IFace.java

/*---

    iGeo - http://igeo.jp

    Copyright (c) 2002-2013 Satoru Sugihara

    This file is part of iGeo.

    iGeo is free software: you can redistribute it and/or modify
    it under the terms of the GNU Lesser General Public License as
    published by the Free Software Foundation, version 3.

    iGeo is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public
    License along with iGeo.  If not, see <http://www.gnu.org/licenses/>.

---*/

package igeo;

import java.util.ArrayList;
import java.awt.Color;

/**
   Class of a face of polygon mesh.
   
   @author Satoru Sugihara
*/
public class IFace{
    public IVertex[] vertices;
    public IEdge[] edges;
    public IVec normal;
    
    /** used in deleting process */
    public boolean deleted=false;
    
    public boolean invalid=false; // in case init fails due to unmatching edge, vertex etc
    
    public IColor clr; // face color
    
    public IFace(IEdge[] e){ init(e); }
    public IFace(IEdge e1, IEdge e2, IEdge e3){ this(new IEdge[]{e1, e2, e3}); }
    public IFace(IEdge e1, IEdge e2, IEdge e3, IEdge e4){ this(new IEdge[]{e1, e2, e3, e4}); }
    
    public IFace(IVertex[] v){
	int num = v.length;
	vertices = v;
	edges = new IEdge[num];
	for(int i=0; i<num; i++){
	    edges[i] = new IEdge(v[i],v[(i+1)%num]);
	    vertices[i].addFace(this);
	    edges[i].addFace(this);
	}
    }
    
    public IFace(IVertex v1, IVertex v2, IVertex v3){ this(new IVertex[]{v1,v2,v3}); }
    public IFace(IVertex v1, IVertex v2, IVertex v3, IVertex v4){ this(new IVertex[]{v1,v2,v3,v4}); }
    
    /**
       Copis a face but shareing same vertices and edges with the original
    */
    public IFace(IFace f){
	vertices = new IVertex[f.vertices.length];
	for(int i=0; i<vertices.length; i++) vertices[i]=f.vertices[i];
	edges = new IEdge[f.edges.length];
	for(int i=0; i<edges.length; i++) edges[i]=f.edges[i];
	if(f.normal!=null) normal = f.normal.dup();
    }

    public boolean isValid(){
	if(invalid) return false;
	if(vertices==null || edges==null) return false;
	for(int i=0; i<vertices.length; i++){
	    if(vertices[i]==null) return false;
	}
	for(int i=0; i<edges.length; i++){
	    if(edges[i]==null) return false;
	}
	return true;
    }
    
    public void init(IEdge[] e){
	int num = e.length;
	
	vertices = new IVertex[num];
	edges = new IEdge[num];
	
	for(int i=0; i<num; i++) edges[i] = e[i];
	
	if(edges[1].contains(edges[0].vertices[0])) vertices[0]=edges[0].vertices[1];
	else if(edges[1].contains(edges[0].vertices[1])) vertices[0]=edges[0].vertices[0];
	else{
	    invalid=true;
	    IOut.err("first&second edges don't match");
	    IOut.err("edges[0] = "+edges[0].vertices[0].pos+", "+edges[0].vertices[1].pos); //
	    IOut.err("edges[1] = "+edges[1].vertices[0].pos+", "+edges[1].vertices[1].pos); //
	}
	
	for(int i=1; i<num; i++){
	    if(edges[i-1].contains(vertices[i-1]))
		vertices[i]=edges[i-1].getOtherVertex(vertices[i-1]);
	    else{
		invalid=true;
		IOut.err((i-1)+"&"+i+" edges don't match");
		//IOut.err("vertex["+(i-1)+"] =" + vertices[i-1]); //
		//IOut.err("edges["+(i-1)+"] = "+edges[i-1].vertices[0]+", "+edges[i-1].vertices[1]); //
	    }
	}
	
	if(edges[num-1].getOtherVertex(vertices[num-1]) != vertices[0]){
	    invalid=true;
	    IOut.err("first&last vertex doesn't match");
	    //new ICurve(edges[num-1]).clr(1.0,0,0).weight(5); //
	    //new IPoint(vertices[0]).clr(1.0,0,0).size(6); //
	    //new ISurface(vertices[0],vertices[1],vertices[2]).clr(1.0,0,0); //
	}

	if(invalid) return; // exit in case of error
	
	for(int i=0; i<num; i++){
	    vertices[i].addFace(this);
	    edges[i].addFace(this);
	}
    }
    
    
    public IFace dup(){ return new IFace(this); }
    
    
    /*
    public IFace dup(){ // duplicate vertices, edges  
	int num = vertices.length;
	IVertex v[] = new IVertex[num];
	for(int i=0; i<num; i++) v[i] = vertices[i].dup();
	
	IEdge e[] = new IEdge[num];
	for(int i=0; i<num; i++) e[i] = new IEdge(v[i],v[(i+1)%num]);
	
	IFace f = new IFace(e);
	f.normal = normal;
	return f;
    }
    */
    
    
    public IVertex getVertex(int i){ return vertex(i); }
    public IVertex vertex(int i){ return vertices[i]; }
    public IEdge getEdge(int i){ return edge(i); }
    public IEdge edge(int i){ return edges[i]; }
    
    public int vertexNum(){ return vertices.length; }
    public int edgeNum(){ return edges.length; }
    
    public IEdge getEdge(IVertex v1, IVertex v2){
	for(int i=0; i<edges.length; i++){
	    if( edges[i].vertices[0]==v1 && edges[i].vertices[1]==v2 ||
		edges[i].vertices[0]==v2 && edges[i].vertices[1]==v1 ){
		return edges[i];
	    }
	}
	return null;
    }
    
    /** returns edges which aren't a link between any two of given vertex variable vtx. matching only one is fine to be returned. */
    public /*ArrayList<IEdge>*/ IEdge[] getOtherEdges(IVertex v1, IVertex v2, IVertex... otherVtx){
	IVertex[] vtx = new IVertex[otherVtx.length+2];
	vtx[0] = v1;
	vtx[1] = v2;	
	for(int i=0; i<otherVtx.length; i++) vtx[i+1] = otherVtx[i+2];
	
	ArrayList<IEdge> otherEdges = new ArrayList<IEdge>();
	for(int i=0; i<edges.length; i++){
	    boolean matchAny=false;
	    for(int j=0; j<vtx.length&&!matchAny; j++){
		if(edges[i].vertices[0]==vtx[j]) matchAny=true;

	    }
	    if(!matchAny){ otherEdges.add(edges[i]); }
	    else{
		matchAny=false;
		for(int j=0; j<vtx.length&&!matchAny; j++){
		    if(edges[i].vertices[1]==vtx[j]) matchAny=true;
		}
		if(!matchAny){ otherEdges.add(edges[i]); }
	    }
	}
	//return otherEdges;
	return otherEdges.toArray(new IEdge[otherEdges.size()]);
    }
    
    
    public IEdge[] getOtherEdges(IVertex v){
	ArrayList<IEdge> otherEdges = new ArrayList<IEdge>();
	for(int i=0; i<edges.length; i++){
	    if(!edges[i].contains(v)) otherEdges.add(edges[i]);
	}
	return otherEdges.toArray(new IEdge[otherEdges.size()]);
    }
    
    public IEdge getOtherEdge(IVertex v){
	for(int i=0; i<edges.length; i++){
	    if(!edges[i].contains(v)) return edges[i];
	}
	return null;
    }
    
    public IEdge[] getOtherEdges(IEdge e){
	ArrayList<IEdge> otherEdges = new ArrayList<IEdge>();
	for(int i=0; i<edges.length; i++){
	    if(edges[i]!=e && !edges[i].eq(e)) otherEdges.add(edges[i]);
	}
	return otherEdges.toArray(new IEdge[otherEdges.size()]);
    }
    
    public IEdge getOtherEdge(IEdge e){
	for(int i=0; i<edges.length; i++){ if(edges[i]!=e) return edges[i]; }
	return null;
    }
    
    public IVertex getOtherVertex(IVertex v1, IVertex v2){
	for(int i=0; i<vertices.length; i++){
	    if( (vertices[i] != v1) && (vertices[i] != v2) ) return vertices[i];
	}
	return null;
    }
    
    public IVertex getOtherVertex(IEdge e){
	for(int i=0; i<vertices.length; i++){
	    if( (vertices[i] != e.vertices[0]) && (vertices[i] != e.vertices[1]) ) return vertices[i];
	}
	return null;
    }
    
    public IVertex[] getOtherVertices(IVertex v){
	ArrayList<IVertex> vtx = new ArrayList<IVertex>();
	for(int i=0; i<vertices.length; i++){
	    if(vertices[i] != v) vtx.add(vertices[i]);
	}
	return vtx.toArray(new IVertex[vtx.size()]);
    }
    
    
    public IVertex[] getSharedVertices(IFace f){
	ArrayList<IVertex> vtx = new ArrayList<IVertex>();
	for(int i=0; i<vertices.length; i++){
	    boolean found=false;
	    for(int j=0; j<f.vertexNum()&&!found; j++){
		if(vertices[i] != f.vertex(j)){
		    vtx.add(vertices[i]);
		    found=true;
		}
	    }
	}
	return vtx.toArray(new IVertex[vtx.size()]);
    }
    
    public IEdge getSharedEdge(IFace f){
	for(int i=0; i<edges.length; i++){
	    boolean found=false;
	    for(int j=0; j<f.edgeNum()&&!found; j++){
		if( edges[i] == f.edge(j)){ return edges[i]; }
		
		if( edges[i].vertex(0) == f.edge(j).vertex(0) &&
		    edges[i].vertex(1) == f.edge(j).vertex(1) ||
		    edges[i].vertex(0) == f.edge(j).vertex(1) &&
		    edges[i].vertex(1) == f.edge(j).vertex(0) ){
		    return edges[i];
		}
	    }
	}
	return null;
    }
    
    
    public IVertex[] getAdjacentVertices(IVertex v1, IVertex v2){
	IVertex[] vtx = new IVertex[2];
	for(int i=0; i<vertices.length; i++){
	    
	    if( vertices[i] == v1 ){
		if(vertices[(i+1)%vertices.length] == v2){
		    vtx[0] = vertices[(i-1+vertices.length)%vertices.length];
		    vtx[1] = vertices[(i+2)%vertices.length];
		    return vtx;
		}
		else if(vertices[(i-1+vertices.length)%vertices.length] == v2){
		    vtx[0] = vertices[(i+1)%vertices.length];
		    vtx[1] = vertices[(i-2+vertices.length)%vertices.length];
		    return vtx;
		}
	    }
	}
	return null;
    }
    
    /** check if two faces have shared pair of vertices
	@return -1 if no shared pair of vertices, 
	        0 if shared pair of vertices in the same order (opposite loop direction), 
		1 if shared pair of vertices in the opposite order (opposite loop direction)
    */
    public int sharedVertexOrder(IFace f){
	for(int i=0; i<vertices.length; i++){
	    for(int j=0; j<f.vertices.length; j++){
		if(vertices[i]==f.vertices[j]){
		    if(vertices[(i+1)%vertices.length]==f.vertices[(j+1)%f.vertices.length] ||
		       vertices[(i-1+vertices.length)%vertices.length]==f.vertices[(j-1+f.vertices.length)%f.vertices.length]){
			return 0;
		    }
		    else if(vertices[(i+1)%vertices.length]==f.vertices[(j-1+f.vertices.length)%f.vertices.length] ||
			    vertices[(i-1+vertices.length)%vertices.length]==f.vertices[(j+1)%f.vertices.length]){
			return 1;
		    }
		}
	    }
	}
	return -1;
    }
    
    /** direction of edge based on the sequence of vertices array inside a face 
	@return true if it's same with vertices array sequence, otherwise false and also if edge is not included inside face, false.
    */
    public boolean loopDir(IEdge edge){	
	int startIdx=-1;
	for(int i=0; i<vertices.length && startIdx<0; i++){
	    if(vertices[i].eq(edge.vertex(0))){ startIdx=i; }
	}
	
	if(startIdx<0){
	    IOut.err("edge is not in the face");
	    return false;
	}
	
	if(vertices[(startIdx+1)%vertices.length].eq(edge.vertex(1))){ return true; }
	if(vertices[(startIdx-1+vertices.length)%vertices.length].eq(edge.vertex(1))){ return false; }
	
	IOut.err("edge is not in the face");

	return false;
    }
    
    
    public boolean sameLoopDir(IEdge e1, IEdge e2){	
	boolean d1 = loopDir(e1);
	boolean d2 = loopDir(e2);
	return d1&&d2 || (!d1)&&(!d2);
    }
    
    
    public IVec center(){
	IVec center = new IVec();
	for(int i=0; i<vertices.length; i++) center.add(vertices[i].pos);
	center.div(vertices.length);
	return center;
    }
    
    /** alias of center */
    public IVec getCenter(){ return center(); }
    
    public void del(){
	deleted=true;
	for(int i=0; i<vertices.length; i++){
	    vertices[i].faces.remove(this);
	}
	for(int i=0; i<edges.length; i++){
	    edges[i].faces.remove(this);
	}
    }
    
    
    public boolean contains(IVertex v){
	for(int i=0; i<vertices.length; i++){ if(vertices[i]==v) return true; }
	return false;
    }
    
    /** checks if the edge is inside face's edges array */
    public boolean contains(IEdge e){
	for(int i=0; i<edges.length; i++){ if(edges[i]==e) return true; }
	return false;
    }
    
    
    /** checks if the edge is located on the edge of the face even if it's not inside face's edges array */
    public boolean onFace(IEdge e){
	if(contains(e)) return true;
	for(int i=0; i<vertices.length; i++){
	    if(vertices[i].eq(e.vertex(0))){
		if(vertices[(i+1)%vertices.length].eq(e.vertex(1))) return true;
		if(vertices[(i-1+vertices.length)%vertices.length].eq(e.vertex(1))) return true;
	    }
	}
	return false;
    }
    
    
    public int indexOf(IEdge e){
	for(int i=0; i<edges.length; i++){ if(edges[i]==e) return i; }
	return -1;
    }
    
    public void replaceVertex(IVertex oldVertex, IVertex newVertex){
	//for(int i=0; i<edges.length; i++){
	for(int i=0; i<vertices.length; i++){
	    if(vertices[i] == oldVertex){ vertices[i] = newVertex; return; }
	    // how about edges?
	}
	IOut.err("no such vertex on this face");
    }
    
    public void replaceEdge(IEdge oldEdge, IEdge newEdge){
	for(int i=0; i<edges.length; i++){
	    if(edges[i] == oldEdge){ edges[i] = newEdge; return; }
	}
	IOut.err("no such edge on this face");
    }
    
    /*
    public boolean eq(IFace f){
	if(edges.length!=f.edges.length) return false; 
	ArrayList<IEdge> e = new ArrayList<IEdge>();
	for(int i=0; i<f.edges.length; i++) e.add(f.edges[i]);
	// ?
	for(int i=0; i<edges.length; i++){
	    if(!e.contains(edges[i])) return false;
	    else e.remove(edges[i]);
	}
	if(e.size()>0) return false;
	return true; 
    }
    */
    
    
    public double area(){
	if(vertices.length==3){
	    IVec v1 = vertices[1].pos.get().diff(vertices[0].pos);
	    IVec v2 = vertices[2].pos.get().diff(vertices[0].pos);
	    return v1.cross(v2).len()/2;
	}
	
	ArrayList<Object> edgesAndFaces = triangulate(true, new IMeshType());
	double area=0;
	for(int i=0; i<edgesAndFaces.size(); i++){
	    if(edgesAndFaces.get(i) instanceof IFace){
		area += ((IFace)edgesAndFaces.get(i)).area();
	    }
	}
	
	for(int i=0; i<edgesAndFaces.size(); i++){
	    if(edgesAndFaces.get(i) instanceof IEdge){
		((IEdge)edgesAndFaces.get(i)).del();
	    }
	    else if(edgesAndFaces.get(i) instanceof IFace){
		((IFace)edgesAndFaces.get(i)).del();
	    }
	}
	return area;
    }
    
    /** returns normal. if null, calculate average normal */
    public IVec nml(){
	if(normal==null) calcNormal();
	return normal;
    }
    /** alias of nml() */
    public IVec normal(){ return nml(); }
    
    
    /** average normal */
    public IVec getAverageNormal(){
	int n = vertices.length;
	IVec nrm = new IVec();
	for(int i=0; i<n; i++){
	    IVec diff1 = vertices[(i+1)%n].pos.get().diff(vertices[i].pos);
	    IVec diff2 = vertices[(i+2)%n].pos.get().diff(vertices[(i+1)%n].pos);
	    nrm.add(diff1.cross(diff2));
	}
	nrm.unit();
	return nrm;
    }
    
    public void calcNormal(){
	setNormal(getAverageNormal());
    }
    
    public void setNormal(IVec n){
	normal = n;
	// set normal of vertices too.
	//for(IVertex v: vertices) v.normal(normal); ?
    }
    
    public void flipNormal(){ flipNml(); }
    
    public void flipNml(){
	if(normal!=null) normal.neg();
	
	IVertex[] tmpvtx = new IVertex[vertices.length];
	IEdge[] tmpedg = new IEdge[edges.length];
	
	for(int i=0; i<vertices.length; i++) tmpvtx[vertices.length-i-1] = vertices[i];
	for(int i=0; i<edges.length; i++) tmpedg[edges.length-i-1] = edges[i];
	
	vertices = tmpvtx;
	edges = tmpedg;
    }
    
    
    public ArrayList<Object> triangulate(boolean triangulateDirection, IMeshType creator){
	if(vertices.length==3) return null;
	
	int idx1=0;
	int idx2=vertices.length-1;
	
	int num = vertices.length - 2;
	
	ArrayList<IEdge> newEdges = new ArrayList<IEdge>();
	ArrayList<IFace> newFaces = new ArrayList<IFace>();
	
	for(; (idx1+1)<=(idx2-1); idx1++, idx2--){
	    
	    IEdge edge1=null, edge2=null, edgeExisting1=null, edgeExisting2=null,
		edgeDiagonal=null;
	    
	    IEdge[] triEdges1 = new IEdge[3];
	    IEdge[] triEdges2 = new IEdge[3];
	    
	    edgeExisting1 = edges[idx1];
	    edgeExisting2 = edges[idx2-1];
	    
	    if(idx1==0) edge1 = edges[idx2];
	    else edge1 = newEdges.get(newEdges.size()-1);
	    
	    if( (idx1+1)==(idx2-1) ) edge2 = null;
	    else if( (idx1+1)+1 ==(idx2-1) ) edge2 = edges[idx1+1];
	    else edge2 = creator.createEdge(vertices[idx1+1],vertices[idx2-1]);
	    
	    if(edge2!=null){
		if(triangulateDirection){
		    edgeDiagonal = creator.createEdge(vertices[idx1],vertices[idx2-1]);
		    triEdges1[0] = edge1;
		    triEdges1[1] = edgeDiagonal;
		    triEdges1[2] = edgeExisting2;
		    triEdges2[0] = edgeDiagonal;
		    triEdges2[1] = edgeExisting1;
		    triEdges2[2] = edge2;
		}
		else{
		    edgeDiagonal = creator.createEdge(vertices[idx1+1],vertices[idx2]);
		    triEdges1[0] = edge1;
		    triEdges1[1] = edgeExisting1;
		    triEdges1[2] = edgeDiagonal;
		    triEdges2[0] = edgeDiagonal;
		    triEdges2[1] = edge2;
		    triEdges2[2] = edgeExisting2;
		}
	    }
	    else{
		triEdges1[0] = edge1;
		triEdges1[1] = edgeExisting1;
		triEdges1[2] = edgeExisting2;
	    }
	    
	    IFace face1 = creator.createFace(triEdges1);
	    IFace face2 = null;
	    if(edge2!=null) face2 = creator.createFace(triEdges2);
	    
	    
	    if(edgeDiagonal!=null) newEdges.add(edgeDiagonal);
	    if(edge2!=null &&  (idx1+1)+1!=(idx2-1)) newEdges.add(edge2);
	    
	    newFaces.add(face1);
	    if(face2!=null) newFaces.add(face2);
	}
	
	ArrayList<Object> retval = new ArrayList<Object>(); // mix of edges and faces
	for(int i=0; i<newEdges.size(); i++) retval.add(newEdges.get(i));
	for(int i=0; i<newFaces.size(); i++) retval.add(newFaces.get(i));
	return retval;
    }
    
    
    
    public ArrayList<Object> triangulateAtCenter(IMeshType creator){
	
	if(vertices.length==3) return null;
	
	IVec center = getCenter();
	IVertex cv = creator.createVertex(center);
	
        int num = edges.length;
        IEdge[] newEdges = new IEdge[num];
        for(int i=0; i<num; i++){
            IVertex v1 = edges[i].getSharedVertex(edges[(i+1)%num]);
            newEdges[i] = creator.createEdge(v1,cv);
        }
        
        IFace[] newFaces = new IFace[num];
        for(int i=0; i<num; i++){
	    IEdge[] e = new IEdge[3];
	    e[0] = edges[i];
	    e[1] = newEdges[i];
	    e[2] = newEdges[(i-1+num)%num];
	    newFaces[i] = creator.createFace(e);
        }
	
	ArrayList<Object> retval = new ArrayList<Object>(); // mix of edges and faces
	retval.add(cv);
	for(int i=0; i<newEdges.length; i++) retval.add(newEdges[i]);
	for(int i=0; i<newFaces.length; i++) retval.add(newFaces[i]);
	return retval;
    }
    
    
    static public boolean eq(double v1, double v2){
	if( Math.abs(v1-v2) < IConfig.tolerance) return true;
	return false;
    }
    
    public boolean eq(IFace face){
	if(face.edges.length != this.edges.length) return false;
	
	if(edges.length==3){
	    if( face.edges[0].eq(edges[0]) ){
		if( face.edges[1].eq(edges[1]) ){
		    if( face.edges[2].eq(edges[2]) ) return true;
		    return false;
		}
		if( face.edges[1].eq(edges[2]) ){
		    if( face.edges[2].eq(edges[1]) ) return true;
		    return false;
		}
		return false;
	    }
	    if( face.edges[0].eq(edges[1]) ){
		if( face.edges[1].eq(edges[0]) ){
		    if( face.edges[2].eq(edges[2]) ) return true;
		    return false;
		}
		if( face.edges[1].eq(edges[2]) ){
		    if( face.edges[2].eq(edges[0]) ) return true;
		    return false;
		}
		return false;
	    }
	    if( face.edges[0].eq(edges[2]) ){
		if( face.edges[1].eq(edges[0]) ){
		    if( face.edges[2].eq(edges[1]) ) return true;
		    return false;
		}
		if( face.edges[1].eq(edges[1]) ){
		    if( face.edges[2].eq(edges[0]) ) return true;
		    return false;
		}
		return false;
	    }
	    return false;
	}
	else if(this.edges.length==4){
	    
	    IVertex vertices1[] = this.vertices; // does this work?
	    IVertex vertices2[] = face.vertices; // does this work?
	    
	    double len1[] = new double[4+2];
	    double len2[] = new double[4+2];
            
	    for(int i=0; i<4; i++){
		len1[i] = vertices1[i].pos.dist(vertices1[(i+1)%4].pos);
		len2[i] = vertices2[i].pos.dist(vertices2[(i+1)%4].pos);
	    }
	    
	    // opposite corner
	    len1[4] = vertices1[0].pos.dist(vertices1[2].pos);
	    len2[4] = vertices2[0].pos.dist(vertices2[2].pos);
	    len1[5] = vertices1[1].pos.dist(vertices1[3].pos);
	    len2[5] = vertices2[1].pos.dist(vertices2[3].pos);
	    
	    if(eq(len1[0],len2[0])){
		if(eq(len1[1],len2[1]) &&
		   eq(len1[2],len2[2]) &&
		   eq(len1[3],len2[3]) &&
		   ( eq(len1[4],len2[4])&&
		     eq(len1[5],len2[5])||
		     eq(len1[4],len2[5])&&
		     eq(len1[5],len2[4]) ) ){
		    return true;
		}
		
		if(eq(len1[1],len2[3]) &&
		   eq(len1[2],len2[2]) &&
		   eq(len1[3],len2[1]) &&
		   ( eq(len1[4],len2[4])&&
		     eq(len1[5],len2[5])||
		     eq(len1[4],len2[5])&&
		     eq(len1[5],len2[4]) )){
		    return true;
		}
		
	    }
	    if(eq(len1[0],len2[1])){
		
		if(eq(len1[1],len2[2]) &&
		   eq(len1[2],len2[3]) &&
		   eq(len1[3],len2[0]) &&
		   ( eq(len1[4],len2[4])&&
		     eq(len1[5],len2[5])||
		     eq(len1[4],len2[5])&&
		     eq(len1[5],len2[4]) )){
		    return true;
		}
		if(eq(len1[1],len2[0]) &&
		   eq(len1[2],len2[3]) &&
		   eq(len1[3],len2[2]) &&
		   ( eq(len1[4],len2[4])&&
		     eq(len1[5],len2[5])||
		     eq(len1[4],len2[5])&&
		     eq(len1[5],len2[4]) ) ){
		    return true;
		}
                
	    }
	    if(eq(len1[0],len2[2])){
		
		if(eq(len1[1],len2[3]) &&
		   eq(len1[2],len2[0]) &&
		   eq(len1[3],len2[1]) &&
		   ( eq(len1[4],len2[4])&&
		     eq(len1[5],len2[5])||
		     eq(len1[4],len2[5])&&
		     eq(len1[5],len2[4]) ) ){
		    return true;
		}
		if(eq(len1[1],len2[1]) &&
		   eq(len1[2],len2[0]) &&
		   eq(len1[3],len2[3]) &&
		   ( eq(len1[4],len2[4])&&
		     eq(len1[5],len2[5])||
		     eq(len1[4],len2[5])&&
		     eq(len1[5],len2[4]) ) ){
		    return true;
		}
                
	    }
	    if(eq(len1[0],len2[3])){
		
		if(eq(len1[1],len2[0]) &&
		   eq(len1[2],len2[1]) &&
		   eq(len1[3],len2[2]) &&
		   ( eq(len1[4],len2[4]) &&
		     eq(len1[5],len2[5])||
		     eq(len1[4],len2[5])&&
		     eq(len1[5],len2[4]) ) ){
		    return true;
		}
		
		if(eq(len1[1],len2[2]) &&
		   eq(len1[2],len2[1]) &&
		   eq(len1[3],len2[0]) &&
		   ( eq(len1[4],len2[4])&&
		     eq(len1[5],len2[5])||
		     eq(len1[4],len2[5])&&
		     eq(len1[5],len2[4]) ) ){
		    return true;
		}
                
	    }
	    return false;
	}
	return false; // unknown for other number of edges
    }
    
    
    // retval[0]: min, retval[1]: max
    public IVec[] getBoundary(){
	IVec min = new IVec(vertices[0]);
	IVec max = new IVec(vertices[0]);
	for(int i=1; i<vertices.length; i++){
	    IVec p = vertices[i].pos.get();
	    if(p.x < min.x) min.x = p.x;
	    else if(p.x > max.x) max.x = p.x;
	    if(p.y < min.y) min.y = p.y;
	    else if(p.y > max.y) max.y = p.y;
	    if(p.z < min.z) min.z = p.z;
	    else if(p.z > max.z) max.z = p.z;
	}
	IVec[] retval = new IVec[2];
	retval[0] = min;
	retval[1] = max;
	return retval;
    }
    
    
    /** calculate closest distance to face taking normal into consideration. if input point is different side of normal vector, it returns negative value */
    public double dist(IVecI pt){
	if(vertices.length==3){
	}
	else{
	}
	return 0;
    }
    

    // color
    public IColor clr(){ return clr; }
    
    public IFace clr(IColor c){ clr=c; return this; }
    
    /** to set color, with alpha value overwritten */
    public IFace clr(IColor c, int alpha){
	return clr(new IColor(c,alpha));
    }
    /** to set color, with alpha value overwritten */
    public IFace clr(IColor c, float alpha){
	return clr(new IColor(c,alpha));
    }
    /** to set color, with alpha value overwritten */
    public IFace clr(IColor c, double alpha){
	return clr(new IColor(c,alpha));
    }
    public IFace clr(IObject o){ clr(o.clr()); return this; }
    public IFace clr(IFace f){ clr(f.clr()); return this; }
    
    public IFace clr(Color c){ return clr(new IColor(c)); }
    public IFace clr(Color c, int alpha){ return clr(new IColor(c),alpha); }
    public IFace clr(Color c, float alpha){ return clr(new IColor(c),alpha); }
    public IFace clr(Color c, double alpha){ return clr(new IColor(c),alpha); }
    
    /** @return returns whatever Color of any graphics member. (first found) */
    public IColor getColor(){ return clr(); }
    
    
    public IFace clr(int gray){ return clr(new IColor(gray)); }
    
    public IFace clr(double dgray){ return clr(new IColor(dgray)); }
    public IFace clr(float fgray){ return clr(new IColor(fgray)); }
    public IFace clr(int gray, int alpha){ return clr(new IColor(gray,alpha)); }
    public IFace clr(double dgray, double dalpha){ return clr(new IColor(dgray,dalpha)); }
    public IFace clr(float fgray, float falpha){ return clr(new IColor(fgray,falpha)); }
    public IFace clr(int r, int g, int b){ return clr(new IColor(r,g,b)); }
    public IFace clr(double dr, double dg, double db){ return clr(new IColor(dr,dg,db)); }
    public IFace clr(float fr, float fg, float fb){ return clr(new IColor(fr,fg,fb)); }
    public IFace clr(int r, int g, int b, int a){ return clr(new IColor(r,g,b,a)); }
    public IFace clr(double dr, double dg, double db, double da){
	return clr(new IColor(dr,dg,db,da));
    }
    public IFace clr(float fr, float fg, float fb, float fa){
	return clr(new IColor(fr,fg,fb,fa));
    }
    public IFace hsb(double dh, double ds, double db, double da){
	return clr(IColor.hsb(dh,ds,db,da));
    }
    public IFace hsb(float h, float s, float b, float a){
	return clr(IColor.hsb(h,s,b,a));
    }
    public IFace hsb(double dh, double ds, double db){
	return clr(IColor.hsb(dh,ds,db));
    }
    public IFace hsb(float h, float s, float b){
	return clr(IColor.hsb(h,s,b));
    }

    
}