THREE.ParametricGeometry

With THREE.ParametricGeometry, you can create a geometry based on an equation. Before we dive into our own example, a good thing to start with is to look at the examples already provided by Three.js. When you download the Three.js distribution, you get the examples/js/ParametricGeometries.js file. In this file, you can find a couple of examples of equations you can use together with THREE.ParametricGeometry. The most basic example is the function to create a plane:

plane: function ( width, height ) {
    return function ( u, v, optionalTarget ) {
      var result = optionalTarget || new THREE.Vector3();
      var x = u * width;
      var y = 0;
      var z = v * height;
      return result.set( x, y, z );
    };
  }

This function is called by THREE.ParametricGeometry. The u and v values will range from 0 to 1 and will be called a large number of times for all the values from 0 to 1. In this example, the u value is used to determine the x coordinate of the vector and...