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PathStroke.cpp

/*
 *  PathStroke.cpp
 *  nlivarot
 *
 *  Created by fred on Tue Jun 17 2003.
 *
 */

#include "Path.h"
#include "Shape.h"
#include <libnr/nr-point.h>
#include <libnr/nr-point-fns.h>
#include <libnr/nr-matrix.h>
#include <libnr/nr-rotate.h>
#include <libnr/nr-rotate-ops.h>
#include <math.h>

/*
 * stroking polylines into a Shape instance
 * grunt work.
 * if the goal is to raster the stroke, polyline stroke->polygon->uncrossed polygon->raster is grossly
 * inefficient (but reuse the intersector, so that's what a lazy programmer like me does). the correct way would be
 * to set up a supersampled buffer, raster each polyline stroke's part (one part per segment in the polyline, plus 
 * each join) because these are all convex polygons, then transform in alpha values
 */

// until i find something better
NR::Point StrokeNormalize(const NR::Point value) {
    double length = L2(value); 
    if ( length < 0.0000001 ) { 
        return NR::Point(0, 0);
    } else { 
        return value/length; 
    }
}

// faster version if length is known
NR::Point StrokeNormalize(const NR::Point value, double length) {
    if ( length < 0.0000001 ) { 
        return NR::Point(0, 0);
    } else { 
        return value/length; 
    }
}

void Path::Stroke(Shape *dest, bool doClose, double width, JoinType join,
        ButtType butt, double miter, bool justAdd)
{
    if (dest == NULL) {
        return;
    }

    if (justAdd == false) {
        dest->Reset(3 * pts.size(), 3 * pts.size());
    }

    dest->MakeBackData(false);

    int lastM = 0;
    while (lastM < int(pts.size())) {

        int lastP = lastM + 1;
        while (lastP < int(pts.size()) // select one subpath
                && (pts[lastP].isMoveTo == polyline_lineto
                    || pts[lastP].isMoveTo == polyline_forced))
        {
            lastP++;
        }

        if ( lastP > lastM+1 ) {
            NR::Point sbStart = pts[lastM].p;
            NR::Point sbEnd = pts[lastP - 1].p;
            if ( NR::LInfty(sbEnd-sbStart) < 0.00001 ) {       // why close lines that shouldn't be closed?
                // ah I see, because close is defined here for
                // a whole path and should be defined per subpath.
                // debut==fin => ferme (on devrait garder un element pour les close(), mais tant pis)
                DoStroke(lastM, lastP - lastM, dest, true, width, join, butt, miter, true);
            } else {
                DoStroke(lastM, lastP - lastM, dest, doClose, width, join, butt, miter, true);
            }
        } else if (butt == butt_round) {       // special case: zero length round butt is a circle
            int last[2] = { -1, -1 };
            NR::Point dir;
            dir[0] = 1;
            dir[1] = 0;
            NR::Point pos = pts[lastM].p;
            DoButt(dest, width, butt, pos, dir, last[RIGHT], last[LEFT]);
            int end[2];
            dir = -dir;
            DoButt(dest, width, butt, pos, dir, end[LEFT], end[RIGHT]);
            dest->AddEdge (end[LEFT], last[LEFT]);
            dest->AddEdge (last[RIGHT], end[RIGHT]);
        }
        lastM = lastP;
    }
}

void Path::DoStroke(int off, int N, Shape *dest, bool doClose, double width, JoinType join,
        ButtType butt, double miter, bool justAdd)
{
    if (N <= 1) {
        return;
    }

    NR::Point prevP, nextP;
    int prevI, nextI;
    int upTo;

    int curI = 0;
    NR::Point curP = pts[off].p;

    if (doClose) {

        prevI = N - 1;
        while (prevI > 0) {
            prevP = pts[off + prevI].p;
            NR::Point diff = curP - prevP;
            double dist = dot(diff, diff);
            if (dist > 0.001) {
                break;
            }
            prevI--;
        }
        if (prevI <= 0) {
            return;
        }
        upTo = prevI;

    } else {

        prevP = curP;
        prevI = curI;
        upTo = N - 1;
    }

    {
        nextI = 1;
        while (nextI <= upTo) {
            nextP = pts[off + nextI].p;
            NR::Point diff = curP - nextP;
            double dist = dot(diff, diff);
            if (dist > 0.0) { // more tolerance for the first distance, to give the cap the right direction
                break;
            }
            nextI++;
        }
        if (nextI > upTo) {
            if (butt == butt_round) {  // special case: zero length round butt is a circle
                int last[2] = { -1, -1 };
                NR::Point dir;
                dir[0] = 1;
                dir[1] = 0;
                DoButt(dest, width, butt, curP, dir, last[RIGHT], last[LEFT]);
                int end[2];
                dir = -dir;
                DoButt(dest, width, butt, curP, dir, end[LEFT], end[RIGHT]);
                dest->AddEdge (end[LEFT], last[LEFT]);
                dest->AddEdge (last[RIGHT], end[RIGHT]);
            }
            return;
        }
    }

    int start[2] = { -1, -1 };
    int last[2] = { -1, -1 };
    NR::Point prevD = curP - prevP;
    NR::Point nextD = nextP - curP;
    double prevLe = NR::L2(prevD);
    double nextLe = NR::L2(nextD);
    prevD = StrokeNormalize(prevD, prevLe);
    nextD = StrokeNormalize(nextD, nextLe);

    if (doClose) {
        DoJoin(dest,  width, join, curP, prevD, nextD, miter, prevLe, nextLe, start, last);
    } else {
        nextD = -nextD;
        DoButt(dest,  width, butt, curP, nextD, last[RIGHT], last[LEFT]);
        nextD = -nextD;
    }

    do {
        prevP = curP;
        prevI = curI;
        curP = nextP;
        curI = nextI;
        prevD = nextD;
        prevLe = nextLe;
        nextI++;
        while (nextI <= upTo) {
            nextP = pts[off + nextI].p;
            NR::Point diff = curP - nextP;
            double dist = dot(diff, diff);
            if (dist > 0.001 || (nextI == upTo && dist > 0.0)) { // more tolerance for the last distance too, for the right cap direction
                break;
            }
            nextI++;
        }
        if (nextI > upTo) {
            break;
        }

        nextD = nextP - curP;
        nextLe = NR::L2(nextD);
        nextD = StrokeNormalize(nextD, nextLe);
        int nSt[2] = { -1, -1 };
        int nEn[2] = { -1, -1 };
        DoJoin(dest, width, join, curP, prevD, nextD, miter, prevLe, nextLe, nSt, nEn);
        dest->AddEdge(nSt[LEFT], last[LEFT]);
        last[LEFT] = nEn[LEFT];
        dest->AddEdge(last[RIGHT], nSt[RIGHT]);
        last[RIGHT] = nEn[RIGHT];
    } while (nextI <= upTo);

    if (doClose) {
        /*        prevP=curP;
                        prevI=curI;
                        curP=nextP;
                        curI=nextI;
                        prevD=nextD;*/
        nextP = pts[off].p;

        nextD = nextP - curP;
        nextLe = NR::L2(nextD);
        nextD = StrokeNormalize(nextD, nextLe);
        int nSt[2] = { -1, -1 };
        int nEn[2] = { -1, -1 };
        DoJoin(dest,  width, join, curP, prevD, nextD, miter, prevLe, nextLe, nSt, nEn);
        dest->AddEdge (nSt[LEFT], last[LEFT]);
        last[LEFT] = nEn[LEFT];
        dest->AddEdge (last[RIGHT], nSt[RIGHT]);
        last[RIGHT] = nEn[RIGHT];

        dest->AddEdge (start[LEFT], last[LEFT]);
        dest->AddEdge (last[RIGHT], start[RIGHT]);

    } else {

        int end[2];
        DoButt (dest,  width, butt, curP, prevD, end[LEFT], end[RIGHT]);
        dest->AddEdge (end[LEFT], last[LEFT]);
        dest->AddEdge (last[RIGHT], end[RIGHT]);
    }
}


void Path::DoButt(Shape *dest, double width, ButtType butt, NR::Point pos, NR::Point dir,
        int &leftNo, int &rightNo)
{
    NR::Point nor;
    nor = dir.ccw();

    if (butt == butt_square)
    {
        NR::Point x;
        x = pos + width * dir + width * nor;
        int bleftNo = dest->AddPoint (x);
        x = pos + width * dir - width * nor;
        int brightNo = dest->AddPoint (x);
        x = pos + width * nor;
        leftNo = dest->AddPoint (x);
        x = pos - width * nor;
        rightNo = dest->AddPoint (x);
        dest->AddEdge (rightNo, brightNo);
        dest->AddEdge (brightNo, bleftNo);
        dest->AddEdge (bleftNo, leftNo);
    }
    else if (butt == butt_pointy)
    {
        leftNo = dest->AddPoint (pos + width * nor);
        rightNo = dest->AddPoint (pos - width * nor);
        int mid = dest->AddPoint (pos + width * dir);
        dest->AddEdge (rightNo, mid);
        dest->AddEdge (mid, leftNo);
    }
    else if (butt == butt_round)
    {
        const NR::Point sx = pos + width * nor;
        const NR::Point ex = pos - width * nor;
        leftNo = dest->AddPoint (sx);
        rightNo = dest->AddPoint (ex);

        RecRound (dest, rightNo, leftNo, ex, sx, -nor, nor, pos, width);
    }
    else
    {
        leftNo = dest->AddPoint (pos + width * nor);
        rightNo = dest->AddPoint (pos - width * nor);
        dest->AddEdge (rightNo, leftNo);
    }
}


void Path::DoJoin (Shape *dest, double width, JoinType join, NR::Point pos, NR::Point prev,
        NR::Point next, double miter, double prevL, double nextL,
        int *stNo, int *enNo)
{
    NR::Point pnor = prev.ccw();
    NR::Point nnor = next.ccw();
    double angSi = cross(next, prev);

    /* FIXED: this special case caused bug 1028953 */
    if (angSi > -0.0001 && angSi < 0.0001) {
        double angCo = dot (prev, next);
        if (angCo > 0.9999) {
            // tout droit
            stNo[LEFT] = enNo[LEFT] = dest->AddPoint(pos + width * pnor);
            stNo[RIGHT] = enNo[RIGHT] = dest->AddPoint(pos - width * pnor);
        } else {
            // demi-tour
            const NR::Point sx = pos + width * pnor;
            const NR::Point ex = pos - width * pnor;
            stNo[LEFT] = enNo[RIGHT] = dest->AddPoint (sx);
            stNo[RIGHT] = enNo[LEFT] = dest->AddPoint (ex);
            if (join == join_round) {
                RecRound (dest, enNo[LEFT], stNo[LEFT], ex, sx, -pnor, pnor, pos, width);
                dest->AddEdge(stNo[RIGHT], enNo[RIGHT]);
            } else {
                dest->AddEdge(enNo[LEFT], stNo[LEFT]);
                dest->AddEdge(stNo[RIGHT], enNo[RIGHT]);    // two times because both are crossing each other
            }
        }
        return;
    }

    if (angSi < 0) {
        int midNo = dest->AddPoint(pos);
        stNo[LEFT] = dest->AddPoint(pos + width * pnor);
        enNo[LEFT] = dest->AddPoint(pos + width * nnor);
        dest->AddEdge(enNo[LEFT], midNo);
        dest->AddEdge(midNo, stNo[LEFT]);

        if (join == join_pointy) {

            stNo[RIGHT] = dest->AddPoint(pos - width * pnor);
            enNo[RIGHT] = dest->AddPoint(pos - width * nnor);

            const NR::Point biss = StrokeNormalize(prev - next);
            double c2 = dot(biss, nnor);
            double l = width / c2;
            double emiter = width * c2;
            if (emiter < miter) {
                emiter = miter;
            }

            if (fabs(l) < miter) {
                int const n = dest->AddPoint(pos - l * biss);
                dest->AddEdge(stNo[RIGHT], n);
                dest->AddEdge(n, enNo[RIGHT]);
            } else {
                dest->AddEdge(stNo[RIGHT], enNo[RIGHT]);
            }

        } else if (join == join_round) {
            NR::Point sx = pos - width * pnor;
            stNo[RIGHT] = dest->AddPoint(sx);
            NR::Point ex = pos - width * nnor;
            enNo[RIGHT] = dest->AddPoint(ex);

            RecRound(dest, stNo[RIGHT], enNo[RIGHT], 
                    sx, ex, -pnor, -nnor, pos, width);

        } else {
            stNo[RIGHT] = dest->AddPoint(pos - width * pnor);
            enNo[RIGHT] = dest->AddPoint(pos - width * nnor);
            dest->AddEdge(stNo[RIGHT], enNo[RIGHT]);
        }

    } else {

        int midNo = dest->AddPoint(pos);
        stNo[RIGHT] = dest->AddPoint(pos - width * pnor);
        enNo[RIGHT] = dest->AddPoint(pos - width * nnor);
        dest->AddEdge(stNo[RIGHT], midNo);
        dest->AddEdge(midNo, enNo[RIGHT]);

        if (join == join_pointy) {

            stNo[LEFT] = dest->AddPoint(pos + width * pnor);
            enNo[LEFT] = dest->AddPoint(pos + width * nnor);

            const NR::Point biss = StrokeNormalize(next - prev);
            double c2 = dot(biss, nnor);
            double l = width / c2;
            double emiter = width * c2;
            if (emiter < miter) {
                emiter = miter;
            }
            if ( fabs(l) < miter) {
                int const n = dest->AddPoint (pos + l * biss);
                dest->AddEdge (enNo[LEFT], n);
                dest->AddEdge (n, stNo[LEFT]);
            }
            else
            {
                dest->AddEdge (enNo[LEFT], stNo[LEFT]);
            }

        } else if (join == join_round) {

            NR::Point sx = pos + width * pnor;
            stNo[LEFT] = dest->AddPoint(sx);
            NR::Point ex = pos + width * nnor;
            enNo[LEFT] = dest->AddPoint(ex);

            RecRound(dest, enNo[LEFT], stNo[LEFT], 
                    ex, sx, nnor, pnor, pos, width);

        } else {
            stNo[LEFT] = dest->AddPoint(pos + width * pnor);
            enNo[LEFT] = dest->AddPoint(pos + width * nnor);
            dest->AddEdge(enNo[LEFT], stNo[LEFT]);
        }
    }
}

    void
Path::DoLeftJoin (Shape * dest, double width, JoinType join, NR::Point pos,
        NR::Point prev, NR::Point next, double miter, double prevL, double nextL,
        int &leftStNo, int &leftEnNo,int pathID,int pieceID,double tID)
{
    NR::Point pnor=prev.ccw();
    NR::Point nnor=next.ccw();
    double angSi = cross (next, prev);
    if (angSi > -0.0001 && angSi < 0.0001)
    {
        double angCo = dot (prev, next);
        if (angCo > 0.9999)
        {
            // tout droit
            leftEnNo = leftStNo = dest->AddPoint (pos + width * pnor);
        }
        else
        {
            // demi-tour
            leftStNo = dest->AddPoint (pos + width * pnor);
            leftEnNo = dest->AddPoint (pos - width * pnor);
            int nEdge=dest->AddEdge (leftEnNo, leftStNo);
            if ( dest->hasBackData() ) {
                dest->ebData[nEdge].pathID=pathID;
                dest->ebData[nEdge].pieceID=pieceID;
                dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
            }
        }
        return;
    }
    if (angSi < 0)
    {
        /*        NR::Point     biss;
                        biss.x=next.x-prev.x;
                        biss.y=next.y-prev.y;
                        double   c2=cross(biss,next);
                        double   l=width/c2;
                        double            projn=l*(dot(biss,next));
                        double            projp=-l*(dot(biss,prev));
                        if ( projp <= 0.5*prevL && projn <= 0.5*nextL ) {
                        double   x,y;
                        x=pos.x+l*biss.x;
                        y=pos.y+l*biss.y;
                        leftEnNo=leftStNo=dest->AddPoint(x,y);
                        } else {*/
        leftStNo = dest->AddPoint (pos + width * pnor);
        leftEnNo = dest->AddPoint (pos + width * nnor);
        int midNo = dest->AddPoint (pos);
        int nEdge=dest->AddEdge (leftEnNo, midNo);
        if ( dest->hasBackData() ) {
            dest->ebData[nEdge].pathID=pathID;
            dest->ebData[nEdge].pieceID=pieceID;
            dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
        }
        nEdge=dest->AddEdge (midNo, leftStNo);
        if ( dest->hasBackData() ) {
            dest->ebData[nEdge].pathID=pathID;
            dest->ebData[nEdge].pieceID=pieceID;
            dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
        }
        //              }
    }
    else
    {
        if (join == join_pointy)
        {
            leftStNo = dest->AddPoint (pos + width * pnor);
            leftEnNo = dest->AddPoint (pos + width * nnor);

            const NR::Point biss = StrokeNormalize (pnor + nnor);
            double c2 = dot (biss, nnor);
            double l = width / c2;
            double emiter = width * c2;
            if (emiter < miter)
                emiter = miter;
            if (l <= emiter)
            {
                int nleftStNo = dest->AddPoint (pos + l * biss);
                int nEdge=dest->AddEdge (leftEnNo, nleftStNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
                nEdge=dest->AddEdge (nleftStNo, leftStNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
            }
            else
            {
                double s2 = cross (biss, nnor);
                double dec = (l - emiter) * c2 / s2;
                const NR::Point tbiss=biss.ccw();

                int nleftStNo = dest->AddPoint (pos + emiter * biss + dec * tbiss);
                int nleftEnNo = dest->AddPoint (pos + emiter * biss - dec * tbiss);
                int nEdge=dest->AddEdge (nleftEnNo, nleftStNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
                nEdge=dest->AddEdge (leftEnNo, nleftEnNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
                nEdge=dest->AddEdge (nleftStNo, leftStNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
            }
        }
        else if (join == join_round)
        {
            const NR::Point sx = pos + width * pnor;
            leftStNo = dest->AddPoint (sx);
            const NR::Point ex = pos + width * nnor;
            leftEnNo = dest->AddPoint (ex);

            RecRound(dest, leftEnNo, leftStNo, 
                    sx, ex, pnor, nnor ,pos, width);

        }
        else
        {
            leftStNo = dest->AddPoint (pos + width * pnor);
            leftEnNo = dest->AddPoint (pos + width * nnor);
            int nEdge=dest->AddEdge (leftEnNo, leftStNo);
            if ( dest->hasBackData() ) {
                dest->ebData[nEdge].pathID=pathID;
                dest->ebData[nEdge].pieceID=pieceID;
                dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
            }
        }
    }
}
    void
Path::DoRightJoin (Shape * dest, double width, JoinType join, NR::Point pos,
        NR::Point prev, NR::Point next, double miter, double prevL,
        double nextL, int &rightStNo, int &rightEnNo,int pathID,int pieceID,double tID)
{
    const NR::Point pnor=prev.ccw();
    const NR::Point nnor=next.ccw();
    double angSi = cross (next,prev);
    if (angSi > -0.0001 && angSi < 0.0001)
    {
        double angCo = dot (prev, next);
        if (angCo > 0.9999)
        {
            // tout droit
            rightEnNo = rightStNo = dest->AddPoint (pos - width*pnor);
        }
        else
        {
            // demi-tour
            rightEnNo = dest->AddPoint (pos + width*pnor);
            rightStNo = dest->AddPoint (pos - width*pnor);
            int nEdge=dest->AddEdge (rightStNo, rightEnNo);
            if ( dest->hasBackData() ) {
                dest->ebData[nEdge].pathID=pathID;
                dest->ebData[nEdge].pieceID=pieceID;
                dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
            }
        }
        return;
    }
    if (angSi < 0)
    {
        if (join == join_pointy)
        {
            rightStNo = dest->AddPoint (pos - width*pnor);
            rightEnNo = dest->AddPoint (pos - width*nnor);

            const NR::Point biss = StrokeNormalize (pnor + nnor);
            double c2 = dot (biss, nnor);
            double l = width / c2;
            double emiter = width * c2;
            if (emiter < miter)
                emiter = miter;
            if (l <= emiter)
            {
                int nrightStNo = dest->AddPoint (pos - l * biss);
                int nEdge=dest->AddEdge (rightStNo, nrightStNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
                nEdge=dest->AddEdge (nrightStNo, rightEnNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
            }
            else
            {
                double s2 = cross (biss, nnor);
                double dec = (l - emiter) * c2 / s2;
                const NR::Point tbiss=biss.ccw();

                int nrightStNo = dest->AddPoint (pos - emiter*biss - dec*tbiss);
                int nrightEnNo = dest->AddPoint (pos - emiter*biss + dec*tbiss);
                int nEdge=dest->AddEdge (rightStNo, nrightStNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
                nEdge=dest->AddEdge (nrightStNo, nrightEnNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
                nEdge=dest->AddEdge (nrightEnNo, rightEnNo);
                if ( dest->hasBackData() ) {
                    dest->ebData[nEdge].pathID=pathID;
                    dest->ebData[nEdge].pieceID=pieceID;
                    dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
                }
            }
        }
        else if (join == join_round)
        {
            const NR::Point sx = pos - width * pnor;
            rightStNo = dest->AddPoint (sx);
            const NR::Point ex = pos - width * nnor;
            rightEnNo = dest->AddPoint (ex);

            RecRound(dest, rightStNo, rightEnNo, 
                    sx, ex, -pnor, -nnor ,pos, width);
        }
        else
        {
            rightStNo = dest->AddPoint (pos - width * pnor);
            rightEnNo = dest->AddPoint (pos - width * nnor);
            int nEdge=dest->AddEdge (rightStNo, rightEnNo);
            if ( dest->hasBackData() ) {
                dest->ebData[nEdge].pathID=pathID;
                dest->ebData[nEdge].pieceID=pieceID;
                dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
            }
        }
    }
    else
    {
        /*        NR::Point     biss;
                        biss=next.x-prev.x;
                        biss.y=next.y-prev.y;
                        double   c2=cross(next,biss);
                        double   l=width/c2;
                        double            projn=l*(dot(biss,next));
                        double            projp=-l*(dot(biss,prev));
                        if ( projp <= 0.5*prevL && projn <= 0.5*nextL ) {
                        double   x,y;
                        x=pos.x+l*biss.x;
                        y=pos.y+l*biss.y;
                        rightEnNo=rightStNo=dest->AddPoint(x,y);
                        } else {*/
        rightStNo = dest->AddPoint (pos - width*pnor);
        rightEnNo = dest->AddPoint (pos - width*nnor);
        int midNo = dest->AddPoint (pos);
        int nEdge=dest->AddEdge (rightStNo, midNo);
        if ( dest->hasBackData() ) {
            dest->ebData[nEdge].pathID=pathID;                                  
            dest->ebData[nEdge].pieceID=pieceID;
            dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
        }
        nEdge=dest->AddEdge (midNo, rightEnNo);
        if ( dest->hasBackData() ) {
            dest->ebData[nEdge].pathID=pathID;
            dest->ebData[nEdge].pieceID=pieceID;
            dest->ebData[nEdge].tSt=dest->ebData[nEdge].tEn=tID;
        }
        //              }
    }
}


// a very ugly way to produce round joins: doing one (or two, depend on the angle of the join) quadratic bezier curves
// but since most joins are going to be small, nobody will notice -- but somebody noticed and now the ugly stuff is gone! so:

// a very nice way to produce round joins, caps or dots
void Path::RecRound(Shape *dest, int sNo, int eNo, // start and end index
        NR::Point const &iS, NR::Point const &iE, // start and end point
        NR::Point const &nS, NR::Point const &nE, // start and end normal vector
        NR::Point &origine, float width) // center and radius of round
{
    //NR::Point diff = iS - iE;
    //double dist = dot(diff, diff);
    if (width < 0.5 || dot(iS - iE, iS - iE)/width < 2.0) {
        dest->AddEdge(sNo, eNo);
        return;
    }
    double ang, sia, lod;
    if (nS == -nE) {
        ang = M_PI;
        sia = 1;
    } else {
        double coa = dot(nS, nE);
        sia = cross(nS, nE);
        ang = acos(coa);
        if ( coa >= 1 ) {
            ang = 0;
        }
        if ( coa <= -1 ) {
            ang = M_PI;
        }
    }
    lod = 0.02 + 10 / (10 + width); // limit detail to about 2 degrees (180 * 0.02/Pi degrees)
    ang /= lod;

    int nbS = (int) floor(ang);
    NR::rotate omega(((sia > 0) ? -lod : lod));
    NR::Point cur = iS - origine;
    //  StrokeNormalize(cur);
    //  cur*=width;
    int lastNo = sNo;
    for (int i = 0; i < nbS; i++) {
        cur = cur * omega;
        NR::Point m = origine + cur;
        int mNo = dest->AddPoint(m);
        dest->AddEdge(lastNo, mNo);
        lastNo = mNo;
    }
    dest->AddEdge(lastNo, eNo);
}

/*
   Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0))
indent-tabs-mode:nil
fill-column:99
End:
 */
// vim: filetype=c++:expandtab:shiftwidth=4:tabstop=8:softtabstop=4 :

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