How to draw a 3D sphere?

I wan开发者_运维问答t to draw a 3D ball or sphere in HTML 5.0 canvas. I want to understand the Algorithm about how to draw a 3D sphere. Who can share this with me?

You will need to model a sphere, and have it be varying colors so that as it rotates you can see that it is not only a sphere, but being rendered.

Otherwise, a sphere in space, with not point of reference around it looks like a circle, if it is all one solid color.

To start with you will want to try drawing a circle with rectangles, as that is the main primitive you have.

Once you understand how to do that, or create a new primitive, such as a triangle, using the Path method, and create a circle, then you are ready to move it to 3D.

3D is just a trick, as you will take your model, probably generated by an equation, and then flatten it, as you determine which parts will be seen, and then display it.

But, you will want to change the color of the triangles based on how far they are from a source of light, as well as based on the angle of that part to the light source.

This is where you can start to do optimizations, as, if you do this pixel by pixel then you are raytracing. If you have larger blocks, and a point source of light, and the object is rotating but not moving around then you can recalculate how the color changes for each triangle, then it is just a matter of changing colors to simulate rotating.

The algorithm will depend on what simplifications you want to make, so as you gain experience come back and ask, showing what you have done so far.

Here is an example of doing it, and below I copied the 3D sphere part, but please look at the entire article.

function Sphere3D(radius) {
 this.point = new Array();
 this.color = "rgb(100,0,255)"
 this.radius = (typeof(radius) == "undefined") ? 20.0 : radius;
 this.radius = (typeof(radius) != "number") ? 20.0 : radius;
 this.numberOfVertexes = 0;

 // Loop from 0 to 360 degrees with a pitch of 10 degrees ... 
  for(alpha = 0; alpha <= 6.28; alpha += 0.17) {
   p = this.point[this.numberOfVertexes] = new Point3D();

   p.x = Math.cos(alpha) * this.radius;
   p.y = 0;
   p.z = Math.sin(alpha) * this.radius;

   this.numberOfVertexes++;
 }

 // Loop from 0 to 90 degrees with a pitch of 10 degrees ... 
 // (direction = 1)

 // Loop from 0 to 90 degrees with a pitch of 10 degrees ...
 // (direction = -1)

 for(var direction = 1; direction >= -1; direction -= 2) {
   for(var beta = 0.17; beta < 1.445; beta += 0.17) {

     var radius = Math.cos(beta) * this.radius;
     var fixedY = Math.sin(beta) * this.radius * direction;

     for(var alpha = 0; alpha < 6.28; alpha += 0.17) {
       p = this.point[this.numberOfVertexes] = new Point3D();

       p.x = Math.cos(alpha) * radius;
       p.y = fixedY;
       p.z = Math.sin(alpha) * radius;

       this.numberOfVertexes++;
     }
   }
 }
}

u can try with three.js library , which abstracts a lot of code from core webgl programming. Include three.js library in your html from three.js lib.

u can use canvas renderer for safari browser , webgl works for chrome

please find the JS FIDDLE FOR SPHERE

var camera, scene, material, mesh, geometry, renderer

function drawSphere() {
    init();
    animate();

}

function init() {
    // camera 

    scene = new THREE.Scene()
    camera = new THREE.PerspectiveCamera(50, window.innerWidth / innerHeight, 1, 1000);
    camera.position.z = 300;
    scene.add(camera);

    // sphere object
    var radius = 50,
        segments = 10,
        rings = 10;
    geometry = new THREE.SphereGeometry(radius, segments, rings);
    material = new THREE.MeshNormalMaterial({
        color: 0x002288
    });
    mesh = new THREE.Mesh(geometry, material);

    //scene 
    ;
    scene.add(mesh);


    // renderer
    renderer = new THREE.WebGLRenderer();
    renderer.setSize(window.innerWidth, window.innerHeight);
    document.body.appendChild(renderer.domElement);

}


function animate() {
    requestAnimationFrame(animate);
    render();

}

function render() {

    mesh.rotation.x += .01;
    mesh.rotation.y += .02;
    renderer.render(scene, camera);


}

// fn callin
drawSphere();

Update: This code is quite old and limited. There are libraries for doing 3D spheres now: http://techslides.com/d3-globe-with-canvas-webgl-and-three-js/

Over ten years ago I wrote a Java applet to render a textured sphere by actually doing the math to work out where the surface of the sphere was in the scene (not using triangles).

I've rewritten it in JavaScript for canvas and I've got a demo rendering the earth as a sphere:

I get around 22 fps on my machine. Which is about as fast as the Java version it was based on renders at, if not a little faster!

Now it's a long time since I wrote the Java code - and it was quite obtuse - so I don't really remember exactly how it works, I've just ported it JavaScript. However this is from a slow version of the code and I'm not sure if the faster version was due to optimisations in the Java methods I used to manipulate pixels or from speedups in the math it does to work out which pixel to render from the texture. I was also corresponding at the time with someone who had a similar applet that was much faster than mine but again I don't know if any of the speed improvements they had would be possible in JavaScript as it may have relied on Java libraries. (I never saw their code so I don't know how they did it.)

So it may be possible to improve on the speed. But this works well as a proof of concept.

I'll have a go at converting my faster version some time to see if I can get any speed improvements into the JavaScript version.

Well, an image of a sphere will always have a circular shape on your screen, so the only thing that matters is the shading. This will be determined by where you place your light source.

As for algorithms, ray tracing is the simplest, but also the slowest by far — so you probably wouldn't want to use it to do anything very complicated in a <CANVAS> (especially given the lack of graphics acceleration available in that environment), but it might be fast enough if you just wanted to do a single sphere.