Z-fighting

solutions select, option

HTML

<div id="info">zfight and depth resolution
  <br><br>
  <select id='method'>
    <option value='sol0'>Overlap</option>
    <option value='sol1'>World offset (1,1e4)</option>
    <option value='sol2'>World offset (1e-2,1e6)</option>
    <option value='sol3'>Depth offset</option>
  </select>
</div>
<script src="https://threejs.org/build/three.js"></script>
<script src="https://threejs.org/examples/js/controls/OrbitControls.js"></script>
<script src="https://code.jquery.com/jquery-2.1.4.min.js"></script>

CSS

#info {
  position: absolute;
  top: 2%;
  width: 100%;
  padding: 10px;
  text-align: center;
  color: #ffff00
}

body {
  overflow: hidden;
}

JavaScript

// jQuery, select, option
// reference:
// https://learn.jquery.com/using-jquery-core/faq/how-do-i-get-the-text-value-of-a-selected-option/

var scene, renderer, camera;
var controls;
var angle = 0;
var sector;
var strategy = 'sol0';

init();
animate();

$("#method").change(function() {
  strategy = $('#method option:selected').val();
});

function init() {
  scene = new THREE.Scene();
  renderer = new THREE.WebGLRenderer();
  renderer.setSize(window.innerWidth, window.innerHeight);
  renderer.setClearColor(0x888888);
  document.body.appendChild(renderer.domElement);

  camera = new THREE.PerspectiveCamera(50, window.innerWidth / window.innerHeight, 0.1, 1e6);
  camera.position.z = 150;
  controls = new THREE.OrbitControls(camera, renderer.domElement);
	var axes = new THREE.AxisHelper (30);
  scene.add (axes);
  window.addEventListener('resize', onWindowResize, false);
  ///////////////////////////////////////////////////////////////////////
  var circle = new THREE.Mesh(new THREE.CircleGeometry(50, 20), new THREE.MeshBasicMaterial({
    side: THREE.DoubleSide
  }));
  sector = new THREE.Mesh(new THREE.CircleGeometry(35, 20, 0, Math.PI * 2 / 3), new THREE.MeshBasicMaterial({
    side: THREE.DoubleSide,
    color: 0xff0000,
    polygonOffset: false,
    polygonOffsetFactor: -1.0,
    polygonOffsetUnits: -4.0
  }));
  scene.add(circle);
  scene.add(sector);
}

function onWindowResize() {
  camera.aspect = window.innerWidth / window.innerHeight;
  camera.updateProjectionMatrix();
  renderer.setSize(window.innerWidth, window.innerHeight);
}

function animate() {
  if (strategy === 'sol0') {
  	sector.material.polygonOffset = false;
    sector.position.z = 0.0;
    camera.near = 1;
    camera.far = 1e4;
    camera.updateProjectionMatrix();
  } else if (strategy === 'sol1') {
  	sector.material.polygonOffset = false;
    sector.position.z = 0.01;
    camera.near = 1;
    camera.far = 1e4;
    camera.updateProjectionMatrix();
  } else if (strategy === 'sol2') {
 ...