# Optimize Lots of Objects Animated

This article is a continuation of an article about optimizing lots of objects . If you haven't read that yet please read it before proceeding.

In the previous article we merged around 19000 cubes into a single geometry. This had the advantage that it optimized our drawing of 19000 cubes but it had the disadvantage of make it harder to move any individual cube.

Depending on what we are trying to accomplish there are different solutions. In this case let's graph multiple sets of data and animate between the sets.

The first thing we need to do is get multiple sets of data. Ideally we'd probably pre-process data offline but in this case let's load 2 sets of data and generate 2 more

Here's our old loading code

    loadFile('resources/data/gpw/gpw_v4_basic_demographic_characteristics_rev10_a000_014mt_2010_cntm_1_deg.asc')
      .then(parseData)
      .then(addBoxes)
      .then(render);

Let's change it to something like this

    async function loadData(info) {
      const text = await loadFile(info.url);
      info.file = parseData(text);
    }

    async function loadAll() {
      const fileInfos = [
        {name: 'men',   hueRange: [0.7, 0.3], url: 'resources/data/gpw/gpw_v4_basic_demographic_characteristics_rev10_a000_014mt_2010_cntm_1_deg.asc' },
        {name: 'women', hueRange: [0.9, 1.1], url: 'resources/data/gpw/gpw_v4_basic_demographic_characteristics_rev10_a000_014ft_2010_cntm_1_deg.asc' },
      ];

      await Promise.all(fileInfos.map(loadData));

      ...
    }
    loadAll();

The code above will load all the files in `fileInfos` and when done each object in `fileInfos` will have a `file` property with the loaded file. `name` and `hueRange` we'll use later. `name` will be for a UI field. `hueRange` will be used to choose a range of hues to map over.

The two files above are apparently the number of men per area and the number of women per area as of 2010. Note, I have no idea if this data is correct but it's not important really. The important part is showing different sets of data.

Let's generate 2 more sets of data. One being the places where the number men are greater than the number of women and vice versa, the places where the number of women are greater than the number of men.

The first thing let's write a function that given a 2 dimensional array of arrays like we had before will map over it to generate a new 2 dimensional array of arrays

    function mapValues(data, fn) {
      return data.map((row, rowNdx) => {
        return row.map((value, colNdx) => {
          return fn(value, rowNdx, colNdx);
        });
      });
    }

Like the normal `Array.map` function the `mapValues` function calls a function `fn` for each value in the array of arrays. It passes it the value and both the row and column indices.

Now let's make some code to generate a new file that is a comparison between 2 files

    function makeDiffFile(baseFile, otherFile, compareFn) {
      let min;
      let max;
      const baseData = baseFile.data;
      const otherData = otherFile.data;
      const data = mapValues(baseData, (base, rowNdx, colNdx) => {
        const other = otherData[rowNdx][colNdx];
          if (base === undefined || other === undefined) {
            return undefined;
          }
          const value = compareFn(base, other);
          min = Math.min(min === undefined ? value : min, value);
          max = Math.max(max === undefined ? value : max, value);
          return value;
      });
      // make a copy of baseFile and replace min, max, and data
      // with the new data
      return {...baseFile, min, max, data};
    }

The code above uses `mapValues` to generate a new set of data that is a comparison based on the `compareFn` function passed in. It also tracks the `min` and `max` comparison results. Finally it makes a new file with all the same properties as `baseFile` except with a new `min`, `max` and `data`.

Then let's use that to make 2 new sets of data

    {
      const menInfo = fileInfos[0];
      const womenInfo = fileInfos[1];
      const menFile = menInfo.file;
      const womenFile = womenInfo.file;

      function amountGreaterThan(a, b) {
        return Math.max(a - b, 0);
      }
      fileInfos.push({
        name: '>50%men',
        hueRange: [0.6, 1.1],
        file: makeDiffFile(menFile, womenFile, (men, women) => {
          return amountGreaterThan(men, women);
        }),
      });
      fileInfos.push({
        name: '>50% women',
        hueRange: [0.0, 0.4],
        file: makeDiffFile(womenFile, menFile, (women, men) => {
          return amountGreaterThan(women, men);
        }),
      });
    }

Now let's generate a UI to select between these sets of data. First we need some UI html

    <body>
      <canvas id="c"></canvas>
    +  <div id="ui"></div>
    </body>

and some CSS to make it appear in the top left area

    #ui {
      position: absolute;
      left: 1em;
      top: 1em;
    }
    #ui>div {
      font-size: 20pt;
      padding: 1em;
      display: inline-block;
    }
    #ui>div.selected {
      color: red;
    }

Then we can go over each file and generate a set of merged boxes per set of data and an element which when hovered over will show that set and hide all others.

    // show the selected data, hide the rest
    function showFileInfo(fileInfos, fileInfo) {
      fileInfos.forEach((info) => {
        const visible = fileInfo === info;
        info.root.visible = visible;
        info.elem.className = visible ? 'selected' : '';
      });
      requestRenderIfNotRequested();
    }

    const uiElem = document.querySelector('#ui');
    fileInfos.forEach((info) => {
      const boxes = addBoxes(info.file, info.hueRange);
      info.root = boxes;
      const div = document.createElement('div');
      info.elem = div;
      div.textContent = info.name;
      uiElem.appendChild(div);
      div.addEventListener('mouseover', () => {
        showFileInfo(fileInfos, info);
      });
    });
    // show the first set of data
    showFileInfo(fileInfos, fileInfos[0]);

The one more change we need from the previous example is we need to make `addBoxes` take a `hueRange`

    -function addBoxes(file) {
    +function addBoxes(file, hueRange) {

      ...

        // compute a color
    -    const hue = THREE.MathUtils.lerp(0.7, 0.3, amount);
    +    const hue = THREE.MathUtils.lerp(...hueRange, amount);

      ...

and with that we should be able to show 4 sets of data. Hover the mouse over the labels or touch them to switch sets

click here to open in a separate window

Note, there are a few strange data points that really stick out. I wonder what's up with those!??! In any case how do we animate between these 4 sets of data.

Lots of ideas.

- Just fade between them using `Material.opacity`

  The problem with this solution is the cubes perfectly overlap which means there will be z-fighting issues. It's possible we could fix that by changing the depth function and using blending. We should probably look into it.

- Scale up the set we want to see and scale down the other sets

  Because all the boxes have their origin at the center of the planet if we scale them below 1.0 they will sink into the planet. At first that sounds like a good idea but the issue is all the low height boxes will disappear almost immediately and not be replaced until the new data set scales up to 1.0. This makes the transition not very pleasant. We could maybe fix that with a fancy custom shader.

- Use Morphtargets

  Morphtargets are a way were we supply multiple values for each vertex in the geometry and morph or lerp (linear interpolate) between them. Morphtargets are most commonly used for facial animation of 3D characters but that's not their only use.

Let's try morphtargets.

We'll still make a geometry for each set of data but we'll then extract the `position` attribute from each one and use them as morphtargets.

First let's change `addBoxes` to just make and return the merged geometry.

    -function addBoxes(file, hueRange) {
    +function makeBoxes(file, hueRange) {
      const {min, max, data} = file;
      const range = max - min;

      ...

    -  const mergedGeometry = BufferGeometryUtils.mergeGeometries(
    -      geometries, false);
    -  const material = new THREE.MeshBasicMaterial({
    -    vertexColors: true,
    -  });
    -  const mesh = new THREE.Mesh(mergedGeometry, material);
    -  scene.add(mesh);
    -  return mesh;
    +  return BufferGeometryUtils.mergeGeometries(
    +     geometries, false);
    }

There's one more thing we need to do here though. Morphtargets are required to all have exactly the same number of vertices. Vertex #123 in one target needs have a corresponding Vertex #123 in all other targets. But, as it is now different data sets might have some data points with no data so no box will be generated for that point which would mean no corresponding vertices for another set. So, we need to check across all data sets and either always generate something if there is data in any set or, generate nothing if there is data missing in any set. Let's do the latter.

    +function dataMissingInAnySet(fileInfos, latNdx, lonNdx) {
    +  for (const fileInfo of fileInfos) {
    +    if (fileInfo.file.data[latNdx][lonNdx] === undefined) {
    +      return true;
    +    }
    +  }
    +  return false;
    +}

    -function makeBoxes(file, hueRange) {
    +function makeBoxes(file, hueRange, fileInfos) {
      const {min, max, data} = file;
      const range = max - min;

      ...

      const geometries = [];
      data.forEach((row, latNdx) => {
        row.forEach((value, lonNdx) => {
    +      if (dataMissingInAnySet(fileInfos, latNdx, lonNdx)) {
    +        return;
    +      }
          const amount = (value - min) / range;

      ...

Now we'll change the code that was calling `addBoxes` to use `makeBoxes` and setup morphtargets

    +// make geometry for each data set
    +const geometries = fileInfos.map((info) => {
    +  return makeBoxes(info.file, info.hueRange, fileInfos);
    +});
    +
    +// use the first geometry as the base
    +// and add all the geometries as morphtargets
    +const baseGeometry = geometries[0];
    +baseGeometry.morphAttributes.position = geometries.map((geometry, ndx) => {
    +  const attribute = geometry.getAttribute('position');
    +  const name = `target${ndx}`;
    +  attribute.name = name;
    +  return attribute;
    +});
    +baseGeometry.morphAttributes.color = geometries.map((geometry, ndx) => {
    +  const attribute = geometry.getAttribute('color');
    +  const name = `target${ndx}`;
    +  attribute.name = name;
    +  return attribute;
    +});
    +const material = new THREE.MeshBasicMaterial({
    +  vertexColors: true,
    +});
    +const mesh = new THREE.Mesh(baseGeometry, material);
    +scene.add(mesh);

    const uiElem = document.querySelector('#ui');
    fileInfos.forEach((info) => {
    -  const boxes = addBoxes(info.file, info.hueRange);
    -  info.root = boxes;
      const div = document.createElement('div');
      info.elem = div;
      div.textContent = info.name;
      uiElem.appendChild(div);
      function show() {
        showFileInfo(fileInfos, info);
      }
      div.addEventListener('mouseover', show);
      div.addEventListener('touchstart', show);
    });
    // show the first set of data
    showFileInfo(fileInfos, fileInfos[0]);

Above we make geometry for each data set, use the first one as the base, then get a `position` attribute from each geometry and add it as a morphtarget to the base geometry for `position`.

Now we need to change how we're showing and hiding the various data sets. Instead of showing or hiding a mesh we need to change the influence of the morphtargets. For the data set we want to see we need to have an influence of 1 and for all the ones we don't want to see to we need to have an influence of 0.

We could just set them to 0 or 1 directly but if we did that we wouldn't see any animation, it would just snap which would be no different than what we already have. We could also write some custom animation code which would be easy but because the original webgl globe uses an animation library let's use the same one here.

We need to include the library

    import * as THREE from 'three';
    import * as BufferGeometryUtils from 'three/addons/utils/BufferGeometryUtils.js';
    import {OrbitControls} from 'three/addons/controls/OrbitControls.js';
    +import TWEEN from 'three/addons/libs/tween.module.js';

And then create a `Tween` to animate the influences.

    // show the selected data, hide the rest
    function showFileInfo(fileInfos, fileInfo) {
    +  const targets = {};
    -  fileInfos.forEach((info) => {
    +  fileInfos.forEach((info, i) => {
        const visible = fileInfo === info;
    -    info.root.visible = visible;
        info.elem.className = visible ? 'selected' : '';
    +    targets[i] = visible ? 1 : 0;
      });
    +  const durationInMs = 1000;
    +  new TWEEN.Tween(mesh.morphTargetInfluences)
    +    .to(targets, durationInMs)
    +    .start();
      requestRenderIfNotRequested();
    }

We're also suppose to call `TWEEN.update` every frame inside our render loop but that points out a problem. "tween.js" is designed for continuous rendering but we are rendering on demand. We could switch to continuous rendering but it's sometimes nice to only render on demand as it well stop using the user's power when nothing is happening so let's see if we can make it animate on demand.

We'll make a `TweenManager` to help. We'll use it to create the `Tween`s and track them. It will have an `update` method that will return `true` if we need to call it again and `false` if all the animations are finished.

    class TweenManger {
      constructor() {
        this.numTweensRunning = 0;
      }
      _handleComplete() {
        --this.numTweensRunning;
        console.assert(this.numTweensRunning >= 0);
      }
      createTween(targetObject) {
        const self = this;
        ++this.numTweensRunning;
        let userCompleteFn = () => {};
        // create a new tween and install our own onComplete callback
        const tween = new TWEEN.Tween(targetObject).onComplete(function(...args) {
          self._handleComplete();
          userCompleteFn.call(this, ...args);
        });
        // replace the tween's onComplete function with our own
        // so we can call the user's callback if they supply one.
        tween.onComplete = (fn) => {
          userCompleteFn = fn;
          return tween;
        };
        return tween;
      }
      update() {
        TWEEN.update();
        return this.numTweensRunning > 0;
      }
    }

To use it we'll create one

    function main() {
      const canvas = document.querySelector('#c');
      const renderer = new THREE.WebGLRenderer({antialias: true, canvas});
    +  const tweenManager = new TweenManger();

      ...

We'll use it to create our `Tween`s.

    // show the selected data, hide the rest
    function showFileInfo(fileInfos, fileInfo) {
      const targets = {};
      fileInfos.forEach((info, i) => {
        const visible = fileInfo === info;
        info.elem.className = visible ? 'selected' : '';
        targets[i] = visible ? 1 : 0;
      });
      const durationInMs = 1000;
    -  new TWEEN.Tween(mesh.morphTargetInfluences)
    +  tweenManager.createTween(mesh.morphTargetInfluences)
        .to(targets, durationInMs)
        .start();
      requestRenderIfNotRequested();
    }

Then we'll update our render loop to update the tweens and keep rendering if there are still animations running.

    function render() {
      renderRequested = false;

      if (resizeRendererToDisplaySize(renderer)) {
        const canvas = renderer.domElement;
        camera.aspect = canvas.clientWidth / canvas.clientHeight;
        camera.updateProjectionMatrix();
      }

    +  if (tweenManager.update()) {
    +    requestRenderIfNotRequested();
    +  }

      controls.update();
      renderer.render(scene, camera);
    }
    render();

And with that we should be animating between data sets.

click here to open in a separate window

I hope going through this was helpful. Using morphtargets is a common technique to move lots of objects. As an example we could give every cube a random place in another target and morph from that to their first positions on the globe. That might be a cool way to introduce the globe.

Next you might be interested in adding labels to a globe which is covered in Aligning HTML Elements to 3D.

Note: We could try to just graph percent of men or percent of women or the raw difference but based on how we are displaying the info, cubes that grow from the surface of the earth, we'd prefer most cubes to be low. If we used one of these other comparisons most cubes would be about 1/2 their maximum height which would not make a good visualization. Feel free to change the `amountGreaterThan` from `Math.max(a - b, 0)` to something like `(a - b)` "raw difference" or `a / (a + b)` "percent" and you'll see what I mean.