DZone
Thanks for visiting DZone today,
Edit Profile
  • Manage Email Subscriptions
  • How to Post to DZone
  • Article Submission Guidelines
Sign Out View Profile
  • Post an Article
  • Manage My Drafts
Over 2 million developers have joined DZone.
Log In / Join
Refcards Trend Reports Events Over 2 million developers have joined DZone. Join Today! Thanks for visiting DZone today,
Edit Profile Manage Email Subscriptions Moderation Admin Console How to Post to DZone Article Submission Guidelines
View Profile
Sign Out
Refcards
Trend Reports
Events
Zones
Culture and Methodologies Agile Career Development Methodologies Team Management
Data Engineering AI/ML Big Data Data Databases IoT
Software Design and Architecture Cloud Architecture Containers Integration Microservices Performance Security
Coding Frameworks Java JavaScript Languages Tools
Testing, Deployment, and Maintenance Deployment DevOps and CI/CD Maintenance Monitoring and Observability Testing, Tools, and Frameworks
Culture and Methodologies
Agile Career Development Methodologies Team Management
Data Engineering
AI/ML Big Data Data Databases IoT
Software Design and Architecture
Cloud Architecture Containers Integration Microservices Performance Security
Coding
Frameworks Java JavaScript Languages Tools
Testing, Deployment, and Maintenance
Deployment DevOps and CI/CD Maintenance Monitoring and Observability Testing, Tools, and Frameworks
  1. DZone
  2. Coding
  3. Languages
  4. Triangle Mesh for 3D Objects in HTML5

Triangle Mesh for 3D Objects in HTML5

Andrey Prikaznov user avatar by
Andrey Prikaznov
·
Nov. 01, 12 · Interview
Like (0)
Save
Tweet
Share
6.19K Views

Join the DZone community and get the full member experience.

Join For Free

 Today’s lesson is a bridge between two-dimensional graphics in html5 and truly three-dimensional (using WebGL). Today I will show how to draw three-dimensional objects using a polygonal mesh. A polygon mesh or unstructured grid is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D computer graphics and solid modeling. The faces usually consist of triangles, quadrilaterals or other simple convex polygons, since this simplifies rendering, but may also be composed of more general concave polygons, or polygons with holes.

In order to understand what it is about, I recommend to read the basis described in wikipedia.
To demonstrate, we have prepared simple three-dimensional objects – a cube and multi-dimensional sphere (with a variable number of faces).

Live Demo
download in package

If you are ready – let’s start!


Step 1. HTML

As usual (for all canvas-based demos) we have a very basic html markup (with a single canvas object inside):

<html lang="en" >
    <head>
        <meta charset="utf-8" />
        <meta name="author" content="Script Tutorials" />
        <title>Triangle mesh for 3D objects in HTML5 | Script Tutorials</title>

        <!-- add styles -->
        <link href="css/main.css" rel="stylesheet" type="text/css" />

        <!-- add script -->
        <script src="js/meshes.js"></script>
        <script src="js/transform.js"></script>
        <script>
            //var obj = new cube();
            //var obj = new sphere(6);
            var obj = new sphere(16);
        </script>
        <script src="js/main.js"></script>
    </head>
    <body>
        <div class="container">
            <canvas id="scene" height="500" width="700" tabindex="1"></canvas>
            <div class="hint">Please use Up / Down keys to change opacity</div>
        </div>
    </body>
</html>

I extracted a generated object initialization here, look:

<script>
    //var obj = new cube();
    //var obj = new sphere(6);
    var obj = new sphere(16);
</script>

It means that if we need to display a cube – you have to uncomment the first one line, if you’d like to display a sphere with 6 faces – select the second variant.

Step 2. JS

There are three JS files (main.js, meshes.js and transform.js), we will publish two of them, third one (transform.js) contains only math-related functions (to rotate, scale, translate and project objects). It will be available in our package. So, let’s review the code of the first javascript:

js/meshes.js


// get random color
function getRandomColor() {
    var letters = '0123456789ABCDEF'.split('');
    var color = '#';
    for (var i = 0; i < 6; i++ ) {
        color += letters[Math.round(Math.random() * 15)];
    }
    return color;
}

// prepare object
function prepareObject(o) {
    o.colors = new Array();

    // prepare normals
    o.normals = new Array();
    for (var i = 0; i < o.faces.length; i++) {
        o.normals[i] = [0, 0, 0];

        o.colors[i] = getRandomColor();
    }

    // prepare centers: calculate max positions
    o.center = [0, 0, 0];
    for (var i = 0; i < o.points.length; i++) {
        o.center[0] += o.points[i][0];
        o.center[1] += o.points[i][1];
        o.center[2] += o.points[i][2];
    }

    // prepare distances
    o.distances = new Array();
    for (var i = 1; i < o.points.length; i++) {
        o.distances[i] = 0;
    }

    // calculate average center positions
    o.points_number = o.points.length;
    o.center[0] = o.center[0] / (o.points_number - 1);
    o.center[1] = o.center[1] / (o.points_number - 1);
    o.center[2] = o.center[2] / (o.points_number - 1);

    o.faces_number = o.faces.length;
    o.axis_x = [1, 0, 0];
    o.axis_y = [0, 1, 0];
    o.axis_z = [0, 0, 1];
}

// Cube object
function cube() {

    // prepare points and faces for cube
    this.points=[
        [0,0,0],
        [100,0,0],
        [100,100,0],
        [0,100,0],
        [0,0,100],
        [100,0,100],
        [100,100,100],
        [0,100,100],
        [50,50,100],
        [50,50,0],
    ];

    this.faces=[
        [0,4,5],
        [0,5,1],
        [1,5,6],
        [1,6,2],
        [2,6,7],
        [2,7,3],
        [3,7,4],
        [3,4,0],
        [8,5,4],
        [8,6,5],
        [8,7,6],
        [8,4,7],
        [9,5,4],
        [9,6,5],
        [9,7,6],
        [9,4,7],
    ];

    prepareObject(this);
}

// Sphere object
function sphere(n) {
    var delta_angle = 2 * Math.PI / n;

    // prepare vertices (points) of sphere
    var vertices = [];
    for (var j = 0; j < n / 2 - 1; j++) {
        for (var i = 0; i < n; i++) {
            vertices[j * n + i] = [];
            vertices[j * n + i][0] = 100 * Math.sin((j + 1) * delta_angle) * Math.cos(i * delta_angle);
            vertices[j * n + i][1] = 100 * Math.cos((j + 1) * delta_angle);
            vertices[j * n + i][2] = 100 * Math.sin((j + 1) * delta_angle) * Math.sin(i * delta_angle);
        }
    }
    vertices[(n / 2 - 1) * n] = [];
    vertices[(n / 2 - 1) * n + 1] = [];

    vertices[(n / 2 - 1) * n][0] = 0;
    vertices[(n / 2 - 1) * n][1] =  100;
    vertices[(n / 2 - 1) * n][2] =  0;

    vertices[(n / 2 - 1) * n + 1][0] = 0;
    vertices[(n / 2 - 1) * n + 1][1] = -100;
    vertices[(n / 2 - 1) * n + 1][2] = 0;

    this.points = vertices;

    // prepare faces
    var faces = [];
    for (var j = 0; j < n / 2 - 2; j++) {
        for (var i = 0; i < n - 1; i++) {
            faces[j * 2 * n + i] = [];
            faces[j * 2 * n + i + n] = [];

            faces[j * 2 * n + i][0] = j * n + i;
            faces[j * 2 * n + i][1] = j * n + i + 1;
            faces[j * 2 * n + i][2] = (j + 1) * n + i + 1;
            faces[j * 2 * n + i + n][0] = j * n + i;
            faces[j * 2 * n + i + n][1] = (j + 1) * n + i + 1;
            faces[j * 2 * n + i + n][2] = (j + 1) * n + i;
        }

        faces[j * 2 * n + n - 1] = [];
        faces[2 * n * (j + 1) - 1] = [];

        faces[j * 2 * n + n - 1  ][0] = (j + 1) * n - 1;
        faces[j * 2 * n + n - 1  ][1] = (j + 1) * n;
        faces[j * 2 * n + n - 1  ][2] = j * n;
        faces[2 * n * (j + 1) - 1][0] = (j + 1) * n - 1;
        faces[2 * n * (j + 1) - 1][1] = j * n + n;
        faces[2 * n * (j + 1) - 1][2] = (j + 2) * n - 1;
    }
    for (var i = 0; i < n - 1; i++) {
        faces[n * (n - 4) + i] = [];
        faces[n * (n - 3) + i] = [];

        faces[n * (n - 4) + i][0] = (n / 2 - 1) * n;
        faces[n * (n - 4) + i][1] = i;
        faces[n * (n - 4) + i][2] = i + 1;
        faces[n * (n - 3) + i][0] = (n / 2 - 1) * n + 1;
        faces[n * (n - 3) + i][1] = (n / 2 - 2) * n + i + 1;
        faces[n * (n - 3) + i][2] = (n / 2 - 2) * n + i;
    }

    faces[n * (n - 3) - 1] = [];
    faces[n * (n - 2) - 1] = [];

    faces[n * (n - 3) - 1][0] = (n / 2 - 1) * n;
    faces[n * (n - 3) - 1][1] = n - 1;
    faces[n * (n - 3) - 1][2] = 0;
    faces[n * (n - 2) - 1][0] = (n / 2 - 1) * n + 1;
    faces[n * (n - 2) - 1][1] = (n / 2 - 2) * n;
    faces[n * (n - 2) - 1][2] = (n / 2 - 2) * n + n - 1;

    this.faces=faces;

    prepareObject(this);
}

In the most beginning, we should prepare all points and faces of our object. There are 2 functions: cube (which generates initial arrays for a simple cube object) and sphere (to generate sphere). As you see – it is much more difficult to calculate all points and faces for multi-dimensional sphere. Once we get all these points and surfaces we have to calculate other params (like normals, distances, absolute center and three axis).

js/main.js

// inner variables
var canvas, ctx;
var vAlpha = 0.5;
var vShiftX = vShiftY = 0;
var distance = -700;
var vMouseSens = 0.05;
var iHalfX, iHalfY;

// initialization
function sceneInit() {
    // prepare canvas and context objects
    canvas = document.getElementById('scene');
    ctx = canvas.getContext('2d');

    iHalfX = canvas.width / 2;
    iHalfY = canvas.height / 2;

    // initial scale and translate
    scaleObj([3, 3, 3], obj);
    translateObj([-obj.center[0], -obj.center[1], -obj.center[2]],obj);
    translateObj([0, 0, -1000], obj);

    // attach event handlers
    document.onkeydown = handleKeydown;
    canvas.onmousemove = handleMousemove;

    // main scene loop
    setInterval(drawScene, 25);
}

// onKeyDown event handler
function handleKeydown(e) {
    kCode = ((e.which) || (e.keyCode));
    switch (kCode) {
        case 38: vAlpha = (vAlpha <= 0.9) ? (vAlpha + 0.1) : vAlpha; break; // Up key
        case 40: vAlpha = (vAlpha >= 0.2) ? (vAlpha - 0.1) : vAlpha; break; // Down key
    }
}

// onMouseMove event handler
function handleMousemove(e) {
    var x = e.pageX - canvas.offsetLeft;
    var y = e.pageY - canvas.offsetTop;

    if ((x > 0) && (x < canvas.width) && (y > 0) && (y < canvas.height)) {
        vShiftY = vMouseSens * (x - iHalfX) / iHalfX;
        vShiftX = vMouseSens * (y - iHalfY) / iHalfY;
    }
}

// draw main scene function
function drawScene() {
    // clear canvas
    ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);

    // set fill color, stroke color, line width and global alpha
    ctx.strokeStyle = 'rgb(0,0,0)';
    ctx.lineWidth = 0.5;
    ctx.globalAlpha= vAlpha;

    // vertical and horizontal rotate
    var vP1x = getRotationPar([0, 0, -1000], [1, 0, 0], vShiftX);
    var vP2x = getRotationPar([0, 0, 0], [1, 0, 0], vShiftX);
    var vP1y = getRotationPar([0, 0, -1000], [0, 1, 0], vShiftY);
    var vP2y = getRotationPar([0, 0, 0], [0, 1, 0], vShiftY);
    rotateObj(vP1x, vP2x, obj);
    rotateObj(vP1y, vP2y, obj);

    // recalculate distances
    for (var i = 0; i < obj.points_number; i++) {
        obj.distances[i] = Math.pow(obj.points[i][0],2) + Math.pow(obj.points[i][1],2) + Math.pow(obj.points[i][2], 2);
    }

    // prepare array with face triangles (with calculation of max distance for every face)
    var iCnt = 0;
    var aFaceTriangles = new Array();
    for (var i = 0; i < obj.faces_number; i++) {
        var max = obj.distances[obj.faces[i][0]];
        for (var f = 1; f < obj.faces[i].length; f++) {
            if (obj.distances[obj.faces[i][f]] > max)
                max = obj.distances[obj.faces[i][f]];
        }
        aFaceTriangles[iCnt++] = {faceVertex:obj.faces[i], faceColor:obj.colors[i], distance:max};
    }
    aFaceTriangles.sort(sortByDistance);

    // prepare array with projected points
    var aPrjPoints = new Array();
    for (var i = 0; i < obj.points.length; i++) {
        aPrjPoints[i] = project(distance, obj.points[i], iHalfX, iHalfY);
    }

    // draw an object (surfaces)
    for (var i = 0; i < iCnt; i++) {

        ctx.fillStyle = aFaceTriangles[i].faceColor;

        // begin path
        ctx.beginPath();

        // face vertex index
        var iFaceVertex = aFaceTriangles[i].faceVertex;

        // move to initial position
        ctx.moveTo(aPrjPoints[iFaceVertex[0]][0], aPrjPoints[iFaceVertex[0]][1]);

        // and draw three lines (to build a triangle)
        for (var z = 1; z < aFaceTriangles[i].faceVertex.length; z++) {
            ctx.lineTo(aPrjPoints[iFaceVertex[z]][0], aPrjPoints[iFaceVertex[z]][1]);
        }

        // close path, strole and fill a triangle
        ctx.closePath();
        ctx.stroke();
        ctx.fill();
    }
}

// sort function
function sortByDistance(x, y) {
    return (y.distance - x.distance);
}

// initialization
if (window.attachEvent) {
    window.attachEvent('onload', sceneInit);
} else {
    if (window.onload) {
        var curronload = window.onload;
        var newonload = function() {
            curronload();
            sceneInit();
        };
        window.onload = newonload;
    } else {
        window.onload = sceneInit;
    }
}

Well, it’s the time to back to our main page functionality. As soon as the page is loaded, we do main initialization (sceneInit function). We create canvas and context objects, then we perform initial scale and translate of our object which we created in the most beginning (cube or sphere). Then we attach onkeydown and onmousemove event handlers and set timer to draw our main scene (drawScene function). Don’t forget that we can change globalAlpha param with clicking Up/Down buttons.




Object (computer science) HTML

Published at DZone with permission of Andrey Prikaznov, DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

Popular on DZone

  • Promises, Thenables, and Lazy-Evaluation: What, Why, How
  • Choosing the Best Cloud Provider for Hosting DevOps Tools
  • Using JSON Web Encryption (JWE)
  • Unleashing the Power of JavaScript Modules: A Beginner’s Guide

Comments

Partner Resources

X

ABOUT US

  • About DZone
  • Send feedback
  • Careers
  • Sitemap

ADVERTISE

  • Advertise with DZone

CONTRIBUTE ON DZONE

  • Article Submission Guidelines
  • Become a Contributor
  • Visit the Writers' Zone

LEGAL

  • Terms of Service
  • Privacy Policy

CONTACT US

  • 600 Park Offices Drive
  • Suite 300
  • Durham, NC 27709
  • support@dzone.com
  • +1 (919) 678-0300

Let's be friends: