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Last active July 24, 2025 07:28
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Fast Quadric Mesh Simplification JS port
Raw
mesh_simplify.html
<!DOCTYPE html>
<html lang="en">
<head>
<title>three.js webgl - modifier - Fast Quadric Mesh Simplification</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
<style>
body {
font-family: Monospace;
background-color: #f0f0f0;
margin: 0px;
overflow: hidden;
}
</style>
</head>
<body>
<script src="../build/three.js"></script>
<script src="js/controls/OrbitControls.js"></script>
<!-- <script src="js/modifiers/SimplifyModifier.js"></script> -->
<script src="MeshSimplify.js"></script>
<script src="js/libs/stats.min.js"></script>
<script>
var container, stats;
var camera, controls, scene, renderer;
var cube, mesh, material;
var boxGeometry = new THREE.BoxGeometry( 80, 80, 80, 4, 4, 4 );
var torusGeometry = new THREE.TorusGeometry( 50, 25, 256, 256, Math.PI * 2 );
var sphereGeometry = new THREE.SphereGeometry( 50, 15, 15 );
var planeGeometry = new THREE.PlaneGeometry( 100, 100, 6, 6 );
var torusKnotGeometry = new THREE.TorusKnotGeometry(100, 25, 256, 256)
var textGeometry;
var loader = new THREE.FontLoader();
loader.load( 'fonts/helvetiker_regular.typeface.json', function ( font ) {
textGeometry = new THREE.TextGeometry( '&', {
size: 200,
height: 50,
curveSegments: 1,
font: font
} );
} );
var modifer = new THREE.SimplifyModifier();
var meshes = [];
var count = 0;
init();
animate();
function addStuff( geometry ) {
count ++;
var simplified = modifer.modify( geometry, geometry.vertices.length * 0.5 | 0 );
console.error('simplified', simplified.faces.length, simplified.vertices.length);
var wireframe = new THREE.MeshBasicMaterial({
color: Math.random() * 0xffffff,
wireframe: true
});
var materialNormal = new THREE.MeshNormalMaterial({
transparent: true,
opacity: 0.7
});
mesh = THREE.SceneUtils.createMultiMaterialObject( simplified, [
material,
wireframe,
// materialNormal
]);
mesh.position.x = -200;
mesh.position.y = count * 150 - 300;
scene.add( mesh );
meshes.push( mesh );
mesh = THREE.SceneUtils.createMultiMaterialObject( geometry, [
material,
wireframe,
// materialNormal
]);
mesh.position.x = 200;
mesh.position.y = count * 150 - 300;
scene.add( mesh );
meshes.push ( mesh );
}
function init() {
container = document.createElement( 'div' );
document.body.appendChild( container );
info = document.createElement( 'div' );
info.style.position = 'absolute';
info.style.top = '10px';
info.style.width = '100%';
info.style.textAlign = 'center';
info.innerHTML = '50% Vertex Reduction using SimplifyModifier';
container.appendChild( info );
camera = new THREE.PerspectiveCamera( 70, window.innerWidth / window.innerHeight, 1, 1000 );
camera.position.z = 500;
scene = new THREE.Scene();
var light = new THREE.PointLight( 0xffffff, 1.5 );
light.position.set( 1000, 1000, 2000 );
scene.add( light );
// addStuff( boxGeometry );
// addStuff( planeGeometry );
// addStuff( sphereGeometry );
// addStuff( torusGeometry );
addStuff( torusKnotGeometry );
renderer = new THREE.WebGLRenderer( { antialias: true } );
renderer.setClearColor( 0xf0f0f0 );
renderer.setPixelRatio( window.devicePixelRatio );
renderer.setSize( window.innerWidth, window.innerHeight );
container.appendChild( renderer.domElement );
stats = new Stats();
container.appendChild( stats.dom );
//
controls = new THREE.OrbitControls( camera, renderer.domElement );
window.addEventListener( 'resize', onWindowResize, false );
}
function onWindowResize() {
camera.aspect = window.innerWidth / window.innerHeight;
camera.updateProjectionMatrix();
renderer.setSize( window.innerWidth, window.innerHeight );
}
//
function animate() {
meshes.forEach( m => {
m.rotation.x += 0.01;
m.rotation.y += 0.01;
m.rotation.z += 0.01;
})
requestAnimationFrame( animate );
controls.update();
stats.begin();
render();
stats.end();
}
function render() {
renderer.render( scene, camera );
}
</script>
</body>
</html>
Raw
mesh_simplify.js
//
// Mesh Simplification Unit
// (C) by Sven Forstmann in 2014
// License : MIT (http://opensource.org/licenses/MIT)
// https://github.com/sp4cerat/Fast-Quadric-Mesh-Simplification
// http://www.gamedev.net/topic/656486-high-speed-quadric-mesh-simplification-without-problems-resolved/
// http://voxels.blogspot.com/2014/05/quadric-mesh-simplification-with-source.html
// https://github.com/neurolabusc/Fast-Quadric-Mesh-Simplification-Pascal-
//
// JS Port by Joshua Koo in 2016
// https://github.com/zz85 @blurspline
// https://github.com/neurolabusc/Fast-Quadric-Mesh-Simplification-Pascal-/blob/master/meshify_simplify_quadric.pas
THREE.SimplifyModifier = function SimplifyModifier() {
}
THREE.SimplifyModifier.prototype.modify =
(function() {
function SymetricMatrix() {
// init
this.m = new Array(10).fill(0);
}
SymetricMatrix.prototype = {
set: function set(
m11, m12, m13, m14,
m22, m23, m24,
m33, m34,
m44 ) {
this.m[0] = m11;
this.m[1] = m12;
this.m[2] = m13;
this.m[3] = m14;
this.m[4] = m22;
this.m[5] = m23;
this.m[6] = m24;
this.m[7] = m33;
this.m[8] = m34;
this.m[9] = m44;
return this;
},
makePlane: function makePlane( a, b, c, d ) {
return this.set(
a * a, a * b, a * c, a * d,
b * b, b * c, b * d,
c * c, c * d,
d * d
);
},
det: function determinant(
a11, a12, a13,
a21, a22, a23,
a31, a32, a33
) {
var det = this.m[ a11 ] * this.m[ a22 ] * this.m[ a33 ]
+ this.m[ a13 ] * this.m[ a21 ] * this.m[ a32 ]
+ this.m[ a12 ] * this.m[ a23 ] * this.m[ a31 ]
- this.m[ a13 ] * this.m[ a22 ] * this.m[ a31 ]
- this.m[ a11 ] * this.m[ a23 ] * this.m[ a32 ]
- this.m[ a12 ] * this.m[ a21 ] * this.m[ a33 ];
return det;
},
// produces new Matrix
add: function add( n ) {
return new SymetricMatrix().set(
this.m[0] + n.m[0],
this.m[1] + n.m[1],
this.m[2] + n.m[2],
this.m[3] + n.m[3],
this.m[4] + n.m[4],
this.m[5] + n.m[5],
this.m[6] + n.m[6],
this.m[7] + n.m[7],
this.m[8] + n.m[8],
this.m[9] + n.m[9]
);
},
addSelf: function addSelf( n ) {
this.m[0]+=n.m[0]; this.m[1]+=n.m[1]; this.m[2]+=n.m[2]; this.m[3]+=n.m[3];
this.m[4]+=n.m[4]; this.m[5]+=n.m[5]; this.m[6]+=n.m[6]; this.m[7]+=n.m[7];
this.m[8]+=n.m[8]; this.m[9]+=n.m[9]
}
};
/* Model Objects */
function Triangle() {
this.v = new Array(3); // indices for array
this.err = new Array(4); // errors
this.deleted = false;
this.dirty = false;
this.n = new Vector3(); // Normal
}
// function Vector3(x, y, z) {
// this.x = x;
// this.y = y;
// this.z = z;
// };
var Vector3 = THREE.Vector3;
function Vertex() {
this.p = new Vector3();
this.tstart = -1;
this.tcount = -1;
this.q = new SymetricMatrix();
this.border = false;
}
function Ref() {
// this.tid = -1;
// this.tvertex = -1;
}
function init(origVertices, origFaces) {
vertices = origVertices.map(
v => {
var vert = new Vertex();
vert.p.copy( v );
return vert;
}
);
triangles = origFaces.map( f => {
var tri = new Triangle();
tri.v[0] = f.a;
tri.v[1] = f.b;
tri.v[2] = f.c;
return tri;
});
}
var triangles = []; // Triangle
var vertices = []; // Vertex
var refs = []; // Ref
function resize(array, count) {
if (count < array.length) {
return array.splice(count);
}
if (count > array.length) {
// in JS, arrays need not be expanded
// console.log('more');
}
}
//
// Main simplification function
//
// target_count : target nr. of triangles
// agressiveness : sharpness to increase the threshold.
// 5..8 are good numbers
// more iterations yield higher quality
//
function simplify_mesh(target_count, agressiveness) {
if (agressiveness === undefined) agressiveness = 7;
// TODO normalize_mesh to max length 1?
console.time('simplify_mesh');
var i, il;
// set all triangles to non deleted
for ( i = 0, il = triangles.length; i < il; i++ ) {
triangles[ i ].deleted = false;
}
console.timeEnd('simplify_mesh');
// main iteration loop
var deleted_triangles = 0;
var deleted0 = [], deleted1 = []; // std::vector<int>
var triangle_count = triangles.length;
for (var iteration = 0; iteration < 100; iteration++ ) {
console.log("iteration %d - triangles %d, tris\n",
iteration, triangle_count - deleted_triangles, triangles.length);
if ( triangle_count - deleted_triangles <= target_count ) break;
// update mesh once in a while
if( iteration % 5 === 0 ) {
update_mesh(iteration);
}
// clear dirty flag
for(var j = 0; j < triangles.length; j++) {
triangles[ j ].dirty = false;
}
//
// All triangles with edges below the threshold will be removed
//
// The following numbers works well for most models.
// If it does not, try to adjust the 3 parameters
//
var threshold = 0.000000001 * Math.pow( iteration + 3, agressiveness );
// remove vertices & mark deleted triangles
for ( i = 0, il = triangles.length; i < il; i++ ) {
var t = triangles[ i ];
if ( t.err[3] > threshold ||
t.deleted || t.dirty ) continue;
for ( j = 0; j < 3; j ++ ) {
if ( t.err[j] < threshold ) {
var i0 = t.v[ j ];
var v0 = vertices[ i0 ];
var i1 = t.v[ (j + 1) % 3 ];
var v1 = vertices[ i1 ];
// Border check
if (v0.border != v1.border) continue;
// Compute vertex to collapse to
var p = new Vector3();
calculate_error( i0, i1, p );
// console.log('Compute vertex to collapse to', p);
resize(deleted0, v0.tcount); // normals temporarily
resize(deleted1, v1.tcount); // normals temporarily
// dont remove if flipped
if( flipped( p, i0, i1, v0, v1, deleted0 ) ) continue;
if( flipped( p, i1, i0, v1, v0, deleted1 ) ) continue;
// not flipped, so remove edge
// console.log('not flipped, remove edge');
// console.log(v0.p, p);
v0.p = p;
// v0.q = v1.q + v0.q;
v0.q.addSelf( v1.q );
var tstart = refs.length;
// CONTINUE
deleted_triangles = update_triangles( i0, v0, deleted0, deleted_triangles );
// console.log('deleted triangle v0', deleted_triangles);
deleted_triangles = update_triangles( i0, v1, deleted1, deleted_triangles );
// console.log('deleted triangle v1', deleted_triangles);
var tcount = refs.length - tstart;
if (tcount <= v0.tcount ) {
// console.log('save ram?');
// if(tcount)
// move(refs, v0.tstart, tstart, tcount);
}
else
// append
v0.tstart = tstart;
v0.tcount=tcount;
break;
}
} // end for j
// done?
if (triangle_count - deleted_triangles
<= target_count)
break;
}
} // end iteration
function move(refs, dest, source, count) {
for (var i = 0; i < count; i++) {
refs[dest + i] = refs[source + i];
}
}
// clean up mesh
compact_mesh();
// ready
console.timeEnd('simplify_mesh');
// int timeEnd=timeGetTime();
// printf("%s - %d/%d %d%% removed in %d ms\n",__FUNCTION__,
// triangle_count-deleted_triangles,
// triangle_count,deleted_triangles*100/triangle_count,
// timeEnd-timeStart);
}
// Check if a triangle flips when this edge is removed
var n = new Vector3();
var d1 = new Vector3();
var d2 = new Vector3();
function /*bool*/ flipped(
/* vec3f */ p,
/*int*/ i0,
/*int*/ i1,
/*Vertex*/ v0,
/*Vertex*/ v1, // not needed
/*std::vector<int>*/ deleted)
{
// var bordercount = 0;
for ( var k = 0; k < v0.tcount; k ++ ) {
// Triangle &
var t = triangles[refs[v0.tstart+k].tid];
if (t.deleted) continue;
var s = refs[v0.tstart + k].tvertex;
var id1 = t.v[(s+1) % 3];
var id2 = t.v[(s+2) % 3];
if(id1==i1 || id2==i1) // delete ?
{
// bordercount++;
deleted[k] = true;
continue;
}
/* vec3f */
d1.subVectors( vertices[id1].p, p).normalize();
d2.subVectors( vertices[id2].p, p).normalize();
if(Math.abs(d1.dot(d2))>0.999) return true;
/*vec3f n;*/
n.crossVectors(d1,d2).normalize();
deleted[k] = false;
if(n.dot(t.n)<0.2) return true;
}
return false;
}
// Update triangle connections and edge error after a edge is collapsed
function update_triangles(/*int*/ i0,
/*Vertex &*/ v,
/*std::vector<int> & */deleted,
/*int &*/ deleted_triangles )
{
// console.log('update_triangles');
// vec3f p;
var p = new Vector3();
for (var k = 0; k < v.tcount; k++)
{
var /*Ref &*/ r = refs[ v.tstart + k ];
var /*Triangle &*/ t = triangles[ r.tid ];
if( t.deleted ) continue;
if( deleted[k] ) {
t.deleted = true;
deleted_triangles++;
continue;
}
t.v[r.tvertex] = i0;
t.dirty = true;
t.err[0] = calculate_error( t.v[0], t.v[1], p );
t.err[1] = calculate_error( t.v[1], t.v[2], p );
t.err[2] = calculate_error( t.v[2], t.v[0], p );
t.err[3] = Math.min( t.err[0], t.err[1], t.err[2] );
refs.push( r );
}
return deleted_triangles;
}
// compact triangles, compute edge error and build reference list
function update_mesh( iteration ) /*int*/
{
// console.log('update_mesh', iteration, triangles.length);
if ( iteration > 0 ) {
// compact triangles
var dst = 0;
for (var i = 0; i < triangles.length; i++) {
var target = triangles[i];
if(!target.deleted) {
triangles[dst++] = target;
}
}
console.log('not deleted dst', triangles.length, dst);
triangles.splice( dst );
}
//
// Init Quadrics by Plane & Edge Errors
//
// required at the beginning ( iteration == 0 )
// recomputing during the simplification is not required,
// but mostly improves the result for closed meshes
//
if( iteration === 0 ) {
for (var i = 0; i < vertices.length; i++ ) {
// may not need to do this.
vertices[i].q = new SymetricMatrix();
}
for (var i = 0; i < triangles.length; i++) {
var /*Triangle &*/ t = triangles[i];
// var n, p[3]; /* vec3f */
var n = new Vector3();
var p = new Array(3);
var p1p0 = new Vector3();
var p2p0 = new Vector3();
for (var j = 0; j < 3; j++) {
p[j] = vertices[t.v[j]].p;
}
p1p0.subVectors(p[1], p[0]);
p2p0.subVectors(p[2], p[0]);
n.crossVectors(p1p0, p2p0).normalize();
t.n = n;
var tmp = new SymetricMatrix().makePlane(
n.x,
n.y,
n.z,
-n.dot(p[0]))
for (var j = 0; j < 3; j++) {
vertices[t.v[j]].q.addSelf(tmp);
}
// vertices[t.v[j]].q =
// vertices[t.v[j]].q.add(SymetricMatrix(n.x,n.y,n.z,-n.dot(p[0])));
}
for (var i = 0; i < triangles.length; i++) {
// Calc Edge Error
var /*Triangle &*/ t=triangles[i];
// vec3f p;
var p = new Vector3();
for (var j = 0; j < 3; j++) {
t.err[ j ] = calculate_error( t.v[j], t.v[(j+1)%3], p );
}
t.err[ 3 ] = Math.min( t.err[0], t.err[1], t.err[2] );
}
}
// Init Reference ID list
for (var i = 0; i < vertices.length; i++)
{
vertices[i].tstart=0;
vertices[i].tcount=0;
}
for (var i = 0; i < triangles.length; i++)
{
/*Triangle &*/
var t = triangles[i];
for (j = 0; j < 3; j++) vertices[t.v[j]].tcount++;
}
var tstart=0;
for (var i = 0; i < vertices.length; i++)
{
var /*Vertex &*/ v = vertices[i];
v.tstart = tstart;
tstart += v.tcount;
v.tcount = 0;
}
// Write References
// resize(refs, triangles.length * 3)
console.log('pre ref', refs.length, triangles.length * 3);
for (var i = refs.length; i < triangles.length * 3; i++) {
refs[i] = new Ref();
}
for (var i = 0; i < triangles.length; i++)
{
/*Triangle &*/
var t = triangles[i];
for (var j = 0; j < 3; j++)
{
/*Vertex &*/
var v = vertices[ t.v[ j ] ];
refs[ v.tstart + v.tcount ].tid = i;
refs[ v.tstart + v.tcount ].tvertex = j;
v.tcount++;
}
}
// Identify boundary : vertices[].border=0,1
if( iteration == 0 )
{
// std::vector<int> vcount,vids;
var vcount,vids;
for (var i = 0; i < vertices.length; i++) {
vertices[i].border = 0;
}
for (var i = 0; i < vertices.length; i++) {
var /*Vertex &*/ v = vertices[i];
// vcount.clear();
// vids.clear();
vcount = [];
vids = [];
for (var j = 0; j < v.tcount; j++) {
var k = refs[v.tstart + j].tid;
var /*Triangle &*/ t = triangles[k];
for (var k = 0; k < 3; k++) {
var ofs=0,
id=t.v[k];
while(ofs < vcount.length) {
if(vids[ofs]==id) break;
ofs++;
}
if(ofs == vcount.length) {
vcount.push(1);
vids.push(id);
}
else {
vcount[ofs]++;
}
}
}
for (var j = 0; j < vcount.length; j++) {
if(vcount[j]==1) {
vertices[vids[j]].border=1;
}
}
}
}
}
// Finally compact mesh before exiting
function compact_mesh()
{
console.log('compact_mesh');
var /*int */ dst=0;
for (var i = 0; i < vertices.length; i++) {
vertices[i].tcount=0;
}
for (var i = 0; i < triangles.length; i++) {
if(!triangles[i].deleted) {
var /*Triangle &*/ t = triangles[i];
triangles[dst++] = t;
for (var j = 0; j < 3; j++)
vertices[t.v[j]].tcount = 1;
}
}
resize(triangles, dst);
dst = 0;
for (var i = 0; i < vertices.length; i++) {
if (vertices[i].tcount) {
vertices[i].tstart = dst;
vertices[dst].p = vertices[i].p;
dst++;
}
}
for (var i = 0; i < triangles.length; i++) {
var /*Triangle &*/ t = triangles[i];
for (var j = 0; j < 3; j++)
t.v[j] = vertices[t.v[j]].tstart;
}
console.log('%cCompact Mesh', 'background:#f00', vertices.length, dst);
resize(vertices, dst);
console.log('%cCompact Mesh ok', 'background:#f00', vertices.length, dst);
}
// Error between vertex and Quadric
function vertex_error(/*SymetricMatrix*/ q, /*double*/ x, y, z) {
return q.m[0]*x*x + 2*q.m[1]*x*y + 2*q.m[2]*x*z + 2*q.m[3]*x + q.m[4]*y*y
+ 2*q.m[5]*y*z + 2*q.m[6]*y + q.m[7]*z*z + 2*q.m[8]*z + q.m[9];
}
// Error for one edge
// if DECIMATE is defined vertex positions are NOT interpolated
// Luebke Survey of Polygonal Simplification Algorithms: "vertices of a model simplified by the decimation algorithm are a subset of the original model’s vertices."
// http://www.cs.virginia.edu/~luebke/publications/pdf/cg+a.2001.pdf
function calculate_error(id_v1, id_v2, p_result)
{
// compute interpolated vertex
var vertex1 = vertices[id_v1];
var vertex2 = vertices[id_v2];
var q = vertex1.q.add(vertex2.q);
var border = vertex1.border && vertex2.border;
var error = 0;
var det = q.det(0, 1, 2, 1, 4, 5, 2, 5, 7);
if ( det !== 0 && !border ) {
// q_delta is invertible
p_result.x = -1/det*(q.det(1, 2, 3, 4, 5, 6, 5, 7, 8)); // vx = A41/det(q_delta)
p_result.y = 1/det*(q.det(0, 2, 3, 1, 5, 6, 2, 7, 8)); // vy = A42/det(q_delta)
p_result.z = -1/det*(q.det(0, 1, 3, 1, 4, 6, 2, 5, 8)); // vz = A43/det(q_delta)
error = vertex_error(q, p_result.x, p_result.y, p_result.z);
}
else {
// det = 0 -> try to find best result
var /*vec3f*/ p1 = vertex1.p;
var /*vec3f*/ p2 = vertex2.p;
var /*vec3f*/ p3 = new Vector3().addVectors(p1, p2).multiplyScalar(0.5);
var error1 = vertex_error(q, p1.x, p1.y, p1.z);
var error2 = vertex_error(q, p2.x, p2.y, p2.z);
var error3 = vertex_error(q, p3.x, p3.y, p3.z);
error = Math.min(error1, error2, error3);
if (error1 === error) p_result.copy(p1);
if (error2 === error) p_result.copy(p2);
if (error3 === error) p_result.copy(p3);
}
return error;
}
return function simplifyModify(geometry) {
if ( geometry instanceof THREE.BufferGeometry && !geometry.vertices && !geometry.faces ) {
console.log('converting BufferGeometry to Geometry');
geometry = new THREE.Geometry().fromBufferGeometry( geometry );
}
geometry.mergeVertices();
// convert format
init( geometry.vertices, geometry.faces );
// simplify!
// simplify_mesh(geometry.faces.length * 0.5 | 0, 7);
// simplify_mesh(geometry.faces.length - 2, 4);
console.time('simplify')
simplify_mesh(150, 7);
console.timeEnd('simplify')
console.log('old vertices ' + geometry.vertices.length, 'old faces ' + geometry.faces.length);
console.log('new vertices ' + vertices.length, 'old faces ' + triangles.length);
// TODO convert to buffer geometry.
var newGeo = new THREE.Geometry();
for ( i = 0; i < vertices.length; i ++ ) {
var v = vertices[ i ];
newGeo.vertices.push( v.p )
}
for ( i = 0; i < triangles.length; i ++ ) {
var tri = triangles[ i ];
newGeo.faces.push( new THREE.Face3(
tri.v[0],
tri.v[1],
tri.v[2]
) );
}
return newGeo;
}
})()
@r03ert0
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r03ert0 commented Feb 18, 2018

The problem seems to be the mergeVertices function: the distance between vertices in the original mesh is too small and they get merged. If I just scale the original mesh size, let's say x100, the issue of the holes goes away.

screen shot 2018-02-18 at 10 54 51

@r03ert0
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r03ert0 commented Feb 18, 2018

Finally, I commented out the geometry.mergeVertices() call, and lowered the threshold in the simplify mesh function to 1e-11 instead of 1e-9 (the value will depend on the vertex density of the mesh i imagine...):

var threshold = 1e-11 * Math.pow( iteration + 3, agressiveness );

The algorithm is so fast !! 💃

@sp4cerat
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From experience, the method works best if the mesh is size 1 (c++ version). Scaling the mesh before simplifying and scaling back after might be a solution.

@dspdog
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dspdog commented Aug 17, 2020 •
edited
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solution for me is removing the if( iteration % 5 === 0 ) { condition (eg, update the mesh every iteration)

setting thethreshold value lower/higher affects the number of iterations but seems to work stable with lots of values once the condition is gone. affects quality (?)

tried scaling the mesh/geometry bigger/smaller but didnt seem to have any effect.

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