  .style('lineWidth', 8)
+  .tooltip(false);
+
+chart.render();
diff --git a/site/examples/general/venn/demo/venn.ts b/site/examples/general/venn/demo/venn.ts
new file mode 100644
index 0000000000..30637ccfed
--- /dev/null
+++ b/site/examples/general/venn/demo/venn.ts
@@ -0,0 +1,42 @@
+/**
+ * A recreation of this demo: http://benfred.github.io/venn.js/examples/intersection_tooltip.html
+ */
+import { Chart } from '@antv/g2';
+
+const chart = new Chart({
+  container: 'container',
+  theme: 'classic',
+  autoFit: true,
+  paddingLeft: 50,
+  paddingRight: 50,
+});
+
+chart
+  .path()
+  .data({
+    type: 'fetch',
+    value: 'https://assets.antv.antgroup.com/g2/lastfm.json',
+    transform: [
+      {
+        type: 'venn',
+        padding: 8,
+        sets: 'sets',
+        size: 'size',
+        as: ['key', 'path'],
+      },
+    ],
+  })
+  .encode('d', 'path')
+  .encode('color', 'key')
+  .label({
+    position: 'inside',
+    text: (d) => d.label || '',
+    transform: [{ type: 'contrastReverse' }],
+  })
+  .style('opacity', (d) => (d.sets.length > 1 ? 0.001 : 0.5))
+  .state('inactive', { opacity: 0.2 })
+  .state('active', { opacity: 0.8 })
+  .interaction('elementHighlight', true)
+  .legend(false);
+
+chart.render();
diff --git a/site/examples/general/venn/index.en.md b/site/examples/general/venn/index.en.md
new file mode 100644
index 0000000000..ed6e141eb7
--- /dev/null
+++ b/site/examples/general/venn/index.en.md
@@ -0,0 +1,4 @@
+---
+title: Venn
+order: 21
+---
\ No newline at end of file
diff --git a/site/examples/general/venn/index.zh.md b/site/examples/general/venn/index.zh.md
new file mode 100644
index 0000000000..3c768eee78
--- /dev/null
+++ b/site/examples/general/venn/index.zh.md
@@ -0,0 +1,4 @@
+---
+title: 韦恩图
+order: 21
+---
\ No newline at end of file
diff --git a/src/api/mark/index.ts b/src/api/mark/index.ts
index c826cb41c8..3792a9e281 100644
--- a/src/api/mark/index.ts
+++ b/src/api/mark/index.ts
@@ -23,6 +23,7 @@ import {
   Boxplot,
   Density,
   Heatmap,
+  Path,
   Shape,
   Pack,
   ForceGraph,
@@ -57,6 +58,7 @@ export interface Mark {
   boxplot(): Boxplot;
   density(): Density;
   heatmap(): Heatmap;
+  path(): Path;
   shape(): Shape;
   pack(): Pack;
   forceGraph(): ForceGraph;
@@ -92,6 +94,7 @@ export const mark = {
   boxplot: Boxplot,
   density: Density,
   heatmap: Heatmap,
+  path: Path,
   shape: Shape,
   pack: Pack,
   forceGraph: ForceGraph,
diff --git a/src/api/mark/mark.ts b/src/api/mark/mark.ts
index 5af176a643..90558d0a2f 100644
--- a/src/api/mark/mark.ts
+++ b/src/api/mark/mark.ts
@@ -21,6 +21,7 @@ import {
   BoxPlotMark,
   DensityMark,
   HeatmapMark,
+  PathMark,
   ShapeMark,
   TreemapMark,
   ForceGraphMark,
@@ -123,6 +124,10 @@ export interface Heatmap extends API<Concrete<HeatmapMark>, Heatmap> {
   type: 'heatmap';
 }
 
+export interface Path extends API<Concrete<PathMark>, Path> {
+  type: 'path';
+}
+
 export interface Shape extends API<Concrete<ShapeMark>, Shape> {
   type: 'shape';
 }
@@ -347,6 +352,13 @@ export class Heatmap extends MarkNode<HeatmapMark> {
   }
 }
 
+@defineProps(props)
+export class Path extends MarkNode<PathMark> {
+  constructor() {
+    super({}, 'path');
+  }
+}
+
 @defineProps([...props, { name: 'layout', type: 'value' }])
 export class Pack extends MarkNode<PackMark> {
   constructor() {
diff --git a/src/data/index.ts b/src/data/index.ts
index 6d7661d19d..8ff9472234 100644
--- a/src/data/index.ts
+++ b/src/data/index.ts
@@ -16,6 +16,7 @@ export { WordCloud } from './wordCloud';
 export { Join } from './join';
 export { Slice } from './slice';
 export { KDE } from './kde';
+export { Venn } from './venn';
 
 export type { FetchOptions } from './fetch';
 export type { FoldOptions } from './fold';
@@ -35,3 +36,4 @@ export type { WordCloudOptions } from './wordCloud';
 export type { JoinOptions } from './join';
 export type { SliceOptions } from './slice';
 export type { KDEOptions } from './kde';
+export type { VennOptions } from './venn';
diff --git a/src/data/utils/venn/circleintersection.ts b/src/data/utils/venn/circleintersection.ts
new file mode 100644
index 0000000000..1c37f2c837
--- /dev/null
+++ b/src/data/utils/venn/circleintersection.ts
@@ -0,0 +1,235 @@
+const SMALL = 1e-10;
+
+/**
+ * Returns the intersection area of a bunch of circles (where each circle
+ * is an object having an x,y and radius property)
+ */
+export function intersectionArea(circles, stats?: any) {
+  // Get all the intersection points of the circles
+  const intersectionPoints = getIntersectionPoints(circles);
+
+  // Filter out points that aren't included in all the circles
+  const innerPoints = intersectionPoints.filter(function (p) {
+    return containedInCircles(p, circles);
+  });
+
+  let arcArea = 0,
+    polygonArea = 0,
+    i;
+  const arcs = [];
+  // If we have intersection points that are within all the circles,
+  // then figure out the area contained by them
+  if (innerPoints.length > 1) {
+    // Sort the points by angle from the center of the polygon, which lets
+    // us just iterate over points to get the edges
+    const center = getCenter(innerPoints);
+    for (i = 0; i < innerPoints.length; ++i) {
+      const p = innerPoints[i];
+      p.angle = Math.atan2(p.x - center.x, p.y - center.y);
+    }
+    innerPoints.sort(function (a, b) {
+      return b.angle - a.angle;
+    });
+
+    // Iterate over all points, get arc between the points
+    // and update the areas
+    let p2 = innerPoints[innerPoints.length - 1];
+    for (i = 0; i < innerPoints.length; ++i) {
+      const p1 = innerPoints[i];
+
+      // Polygon area updates easily ...
+      polygonArea += (p2.x + p1.x) * (p1.y - p2.y);
+
+      // Updating the arc area is a little more involved
+      const midPoint = { x: (p1.x + p2.x) / 2, y: (p1.y + p2.y) / 2 };
+      let arc = null;
+
+      for (let j = 0; j < p1.parentIndex.length; ++j) {
+        if (p2.parentIndex.indexOf(p1.parentIndex[j]) > -1) {
+          // Figure out the angle halfway between the two points
+          // on the current circle
+          const circle = circles[p1.parentIndex[j]],
+            a1 = Math.atan2(p1.x - circle.x, p1.y - circle.y),
+            a2 = Math.atan2(p2.x - circle.x, p2.y - circle.y);
+
+          let angleDiff = a2 - a1;
+          if (angleDiff < 0) {
+            angleDiff += 2 * Math.PI;
+          }
+
+          // and use that angle to figure out the width of the
+          // arc
+          const a = a2 - angleDiff / 2;
+          let width = distance(midPoint, {
+            x: circle.x + circle.radius * Math.sin(a),
+            y: circle.y + circle.radius * Math.cos(a),
+          });
+
+          // Clamp the width to the largest is can actually be
+          // (sometimes slightly overflows because of FP errors)
+          if (width > circle.radius * 2) {
+            width = circle.radius * 2;
+          }
+
+          // Pick the circle whose arc has the smallest width
+          if (arc === null || arc.width > width) {
+            arc = { circle: circle, width: width, p1: p1, p2: p2 };
+          }
+        }
+      }
+
+      if (arc !== null) {
+        arcs.push(arc);
+        arcArea += circleArea(arc.circle.radius, arc.width);
+        p2 = p1;
+      }
+    }
+  } else {
+    // No intersection points, is either disjoint - or is completely
+    // overlapped. figure out which by examining the smallest circle
+    let smallest = circles[0];
+    for (i = 1; i < circles.length; ++i) {
+      if (circles[i].radius < smallest.radius) {
+        smallest = circles[i];
+      }
+    }
+
+    // Make sure the smallest circle is completely contained in all
+    // the other circles
+    let disjoint = false;
+    for (i = 0; i < circles.length; ++i) {
+      if (
+        distance(circles[i], smallest) >
+        Math.abs(smallest.radius - circles[i].radius)
+      ) {
+        disjoint = true;
+        break;
+      }
+    }
+
+    if (disjoint) {
+      arcArea = polygonArea = 0;
+    } else {
+      arcArea = smallest.radius * smallest.radius * Math.PI;
+      arcs.push({
+        circle: smallest,
+        p1: { x: smallest.x, y: smallest.y + smallest.radius },
+        p2: { x: smallest.x - SMALL, y: smallest.y + smallest.radius },
+        width: smallest.radius * 2,
+      });
+    }
+  }
+
+  polygonArea /= 2;
+  if (stats) {
+    stats.area = arcArea + polygonArea;
+    stats.arcArea = arcArea;
+    stats.polygonArea = polygonArea;
+    stats.arcs = arcs;
+    stats.innerPoints = innerPoints;
+    stats.intersectionPoints = intersectionPoints;
+  }
+
+  return arcArea + polygonArea;
+}
+
+/**
+ * Returns whether a point is contained by all of a list of circles
+ */
+export function containedInCircles(point, circles) {
+  for (let i = 0; i < circles.length; ++i) {
+    if (distance(point, circles[i]) > circles[i].radius + SMALL) {
+      return false;
+    }
+  }
+  return true;
+}
+
+/** Gets all intersection points between a bunch of circles */
+function getIntersectionPoints(circles) {
+  const ret = [];
+  for (let i = 0; i < circles.length; ++i) {
+    for (let j = i + 1; j < circles.length; ++j) {
+      const intersect = circleCircleIntersection(circles[i], circles[j]);
+      for (let k = 0; k < intersect.length; ++k) {
+        const p: any = intersect[k];
+        p.parentIndex = [i, j];
+        ret.push(p);
+      }
+    }
+  }
+  return ret;
+}
+
+/** Circular segment area calculation. See http://mathworld.wolfram.com/CircularSegment.html */
+export function circleArea(r, width) {
+  return (
+    r * r * Math.acos(1 - width / r) -
+    (r - width) * Math.sqrt(width * (2 * r - width))
+  );
+}
+
+/** Euclidean distance between two points */
+export function distance(p1, p2) {
+  return Math.sqrt(
+    (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y),
+  );
+}
+
+/** Returns the overlap area of two circles of radius r1 and r2 - that
+have their centers separated by distance d. Simpler faster
+circle intersection for only two circles */
+export function circleOverlap(r1, r2, d) {
+  // no overlap
+  if (d >= r1 + r2) {
+    return 0;
+  }
+
+  // Completely overlapped
+  if (d <= Math.abs(r1 - r2)) {
+    return Math.PI * Math.min(r1, r2) * Math.min(r1, r2);
+  }
+
+  const w1 = r1 - (d * d - r2 * r2 + r1 * r1) / (2 * d),
+    w2 = r2 - (d * d - r1 * r1 + r2 * r2) / (2 * d);
+  return circleArea(r1, w1) + circleArea(r2, w2);
+}
+
+/** Given two circles (containing a x/y/radius attributes),
+returns the intersecting points if possible.
+note: doesn't handle cases where there are infinitely many
+intersection points (circles are equivalent):, or only one intersection point*/
+export function circleCircleIntersection(p1, p2) {
+  const d = distance(p1, p2),
+    r1 = p1.radius,
+    r2 = p2.radius;
+
+  // If to far away, or self contained - can't be done
+  if (d >= r1 + r2 || d <= Math.abs(r1 - r2)) {
+    return [];
+  }
+
+  const a = (r1 * r1 - r2 * r2 + d * d) / (2 * d),
+    h = Math.sqrt(r1 * r1 - a * a),
+    x0 = p1.x + (a * (p2.x - p1.x)) / d,
+    y0 = p1.y + (a * (p2.y - p1.y)) / d,
+    rx = -(p2.y - p1.y) * (h / d),
+    ry = -(p2.x - p1.x) * (h / d);
+
+  return [
+    { x: x0 + rx, y: y0 - ry },
+    { x: x0 - rx, y: y0 + ry },
+  ];
+}
+
+/** Returns the center of a bunch of points */
+export function getCenter(points) {
+  const center = { x: 0, y: 0 };
+  for (let i = 0; i < points.length; ++i) {
+    center.x += points[i].x;
+    center.y += points[i].y;
+  }
+  center.x /= points.length;
+  center.y /= points.length;
+  return center;
+}
diff --git a/src/data/utils/venn/diagram.ts b/src/data/utils/venn/diagram.ts
new file mode 100644
index 0000000000..44e010cb35
--- /dev/null
+++ b/src/data/utils/venn/diagram.ts
@@ -0,0 +1,47 @@
+import { intersectionArea } from './circleintersection';
+
+/**
+ * 根据圆心(x, y) 半径 r 返回圆的绘制 path
+ * @param x 圆心点 x
+ * @param y 圆心点 y
+ * @param r 圆的半径
+ * @returns 圆的 path
+ */
+function circlePath(x, y, r) {
+  const ret = [];
+  // ret.push('\nM', x, y);
+  // ret.push('\nm', -r, 0);
+  // ret.push('\na', r, r, 0, 1, 0, r * 2, 0);
+  // ret.push('\na', r, r, 0, 1, 0, -r * 2, 0);
+  const x0 = x - r;
+  const y0 = y;
+  ret.push('M', x0, y0);
+  ret.push('A', r, r, 0, 1, 0, x0 + 2 * r, y0);
+  ret.push('A', r, r, 0, 1, 0, x0, y0);
+
+  return ret.join(' ');
+}
+
+/** returns a svg path of the intersection area of a bunch of circles */
+export function intersectionAreaPath(circles) {
+  const stats: any = {};
+  intersectionArea(circles, stats);
+  const arcs = stats.arcs;
+
+  if (arcs.length === 0) {
+    return 'M 0 0';
+  } else if (arcs.length == 1) {
+    const circle = arcs[0].circle;
+    return circlePath(circle.x, circle.y, circle.radius);
+  } else {
+    // draw path around arcs
+    const ret = ['\nM', arcs[0].p2.x, arcs[0].p2.y];
+    for (let i = 0; i < arcs.length; ++i) {
+      const arc = arcs[i],
+        r = arc.circle.radius,
+        wide = arc.width > r;
+      ret.push('\nA', r, r, 0, wide ? 1 : 0, 1, arc.p1.x, arc.p1.y);
+    }
+    return ret.join(' ');
+  }
+}
diff --git a/src/data/utils/venn/index.ts b/src/data/utils/venn/index.ts
new file mode 100644
index 0000000000..c37b2c63e8
--- /dev/null
+++ b/src/data/utils/venn/index.ts
@@ -0,0 +1,5 @@
+/**
+ * Code from https://github.com/benfred/venn.js/blob/master/src/.
+ */
+export { scaleSolution, venn } from './layout';
+export { intersectionAreaPath } from './diagram';
diff --git a/src/data/utils/venn/layout.ts b/src/data/utils/venn/layout.ts
new file mode 100644
index 0000000000..2807dacea7
--- /dev/null
+++ b/src/data/utils/venn/layout.ts
@@ -0,0 +1,769 @@
+import {
+  bisect,
+  conjugateGradient,
+  nelderMead,
+  norm2,
+  scale,
+  zeros,
+  zerosM,
+} from 'fmin';
+import {
+  circleCircleIntersection,
+  circleOverlap,
+  distance,
+  intersectionArea,
+} from './circleintersection';
+
+/** given a list of set objects, and their corresponding overlaps.
+updates the (x, y, radius) attribute on each set such that their positions
+roughly correspond to the desired overlaps */
+export function venn(areas, parameters?: any) {
+  parameters = parameters || {};
+  parameters.maxIterations = parameters.maxIterations || 500;
+  const initialLayout = parameters.initialLayout || bestInitialLayout;
+  const loss = parameters.lossFunction || lossFunction;
+
+  // add in missing pairwise areas as having 0 size
+  areas = addMissingAreas(areas);
+
+  // initial layout is done greedily
+  const circles = initialLayout(areas, parameters);
+
+  // transform x/y coordinates to a vector to optimize
+  const initial = [],
+    setids = [];
+  let setid;
+  for (setid in circles) {
+    // eslint-disable-next-line
+    if (circles.hasOwnProperty(setid)) {
+      initial.push(circles[setid].x);
+      initial.push(circles[setid].y);
+      setids.push(setid);
+    }
+  }
+
+  // optimize initial layout from our loss function
+  const solution = nelderMead(
+    function (values) {
+      const current = {};
+      for (let i = 0; i < setids.length; ++i) {
+        const setid = setids[i];
+        current[setid] = {
+          x: values[2 * i],
+          y: values[2 * i + 1],
+          radius: circles[setid].radius,
+        };
+      }
+      return loss(current, areas);
+    },
+    initial,
+    parameters,
+  );
+
+  // transform solution vector back to x/y points
+  const positions = solution.x;
+  for (let i = 0; i < setids.length; ++i) {
+    setid = setids[i];
+    circles[setid].x = positions[2 * i];
+    circles[setid].y = positions[2 * i + 1];
+  }
+
+  return circles;
+}
+
+const SMALL = 1e-10;
+
+/** Returns the distance necessary for two circles of radius r1 + r2 to
+have the overlap area 'overlap' */
+export function distanceFromIntersectArea(r1, r2, overlap) {
+  // handle complete overlapped circles
+  if (Math.min(r1, r2) * Math.min(r1, r2) * Math.PI <= overlap + SMALL) {
+    return Math.abs(r1 - r2);
+  }
+
+  return bisect(
+    function (distance) {
+      return circleOverlap(r1, r2, distance) - overlap;
+    },
+    0,
+    r1 + r2,
+  );
+}
+
+/** Missing pair-wise intersection area data can cause problems:
+ treating as an unknown means that sets will be laid out overlapping,
+ which isn't what people expect. To reflect that we want disjoint sets
+ here, set the overlap to 0 for all missing pairwise set intersections */
+function addMissingAreas(areas) {
+  areas = areas.slice();
+
+  // two circle intersections that aren't defined
+  const ids: number[] = [],
+    pairs: any = {};
+  let i, j, a, b;
+  for (i = 0; i < areas.length; ++i) {
+    const area = areas[i];
+    if (area.sets.length == 1) {
+      ids.push(area.sets[0]);
+    } else if (area.sets.length == 2) {
+      a = area.sets[0];
+      b = area.sets[1];
+      // @ts-ignore
+      pairs[[a, b]] = true;
+      // @ts-ignore
+      pairs[[b, a]] = true;
+    }
+  }
+  ids.sort((a, b) => {
+    return a > b ? 1 : -1;
+  });
+
+  for (i = 0; i < ids.length; ++i) {
+    a = ids[i];
+    for (j = i + 1; j < ids.length; ++j) {
+      b = ids[j];
+      // @ts-ignore
+      if (!([a, b] in pairs)) {
+        areas.push({ sets: [a, b], size: 0 });
+      }
+    }
+  }
+  return areas;
+}
+
+/// Returns two matrices, one of the euclidean distances between the sets
+/// and the other indicating if there are subset or disjoint set relationships
+export function getDistanceMatrices(areas, sets, setids) {
+  // initialize an empty distance matrix between all the points
+  const distances = zerosM(sets.length, sets.length),
+    constraints = zerosM(sets.length, sets.length);
+
+  // compute required distances between all the sets such that
+  // the areas match
+  areas
+    .filter(function (x) {
+      return x.sets.length == 2;
+    })
+    .map(function (current) {
+      const left = setids[current.sets[0]],
+        right = setids[current.sets[1]],
+        r1 = Math.sqrt(sets[left].size / Math.PI),
+        r2 = Math.sqrt(sets[right].size / Math.PI),
+        distance = distanceFromIntersectArea(r1, r2, current.size);
+
+      distances[left][right] = distances[right][left] = distance;
+
+      // also update constraints to indicate if its a subset or disjoint
+      // relationship
+      let c = 0;
+      if (current.size + 1e-10 >= Math.min(sets[left].size, sets[right].size)) {
+        c = 1;
+      } else if (current.size <= 1e-10) {
+        c = -1;
+      }
+      constraints[left][right] = constraints[right][left] = c;
+    });
+
+  return { distances: distances, constraints: constraints };
+}
+
+/// computes the gradient and loss simulatenously for our constrained MDS optimizer
+function constrainedMDSGradient(x, fxprime, distances, constraints) {
+  let loss = 0,
+    i;
+  for (i = 0; i < fxprime.length; ++i) {
+    fxprime[i] = 0;
+  }
+
+  for (i = 0; i < distances.length; ++i) {
+    const xi = x[2 * i],
+      yi = x[2 * i + 1];
+    for (let j = i + 1; j < distances.length; ++j) {
+      const xj = x[2 * j],
+        yj = x[2 * j + 1],
+        dij = distances[i][j],
+        constraint = constraints[i][j];
+
+      const squaredDistance = (xj - xi) * (xj - xi) + (yj - yi) * (yj - yi),
+        distance = Math.sqrt(squaredDistance),
+        delta = squaredDistance - dij * dij;
+
+      if (
+        (constraint > 0 && distance <= dij) ||
+        (constraint < 0 && distance >= dij)
+      ) {
+        continue;
+      }
+
+      loss += 2 * delta * delta;
+
+      fxprime[2 * i] += 4 * delta * (xi - xj);
+      fxprime[2 * i + 1] += 4 * delta * (yi - yj);
+
+      fxprime[2 * j] += 4 * delta * (xj - xi);
+      fxprime[2 * j + 1] += 4 * delta * (yj - yi);
+    }
+  }
+  return loss;
+}
+
+/// takes the best working variant of either constrained MDS or greedy
+export function bestInitialLayout(areas, params) {
+  let initial = greedyLayout(areas, params);
+  const loss = params.lossFunction || lossFunction;
+
+  // greedylayout is sufficient for all 2/3 circle cases. try out
+  // constrained MDS for higher order problems, take its output
+  // if it outperforms. (greedy is aesthetically better on 2/3 circles
+  // since it axis aligns)
+  if (areas.length >= 8) {
+    const constrained = constrainedMDSLayout(areas, params),
+      constrainedLoss = loss(constrained, areas),
+      greedyLoss = loss(initial, areas);
+
+    if (constrainedLoss + 1e-8 < greedyLoss) {
+      initial = constrained;
+    }
+  }
+  return initial;
+}
+
+/// use the constrained MDS variant to generate an initial layout
+export function constrainedMDSLayout(areas, params) {
+  params = params || {};
+  const restarts = params.restarts || 10;
+
+  // bidirectionally map sets to a rowid  (so we can create a matrix)
+  const sets = [],
+    setids = {};
+  let i;
+  for (i = 0; i < areas.length; ++i) {
+    const area = areas[i];
+    if (area.sets.length == 1) {
+      setids[area.sets[0]] = sets.length;
+      sets.push(area);
+    }
+  }
+
+  const matrices = getDistanceMatrices(areas, sets, setids);
+  let distances = matrices.distances;
+  const constraints = matrices.constraints;
+
+  // keep distances bounded, things get messed up otherwise.
+  // TODO: proper preconditioner?
+  const norm = norm2(distances.map(norm2)) / distances.length;
+  distances = distances.map(function (row) {
+    return row.map(function (value) {
+      return value / norm;
+    });
+  });
+
+  const obj = function (x, fxprime) {
+    return constrainedMDSGradient(x, fxprime, distances, constraints);
+  };
+
+  let best, current;
+  for (i = 0; i < restarts; ++i) {
+    const initial = zeros(distances.length * 2).map(Math.random);
+
+    current = conjugateGradient(obj, initial, params);
+    if (!best || current.fx < best.fx) {
+      best = current;
+    }
+  }
+  const positions = best.x;
+
+  // translate rows back to (x,y,radius) coordinates
+  const circles = {};
+  for (i = 0; i < sets.length; ++i) {
+    const set = sets[i];
+    circles[set.sets[0]] = {
+      x: positions[2 * i] * norm,
+      y: positions[2 * i + 1] * norm,
+      radius: Math.sqrt(set.size / Math.PI),
+    };
+  }
+
+  if (params.history) {
+    for (i = 0; i < params.history.length; ++i) {
+      scale(params.history[i].x, norm);
+    }
+  }
+  return circles;
+}
+
+/** Lays out a Venn diagram greedily, going from most overlapped sets to
+least overlapped, attempting to position each new set such that the
+overlapping areas to already positioned sets are basically right */
+export function greedyLayout(areas, params) {
+  const loss =
+    params && params.lossFunction ? params.lossFunction : lossFunction;
+  // define a circle for each set
+  const circles = {},
+    setOverlaps = {};
+  let set;
+  for (let i = 0; i < areas.length; ++i) {
+    const area = areas[i];
+    if (area.sets.length == 1) {
+      set = area.sets[0];
+      circles[set] = {
+        x: 1e10,
+        y: 1e10,
+        // rowid: circles.length, // fix to ->
+        rowid: Object.keys(circles).length,
+        size: area.size,
+        radius: Math.sqrt(area.size / Math.PI),
+      };
+      setOverlaps[set] = [];
+    }
+  }
+  areas = areas.filter(function (a) {
+    return a.sets.length == 2;
+  });
+
+  // map each set to a list of all the other sets that overlap it
+  for (let i = 0; i < areas.length; ++i) {
+    const current = areas[i];
+    // eslint-disable-next-line
+    let weight = current.hasOwnProperty('weight') ? current.weight : 1.0;
+    const left = current.sets[0],
+      right = current.sets[1];
+
+    // completely overlapped circles shouldn't be positioned early here
+    if (
+      current.size + SMALL >=
+      Math.min(circles[left].size, circles[right].size)
+    ) {
+      weight = 0;
+    }
+
+    setOverlaps[left].push({ set: right, size: current.size, weight: weight });
+    setOverlaps[right].push({ set: left, size: current.size, weight: weight });
+  }
+
+  // get list of most overlapped sets
+  const mostOverlapped = [];
+  for (set in setOverlaps) {
+    // eslint-disable-next-line
+    if (setOverlaps.hasOwnProperty(set)) {
+      let size = 0;
+      for (let i = 0; i < setOverlaps[set].length; ++i) {
+        size += setOverlaps[set][i].size * setOverlaps[set][i].weight;
+      }
+
+      mostOverlapped.push({ set: set, size: size });
+    }
+  }
+
+  // sort by size desc
+  function sortOrder(a, b) {
+    return b.size - a.size;
+  }
+  mostOverlapped.sort(sortOrder);
+
+  // keep track of what sets have been laid out
+  const positioned = {};
+  function isPositioned(element) {
+    return element.set in positioned;
+  }
+
+  // adds a point to the output
+  function positionSet(point, index) {
+    circles[index].x = point.x;
+    circles[index].y = point.y;
+    positioned[index] = true;
+  }
+
+  // add most overlapped set at (0,0)
+  positionSet({ x: 0, y: 0 }, mostOverlapped[0].set);
+
+  // get distances between all points. TODO, necessary?
+  // answer: probably not
+  // var distances = venn.getDistanceMatrices(circles, areas).distances;
+  for (let i = 1; i < mostOverlapped.length; ++i) {
+    const setIndex = mostOverlapped[i].set,
+      overlap = setOverlaps[setIndex].filter(isPositioned);
+    set = circles[setIndex];
+    overlap.sort(sortOrder);
+
+    if (overlap.length === 0) {
+      // this shouldn't happen anymore with addMissingAreas
+      throw 'ERROR: missing pairwise overlap information';
+    }
+
+    const points = [];
+    for (let j = 0; j < overlap.length; ++j) {
+      // get appropriate distance from most overlapped already added set
+      const p1 = circles[overlap[j].set],
+        d1 = distanceFromIntersectArea(set.radius, p1.radius, overlap[j].size);
+
+      // sample positions at 90 degrees for maximum aesthetics
+      points.push({ x: p1.x + d1, y: p1.y });
+      points.push({ x: p1.x - d1, y: p1.y });
+      points.push({ y: p1.y + d1, x: p1.x });
+      points.push({ y: p1.y - d1, x: p1.x });
+
+      // if we have at least 2 overlaps, then figure out where the
+      // set should be positioned analytically and try those too
+      for (let k = j + 1; k < overlap.length; ++k) {
+        const p2 = circles[overlap[k].set],
+          d2 = distanceFromIntersectArea(
+            set.radius,
+            p2.radius,
+            overlap[k].size,
+          );
+
+        const extraPoints = circleCircleIntersection(
+          { x: p1.x, y: p1.y, radius: d1 },
+          { x: p2.x, y: p2.y, radius: d2 },
+        );
+
+        for (let l = 0; l < extraPoints.length; ++l) {
+          points.push(extraPoints[l]);
+        }
+      }
+    }
+
+    // we have some candidate positions for the set, examine loss
+    // at each position to figure out where to put it at
+    let bestLoss = 1e50,
+      bestPoint = points[0];
+    for (let j = 0; j < points.length; ++j) {
+      circles[setIndex].x = points[j].x;
+      circles[setIndex].y = points[j].y;
+      const localLoss = loss(circles, areas);
+      if (localLoss < bestLoss) {
+        bestLoss = localLoss;
+        bestPoint = points[j];
+      }
+    }
+
+    positionSet(bestPoint, setIndex);
+  }
+
+  return circles;
+}
+
+/** Given a bunch of sets, and the desired overlaps between these sets - computes
+the distance from the actual overlaps to the desired overlaps. Note that
+this method ignores overlaps of more than 2 circles */
+export function lossFunction(sets, overlaps) {
+  let output = 0;
+
+  function getCircles(indices) {
+    return indices.map(function (i) {
+      return sets[i];
+    });
+  }
+
+  for (let i = 0; i < overlaps.length; ++i) {
+    const area = overlaps[i];
+    let overlap;
+    if (area.sets.length == 1) {
+      continue;
+    } else if (area.sets.length == 2) {
+      const left = sets[area.sets[0]],
+        right = sets[area.sets[1]];
+      overlap = circleOverlap(left.radius, right.radius, distance(left, right));
+    } else {
+      overlap = intersectionArea(getCircles(area.sets));
+    }
+
+    // eslint-disable-next-line
+    const weight = area.hasOwnProperty('weight') ? area.weight : 1.0;
+    output += weight * (overlap - area.size) * (overlap - area.size);
+  }
+
+  return output;
+}
+
+// orientates a bunch of circles to point in orientation
+function orientateCircles(circles, orientation, orientationOrder) {
+  if (orientationOrder === null) {
+    circles.sort(function (a, b) {
+      return b.radius - a.radius;
+    });
+  } else {
+    circles.sort(orientationOrder);
+  }
+
+  let i;
+  // shift circles so largest circle is at (0, 0)
+  if (circles.length > 0) {
+    const largestX = circles[0].x,
+      largestY = circles[0].y;
+
+    for (i = 0; i < circles.length; ++i) {
+      circles[i].x -= largestX;
+      circles[i].y -= largestY;
+    }
+  }
+
+  if (circles.length == 2) {
+    // if the second circle is a subset of the first, arrange so that
+    // it is off to one side. hack for https://github.com/benfred/venn.js/issues/120
+    const dist = distance(circles[0], circles[1]);
+    if (dist < Math.abs(circles[1].radius - circles[0].radius)) {
+      circles[1].x =
+        circles[0].x + circles[0].radius - circles[1].radius - 1e-10;
+      circles[1].y = circles[0].y;
+    }
+  }
+
+  // rotate circles so that second largest is at an angle of 'orientation'
+  // from largest
+  if (circles.length > 1) {
+    const rotation = Math.atan2(circles[1].x, circles[1].y) - orientation;
+    let x, y;
+    const c = Math.cos(rotation),
+      s = Math.sin(rotation);
+    for (i = 0; i < circles.length; ++i) {
+      x = circles[i].x;
+      y = circles[i].y;
+      circles[i].x = c * x - s * y;
+      circles[i].y = s * x + c * y;
+    }
+  }
+
+  // mirror solution if third solution is above plane specified by
+  // first two circles
+  if (circles.length > 2) {
+    let angle = Math.atan2(circles[2].x, circles[2].y) - orientation;
+    while (angle < 0) {
+      angle += 2 * Math.PI;
+    }
+    while (angle > 2 * Math.PI) {
+      angle -= 2 * Math.PI;
+    }
+    if (angle > Math.PI) {
+      const slope = circles[1].y / (1e-10 + circles[1].x);
+      for (i = 0; i < circles.length; ++i) {
+        const d = (circles[i].x + slope * circles[i].y) / (1 + slope * slope);
+        circles[i].x = 2 * d - circles[i].x;
+        circles[i].y = 2 * d * slope - circles[i].y;
+      }
+    }
+  }
+}
+
+export function disjointCluster(circles) {
+  // union-find clustering to get disjoint sets
+  circles.map(function (circle) {
+    circle.parent = circle;
+  });
+
+  // path compression step in union find
+  function find(circle) {
+    if (circle.parent !== circle) {
+      circle.parent = find(circle.parent);
+    }
+    return circle.parent;
+  }
+
+  function union(x, y) {
+    const xRoot = find(x),
+      yRoot = find(y);
+    xRoot.parent = yRoot;
+  }
+
+  // get the union of all overlapping sets
+  for (let i = 0; i < circles.length; ++i) {
+    for (let j = i + 1; j < circles.length; ++j) {
+      const maxDistance = circles[i].radius + circles[j].radius;
+      if (distance(circles[i], circles[j]) + 1e-10 < maxDistance) {
+        union(circles[j], circles[i]);
+      }
+    }
+  }
+
+  // find all the disjoint clusters and group them together
+  const disjointClusters = {};
+  let setid;
+  for (let i = 0; i < circles.length; ++i) {
+    setid = find(circles[i]).parent.setid;
+    if (!(setid in disjointClusters)) {
+      disjointClusters[setid] = [];
+    }
+    disjointClusters[setid].push(circles[i]);
+  }
+
+  // cleanup bookkeeping
+  circles.map(function (circle) {
+    delete circle.parent;
+  });
+
+  // return in more usable form
+  const ret = [];
+  for (setid in disjointClusters) {
+    // eslint-disable-next-line
+    if (disjointClusters.hasOwnProperty(setid)) {
+      ret.push(disjointClusters[setid]);
+    }
+  }
+  return ret;
+}
+
+function getBoundingBox(circles) {
+  const minMax = function (d) {
+    const hi = Math.max.apply(
+        null,
+        circles.map(function (c) {
+          return c[d] + c.radius;
+        }),
+      ),
+      lo = Math.min.apply(
+        null,
+        circles.map(function (c) {
+          return c[d] - c.radius;
+        }),
+      );
+    return { max: hi, min: lo };
+  };
+
+  return { xRange: minMax('x'), yRange: minMax('y') };
+}
+
+export function normalizeSolution(solution, orientation, orientationOrder) {
+  if (orientation === null) {
+    orientation = Math.PI / 2;
+  }
+
+  // work with a list instead of a dictionary, and take a copy so we
+  // don't mutate input
+  let circles = [],
+    i,
+    setid;
+  for (setid in solution) {
+    // eslint-disable-next-line
+    if (solution.hasOwnProperty(setid)) {
+      const previous = solution[setid];
+      circles.push({
+        x: previous.x,
+        y: previous.y,
+        radius: previous.radius,
+        setid: setid,
+      });
+    }
+  }
+
+  // get all the disjoint clusters
+  const clusters = disjointCluster(circles);
+
+  // orientate all disjoint sets, get sizes
+  for (i = 0; i < clusters.length; ++i) {
+    orientateCircles(clusters[i], orientation, orientationOrder);
+    const bounds = getBoundingBox(clusters[i]);
+    clusters[i].size =
+      (bounds.xRange.max - bounds.xRange.min) *
+      (bounds.yRange.max - bounds.yRange.min);
+    clusters[i].bounds = bounds;
+  }
+  clusters.sort(function (a, b) {
+    return b.size - a.size;
+  });
+
+  // orientate the largest at 0,0, and get the bounds
+  circles = clusters[0];
+  // @ts-ignore fixme 从逻辑上看似乎是不对的，后续看看
+  let returnBounds = circles.bounds;
+
+  const spacing = (returnBounds.xRange.max - returnBounds.xRange.min) / 50;
+
+  function addCluster(cluster, right, bottom) {
+    if (!cluster) return;
+
+    const bounds = cluster.bounds;
+    let xOffset, yOffset, centreing;
+
+    if (right) {
+      xOffset = returnBounds.xRange.max - bounds.xRange.min + spacing;
+    } else {
+      xOffset = returnBounds.xRange.max - bounds.xRange.max;
+      centreing =
+        (bounds.xRange.max - bounds.xRange.min) / 2 -
+        (returnBounds.xRange.max - returnBounds.xRange.min) / 2;
+      if (centreing < 0) xOffset += centreing;
+    }
+
+    if (bottom) {
+      yOffset = returnBounds.yRange.max - bounds.yRange.min + spacing;
+    } else {
+      yOffset = returnBounds.yRange.max - bounds.yRange.max;
+      centreing =
+        (bounds.yRange.max - bounds.yRange.min) / 2 -
+        (returnBounds.yRange.max - returnBounds.yRange.min) / 2;
+      if (centreing < 0) yOffset += centreing;
+    }
+
+    for (let j = 0; j < cluster.length; ++j) {
+      cluster[j].x += xOffset;
+      cluster[j].y += yOffset;
+      circles.push(cluster[j]);
+    }
+  }
+
+  let index = 1;
+  while (index < clusters.length) {
+    addCluster(clusters[index], true, false);
+    addCluster(clusters[index + 1], false, true);
+    addCluster(clusters[index + 2], true, true);
+    index += 3;
+
+    // have one cluster (in top left). lay out next three relative
+    // to it in a grid
+    returnBounds = getBoundingBox(circles);
+  }
+
+  // convert back to solution form
+  const ret = {};
+  for (i = 0; i < circles.length; ++i) {
+    ret[circles[i].setid] = circles[i];
+  }
+  return ret;
+}
+
+/** Scales a solution from venn.venn or venn.greedyLayout such that it fits in
+a rectangle of width/height - with padding around the borders. also
+centers the diagram in the available space at the same time */
+export function scaleSolution(solution, width, height, padding) {
+  const circles = [],
+    setids = [];
+  for (const setid in solution) {
+    // eslint-disable-next-line
+    if (solution.hasOwnProperty(setid)) {
+      setids.push(setid);
+      circles.push(solution[setid]);
+    }
+  }
+
+  width -= 2 * padding;
+  height -= 2 * padding;
+
+  const bounds = getBoundingBox(circles),
+    xRange = bounds.xRange,
+    yRange = bounds.yRange;
+
+  if (xRange.max == xRange.min || yRange.max == yRange.min) {
+    console.log('not scaling solution: zero size detected');
+    return solution;
+  }
+
+  const xScaling = width / (xRange.max - xRange.min),
+    yScaling = height / (yRange.max - yRange.min),
+    scaling = Math.min(yScaling, xScaling),
+    // while we're at it, center the diagram too
+    xOffset = (width - (xRange.max - xRange.min) * scaling) / 2,
+    yOffset = (height - (yRange.max - yRange.min) * scaling) / 2;
+
+  const scaled = {};
+  for (let i = 0; i < circles.length; ++i) {
+    const circle = circles[i];
+    scaled[setids[i]] = {
+      radius: scaling * circle.radius,
+      x: padding + xOffset + (circle.x - xRange.min) * scaling,
+      y: padding + yOffset + (circle.y - yRange.min) * scaling,
+    };
+  }
+
+  return scaled;
+}
diff --git a/src/data/venn.ts b/src/data/venn.ts
new file mode 100644
index 0000000000..018f7fc566
--- /dev/null
+++ b/src/data/venn.ts
@@ -0,0 +1,58 @@
+import { DataComponent as DC } from '../runtime';
+import { VennDataTransform } from '../spec';
+import { intersectionAreaPath, scaleSolution, venn } from './utils/venn';
+
+export type VennOptions = Omit<VennDataTransform, 'type'>;
+
+type VennData = {
+  key?: string;
+  sets: string[];
+  size: number;
+};
+
+/**
+ * Layout venn data, get the path string for each set.
+ */
+export const Venn: DC<VennOptions> = (options) => {
+  const {
+    sets = 'sets',
+    size = 'size',
+    as = ['key', 'path'],
+    padding = 0,
+  } = options;
+  const [key, path] = as;
+  return (data) => {
+    // Transform the data, venn layout use `sets` and `size` field.
+    const vennData: VennData[] = data.map((d) => ({
+      ...d,
+      sets: d[sets],
+      size: d[size],
+      [key]: d.sets.join('&'),
+    }));
+    // Sort data, avoid data occlusion.
+    vennData.sort((a, b) => a.sets.length - b.sets.length);
+
+    // Layout venn data.
+    const solution = venn(vennData);
+
+    let circles;
+
+    return vennData.map((datum) => {
+      const setsValue = datum[sets];
+      const pathFunc = ({ width, height }) => {
+        circles = circles
+          ? circles
+          : scaleSolution(solution, width, height, padding);
+        const setCircles = setsValue.map((set) => circles[set]);
+        let p = intersectionAreaPath(setCircles);
+        // Close the path for event picker.
+        if (!/[zZ]$/.test(p)) p += ' Z';
+        return p;
+      };
+
+      return { ...datum, [path]: pathFunc };
+    });
+  };
+};
+
+Venn.props = {};
diff --git a/src/shape/path/color.ts b/src/shape/path/color.ts
index 49f6f965b8..da579b98a6 100644
--- a/src/shape/path/color.ts
+++ b/src/shape/path/color.ts
@@ -22,12 +22,16 @@ export const Color: SC<ColorOptions> = (options) => {
       defaultShape,
     );
     const { d, color } = value;
-    return select(new GPath())
-      .call(applyStyle, shapeTheme)
-      .style('d', d)
-      .style(colorAttribute, color)
-      .call(applyStyle, style)
-      .node();
+    const [width, height] = coordinate.getSize();
+    return (
+      select(new GPath())
+        .call(applyStyle, shapeTheme)
+        // Path support string, function with parameter { width, height }.
+        .style('d', typeof d === 'function' ? d({ width, height }) : d)
+        .style(colorAttribute, color)
+        .call(applyStyle, style)
+        .node()
+    );
   };
 };
 
diff --git a/src/spec/dataTransform.ts b/src/spec/dataTransform.ts
index 63c4612e6f..41dc4980f4 100644
--- a/src/spec/dataTransform.ts
+++ b/src/spec/dataTransform.ts
@@ -11,6 +11,7 @@ export type DataTransform =
   | MapTransform
   | SliceTransform
   | KDEDataTransform
+  | VennDataTransform
   | CustomTransform;
 
 export type DataTransformTypes =
@@ -24,6 +25,7 @@ export type DataTransformTypes =
   | 'map'
   | 'slice'
   | 'kde'
+  | 'venn'
   | 'custom'
   | DataComponent;
 
@@ -154,6 +156,29 @@ export type KDEDataTransform = {
   width?: number;
 };
 
+export type VennDataTransform = {
+  type?: 'venn';
+  /**
+   * Canvas padding for 4 direction.
+   * Default is `0`.
+   */
+  padding?: number;
+  /**
+   * Set the sets field.
+   * Default is `sets`.
+   */
+  sets?: string;
+  /**
+   * Set the size field for each set.
+   * Default is `size`.
+   */
+  size?: string;
+  /**
+   * Set the generated fields, includes: [key, x, y, path]
+   */
+  as?: [string, string];
+};
+
 export type CustomTransform = {
   type?: DataComponent;
   [key: string]: any;
diff --git a/src/stdlib/index.ts b/src/stdlib/index.ts
index a25dd0acaf..a87365b36c 100644
--- a/src/stdlib/index.ts
+++ b/src/stdlib/index.ts
@@ -244,6 +244,7 @@ import {
   Join,
   Sort,
   KDE,
+  Venn,
 } from '../data';
 import {
   OverlapDodgeY,
@@ -273,6 +274,7 @@ export function createLibrary(): G2Library {
     'data.wordCloud': WordCloud,
     'data.join': Join,
     'data.kde': KDE,
+    'data.venn': Venn,
     // 'transform.voronoi': Voronoi,
     'transform.maybeZeroY1': MaybeZeroY1,
     'transform.maybeZeroX': MaybeZeroX,