threejs/examples/js/modifiers/SimplifyModifier.js

( 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;

} )();