/*---

    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;

/**
   Geometry of NURBS curve.
   
   @author Satoru Sugihara
*/
public class ICurveGeo extends INurbsGeo implements ICurveI, IEntityParameter{
    
    /** control points */
    public IVecI[] controlPoints;
    
    // degree and knots should not be parameterized
    // because number of control points, degree and knots are intertwined together: 
    // changing them independently doesn't make sense
    /** degree of NURBS curve */
    public int degree;
    
    /** normalized knot vector (start value in knot vector is 0, end value is 1) */
    public double[] knots;
    
    /** ustart and uend are not normalized, keeping original value in input files */
    public double ustart, uend;
    
    /** flag to determine to use default weight value (1.0) */
    public boolean[] defaultWeights;
    
    /** bernstein basis function */
    public IBSplineBasisFunction basisFunction;
    /** derivative of bernstein basis function */
    public IBSplineBasisFunction derivativeFunction;
    
    public ICurveCache uSearchCache;
    
    
    
    public ICurveGeo(){}
    
    public ICurveGeo(IVecI[] cpts, int degree, double[] knots, double ustart, double uend){
	this.ustart=ustart;
	this.uend=uend;
	//if(IConfig.normalizeKnots) normalizeKnots(knots, ustart, uend);
	if(ustart!=0.0 || uend!=1.0) normalizeKnots(knots, ustart, uend);
	init(cpts, degree, knots);
    }
    
    public ICurveGeo(IVecI[] cpts, int degree, double[] knots){
	ustart=knots[0];
	uend=knots[knots.length-1];
	//if(IConfig.normalizeKnots && (knots[0]!=0. || knots[knots.length-1]!=1.)) 
	//  normalizeKnots(knots, knots[0], knots[knots.length-1]);
	if(knots[0]!=0.0 || knots[knots.length-1]!=1.0)
	    normalizeKnots(knots, knots[0], knots[knots.length-1]);
	init(cpts, degree, knots);
    }
    
    public ICurveGeo(IVecI[] cpts, int degree){
	ustart=0.; uend=1.;
	init(cpts, degree, createKnots(degree, cpts.length));
    }
    
    public ICurveGeo(IVecI[] cpts){
	ustart=0.; uend=1.;
	init(cpts, 1, createKnots(1, cpts.length));
    }
    
    public ICurveGeo(IVecI[] cpts, int degree, boolean close){
	ustart=0.; uend=1.;
	init(cpts, degree, close);
    }
    
    public ICurveGeo(IVecI[] cpts, boolean close){
	ustart=0.; uend=1.;
	init(cpts, 1, close);
    }
    
    public ICurveGeo(IVecI pt1, IVecI pt2){
	ustart=0.; uend=1.;
	init(new IVecI[]{ pt1, pt2 }, 1, createKnots(1, 2));
    }
    
    //this creates line between a same point
    public ICurveGeo(IVecI pt){
	ustart=0.; uend=1.;
	init(new IVecI[]{ pt, pt.dup() }, 1, createKnots(1, 2));
    }
    
    public ICurveGeo(double x1,double y1,double z1,double x2,double y2,double z2){
	this(new IVec(x1,y1,z1),new IVec(x2,y2,z2));
    }
    
    public ICurveGeo(double[][] xyzValues){
	ustart=0.; uend=1.;
	init(getPointsFromArray(xyzValues), 1);
    }
    
    public ICurveGeo(double[][] xyzValues, int degree){
	ustart=0.; uend=1.;
	init(getPointsFromArray(xyzValues), degree);
    }
    
    public ICurveGeo(double[][] xyzValues, boolean close){
	ustart=0.; uend=1.;
	init(getPointsFromArray(xyzValues), 1, close);
    }
    
    public ICurveGeo(double[][] xyzValues, int degree, boolean close){
	ustart=0.; uend=1.;
	init(getPointsFromArray(xyzValues), degree, close);
    }
    
    public ICurveGeo(IEdge edge){ this(edge.vertex(0), edge.vertex(1)); }
    
    
    public ICurveGeo(ICurveGeo crv){
	// duplicate points
	controlPoints = new IVecI[crv.controlPoints.length];
	for(int i=0; i<controlPoints.length; i++)
	    controlPoints[i] = crv.controlPoints[i].dup();
	knots = new double[crv.knots.length];
	System.arraycopy(crv.knots, 0, knots, 0, knots.length);
	degree = crv.degree;
	ustart=crv.ustart; uend=crv.uend;
	init(controlPoints, degree, knots);
    }
    
    
    public void init(IVecI[] cpts){
	init(cpts, 1, createKnots(1, cpts.length));
    }
    
    public void init(IVecI[] cpts, int degree){
	init(cpts, degree, createKnots(degree, cpts.length));
    }
    
    public void init(IVecI[] cpts, boolean close){
	init(cpts, 1, close);
    }
    
    public void init(IVecI[] cpts, int degree, boolean close){
	if(close){
	    IVecI[] cpts2 = createClosedCP(cpts,degree);
	    init(cpts2, degree, createClosedKnots(degree, cpts2.length));
	}
	else{
	    init(cpts, degree, createKnots(degree, cpts.length));
	}
    }
    
    public void init(IVecI[] cpts, int degree, double[] knots){
	
	if(IConfig.checkValidControlPoint){ isValidCP(cpts, degree, knots); }
	
	// duplicate of control points is avoided
	if(IConfig.checkDuplicatedControlPoint){ checkDuplicatedCP(cpts); }
	else if(IConfig.checkDuplicatedControlPointOnEdge){ checkDuplicatedCPOnEdge(cpts); }
	
	controlPoints = cpts;
	this.degree = degree;
	this.knots = knots;
	basisFunction = new IBSplineBasisFunction(degree, knots);
	
	defaultWeights = new boolean[cpts.length];
	for(int i=0; i<cpts.length; i++){
	    defaultWeights[i] = !(cpts[i] instanceof IVec4I);
	}
    }
    
    public boolean isValid(){
	return isValidCP(controlPoints, degree, knots);
    }
    
    public static boolean isValidCP(IVecI[] cpts, int deg, double[] knots){
	if(cpts==null){
	    IOut.err("control points are null");
	    return false;
	}
	
	if(knots==null){
	    IOut.err("knots are null");
	    return false;
	}
	
	if(deg <= 0){
	    IOut.err("invalid degree ("+deg+")");
	    return false;
	}
	
	int num = cpts.length;
	
	if(num <= deg){
	    IOut.err("too less control points ("+num+") for degree "+deg+". it needs minimum "+(deg+1));
	    return false;
	}
	
	if(knots.length != (deg+num+1)){
	    IOut.err("knot array length is invalid. it needs to be "+(deg+num+1));
	    return false;
	}
	
	if(!isValidCP(cpts)) return false;
	
	if(!isValidKnots(knots)){
	    IOut.err("knot has invalid value");
	    return false;
	}
	
	return true;
    }
    
    public static boolean isValidCP(IVecI[] cpts){
	for(int i=0; i<cpts.length; i++){
	    if(!cpts[i].isValid()){
		IOut.err("controlPoint at "+i+" is invalid");
		return false;
	    }
	}
	return true;
    }
    
    static public void checkDuplicatedCP(IVecI[] cpts){
	for(int i=0; i<cpts.length; i++)
	    for(int j=i+1; j<cpts.length; j++)
		if(cpts[j]==cpts[i]) cpts[j] = cpts[i].dup();
    }
    
    static public void checkDuplicatedCP(IVecI[] origCPs, IVecI newCP){
	for(int i=0; i<origCPs.length; i++)
	    if(origCPs[i]==newCP) origCPs[i] = newCP.dup();
    }
    
    static public void checkDuplicatedCP(IVecI[] origCPs, IVecI[] newCPs){
	for(int i=0; i<origCPs.length; i++)
	    for(int j=0; j<newCPs.length; j++)
		if(origCPs[i]==newCPs[j]) origCPs[i] = newCPs[j].dup();
    }
    
    static public void checkDuplicatedCPOnEdge(IVecI[] cpts){
	if(cpts[0]==cpts[cpts.length-1]) cpts[cpts.length-1] = cpts[0].dup();
    }
    
    static public IVec[] getPointsFromArray(double[][] xyzvalues){
	IVec[] cpts = new IVec[xyzvalues.length];
	for(int i=0; i<cpts.length; i++){
	    if(xyzvalues[i].length==4){
		cpts[i] = new IVec4(xyzvalues[i][0], xyzvalues[i][1], xyzvalues[i][2],xyzvalues[i][3]);
	    }
	    else{
		cpts[i] = new IVec();
		if(xyzvalues[i].length>=1) cpts[i].x = xyzvalues[i][0];
		if(xyzvalues[i].length>=2) cpts[i].y = xyzvalues[i][1];
		if(xyzvalues[i].length>=3) cpts[i].z = xyzvalues[i][2];
	    }
	}
	return cpts;
    }
    
    public ICurveGeo get(){ return this; }
    
    public ICurveGeo dup(){ return new ICurveGeo(this); }
    
    
    public IVec pt(IDoubleI u){ return pt(u.x()); }
    public IVec pt(double u){
	IVec retval = new IVec();
	pt(u, retval);
	return retval;
    }
    public void pt(double u, IVec retval){
	//IOut.p("u="+u); //
        int index = basisFunction.index(u);
        double n[] = basisFunction.eval(index, u);
        double weight=0;
        for(int i=0; i<=degree; i++){
            IVec cpt=controlPoints[index-degree+i].get();
	    double w=1.;
	    if(!defaultWeights[index-degree+i]) w=((IVec4)cpt).w;
            retval.x += cpt.x*w*n[i];
            retval.y += cpt.y*w*n[i];
            retval.z += cpt.z*w*n[i];
            weight += w*n[i];
        }
        retval.x/=weight;
        retval.y/=weight;
        retval.z/=weight;
    }
    
    public IVec tan(IDoubleI u){ return tan(u.x()); }
    public IVec tan(double u){
	IVec retval = new IVec();
	tan(u, retval);
	return retval;
    }
    public void tan(double u, IVec retval){
	if(derivativeFunction==null){
            derivativeFunction=new IBSplineBasisFunction(basisFunction);
            derivativeFunction.differentiate();
        }
        int index = derivativeFunction.index(u);
	
        double dn[] = derivativeFunction.eval(index, u);
        double n[] = basisFunction.eval(index, u);
        
        IVec4 val1 = new IVec4();
        IVec4 val2 = new IVec4();
        
        for(int i=0; i<=degree; i++){
            IVec cpt=controlPoints[index-degree+i].get();
	    
            double w=1.;
            if(!defaultWeights[index-degree+i]) w=((IVec4)cpt).w;
            
            val1.x += cpt.x*w*n[i];
            val1.y += cpt.y*w*n[i];
            val1.z += cpt.z*w*n[i];
            val1.w += w*n[i];
	    
	    val2.x += cpt.x*w*dn[i];
            val2.y += cpt.y*w*dn[i];
            val2.z += cpt.z*w*dn[i];
            val2.w += w*dn[i];
        }
        val1.x*=val2.w;
        val1.y*=val2.w;
        val1.z*=val2.w;
        
        val2.x*=val1.w;
        val2.y*=val1.w;
        val2.z*=val1.w;
        
        val1.w*=val1.w;
        
        retval.x = (val2.x-val1.x)/val1.w;
        retval.y = (val2.y-val1.y)/val1.w;
        retval.z = (val2.z-val1.z)/val1.w;
    }
    
    /** getting i-th control point */
    public IVecI cp(int i){ return controlPoints[i]/*.get()*/; }
    /** getting i-th control point */
    public IVecI cp(IIntegerI i){ return controlPoints[i.x()]; }
    
    public IVecI[] cps(){ return controlPoints; }
    
    
    
    
    /** add control point at the end and rebuild the curve and change degree if possible.
	note that a knots is rebuilt with default equal intervals
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo addCP(IVecI pt, int newDegree){
	if(degree==newDegree || 
	   (controlPoints.length==2 && controlPoints[0].eq(controlPoints[1]))) return addCP(pt);
	
	if(controlPoints.length+1 > newDegree){ degree=newDegree; } 
	return addCP(pt); // if pt is invalid, it'd crash
    }
    
    /** add control point at the end and rebuild the curve.
	note that a knots is rebuilt with default equal intervals
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo addCP(IVecI pt){
	if(!pt.isValid()){
	    IOut.err("input pt is invalid. not added");
	    return this; 
	}
	
	// in case of first addition after the curve is instantiated with one point.
	if(controlPoints.length==2 &&
	   controlPoints[0].x()==controlPoints[1].x() &&
	   controlPoints[0].y()==controlPoints[1].y() &&
	   controlPoints[0].z()==controlPoints[1].z()){ // replace the second point with new one
	    
	    if(IConfig.checkDuplicatedControlPoint){ checkDuplicatedCP(controlPoints, pt); } // added 20121111
	    
	    controlPoints[1] = pt;
	    defaultWeights[1] = !(pt instanceof IVec4I);
	    return this;
	}
	
	if(IConfig.checkDuplicatedControlPoint){ checkDuplicatedCP(controlPoints, pt); }
	int num = controlPoints.length;
	//check if it started with duplicated 2 points and if so, remove one of them.
	if( num==2 && controlPoints[0].eq(controlPoints[1])){ num=1; } // isn't taken care of already above?
	
	IVecI[] controlPoints2 = new IVecI[num+1];
	for(int i=0; i<num; i++){ controlPoints2[i] = controlPoints[i]; }
	controlPoints2[num] = pt;
	// rebuild knots; because it's adding, ignoring the case of closed curve.
	double[] knots2  =createKnots(degree, num+1);
	IBSplineBasisFunction basisFunction2 = new IBSplineBasisFunction(degree, knots2);
	boolean[] defaultWeights2 = new boolean[num+1];
	for(int i=0; i<num; i++) defaultWeights2[i] = defaultWeights[i];
	defaultWeights2[num] = !(pt instanceof IVec4I);
	
	controlPoints = controlPoints2;
	knots = knots2;
	basisFunction = basisFunction2;
	defaultWeights = defaultWeights2;
	
	uSearchCache = null; // to update cache when used. // added 20130318
	
	return this;
    }
    
    /** add control point at i and rebuild the curve and change degree.
     	note that a knots is rebuilt with default equal intervals
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo addCP(int index, IVecI pt, int newDegree){
	if(degree==newDegree || 
	   (controlPoints.length==2 && controlPoints[0].eq(controlPoints[1]))) return addCP(index,pt);
	
	if(controlPoints.length+1 > newDegree){ degree=newDegree; } 
	return addCP(index,pt); // if pt is invalid, it'd crash
    }
    
    /** add control point at i and rebuild the curve.
     	note that a knots is rebuilt with default equal intervals
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo addCP(int index, IVecI pt){
	int num = controlPoints.length;
	if(index<0 || index>=num){
	    IOut.err("index "+index+" is out of range. not added");
	    return this;
	}
	if(!pt.isValid()){
	    IOut.err("input pt is invalid. not added");
	    return this; 
	}
	if(IConfig.checkDuplicatedControlPoint){ checkDuplicatedCP(controlPoints, pt); }
	
	//check if it started with duplicated 2 points and if so, remove one of them.
	if( num==2 && controlPoints[0].eq(controlPoints[1])){ num=1; }
	
	IVecI[] controlPoints2 = new IVecI[num+1];
	int i=0; 
	for(; i<index; i++) controlPoints2[i] = controlPoints[i];
	controlPoints2[i++] = pt;
	for(; i<num+1; i++) controlPoints2[i] = controlPoints[i-1];
	// rebuild knots; because it's adding, ignoring the case of closed curve.
	double[] knots2  =createKnots(degree, num+1);
	IBSplineBasisFunction basisFunction2 = new IBSplineBasisFunction(degree, knots2);
	boolean[] defaultWeights2 = new boolean[num+1];
	i=0;
	for(; i<index; i++) defaultWeights2[i] = defaultWeights[i];
	defaultWeights2[i++] = !(pt instanceof IVec4I);
	for(; i<num+1; i++) defaultWeights2[i] = defaultWeights[i-1];
	
	controlPoints = controlPoints2;
	knots = knots2;
	basisFunction = basisFunction2;
	defaultWeights = defaultWeights2;
	
	uSearchCache = null; // to update cache when used. // added 20130318
	
	return this;
    }
    
    /** add control point at i and rebuild the curve and change degree.
     	note that a knots is rebuilt with default equal intervals
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo addCP(IVecI[] pts, int newDegree){
	if(degree==newDegree || 
	   (controlPoints.length==2 && controlPoints[0].eq(controlPoints[1]))) return addCP(pts);
	if(controlPoints.length+1 > newDegree){ degree=newDegree; } 
	return addCP(pts); // if pt is invalid, it'd crash
    }
    
    /** add control points at the end and rebuild the curve.
	note that a knots is rebuilt with default equal intervals
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo addCP(IVecI[] pts){
	int num2 = pts.length;
	for(int i=0; i < num2; i++){
	    if(!pts[i].isValid()){
		IOut.err("input pts["+i+"] is invalid. not added");
		return this; 
	    }
	}
	if(IConfig.checkDuplicatedControlPoint){ checkDuplicatedCP(controlPoints, pts); }
	int num = controlPoints.length;
	
	//check if it started with duplicated 2 points and if so, remove one of them.
	if( num==2 && controlPoints[0].eq(controlPoints[1])){ num=1; }
	
	IVecI[] controlPoints2 = new IVecI[num+num2];
	int i=0;
	for(; i<num; i++){ controlPoints2[i] = controlPoints[i]; }
	for(; i<num+num2; i++){ controlPoints2[i] =  pts[i-num]; }
	// rebuild knots; because it's adding, ignoring the case of closed curve.
	double[] knots2  =createKnots(degree, num+num2);
	IBSplineBasisFunction basisFunction2 = new IBSplineBasisFunction(degree, knots2);
	boolean[] defaultWeights2 = new boolean[num+num2];
	i=0;
	for(; i<num; i++) defaultWeights2[i] = defaultWeights[i];
	for(; i<num+num2; i++) defaultWeights2[i] = !(pts[i-num] instanceof IVec4I);
	
	controlPoints = controlPoints2;
	knots = knots2;
	basisFunction = basisFunction2;
	defaultWeights = defaultWeights2;
	
	uSearchCache = null; // to update cache when used. // added 20130318
	
	return this;
    }
    
    /** add control point at i and rebuild the curve and change degree.
     	note that a knots is rebuilt with default equal intervals
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo addCP(int index, IVecI[] pts, int newDegree){
	if(degree==newDegree || 
	   (controlPoints.length==2 && controlPoints[0].eq(controlPoints[1]))) return addCP(index,pts);
	if(controlPoints.length+1 > newDegree){ degree=newDegree; } 
	return addCP(index,pts); // if pt is invalid, it'd crash
    }
    
    /** add control points at i and rebuild the curve.
     	note that a knots is rebuilt with default equal intervals
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo addCP(int index, IVecI[] pts){
	int num = controlPoints.length;
	if(index<0 || index>=num){
	    IOut.err("index "+index+" is out of range. not added");
	    return this;
	}
	int num2 = pts.length;
	for(int i=0; i < num2; i++){
	    if(!pts[i].isValid()){
		IOut.err("input pts["+i+"] is invalid. not added");
		return this; 
	    }
	}
	if(IConfig.checkDuplicatedControlPoint){ checkDuplicatedCP(controlPoints, pts); }
	
	//check if it started with duplicated 2 points and if so, remove one of them.
	if( num==2 && controlPoints[0].eq(controlPoints[1])){ num=1; }
		
	IVecI[] controlPoints2 = new IVecI[num+num2];
	int i=0;
	for(; i<index; i++){ controlPoints2[i] = controlPoints[i]; }
	for(; i<index+num2; i++){ controlPoints2[i] = pts[i-index]; }
	for(; i<num+num2; i++){ controlPoints2[i] =  controlPoints[i-num2]; }
	// rebuild knots; because it's adding, ignoring the case of closed curve.
	double[] knots2  =createKnots(degree, num+num2);
	IBSplineBasisFunction basisFunction2 = new IBSplineBasisFunction(degree, knots2);
	boolean[] defaultWeights2 = new boolean[num+num2];
	i=0;
	for(; i<index; i++) defaultWeights2[i] = defaultWeights[i];
	for(; i<index+num2; i++) defaultWeights2[i] = !(pts[i-index] instanceof IVec4I);
	for(; i<num+num2; i++) defaultWeights2[i] = defaultWeights[i-num2];
	
	controlPoints = controlPoints2;
	knots = knots2;
	basisFunction = basisFunction2;
	defaultWeights = defaultWeights2;

	uSearchCache = null; // to update cache when used. // added 20130318
	
	return this;
    }
    
    /** alias of addCP(int,IVecI) */
    public ICurveGeo insertCP(int i, IVecI pt){ return addCP(i,pt); }
    /** alias of addCP(int,IVecI[]) */
    public ICurveGeo insertCP(int i, IVecI[] pts){ return addCP(i,pts); }
    
    /** removing control point at the end and rebuild the curve.
	note that a knots is rebuilt with default equal interval
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo removeCP(){
	int num = controlPoints.length;
	IVecI[] controlPoints2 = new IVecI[num-1];
	for(int i=0; i<num-1; i++){ controlPoints2[i] = controlPoints[i]; }
	// rebuild knots; because it's adding, ignoring the case of closed curve.
	double[] knots2=createKnots(degree, num-1);
	IBSplineBasisFunction basisFunction2 = new IBSplineBasisFunction(degree, knots2);
	boolean[] defaultWeights2 = new boolean[num-1];
	for(int i=0; i<num-1; i++) defaultWeights2[i] = defaultWeights[i];
	
	controlPoints = controlPoints2;
	knots = knots2;
	basisFunction = basisFunction2;
	defaultWeights = defaultWeights2;
	
	uSearchCache = null; // to update cache when used. // added 20130318
	
	return this;
    }
    /** removing control point at i and rebuild the curve 
	note that a knots is rebuilt with default equal interval
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo removeCP(int index){
	int num = controlPoints.length;
	if(index<0 || index>=num){
	    IOut.err("index "+index+" is out of range. not removed");
	    return this;
	}
	IVecI[] controlPoints2 = new IVecI[num-1];
	int i=0;
	for(; i<index; i++){ controlPoints2[i] = controlPoints[i]; }
	for(; i<num-1; i++){ controlPoints2[i] = controlPoints[i+1]; }
	// rebuild knots; because it's adding, ignoring the case of closed curve.
	double[] knots2 = createKnots(degree, num-1);
	IBSplineBasisFunction basisFunction2 = new IBSplineBasisFunction(degree, knots2);
	boolean[] defaultWeights2 = new boolean[num-1];
	i=0;
	for(; i<index; i++) defaultWeights2[i] = defaultWeights[i];
	for(; i<num-1; i++) defaultWeights2[i] = defaultWeights[i+1];
	
	controlPoints = controlPoints2;
	knots = knots2;
	basisFunction = basisFunction2;
	defaultWeights = defaultWeights2;
	
	uSearchCache = null; // to update cache when used. // added 20130318
	
	return this;
    }
    /** removing control point from indexFrom to indexTo-1 and rebuild the curve.
	note taht point at indexTo is not removed.
	note that a knots is rebuilt with default equal interval
	and destroy original knot intervals if variable, like circle.
    */
    public ICurveGeo removeCP(int indexFrom, int indexTo){
	int num = controlPoints.length;
	if(indexFrom<0 || indexFrom>=num || indexTo<0 || indexFrom>=num || indexFrom>=indexTo){
	    IOut.err("index range ["+indexFrom+"-"+indexTo+" is invalid. not removed");
	    return this;
	}
	int num2 = indexTo-indexFrom;
	IVecI[] controlPoints2 = new IVecI[num-num2];
	int i=0;
	for(; i<indexFrom; i++){ controlPoints2[i] = controlPoints[i]; }
	for(; i<num-num2; i++){ controlPoints2[i] = controlPoints[i+num2]; }
	// rebuild knots; because it's adding, ignoring the case of closed curve.
	double[] knots2 = createKnots(degree, num-num2);
	IBSplineBasisFunction basisFunction2 = new IBSplineBasisFunction(degree, knots2);
	boolean[] defaultWeights2 = new boolean[num-num2];
	i=0;
	for(; i<indexFrom; i++) defaultWeights2[i] = defaultWeights[i];
	for(; i<num-num2; i++) defaultWeights2[i] = defaultWeights[i+num2];
	
	controlPoints = controlPoints2;
	knots = knots2;
	basisFunction = basisFunction2;
	defaultWeights = defaultWeights2;
	
	uSearchCache = null; // to update cache when used. // added 20130318
	
	return this;
    }
    
    
    /** close curve with the current control points.
	it changes total number of control points and knot vector dependng on the degree.
	new knot vector has equal default intervals destroying original variable intervals.
    */
    //public ICurveGeo close();
    
    
    
    public IVec ep(int i){ return pt(knots[i+degree]); }
    public IVec ep(IIntegerI i){ return pt(knots[i.x()+degree]); }
    
    public IVec start(){ return pt(0.); }
    public IVec end(){ return pt(1.); }
    
    public IVec startCP(){ return controlPoints[0].get(); }
    public IVec endCP(){ return controlPoints[controlPoints.length-1].get(); }
    
    
    /** parametrically mid point of a curve */
    public IVec mid(){ return pt(0.5); }
    
    /** Returns center of geometry object.
	This is approximation calculated only by control points */
    public IVec center(){
	int count = cpNum();
	
	// check if it's closed and having overlapping control points
	//if(knots[0] != 0.0 || knots[knots.length-1] != 1.0){
	//    if(cp(0).eq(cp(cpNum()-deg()))){ count = cpNum()-deg(); }// check by cp
	//}
	//else if(cp(0).eq(cp(cpNum()-1))){ count = cpNum()-1; }
	
	if(isClosed()){ count -= overlapCPNum(); }
	
	// calc average of control points
	IVec cnt = new IVec();
	for(int i=0; i<count; i++){ cnt.add(cp(i)); }
	cnt.div(count);
	return cnt;
    }
    
    
    
    /** approximate invert projection from 3D location to interanl parameter U (closest point on curve) */
    synchronized public double u(IVecI pt){
	if(uSearchCache==null){ uSearchCache = new ICurveCache(this); }
	return uSearchCache.u(pt.get());
    }
    public double u(ISwitchE r, IVecI pt){ return u(pt); }
    public IDouble u(ISwitchR r, IVecI pt){ return new IDouble(u(pt)); }
    
    /** approximate invert projection from 2D location to interanl parameter U */
    public double u(IVec2I pt){
	if(uSearchCache==null){ uSearchCache = new ICurveCache(this); }
	return uSearchCache.u(pt.get());
    }
    public double u(ISwitchE r, IVec2I pt){ return u(pt); }
    public IDouble u(ISwitchR r, IVec2I pt){ return new IDouble(u(pt)); }
    
    
    /** find approximately closest point on a curve */
    public IVec closePt(IVecI pt){ return pt(u(pt)); }
    
    /** find approximately closest point on a curve on 2D */
    public IVec closePt(IVec2I pt){ return pt(u(pt)); }
    
    /** distance to the closest point on a curve */
    public double dist(IVecI pt){ return closePt(pt).dist(pt); }
    /** distance to the closest point on a curve on 2D*/
    public double dist(IVec2I pt){ return closePt(pt).to2d().dist(pt); }
    
    
    public double knot(int i){ return knots[i]; }
    public IDouble knot(IIntegerI i){ return new IDouble(knots[i.x()]); }

    public double[] knots(){ return knots; }
    public double[] knots(ISwitchE e){ return knots(); }
    public IDouble[] knots(ISwitchR r){
	IDouble[] kn = new IDouble[knots.length];
	for(int i=0; i<knots.length; i++) kn[i] = new IDouble(knots[i]);
	return kn;
    }
    
    public int knotNum(){ return knots.length; }
    //public IInteger knotNumR(){ return new IInteger(knots.length); }
    public int knotNum(ISwitchE e){ return knotNum(); }
    public IInteger knotNum(ISwitchR r){ return new IInteger(knotNum()); }
    
    public int deg(){ return degree; }
    //public IInteger degR(){ return new IInteger(degree); }
    public int deg(ISwitchE e){ return deg(); }
    public IInteger deg(ISwitchR r){ return new IInteger(deg()); }
    
    public int num(){ return controlPoints.length; }
    //public IInteger numR(){ return new IInteger(controlPoints.length); }
    public int num(ISwitchE e){ return num(); }
    public IInteger num(ISwitchR r){ return new IInteger(num()); }
    
    public int cpNum(){ return num(); }
    //public IInteger cpNumR(){ return new IInteger(num()); }
    public int cpNum(ISwitchE e){ return cpNum(); }
    public IInteger cpNum(ISwitchR r){ return new IInteger(cpNum()); }
    
    public int epNum(){ return knots.length-2*degree; }
    //public IInteger epNumR(){ return new IInteger(epNum()); }
    public int epNum(ISwitchE e){ return epNum(); }
    public IInteger epNum(ISwitchR r){ return new IInteger(epNum()); }
    
    public boolean isRational(){
	if(defaultWeights==null){ IOut.err("defaultWeights is null"); return false; }
	for(int i=0; i<defaultWeights.length; i++) if(!defaultWeights[i]) return true; 
	return false;
    }
    public boolean isRational(ISwitchE e){ return isRational(); }
    public IBool isRational(ISwitchR r){ return new IBool(isRational()); }
    
    
    public double len(double resolutionPerEP){
	double ln = 0;
	if(degree==1){
	    for(int i=0; i<num()-1; i++) ln += cp(i+1).dist(cp(i));
	    return ln;
	}
	int epnum = epNum();
	int rnum = (int)(1.0/resolutionPerEP);
	if(rnum<1) rnum=1;
	IVec p1=null, p2=null;
	for(int i=0; i<epnum; i++){
	    for(int j=0; j<rnum && i<epnum-1 || j<=0; j++){
		p2 = pt(u(i,(double)j/rnum));
		if(p1!=null) ln += p2.dist(p1);
		p1 = p2;
	    }
	}
	return ln;
    }
    
    public double len(){
	// default resolution per EP. not refined. ; should it be IConfig.parameterTolerance? Is it too small?
	final double defaultResolution = 0.01; // 1/100
	return len(defaultResolution);
    }
    //public IDouble lenR(){ return null; }
    public double len(ISwitchE e){ return len(); }
    public IDouble len(ISwitchR r){ return new IDouble(len()); }
    
    // epIdx: 0-epNum, epFraction: 0-1 or -1-0
    public double u(int epIdx, double epFraction){
        if(epFraction>=0) return knots[epIdx+degree] +
            (knots[epIdx+degree+1]-knots[epIdx+degree])*epFraction;
	return knots[epIdx+degree] +
            (knots[epIdx+degree]-knots[epIdx+degree-1])*epFraction;	
    }
    public IDouble u(IInteger epIdx, IDouble epFraction){
	return new IDouble(u(epIdx.x(),epFraction.x()));
    }
    
    public double ustart(){ return ustart; }
    public double uend(){ return uend; }
    //public IDouble ustartR(){ return new IDouble(ustart); }
    //public IDouble uendR(){ return new IDouble(uend); }
    public double ustart(ISwitchE e){ return ustart(); }
    public double uend(ISwitchE e){ return uend(); }
    public IDouble ustart(ISwitchR r){ return new IDouble(ustart()); }
    public IDouble uend(ISwitchR r){ return new IDouble(uend()); }
    
    
    // not tested; test this
    public boolean isClosed(){
	// check if start and end of parameter match with knots[0] and knots[knots.length-1]
	//boolean knotsEndMatch=true;
	/*
	if(IConfig.normalizeKnots){
	    if(knots[0] != 0.0 || knots[knots.length-1] != 1.0) knotsEndMatch=false;
	}
	else{
	    if(knots[0] != ustart || knots[knots.length-1] != uend) knotsEndMatch=false;
	}
	*/
	//if(knots[0] != 0.0 || knots[knots.length-1] != 1.0) knotsEndMatch=false;
	
	/*
	//this is not necessarily true. sometimes just the end points match with non standard knots and non overlapping control points
	if(knots[0] != 0.0 || knots[knots.length-1] != 1.0){
	    // check by cp
	    //if(cp(0).eq(cp(cpNum()-1))) return true;
	    if(cp(0).eq(cp(cpNum()-degree))) return true; // added 20120310
	    return false;
	}
	*/
	// check by ep
	//if(ep(0).eq(ep(epNum()-1))) return true;
	//return true;
	
	// check by pt
	if(pt(0.).eq(pt(1.))) return true;
	return false;
    }
    
    public boolean isClosed(ISwitchE e){ return isClosed(); }
    public IBool isClosed(ISwitchR r){ return new IBool(isClosed()); }
    
    public ICurveGeo rev(){
	synchronized(IG.lock){
	    IVecI[] cpts2 = new IVecI[controlPoints.length];
	    
	    for(int i=0; i<controlPoints.length; i++){
		cpts2[i] = controlPoints[controlPoints.length-1-i];
	    }
	    
	    double[] knots2 = new double[knots.length];
	    for(int i=0; i<knots.length; i++){
		knots2[i] = 1.0 - knots[knots.length-1-i]; // [0-1] to [1-0]
	    }

	    boolean[] defaultWeights2 = new boolean[defaultWeights.length];
	    for(int i=0; i<defaultWeights.length; i++){
		defaultWeights2[i] = defaultWeights[defaultWeights.length-1-i];
	    }
	    
	    
	    controlPoints = cpts2;
	    knots = knots2;
	    defaultWeights = defaultWeights2;
	    if(ustart!=0. || uend!=1.){
		double ustart2 = -uend;
		double uend2 = -ustart;
		ustart = ustart2;
		uend = uend2;
	    }
	    basisFunction = new IBSplineBasisFunction(degree, knots);
	    derivativeFunction = null;
	}
	return this;
    }
    
    /** alias of rev() */
    public ICurveGeo revU(){ return rev(); }
    /** alias of rev() */
    public ICurveGeo flipU(){ return rev(); }


    /**
       number of overlapping control points at the end and the beginning when the curve is closed.
       this should be used after checking curve is closed. if it's open it checks all the control points.
    */
    public int overlapCPNum(){
	int i=0;
	for(; i<num()-1 && !cp(i).eq(cp(num()-1)); i++);
	// each point of overlapping sequence needs to be all matching.
	if(i>=num()-1) return 0; // none matches
	for(int j=0; j<i; j++){
	    if(!cp(j).eq(cp(num()-1-i+j))) return 0; // one of them not matching -> 0
	}
	return i+1;
    }
    
    
    /** check if the input point is inside a closed curve. if not closed, it supposes closed by connecting the start and end point */
    public boolean isInside2d(IVecI pt, IVecI projectionDir){
	IVec2[] pts2 = null;
	if(deg()==1){
	    if(isClosed()){
		pts2 = new IVec2[cpNum()-1];
		for(int i=0; i<cpNum()-1; i++) pts2[i] = cp(i).get().to2d(projectionDir);
	    }
	    else{
		pts2 = new IVec2[cpNum()];
		for(int i=0; i<cpNum(); i++) pts2[i] = cp(i).get().to2d(projectionDir);
	    }
	}
	else{
	    int reso = IConfig.segmentResolution;
            int epnum = epNum() ;
            pts2 = new IVec2[(epnum-1)*reso+1];
            for(int i=0; i<epnum; i++){
                for(int j=0; j<reso; j++){
                    if(i<epnum-1 || j==0){
			pts2[i*reso + j] = pt(u(i,(double)j/reso)).to2d(projectionDir);
                    }
                }
            }
	}
	return pt.get().to2d(projectionDir).isInside(pts2);
    }

    /** check if the input point is inside a closed curve. if not closed, it supposes closed by connecting the start and end point */
    public boolean isInside2d(IVecI pt){
	IVec2[] pts2 = null;
	if(deg()==1){
	    if(isClosed()){
		pts2 = new IVec2[cpNum()-1];
		for(int i=0; i<cpNum()-1; i++) pts2[i] = cp(i).get().to2d();
	    }
	    else{
		pts2 = new IVec2[cpNum()];
		for(int i=0; i<cpNum(); i++) pts2[i] = cp(i).get().to2d();
	    }
	}
	else{
	    int reso = IConfig.segmentResolution;
            int epnum = epNum() ;
            pts2 = new IVec2[(epnum-1)*reso+1];
            for(int i=0; i<epnum; i++){
                for(int j=0; j<reso; j++){
                    if(i<epnum-1 || j==0){ pts2[i*reso + j] = pt(u(i,(double)j/reso)).to2d(); }
                }
            }
	}
	return pt.get().to2d().isInside(pts2);
    }
    
    
    
    synchronized public ICurveGeo updateCache(){ uSearchCache = new ICurveCache(this); return this; }

    
    
    
    // intersection
    
    /** intersection of curve and plane.
	@param segmentResolution segmentation resolution per EP count in degree &gt;= 1 curve. */
    public IVec[] intersectPlane(IVecI planeDir, IVecI planePt, int segmentResolution){
	ArrayList<IVec> itxns = new ArrayList<IVec>();
	if(deg()>1){
	    IVec prevPt = pt(u(0,0.0));
	    double prevDot = prevPt.dif(planePt).dot(planeDir);
	    if(prevDot==0) itxns.add(prevPt);
	    for(int i=0; i<epNum(); i++){
		int j=0;
		if(i==0) j=1;
		for(;j<segmentResolution; j++){
		    IVec pt =  pt(u(i,(double)j/segmentResolution));
		    double dot = pt.dif(planePt).dot(planeDir);
		    if(dot==0) itxns.add(pt);
		    else if(dot<0 && prevDot>0 || dot>0 && prevDot<0 ){
			itxns.add(IVec.intersectPlaneAndLine(planeDir.get(),planePt.get(),
							     pt.dif(prevPt),pt));
		    }
		    prevPt = pt;
		    prevDot = dot;
		}
	    }
	}
	else{ // polyline
	    double prevDot = cp(0).dif(planePt).dot(planeDir);
	    if(prevDot==0) itxns.add(cp(0).get().dup());
	    for(int i=1; i<cpNum(); i++){
		double dot = cp(i).dif(planePt).dot(planeDir);
		if(dot==0) itxns.add(cp(i).get().dup());
		else if(dot<0 && prevDot>0 || dot>0 && prevDot<0 ){
		    itxns.add(IVec.intersectPlaneAndLine(planeDir.get(), planePt.get(),
							 cp(i).get().dif(cp(i-1)), cp(i).get()));
		}
		prevDot = dot;
	    }
	}
	return itxns.toArray(new IVec[itxns.size()]);
    }
    
    /** intersection of curve and plane. */
    public IVec[] intersectPlane(IVecI planeDir, IVecI planePt){
	return intersectPlane(planeDir, planePt, IConfig.segmentResolution);
    }
    
    
    
    
    
    /********************************************************************************
     * transformation methods
     *******************************************************************************/
    
    public ICurveGeo add(double x, double y, double z){
	for(IVecI p:controlPoints){ p.add(x,y,z); } return this;
    }
    public ICurveGeo add(IDoubleI x, IDoubleI y, IDoubleI z){
	for(IVecI p:controlPoints){ p.add(x,y,z); } return this;
    }
    public ICurveGeo add(IVecI v){ for(IVecI p:controlPoints){ p.add(v); } return this; }
    public ICurveGeo sub(double x, double y, double z){
	for(IVecI p:controlPoints){ p.sub(x,y,z); } return this;
    }
    public ICurveGeo sub(IDoubleI x, IDoubleI y, IDoubleI z){
	for(IVecI p:controlPoints){ p.sub(x,y,z); } return this;
    }
    public ICurveGeo sub(IVecI v){ for(IVecI p:controlPoints){ p.sub(v); } return this; }
    public ICurveGeo mul(IDoubleI v){ for(IVecI p:controlPoints){ p.mul(v); } return this; }
    public ICurveGeo mul(double v){ for(IVecI p:controlPoints){ p.mul(v); } return this; }
    public ICurveGeo div(IDoubleI v){ for(IVecI p:controlPoints){ p.div(v); } return this; }
    public ICurveGeo div(double v){ for(IVecI p:controlPoints){ p.div(v); } return this; }
    
    public ICurveGeo neg(){ for(IVecI p:controlPoints){ p.neg(); } return this; }
    /** alias of neg */
    public ICurveGeo flip(){ return neg(); }
    
    /** scale add */
    public ICurveGeo add(IVecI v, double f){ for(IVecI p:controlPoints){ p.add(v,f); } return this; }
    public ICurveGeo add(IVecI v, IDoubleI f){ for(IVecI p:controlPoints){ p.add(v,f); } return this; }
    /** scale add alias */
    public ICurveGeo add(double f, IVecI v){ return add(v,f); }
    public ICurveGeo add(IDoubleI f, IVecI v){ return add(v,f); }
    
    public ICurveGeo rot(IDoubleI angle){ for(IVecI p:controlPoints){ p.rot(angle); } return this; }
    public ICurveGeo rot(double angle){ for(IVecI p:controlPoints){ p.rot(angle); } return this; }
    public ICurveGeo rot(IVecI axis, IDoubleI angle){
	for(IVecI p:controlPoints){ p.rot(axis,angle); } return this;
    }
    public ICurveGeo rot(IVecI axis, double angle){
	for(IVecI p:controlPoints){ p.rot(axis,angle); } return this;
    }
    public ICurveGeo rot(IVecI center, IVecI axis, IDoubleI angle){
	for(IVecI p:controlPoints){ p.rot(center,axis,angle); } return this;
    }
    public ICurveGeo rot(IVecI center, IVecI axis, double angle){
	for(IVecI p:controlPoints){ p.rot(center,axis,angle); } return this;
    }
    /** rotate to destination direction vector */
    public ICurveGeo rot(IVecI axis, IVecI destDir){
	for(IVecI p:controlPoints){ p.rot(axis,destDir); } return this;
    }
    /** rotate to destination point location */
    public ICurveGeo rot(IVecI center, IVecI axis, IVecI destPt){
	for(IVecI p:controlPoints){ p.rot(center,axis,destPt); } return this;
    }

    public ICurveGeo rot2(IDoubleI angle){ return rot(angle); }
    public ICurveGeo rot2(double angle){ return rot(angle); }
    public ICurveGeo rot2(IVecI center, IDoubleI angle){
	for(IVecI p:controlPoints){ p.rot2(center,angle); } return this;
    }
    public ICurveGeo rot2(IVecI center, double angle){
	for(IVecI p:controlPoints){ p.rot2(center,angle); } return this;
    }
    /** rotation on xy-plane to destination direction vector */
    public ICurveGeo rot2(IVecI destDir){ for(IVecI p:controlPoints){ p.rot2(destDir); } return this; }
    /** rotation on xy-plane to destination point location */
    public ICurveGeo rot2(IVecI center, IVecI destPt){
	for(IVecI p:controlPoints){ p.rot2(center,destPt); } return this;
    }
    
    
    /** alias of mul */
    public ICurveGeo scale(IDoubleI f){ return mul(f); }
    public ICurveGeo scale(double f){ return mul(f); }
    public ICurveGeo scale(IVecI center, IDoubleI f){
	for(IVecI p:controlPoints){ p.scale(center,f); } return this;
    }
    public ICurveGeo scale(IVecI center, double f){
	for(IVecI p:controlPoints){ p.scale(center,f); } return this;
    }
    
    /** scale only in 1 direction */
    public ICurveGeo scale1d(IVecI axis, double f){
	for(IVecI p:controlPoints){ p.scale1d(axis,f); } return this;
    }
    public ICurveGeo scale1d(IVecI axis, IDoubleI f){
	for(IVecI p:controlPoints){ p.scale1d(axis,f); } return this;
    }
    public ICurveGeo scale1d(IVecI center, IVecI axis, double f){
	for(IVecI p:controlPoints){ p.scale1d(center,axis,f); } return this;
    }
    public ICurveGeo scale1d(IVecI center, IVecI axis, IDoubleI f){
	for(IVecI p:controlPoints){ p.scale1d(center,axis,f); } return this;
    }
    
    
    /** reflect(mirror) 3 dimensionally to the other side of the plane */
    public ICurveGeo ref(IVecI planeDir){
	for(IVecI p:controlPoints){ p.ref(planeDir); } return this;
    }
    public ICurveGeo ref(IVecI center, IVecI planeDir){
	for(IVecI p:controlPoints){ p.ref(center,planeDir); } return this;
    }
    /** mirror is alias of ref */
    public ICurveGeo mirror(IVecI planeDir){ return ref(planeDir); }
    public ICurveGeo mirror(IVecI center, IVecI planeDir){ return ref(center,planeDir); }
    
    
    /** shear operation */
    public ICurveGeo shear(double sxy, double syx, double syz,
			   double szy, double szx, double sxz){
	for(IVecI p:controlPoints){ p.shear(sxy,syx,syz,szy,szx,sxz); } return this;
    }
    public ICurveGeo shear(IDoubleI sxy, IDoubleI syx, IDoubleI syz,
			   IDoubleI szy, IDoubleI szx, IDoubleI sxz){
	for(IVecI p:controlPoints){ p.shear(sxy,syx,syz,szy,szx,sxz); } return this;
    }
    public ICurveGeo shear(IVecI center, double sxy, double syx, double syz,
			   double szy, double szx, double sxz){
	for(IVecI p:controlPoints){ p.shear(center,sxy,syx,syz,szy,szx,sxz); } return this;
    }
    public ICurveGeo shear(IVecI center, IDoubleI sxy, IDoubleI syx, IDoubleI syz,
			   IDoubleI szy, IDoubleI szx, IDoubleI sxz){
	for(IVecI p:controlPoints){ p.shear(center,sxy,syx,syz,szy,szx,sxz); } return this;
    }
    
    public ICurveGeo shearXY(double sxy, double syx){
	for(IVecI p:controlPoints){ p.shearXY(sxy,syx); } return this;
    }
    public ICurveGeo shearXY(IDoubleI sxy, IDoubleI syx){
	for(IVecI p:controlPoints){ p.shearXY(sxy,syx); } return this;
    }
    public ICurveGeo shearXY(IVecI center, double sxy, double syx){
	for(IVecI p:controlPoints){ p.shearXY(center,sxy,syx); } return this;
    }
    public ICurveGeo shearXY(IVecI center, IDoubleI sxy, IDoubleI syx){
	for(IVecI p:controlPoints){ p.shearXY(center,sxy,syx); } return this;
    }
    
    public ICurveGeo shearYZ(double syz, double szy){
	for(IVecI p:controlPoints){ p.shearYZ(syz,szy); } return this;
    }
    public ICurveGeo shearYZ(IDoubleI syz, IDoubleI szy){
	for(IVecI p:controlPoints){ p.shearYZ(syz,szy); } return this;
    }
    public ICurveGeo shearYZ(IVecI center, double syz, double szy){
	for(IVecI p:controlPoints){ p.shearYZ(center,syz,szy); } return this;
    }
    public ICurveGeo shearYZ(IVecI center, IDoubleI syz, IDoubleI szy){
	for(IVecI p:controlPoints){ p.shearYZ(center,syz,szy); } return this;
    }
    
    public ICurveGeo shearZX(double szx, double sxz){
	for(IVecI p:controlPoints){ p.shearZX(szx,sxz); } return this;
    }
    public ICurveGeo shearZX(IDoubleI szx, IDoubleI sxz){
	for(IVecI p:controlPoints){ p.shearZX(szx,sxz); } return this;
    }
    public ICurveGeo shearZX(IVecI center, double szx, double sxz){
	for(IVecI p:controlPoints){ p.shearZX(center,szx,sxz); } return this;
    }
    public ICurveGeo shearZX(IVecI center, IDoubleI szx, IDoubleI sxz){
	for(IVecI p:controlPoints){ p.shearZX(center,szx,sxz); } return this;
    }
    
    /** translate is alias of add() */
    public ICurveGeo translate(double x, double y, double z){ return add(x,y,z); }
    public ICurveGeo translate(IDoubleI x, IDoubleI y, IDoubleI z){ return add(x,y,z); }
    public ICurveGeo translate(IVecI v){ return add(v); }
    
    
    public ICurveGeo transform(IMatrix3I mat){
	for(IVecI p:controlPoints){ p.transform(mat); } return this;
    }
    public ICurveGeo transform(IMatrix4I mat){
	for(IVecI p:controlPoints){ p.transform(mat); } return this;
    }
    public ICurveGeo transform(IVecI xvec, IVecI yvec, IVecI zvec){
	for(IVecI p:controlPoints){ p.transform(xvec,yvec,zvec); } return this;
    }
    public ICurveGeo transform(IVecI xvec, IVecI yvec, IVecI zvec, IVecI translate){
	for(IVecI p:controlPoints){ p.transform(xvec,yvec,zvec,translate); } return this;
    }
    
    
    /** mv() is alias of add() */
    public ICurveGeo mv(double x, double y, double z){ return add(x,y,z); }
    public ICurveGeo mv(IDoubleI x, IDoubleI y, IDoubleI z){ return add(x,y,z); }
    public ICurveGeo mv(IVecI v){ return add(v); }
    
    // method name cp() is used as getting control point method in curve and surface but here used also as copy because of the priority of variable fitting of diversed users' mind set over the clarity of the code organization
    /** cp() is alias of dup() */ 
    public ICurveGeo cp(){ return dup(); }
    
    /** cp() is alias of dup().add() */
    public ICurveGeo cp(double x, double y, double z){ return dup().add(x,y,z); }
    /** cp() is alias of dup().add() */
    public ICurveGeo cp(IDoubleI x, IDoubleI y, IDoubleI z){ return dup().add(x,y,z); }
    /** cp() is alias of dup().add() */
    public ICurveGeo cp(IVecI v){ return dup().add(v); }
    
    
    
    
}
