Drawing parametric shapes in webGL (without three.js)

Question

I've written a program that draws some parametric shapes (spheres, toruses, and cylinders) just using HTML5 and regular Javascript. I'm trying to convert this code so that it uses WebGL, implementing the shapes with triangle strips as is done in this tutorial. My point of confusion is how triangle strips are even being used to create spheres at all. The way I was doing it before just featured the calculation of where to draw each horizontal slice or circle based on the latitude lines in a for loop and nested inside of that loop was the calculation of each point on that circle. After all of those points were generated, I passed them to a function which adds all of the vertices to an array which is returned and passed to a curve plotting function that used moveTo() and lineTo() in order to draw lines between each point. The problem is that I don't know what the equivalent of moveTo() and lineTo() is in webGL when using triangle shapes. How can I translate my implementation to WebGL?

Here is some of the code from my original implementation:

//Calculates point on sphere
   function spherePoint(uv) {
      var u = uv[0];
      var v = uv[1];
      var phi = -Math.PI/2 + Math.PI * v;
      var theta = 2 * Math.PI * u;
      return [ Math.cos(phi) * Math.cos(theta),
               Math.cos(phi) * Math.sin(theta),
               Math.sin(phi)];
   }

// Takes the parametric function as an argument and constructs 3D shape

   function makeShape(num_u, num_v, eq, possRad) {
      var shell = [];
      for (var j = 0 ; j <= num_v ; j++) {
          var v = j / num_v;
          shell.push([]);
         for (var i = 0 ; i <= num_u ; i++) {
             var u = i / num_u;
             var p = eq([u, v], possRad);
            shell[j].push(p);
         }
      }
      return shell;
   }
// Used to create shapes to render parametric surface

   function renderShape(shape) {
       var num_j = shape.length;
       var num_i = shape[0].length;
       for (var j = 0 ; j < num_j - 1 ; j++)
           for (var i = 0 ; i < num_i - 1 ; i++) {

              plotCurve([shape[j][i],
                          shape[j + 1][i],
                          shape[j + 1][i + 1],
                          shape[j][i + 1]]);
          }
   }
 //plot curve on canvas
   function plotCurve(C) {
      g.beginPath();
      for (var i = 0 ; i < C.length ; i++)
         if (i == 0)
            moveTo(C[i]);
         else
            lineTo(C[i]);
      g.stroke();
   }

  function moveTo(p) {
      var q = m.transform(p);  // APPLY 3D MATRIX TRANFORMATION
      var xy = viewport(q);    // APPLY VIEWPORT TRANSFORM
      g.moveTo(xy[0], xy[1]);
   }

   function lineTo(p) {
      var q = m.transform(p);  // APPLY 3D MATRIX TRANFORMATION
      var xy = viewport(q);    // APPLY VIEWPORT TRANSFORM
      g.lineTo(xy[0], xy[1]);
   }

The webGL version should look something like this I would think:

The plain Javascript version looks like this:

gman · Accepted Answer · 2017-03-17T12:20:51.520

That's a pretty basic WebGL question. Some more tutorials on webgl might be helpful.

WebGL only draws chunks of data. It doesn't really have a lineTo or a moveTo. Instead you give it buffers of data, tell it how to pull data out of those buffers, then you write a function (a vertex shader) to use that data to tell WebGL how convert it to clip space coordinates and whether to draw points, lines, or triangles with the result. You also supply a function (a fragment shader) to tell it what colors to use for the points, lines or triangles.

Basically to draw the thing you want to draw you need to generate 2 triangles for every rectangle on that sphere. In other words you need to generate 6 vertices for every rectangle. The reason is in order to draw each triangle in a different color you can't share any vertices since the colors are associated with the vertices.

So for one rectangle you need to generate these points

0--1 4
| / /|
|/ / |
2 3--5

Where 0, 1, and 2 are pink points and 3, 4, 5 are green points. 1 and 4 have the same position but because their colors are different they have to be different points. The same with points 2 and 3.

var pink   = [1, 0.5, 0.5, 1];
var green  = [0.5, 1, 0.5, 1];
var positions = [];
var colors = [];
var across = 20;
var down = 10;

function addPoint(x, y, color) {
  var u = x / across;
  var v = y / down;
  var radius = Math.sin(v * Math.PI);
  var angle = u * Math.PI * 2;
  var nx = Math.cos(angle);
  var ny = Math.cos(v * Math.PI);
  var nz = Math.sin(angle);
  positions.push(
     nx * radius,   // x
     ny,            // y
     nz * radius);  // z
  colors.push(color[0], color[1], color[2], color[3]);
}

for (var y = 0; y < down; ++y) {
  for (var x = 0; x < across; ++x) {
    // for each rect we need 6 points
    addPoint(x    , y    , pink);
    addPoint(x + 1, y    , pink);
    addPoint(x    , y + 1, pink);

    addPoint(x    , y + 1, green);
    addPoint(x + 1, y    , green);
    addPoint(x + 1, y + 1, green);
  }
}

Here's the sphere above rendered but without any lighting, perspective or anything.

var pink   = [1, 0.5, 0.5, 1];
var green  = [0.5, 1, 0.5, 1];
var positions = [];
var colors = [];
var across = 20;
var down = 10;

function addPoint(x, y, color) {
  var u = x / across;
  var v = y / down;
  var radius = Math.sin(v * Math.PI);
  var angle = u * Math.PI * 2;
  var nx = Math.cos(angle);
  var ny = Math.cos(v * Math.PI);
  var nz = Math.sin(angle);
  positions.push(
    nx * radius,   // x
    ny,            // y
    nz * radius);  // z
  colors.push(color[0], color[1], color[2], color[3]);
}

for (var y = 0; y < down; ++y) {
  for (var x = 0; x < across; ++x) {
    // for each rect we need 6 points
    addPoint(x    , y    , pink);
    addPoint(x + 1, y    , pink);
    addPoint(x    , y + 1, pink);

    addPoint(x    , y + 1, green);
    addPoint(x + 1, y    , green);
    addPoint(x + 1, y + 1, green);
  }
}

var gl = twgl.getWebGLContext(document.getElementById("c"));
var programInfo = twgl.createProgramInfo(gl, ["vs", "fs"]);
 
var arrays = {
  position: positions,
  color: colors,
};
var bufferInfo = twgl.createBufferInfoFromArrays(gl, arrays);

var uniforms = {
  resolution: [gl.canvas.width, gl.canvas.height],
};

gl.useProgram(programInfo.program);
twgl.setBuffersAndAttributes(gl, programInfo, bufferInfo);
twgl.setUniforms(programInfo, uniforms);
twgl.drawBufferInfo(gl, bufferInfo);

canvas { border: 1px solid black; }

<canvas id="c"></canvas>  

<script id="vs" type="not-js">
attribute vec4 position;
attribute vec4 color;

uniform vec2 resolution;

varying vec4 v_color;

void main() {
  gl_Position = position * vec4(resolution.y / resolution.x, 1, 1, 1);
  v_color = color;
}
</script>
<script id="fs" type="not-js">
precision mediump float;

varying vec4 v_color;

void main() {
  gl_FragColor = v_color;
}
</script>
<script src="https://twgljs.org/dist/3.x/twgl-full.min.js"></script>

If you later want to light it you'll also need normals (values that you can use to tell which direction something is facing). We can add those in by adding

var normals = [];

and inside addPoint

function addPoint(x, y, color) {
  var u = x / across;
  var v = y / down;
  var radius = Math.sin(v * Math.PI);
  var angle = u * Math.PI * 2;
  var nx = Math.cos(angle);
  var ny = Math.cos(v * Math.PI);
  var nz = Math.sin(angle);
  positions.push(
     nx * radius,   // x
     ny,            // y
     nz * radius);  // z
  colors.push(color[0], color[1], color[2], color[3]);
  normals.push(nx, ny, nz);
}

Here's a sample with hacked lighting

var pink   = [1, 0.5, 0.5, 1];
var green  = [0.5, 1, 0.5, 1];
var positions = [];
var colors = [];
var normals = [];
var across = 20;
var down = 10;

function addPoint(x, y, color) {
  var u = x / across;
  var v = y / down;
  var radius = Math.sin(v * Math.PI);
  var angle = u * Math.PI * 2;
  var nx = Math.cos(angle);
  var ny = Math.cos(v * Math.PI);
  var nz = Math.sin(angle);
  positions.push(
    nx * radius,   // x
    ny,            // y
    nz * radius);  // z
  normals.push(nx, ny, nz);
  colors.push(color[0], color[1], color[2], color[3]);
}

for (var y = 0; y < down; ++y) {
  for (var x = 0; x < across; ++x) {
    // for each rect we need 6 points
    addPoint(x    , y    , pink);
    addPoint(x + 1, y    , pink);
    addPoint(x    , y + 1, pink);

    addPoint(x    , y + 1, green);
    addPoint(x + 1, y    , green);
    addPoint(x + 1, y + 1, green);
  }
}

var gl = document.getElementById("c").getContext("webgl");
var programInfo = twgl.createProgramInfo(gl, ["vs", "fs"]);
 
var arrays = {
  position: positions,
  normal: normals,
  color: colors,
};
var bufferInfo = twgl.createBufferInfoFromArrays(gl, arrays);

var uniforms = {
  resolution: [gl.canvas.width, gl.canvas.height],
  lightDirection: [0.5, 0.5, -1],
};

gl.useProgram(programInfo.program);
twgl.setBuffersAndAttributes(gl, programInfo, bufferInfo);
twgl.setUniforms(programInfo, uniforms);
twgl.drawBufferInfo(gl, bufferInfo);

canvas { border: 1px solid black; }

<canvas id="c"></canvas>  

<script id="vs" type="not-js">
attribute vec4 position;
attribute vec4 color;
attribute vec3 normal;

uniform vec2 resolution;

varying vec4 v_color;
varying vec3 v_normal;

void main() {
  gl_Position = position * vec4(resolution.y / resolution.x, 1, 1, 1);
  v_color = color;
  v_normal = normal;
}
</script>
<script id="fs" type="not-js">
precision mediump float;

varying vec4 v_color;
varying vec3 v_normal;

uniform vec3 lightDirection;

void main() {
  float light = pow(abs(dot(v_normal, normalize(lightDirection))), 2.0);
  gl_FragColor = vec4(v_color.xyz * light, v_color.a);
}
</script>
<script src="https://twgljs.org/dist/3.x/twgl-full.min.js"></script>

PS: The picture you posted is actually drawing more triangles per rectangle. The division between green and pink is not straight.

You might also find [this site interesting since it's arguably 100% parametric geometry](http://vertexshaderart.com). — gman, Nov 19 '15 at 07:04
Thanks! This was a really full and comprehensive answer to the question! Just to follow up though, if I were to use ```gl.TRIANGLE_STRIPS``` instead of just ```gl.TRIANGLES``` in order to make the squares, would the code provided still be correct? Thanks for all of the code btw, the stuff for lighting will come in handy soon. — loremIpsum1771, Nov 21 '15 at 23:49
You can't use `TRIANGLE_STRIP` to get the same result because strips share vertices so you couldn't get pink and green triangles because some triangles would have to share both pink and green vertices. FYI: No games (ie, no professional graphics programmers) use strips — gman, Nov 23 '15 at 00:56
Ok that makes sense. I'm actually doing something similar with toruses and cylinders (without different colors) but I'm having trouble with rendering them properly. It seems like you have a lot of experience with this subject so maybe you might be able to [help here](http://stackoverflow.com/questions/33860167/issue-when-rendering-a-torus-in-webgl?noredirect=1#comment55485165_33860167) , thanks again. — loremIpsum1771, Nov 23 '15 at 01:05

score 1 · Answer 2 · answered Nov 18 '15 at 22:14

There is gl.LINES that well, pretty much draw connected lines. So lineTo(x,y,z) would just be add one more vertex to the VBO you use to store the lines data. moveTo(x,y,z) would be just to create a "break" between the lines. This can be accomplished with a new drawArrays call.

Drawing parametric shapes in webGL (without three.js)

2 Answers2

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