( function () {
/**
* Simplification Geometry Modifier
* - based on code and technique
* - by Stan Melax in 1998
* - Progressive Mesh type Polygon Reduction Algorithm
* - http://www.melax.com/polychop/
*/
const _cb = new THREE.Vector3(),
_ab = new THREE.Vector3();
class SimplifyModifier {
modify( geometry, count ) {
geometry = geometry.clone();
const attributes = geometry.attributes; // this modifier can only process indexed and non-indexed geomtries with a position attribute
for ( const name in attributes ) {
if ( name !== 'position' ) geometry.deleteAttribute( name );
}
geometry = THREE.BufferGeometryUtils.mergeVertices( geometry ); //
// put data of original geometry in different data structures
//
const vertices = [];
const faces = []; // add vertices
const positionAttribute = geometry.getAttribute( 'position' );
for ( let i = 0; i < positionAttribute.count; i ++ ) {
const v = new THREE.Vector3().fromBufferAttribute( positionAttribute, i );
const vertex = new Vertex( v );
vertices.push( vertex );
} // add faces
let index = geometry.getIndex();
if ( index !== null ) {
for ( let i = 0; i < index.count; i += 3 ) {
const a = index.getX( i );
const b = index.getX( i + 1 );
const c = index.getX( i + 2 );
const triangle = new Triangle( vertices[ a ], vertices[ b ], vertices[ c ], a, b, c );
faces.push( triangle );
}
} else {
for ( let i = 0; i < positionAttribute.count; i += 3 ) {
const a = i;
const b = i + 1;
const c = i + 2;
const triangle = new Triangle( vertices[ a ], vertices[ b ], vertices[ c ], a, b, c );
faces.push( triangle );
}
} // compute all edge collapse costs
for ( let i = 0, il = vertices.length; i < il; i ++ ) {
computeEdgeCostAtVertex( vertices[ i ] );
}
let nextVertex;
let z = count;
while ( z -- ) {
nextVertex = minimumCostEdge( vertices );
if ( ! nextVertex ) {
console.log( 'THREE.SimplifyModifier: No next vertex' );
break;
}
collapse( vertices, faces, nextVertex, nextVertex.collapseNeighbor );
} //
const simplifiedGeometry = new THREE.BufferGeometry();
const position = [];
index = []; //
for ( let i = 0; i < vertices.length; i ++ ) {
const vertex = vertices[ i ].position;
position.push( vertex.x, vertex.y, vertex.z ); // cache final index to GREATLY speed up faces reconstruction
vertices[ i ].id = i;
} //
for ( let i = 0; i < faces.length; i ++ ) {
const face = faces[ i ];
index.push( face.v1.id, face.v2.id, face.v3.id );
} //
simplifiedGeometry.setAttribute( 'position', new THREE.Float32BufferAttribute( position, 3 ) );
simplifiedGeometry.setIndex( index );
return simplifiedGeometry;
}
}
function pushIfUnique( array, object ) {
if ( array.indexOf( object ) === - 1 ) array.push( object );
}
function removeFromArray( array, object ) {
const k = array.indexOf( object );
if ( k > - 1 ) array.splice( k, 1 );
}
function computeEdgeCollapseCost( u, v ) {
// if we collapse edge uv by moving u to v then how
// much different will the model change, i.e. the "error".
const edgelength = v.position.distanceTo( u.position );
let curvature = 0;
const sideFaces = []; // find the "sides" triangles that are on the edge uv
for ( let i = 0, il = u.faces.length; i < il; i ++ ) {
const face = u.faces[ i ];
if ( face.hasVertex( v ) ) {
sideFaces.push( face );
}
} // use the triangle facing most away from the sides
// to determine our curvature term
for ( let i = 0, il = u.faces.length; i < il; i ++ ) {
let minCurvature = 1;
const face = u.faces[ i ];
for ( let j = 0; j < sideFaces.length; j ++ ) {
const sideFace = sideFaces[ j ]; // use dot product of face normals.
const dotProd = face.normal.dot( sideFace.normal );
minCurvature = Math.min( minCurvature, ( 1.001 - dotProd ) / 2 );
}
curvature = Math.max( curvature, minCurvature );
} // crude approach in attempt to preserve borders
// though it seems not to be totally correct
const borders = 0;
if ( sideFaces.length < 2 ) {
// we add some arbitrary cost for borders,
// borders += 10;
curvature = 1;
}
const amt = edgelength * curvature + borders;
return amt;
}
function computeEdgeCostAtVertex( v ) {
// compute the edge collapse cost for all edges that start
// from vertex v. Since we are only interested in reducing
// the object by selecting the min cost edge at each step, we
// only cache the cost of the least cost edge at this vertex
// (in member variable collapse) as well as the value of the
// cost (in member variable collapseCost).
if ( v.neighbors.length === 0 ) {
// collapse if no neighbors.
v.collapseNeighbor = null;
v.collapseCost = - 0.01;
return;
}
v.collapseCost = 100000;
v.collapseNeighbor = null; // search all neighboring edges for "least cost" edge
for ( let i = 0; i < v.neighbors.length; i ++ ) {
const collapseCost = computeEdgeCollapseCost( v, v.neighbors[ i ] );
if ( ! v.collapseNeighbor ) {
v.collapseNeighbor = v.neighbors[ i ];
v.collapseCost = collapseCost;
v.minCost = collapseCost;
v.totalCost = 0;
v.costCount = 0;
}
v.costCount ++;
v.totalCost += collapseCost;
if ( collapseCost < v.minCost ) {
v.collapseNeighbor = v.neighbors[ i ];
v.minCost = collapseCost;
}
} // we average the cost of collapsing at this vertex
v.collapseCost = v.totalCost / v.costCount; // v.collapseCost = v.minCost;
}
function removeVertex( v, vertices ) {
console.assert( v.faces.length === 0 );
while ( v.neighbors.length ) {
const n = v.neighbors.pop();
removeFromArray( n.neighbors, v );
}
removeFromArray( vertices, v );
}
function removeFace( f, faces ) {
removeFromArray( faces, f );
if ( f.v1 ) removeFromArray( f.v1.faces, f );
if ( f.v2 ) removeFromArray( f.v2.faces, f );
if ( f.v3 ) removeFromArray( f.v3.faces, f ); // TODO optimize this!
const vs = [ f.v1, f.v2, f.v3 ];
for ( let i = 0; i < 3; i ++ ) {
const v1 = vs[ i ];
const v2 = vs[ ( i + 1 ) % 3 ];
if ( ! v1 || ! v2 ) continue;
v1.removeIfNonNeighbor( v2 );
v2.removeIfNonNeighbor( v1 );
}
}
function collapse( vertices, faces, u, v ) {
// u and v are pointers to vertices of an edge
// Collapse the edge uv by moving vertex u onto v
if ( ! v ) {
// u is a vertex all by itself so just delete it..
removeVertex( u, vertices );
return;
}
const tmpVertices = [];
for ( let i = 0; i < u.neighbors.length; i ++ ) {
tmpVertices.push( u.neighbors[ i ] );
} // delete triangles on edge uv:
for ( let i = u.faces.length - 1; i >= 0; i -- ) {
if ( u.faces[ i ] && u.faces[ i ].hasVertex( v ) ) {
removeFace( u.faces[ i ], faces );
}
} // update remaining triangles to have v instead of u
for ( let i = u.faces.length - 1; i >= 0; i -- ) {
u.faces[ i ].replaceVertex( u, v );
}
removeVertex( u, vertices ); // recompute the edge collapse costs in neighborhood
for ( let i = 0; i < tmpVertices.length; i ++ ) {
computeEdgeCostAtVertex( tmpVertices[ i ] );
}
}
function minimumCostEdge( vertices ) {
// O(n * n) approach. TODO optimize this
let least = vertices[ 0 ];
for ( let i = 0; i < vertices.length; i ++ ) {
if ( vertices[ i ].collapseCost < least.collapseCost ) {
least = vertices[ i ];
}
}
return least;
} // we use a triangle class to represent structure of face slightly differently
class Triangle {
constructor( v1, v2, v3, a, b, c ) {
this.a = a;
this.b = b;
this.c = c;
this.v1 = v1;
this.v2 = v2;
this.v3 = v3;
this.normal = new THREE.Vector3();
this.computeNormal();
v1.faces.push( this );
v1.addUniqueNeighbor( v2 );
v1.addUniqueNeighbor( v3 );
v2.faces.push( this );
v2.addUniqueNeighbor( v1 );
v2.addUniqueNeighbor( v3 );
v3.faces.push( this );
v3.addUniqueNeighbor( v1 );
v3.addUniqueNeighbor( v2 );
}
computeNormal() {
const vA = this.v1.position;
const vB = this.v2.position;
const vC = this.v3.position;
_cb.subVectors( vC, vB );
_ab.subVectors( vA, vB );
_cb.cross( _ab ).normalize();
this.normal.copy( _cb );
}
hasVertex( v ) {
return v === this.v1 || v === this.v2 || v === this.v3;
}
replaceVertex( oldv, newv ) {
if ( oldv === this.v1 ) this.v1 = newv; else if ( oldv === this.v2 ) this.v2 = newv; else if ( oldv === this.v3 ) this.v3 = newv;
removeFromArray( oldv.faces, this );
newv.faces.push( this );
oldv.removeIfNonNeighbor( this.v1 );
this.v1.removeIfNonNeighbor( oldv );
oldv.removeIfNonNeighbor( this.v2 );
this.v2.removeIfNonNeighbor( oldv );
oldv.removeIfNonNeighbor( this.v3 );
this.v3.removeIfNonNeighbor( oldv );
this.v1.addUniqueNeighbor( this.v2 );
this.v1.addUniqueNeighbor( this.v3 );
this.v2.addUniqueNeighbor( this.v1 );
this.v2.addUniqueNeighbor( this.v3 );
this.v3.addUniqueNeighbor( this.v1 );
this.v3.addUniqueNeighbor( this.v2 );
this.computeNormal();
}
}
class Vertex {
constructor( v ) {
this.position = v;
this.id = - 1; // external use position in vertices list (for e.g. face generation)
this.faces = []; // faces vertex is connected
this.neighbors = []; // neighbouring vertices aka "adjacentVertices"
// these will be computed in computeEdgeCostAtVertex()
this.collapseCost = 0; // cost of collapsing this vertex, the less the better. aka objdist
this.collapseNeighbor = null; // best candinate for collapsing
}
addUniqueNeighbor( vertex ) {
pushIfUnique( this.neighbors, vertex );
}
removeIfNonNeighbor( n ) {
const neighbors = this.neighbors;
const faces = this.faces;
const offset = neighbors.indexOf( n );
if ( offset === - 1 ) return;
for ( let i = 0; i < faces.length; i ++ ) {
if ( faces[ i ].hasVertex( n ) ) return;
}
neighbors.splice( offset, 1 );
}
}
THREE.SimplifyModifier = SimplifyModifier;
} )();
