path: root/contrib/python/contourpy/src/mpl2005_original.cpp

/*
  cntr.c
  General purpose contour tracer for quadrilateral meshes.
  Handles single level contours, or region between a pair of levels.

    The routines that do all the work, as well as the explanatory
    comments, came from gcntr.c, part of the GIST package. The
    original mpl interface was also based on GIST.  The present
    interface uses parts of the original, but places them in
    the entirely different framework of a Python type.  It
    was written by following the Python "Extending and Embedding"
    tutorial.
 */

#include "mpl2005_original.h"
#include "mpl_kind_code.h"

/* Note that all arrays in these routines are Fortran-style,
   in the sense that the "i" index varies fastest; the dimensions
   of the corresponding C array are z[jmax][imax] in the notation
   used here.  We can identify i and j with the x and y dimensions,
   respectively.

*/

/* What is a contour?
 *
 * Given a quadrilateral mesh (x,y), and values of a z at the points
 * of that mesh, we seek a set of polylines connecting points at a
 * particular value of z.  Each point on such a contour curve lies
 * on an edge of the mesh, at a point linearly interpolated to the
 * contour level z0 between the given values of z at the endpoints
 * of the edge.
 *
 * Identifying these points is easy.  Figuring out how to connect them
 * into a curve -- or possibly a set of disjoint curves -- is difficult.
 * Each disjoint curve may be either a closed circuit, or it may begin
 * and end on a mesh boundary.
 *
 * One of the problems with a quadrilateral mesh is that when the z
 * values at one pair of diagonally opposite points lie below z0, and
 * the values at the other diagonal pair of the same zone lie above z0,
 * all four edges of the zone are cut, and there is an ambiguity in
 * how we should connect the points.  I call this a saddle zone.
 * The problem is that two disjoint curves cut through a saddle zone
 * (I reject the alternative of connecting the opposite points to make
 * a single self-intersecting curve, since those make ugly contour plots
 * -- I've tried it).  The solution is to determine the z value of the
 * centre of the zone, which is the mean of the z values of the four
 * corner points.  If the centre z is higher than the contour level of
 * interest and you are moving along the line with higher values on the
 * left, turn right to leave the saddle zone.  If the centre z is lower
 * than the contour level turn left.  Whether the centre z is higher
 * than the 1 or 2 contour levels is stored in the saddle array so that
 * it does not need to be recalculated in subsequent passes.
 *
 * Another complicating factor is that there may be logical holes in
 * the mesh -- zones which do not exist.  We want our contours to stop
 * if they hit the edge of such a zone, just as if they'd hit the edge
 * of the whole mesh.  The input region array addresses this issue.
 *
 * Yet another complication: We may want a list of closed polygons which
 * outline the region between two contour levels z0 and z1.  These may
 * include sections of the mesh boundary (including edges of logical
 * holes defined by the region array), in addition to sections of the
 * contour curves at one or both levels.  This introduces a huge
 * topological problem -- if one of the closed contours (possibly
 * including an interior logical hole in the mesh, but not any part of
 * the boundary of the whole mesh) encloses a region which is not
 * between z0 and z1, that curve must be connected by a slit (or "branch
 * cut") to the enclosing curve, so that the list of disjoint polygons
 * we return is each simply connected.
 *
 * Okay, one final stunning difficulty: For the two level case, no
 * individual polygon should have more than a few thousand sides, since
 * huge filled polygons place an inordinate load on rendering software,
 * which needs an amount of scratch space proportional to the number
 * of sides it needs to fill.  So in the two level case, we want to
 * chunk the mesh into rectangular pieces of no more than, say, 30x30
 * zones, which keeps each returned polygon to less than a few thousand
 * sides (the worst case is very very bad -- you can easily write down
 * a function and two level values which produce a polygon that cuts
 * every edge of the mesh twice).
 */

/*
 * Here is the numbering scheme for points, edges, and zones in
 * the mesh -- note that each ij corresponds to one point, one zone,
 * one i-edge (i=constant edge) and one j-edge (j=constant edge):
 *
 *             (ij-1)-------(ij)-------(ij)
 *                |                     |
 *                |                     |
 *                |                     |
 *             (ij-1)       (ij)       (ij)
 *                |                     |
 *                |                     |
 *                |                     |
 *           (ij-iX-1)----(ij-iX)----(ij-iX)
 *
 * At each point, the function value is either 0, 1, or 2, depending
 * on whether it is below z0, between z0 and z1, or above z1.
 * Each zone either exists (1) or not (0).
 * From these three bits of data, all of the curve connectivity follows.
 *
 * The tracing algorithm is naturally edge-based: Either you are at a
 * point where a level cuts an edge, ready to step across a zone to
 * another edge, or you are drawing the edge itself, if it happens to
 * be a boundary with at least one section between z0 and z1.
 *
 * In either case, the edge is a directed edge -- either the zone
 * you are advancing into is to its left or right, or you are actually
 * drawing it.  I always trace curves keeping the region between z0 and
 * z1 to the left of the curve.  If I'm tracing a boundary, I'm always
 * moving CCW (counter clockwise) around the zone that exists.  And if
 * I'm about to cross a zone, I'll make the direction of the edge I'm
 * sitting on be such that the zone I'm crossing is to its left.
 *
 * I start tracing each curve near its lower left corner (mesh oriented
 * as above), which is the first point I encounter scanning through the
 * mesh in order.  When I figure the 012 z values and zonal existence,
 * I also mark the potential starting points: Each edge may harbor a
 * potential starting point corresponding to either direction, so there
 * are four start possibilities at each ij point.  Only the following
 * possibilities need to be marked as potential starting edges:
 *
 *     +-+-+-+
 *     | | | |
 *     A-0-C-+    One or both levels cut E and have z=1 above them, and
 *     | EZ| |    0A is cut and either 0C is cut or CD is cut.
 *     +-B-D-+    Or, one or both levels cut E and E is a boundary edge.
 *     | | | |    (and Z exists)
 *     +-+-+-+
 *
 *     +-+-+-+
 *     | | | |
 *     +-A-0-C    One or both levels cut E and have z=1 below them, and
 *     | |ZE |    0A is cut and either 0C is cut or CD is cut.
 *     +-+-B-D    Or, one or both levels cut E and E is a boundary edge.
 *     | | | |    (and Z exists)
 *     +-+-+-+
 *
 *     +-+-+-+
 *     | | | |
 *     +-+-+-+    E is a boundary edge, Z exists, at some point on E
 *     | |Z| |    lies between the levels.
 *     +-+E+-+
 *     | | | |
 *     +-+-+-+
 *
 *     +-+-+-+
 *     | | | |
 *     +-+E+-+    E is a boundary edge, Z exists, at some point on E
 *     | |Z| |    lies between the levels.
 *     +-+-+-+
 *     | | | |
 *     +-+-+-+
 *
 * During the first tracing pass, the start mark is erased whenever
 * any non-starting edge is encountered, reducing the number of points
 * that need to be considered for the second pass.  The first pass
 * makes the basic connectivity decisions.  It figures out how many
 * disjoint curves there will be, and identifies slits for the two level
 * case or open contours for the single level case, and removes all but
 * the actual start markers.  A second tracing pass can perform the
 * actual final trace.
 */

/* ------------------------------------------------------------------------ */

namespace contourpy {

void print_Csite(Csite *Csite)
{
    Cdata *data = Csite->data;
    int i, j, ij;
    int nd = Csite->imax * (Csite->jmax + 1) + 1;
    printf("zlevels: %8.2lg %8.2lg\n", Csite->zlevel[0], Csite->zlevel[1]);
    printf("edge %ld, left %ld, n %ld, count %ld, edge0 %ld, left0 %ld\n",
            Csite->edge, Csite->left, Csite->n, Csite->count,
            Csite->edge0, Csite->left0);
    printf("  level0 %d, edge00 %ld\n", Csite->level0, Csite->edge00);
    printf("%04x\n", data[nd-1]);
    for (j = Csite->jmax; j >= 0; j--)
    {
        for (i=0; i < Csite->imax; i++)
        {
            ij = i + j * Csite->imax;
            printf("%04x ", data[ij]);
        }
        printf("\n");
    }
    printf("\n");
}


/* the Cdata array consists of the following bits:
 * Z_VALUE     (2 bits) 0, 1, or 2 function value at point
 * ZONE_EX     1 zone exists, 0 zone doesn't exist
 * I_BNDY      this i-edge (i=constant edge) is a mesh boundary
 * J_BNDY      this j-edge (i=constant edge) is a mesh boundary
 * I0_START    this i-edge is a start point into zone to left
 * I1_START    this i-edge is a start point into zone to right
 * J0_START    this j-edge is a start point into zone below
 * J1_START    this j-edge is a start point into zone above
 * START_ROW   next start point is in current row (accelerates 2nd pass)
 * SLIT_UP     marks this i-edge as the beginning of a slit upstroke
 * SLIT_DN     marks this i-edge as the beginning of a slit downstroke
 * OPEN_END    marks an i-edge start point whose other endpoint is
 *             on a boundary for the single level case
 * ALL_DONE    marks final start point
 * SLIT_DN_VISITED this slit downstroke hasn't/has been visited in pass 2
 */
#define Z_VALUE   0x0003
#define ZONE_EX   0x0004
#define I_BNDY    0x0008
#define J_BNDY    0x0010
#define I0_START  0x0020
#define I1_START  0x0040
#define J0_START  0x0080
#define J1_START  0x0100
#define START_ROW 0x0200
#define SLIT_UP   0x0400
#define SLIT_DN   0x0800
#define OPEN_END  0x1000
#define ALL_DONE  0x2000
#define SLIT_DN_VISITED 0x4000

/* some helpful macros to find points relative to a given directed
 * edge -- points are designated 0, 1, 2, 3 CCW around zone with 0 and
 * 1 the endpoints of the current edge */
#define FORWARD(left,ix) ((left)>0?((left)>1?1:-(ix)):((left)<-1?-1:(ix)))
#define POINT0(edge,fwd) ((edge)-((fwd)>0?fwd:0))
#define POINT1(edge,fwd) ((edge)+((fwd)<0?fwd:0))
#define IS_JEDGE(edge,left) ((left)>0?((left)>1?1:0):((left)<-1?1:0))
#define ANY_START (I0_START|I1_START|J0_START|J1_START)
#define START_MARK(left) \
  ((left)>0?((left)>1?J1_START:I1_START):((left)<-1?J0_START:I0_START))

enum {kind_zone, kind_edge1, kind_edge2,
        kind_slit_up, kind_slit_down, kind_start_slit=16};

/* Saddle zone array consists of the following bits:
 * SADDLE_SET  whether zone's saddle data has been set.
 * SADDLE_GT0  whether z of centre of zone is higher than site->level[0].
 * SADDLE_GT1  whether z of centre of zone is higher than site->level[1].
 */
#define SADDLE_SET 0x01
#define SADDLE_GT0 0x02
#define SADDLE_GT1 0x04

/* ------------------------------------------------------------------------ */

/* these actually mark points */
static int zone_crosser (Csite * site, int level, int pass2);
static int edge_walker (Csite * site, int pass2);
static int slit_cutter (Csite * site, int up, int pass2);

/* this calls the first three to trace the next disjoint curve
 * -- return value is number of points on this curve, or
 *    0 if there are no more curves this pass
 *    -(number of points) on first pass if:
 *      this is two level case, and the curve closed on a hole
 *      this is single level case, curve is open, and will start from
 *      a different point on the second pass
 *      -- in both cases, this curve will be combined with another
 *         on the second pass */
static long curve_tracer (Csite * site, int pass2);

/* this initializes the data array for curve_tracer */
static void data_init (Csite * site);

/* ------------------------------------------------------------------------ */

/* zone_crosser assumes you are sitting at a cut edge about to cross
 * the current zone.  It always marks the initial point, crosses at
 * least one zone, and marks the final point.  On non-boundary i-edges,
 * it is responsible for removing start markers on the first pass.  */
static int
zone_crosser (Csite * site, int level, int pass2)
{
    Cdata * data = site->data;
    long edge = site->edge;
    long left = site->left;
    long n = site->n;
    long fwd = FORWARD (left, site->imax);
    long p0, p1;
    int jedge = IS_JEDGE (edge, left);
    long edge0 = site->edge0;
    long left0 = site->left0;
    int level0 = site->level0 == level;
    int two_levels = site->zlevel[1] > site->zlevel[0];
    Saddle* saddle = site->saddle;

    const double *x = pass2 ? site->x : 0;
    const double *y = pass2 ? site->y : 0;
    const double *z = site->z;
    double zlevel = site->zlevel[level];
    double *xcp = pass2 ? site->xcp : 0;
    double *ycp = pass2 ? site->ycp : 0;
    short *kcp = pass2 ? site->kcp : 0;

    int z0, z1, z2, z3;
    int done = 0;
    int n_kind;

    if (level)
        level = 2;

    for (;;)
    {
        n_kind = 0;
        /* set edge endpoints */
        p0 = POINT0 (edge, fwd);
        p1 = POINT1 (edge, fwd);

        /* always mark cut on current edge */
        if (pass2)
        {
            /* second pass actually computes and stores the point */
            double zcp = (zlevel - z[p0]) / (z[p1] - z[p0]);
            xcp[n] = zcp * (x[p1] - x[p0]) + x[p0];
            ycp[n] = zcp * (y[p1] - y[p0]) + y[p0];
            kcp[n] = kind_zone;
            n_kind = n;
        }
        if (!done && !jedge)
        {
            if (n)
            {
                /* if this is not the first point on the curve, and we're
                 * not done, and this is an i-edge, check several things */
                if (!two_levels && !pass2 && (data[edge] & OPEN_END))
                {
                    /* reached an OPEN_END mark, skip the n++ */
                    done = 4;   /* same return value 4 used below */
                    break;
                }

                /* check for curve closure -- if not, erase any start mark */
                if (edge == edge0 && left == left0)
                {
                    /* may signal closure on a downstroke */
                    if (level0)
                        done = (!pass2 && two_levels && left < 0) ? 5 : 3;
                }
                else if (!pass2)
                {
                    Cdata start =
                        data[edge] & (fwd > 0 ? I0_START : I1_START);
                    if (start)
                    {
                        data[edge] &= ~start;
                        site->count--;
                    }
                    if (!two_levels)
                    {
                        start = data[edge] & (fwd > 0 ? I1_START : I0_START);
                        if (start)
                        {
                            data[edge] &= ~start;
                            site->count--;
                        }
                    }
                }
            }
        }
        n++;
        if (done)
            break;

        /* cross current zone to another cut edge */
        z0 = (data[p0] & Z_VALUE) != level;     /* 1 if fill toward p0 */
        z1 = !z0;               /* know level cuts edge */
        z2 = (data[p1 + left] & Z_VALUE) != level;
        z3 = (data[p0 + left] & Z_VALUE) != level;
        if (z0 == z2)
        {
            if (z1 == z3)
            {
                /* this is a saddle zone, determine whether to turn left or
                 * right depending on height of centre of zone relative to
                 * contour level.  Set saddle[zone] if not already decided. */
                int turnRight;
                long zone = edge + (left > 0 ? left : 0);
                if (!(saddle[zone] & SADDLE_SET))
                {
                    double zcentre;
                    saddle[zone] = SADDLE_SET;
                    zcentre = (z[p0] + z[p0+left] + z[p1] + z[p1+left])/4.0;
                    if (zcentre > site->zlevel[0])
                        saddle[zone] |=
                            (two_levels && zcentre > site->zlevel[1])
                            ? SADDLE_GT0 | SADDLE_GT1 : SADDLE_GT0;
                }

                turnRight = level == 2 ? (saddle[zone] & SADDLE_GT1)
                                       : (saddle[zone] & SADDLE_GT0);
                if (z1 ^ (level == 2))
                    turnRight = !turnRight;
                if (!turnRight)
                    goto bkwd;
            }
            /* bend forward (right along curve) */
            jedge = !jedge;
            edge = p1 + (left > 0 ? left : 0);
            {
                long tmp = fwd;
                fwd = -left;
                left = tmp;
            }
        }
        else if (z1 == z3)
        {
          bkwd:
            /* bend backward (left along curve) */
            jedge = !jedge;
            edge = p0 + (left > 0 ? left : 0);
            {
                long tmp = fwd;
                fwd = left;
                left = -tmp;
            }
        }
        else
        {
            /* straight across to opposite edge */
            edge += left;
        }
        /* after crossing zone, edge/left/fwd is oriented CCW relative to
         * the next zone, assuming we will step there */

        /* now that we've taken a step, check for the downstroke
         * of a slit on the second pass (upstroke checked above)
         * -- taking step first avoids a race condition */
        if (pass2 && two_levels && !jedge)
        {
            if (left > 0)
            {
                if (data[edge] & SLIT_UP)
                    done = 6;
            }
            else
            {
                if (data[edge] & SLIT_DN)
                    done = 5;
            }
        }

        if (!done)
        {
            /* finally, check if we are on a boundary */
            if (data[edge] & (jedge ? J_BNDY : I_BNDY))
            {
                done = two_levels ? 2 : 4;
                /* flip back into the zone that exists */
                left = -left;
                fwd = -fwd;
                if (!pass2 && (edge != edge0 || left != left0))
                {
                    Cdata start = data[edge] & START_MARK (left);
                    if (start)
                    {
                        data[edge] &= ~start;
                        site->count--;
                    }
                }
            }
        }
    }

    site->edge = edge;
    site->n = n;
    site->left = left;
    if (done <= 4)
    {
        return done;
    }
    if (pass2 && n_kind)
    {
        kcp[n_kind] += kind_start_slit;
    }
    return slit_cutter (site, done - 5, pass2);
}

/* edge_walker assumes that the current edge is being drawn CCW
 * around the current zone.  Since only boundary edges are drawn
 * and we always walk around with the filled region to the left,
 * no edge is ever drawn CW.  We attempt to advance to the next
 * edge on this boundary, but if current second endpoint is not
 * between the two contour levels, we exit back to zone_crosser.
 * Note that we may wind up marking no points.
 * -- edge_walker is never called for single level case */
static int
edge_walker (Csite * site,  int pass2)
{
    Cdata * data = site->data;
    long edge = site->edge;
    long left = site->left;
    long n = site->n;
    long fwd = FORWARD (left, site->imax);
    long p0 = POINT0 (edge, fwd);
    long p1 = POINT1 (edge, fwd);
    int jedge = IS_JEDGE (edge, left);
    long edge0 = site->edge0;
    long left0 = site->left0;
    int level0 = site->level0 == 2;
    int marked;
    int n_kind = 0;

    const double *x = pass2 ? site->x : 0;
    const double *y = pass2 ? site->y : 0;
    double *xcp = pass2 ? site->xcp : 0;
    double *ycp = pass2 ? site->ycp : 0;
    short *kcp = pass2 ? site->kcp : 0;

    int z0, z1, heads_up = 0;

    for (;;)
    {
        /* mark endpoint 0 only if value is 1 there, and this is a
         * two level task */
        z0 = data[p0] & Z_VALUE;
        z1 = data[p1] & Z_VALUE;
        marked = 0;
        n_kind = 0;
        if (z0 == 1)
        {
            /* mark current boundary point */
            if (pass2)
            {
                xcp[n] = x[p0];
                ycp[n] = y[p0];
                kcp[n] = kind_edge1;
                n_kind = n;
            }
            marked = 1;
        }
        else if (!n)
        {
            /* if this is the first point is not between the levels
             * must do the job of the zone_crosser and mark the first cut here,
             * so that it will be marked again by zone_crosser as it closes */
            if (pass2)
            {
                double zcp = site->zlevel[(z0 != 0)];
                zcp = (zcp - site->z[p0]) / (site->z[p1] - site->z[p0]);
                xcp[n] = zcp * (x[p1] - x[p0]) + x[p0];
                ycp[n] = zcp * (y[p1] - y[p0]) + y[p0];
                kcp[n] = kind_edge2;
                n_kind = n;
            }
            marked = 1;
        }
        if (n)
        {
            /* check for closure */
            if (level0 && edge == edge0 && left == left0)
            {
                site->edge = edge;
                site->left = left;
                site->n = n + marked;
                /* if the curve is closing on a hole, need to make a downslit */
                if (fwd < 0 && !(data[edge] & (jedge ? J_BNDY : I_BNDY)))
                {
                    if (n_kind) kcp[n_kind] += kind_start_slit;
                    return slit_cutter (site, 0, pass2);
                }
                if (fwd < 0 && level0 && left < 0)
                {
                    /* remove J0_START from this boundary edge as boundary is
                     * included by the upwards slit from contour line below. */
                    data[edge] &= ~J0_START;
                    if (n_kind) kcp[n_kind] += kind_start_slit;
                    return slit_cutter (site, 0, pass2);
                }
                return 3;
            }
            else if (pass2)
            {
                if (heads_up || (fwd < 0 && (data[edge] & SLIT_DN)))
                {
                    if (!heads_up && !(data[edge] & SLIT_DN_VISITED))
                        data[edge] |= SLIT_DN_VISITED;
                    else
                    {
                        site->edge = edge;
                        site->left = left;
                        site->n = n + marked;
                        if (n_kind) kcp[n_kind] += kind_start_slit;
                        return slit_cutter (site, heads_up, pass2);
                    }
                }
            }
            else
            {
                /* if this is not first point, clear start mark for this edge */
                Cdata start = data[edge] & START_MARK (left);
                if (start)
                {
                    data[edge] &= ~start;
                    site->count--;
                }
            }
        }
        if (marked)
            n++;

        /* if next endpoint not between levels, need to exit to zone_crosser */
        if (z1 != 1)
        {
            site->edge = edge;
            site->left = left;
            site->n = n;
            return (z1 != 0);   /* return level closest to p1 */
        }

        /* step to p1 and find next edge
         * -- turn left if possible, else straight, else right
         * -- check for upward slit beginning at same time */
        edge = p1 + (left > 0 ? left : 0);
        if (pass2 && jedge && fwd > 0 && (data[edge] & SLIT_UP))
        {
            jedge = !jedge;
            heads_up = 1;
        }
        else if (data[edge] & (jedge ? I_BNDY : J_BNDY))
        {
            long tmp = fwd;
            fwd = left;
            left = -tmp;
            jedge = !jedge;
        }
        else
        {
            edge = p1 + (fwd > 0 ? fwd : 0);
            if (pass2 && !jedge && fwd > 0 && (data[edge] & SLIT_UP))
            {
                heads_up = 1;
            }
            else if (!(data[edge] & (jedge ? J_BNDY : I_BNDY)))
            {
                edge = p1 - (left < 0 ? left : 0);
                jedge = !jedge;
                {
                    long tmp = fwd;
                    fwd = -left;
                    left = tmp;
                }
            }
        }
        p0 = p1;
        p1 = POINT1 (edge, fwd);
    }
}

/* -- slit_cutter is never called for single level case */
static int
slit_cutter (Csite * site, int up, int pass2)
{
    Cdata * data = site->data;
    long imax = site->imax;
    long n = site->n;

    const double *x = pass2 ? site->x : 0;
    const double *y = pass2 ? site->y : 0;
    double *xcp = pass2 ? site->xcp : 0;
    double *ycp = pass2 ? site->ycp : 0;
    short *kcp = pass2 ? site->kcp : 0;

    if (up && pass2)
    {
        /* upward stroke of slit proceeds up left side of slit until
         * it hits a boundary or a point not between the contour levels
         * -- this never happens on the first pass */
        long p1 = site->edge;
        int z1;

        for (;;)
        {
            z1 = data[p1] & Z_VALUE;
            if (z1 != 1)
            {
                site->edge = p1;
                site->left = -1;
                site->n = n;
                return (z1 != 0);
            }
            else if (data[p1] & J_BNDY)
            {
                /* this is very unusual case of closing on a mesh hole */
                site->edge = p1;
                site->left = -imax;
                site->n = n;
                return 2;
            }
            xcp[n] = x[p1];
            ycp[n] = y[p1];
            kcp[n] = kind_slit_up;
            n++;
            p1 += imax;
        }

    }
    else
    {
        /* downward stroke proceeds down right side of slit until it
         * hits a boundary or point not between the contour levels */
        long p0 = site->edge;
        int z0;
        /* at beginning of first pass, mark first i-edge with SLIT_DN */
        data[p0] |= SLIT_DN;
        p0 -= imax;
        for (;;)
        {
            z0 = data[p0] & Z_VALUE;
            if (!pass2)
            {
                if (z0 != 1 || (data[p0] & I_BNDY) || (data[p0 + 1] & J_BNDY))
                {
                    /* at end of first pass, mark final i-edge with SLIT_UP */
                    data[p0 + imax] |= SLIT_UP;
                    /* one extra count for splicing at outer curve */
                    site->n = n + 1;
                    return 4;   /* return same special value as for OPEN_END */
                }
            }
            else
            {
                if (z0 != 1)
                {
                    site->edge = p0 + imax;
                    site->left = 1;
                    site->n = n;
                    return (z0 != 0);
                }
                else if (data[p0 + 1] & J_BNDY)
                {
                    site->edge = p0 + 1;
                    site->left = imax;
                    site->n = n;
                    return 2;
                }
                else if (data[p0] & I_BNDY)
                {
                    site->edge = p0;
                    site->left = 1;
                    site->n = n;
                    return 2;
                }
            }
            if (pass2)
            {
                xcp[n] = x[p0];
                ycp[n] = y[p0];
                kcp[n] = kind_slit_down;
                n++;
            }
            else
            {
                /* on first pass need to count for upstroke as well */
                n += 2;
            }
            p0 -= imax;
        }
    }
}

/* ------------------------------------------------------------------------ */

/* curve_tracer finds the next starting point, then traces the curve,
 * returning the number of points on this curve
 * -- in a two level trace, the return value is negative on the
 *    first pass if the curve closed on a hole
 * -- in a single level trace, the return value is negative on the
 *    first pass if the curve is an incomplete open curve
 * -- a return value of 0 indicates no more curves */
static long
curve_tracer (Csite * site, int pass2)
{
    Cdata * data = site->data;
    long imax = site->imax;
    long edge0 = site->edge0;
    long left0 = site->left0;
    long edge00 = site->edge00;
    int two_levels = site->zlevel[1] > site->zlevel[0];
    int level, level0, mark_row;
    long n;

    /* it is possible for a single i-edge to serve as two actual start
     * points, one to the right and one to the left
     * -- for the two level case, this happens on the first pass for
     *    a doubly cut edge, or on a chunking boundary
     * -- for single level case, this is impossible, but a similar
     *    situation involving open curves is handled below
     * a second two start possibility is when the edge0 zone does not
     * exist and both the i-edge and j-edge boundaries are cut
     * yet another possibility is three start points at a junction
     * of chunk cuts
     * -- sigh, several other rare possibilities,
     *    allow for general case, just go in order i1, i0, j1, j0 */
    int two_starts;
    /* printf("curve_tracer pass %d\n", pass2); */
    /* print_Csite(site); */
    if (left0 == 1)
        two_starts = data[edge0] & (I0_START | J1_START | J0_START);
    else if (left0 == -1)
        two_starts = data[edge0] & (J1_START | J0_START);
    else if (left0 == imax)
        two_starts = data[edge0] & J0_START;
    else
        two_starts = 0;

    if (pass2 || edge0 == 0)
    {
        /* zip up to row marked on first pass (or by data_init if edge0==0)
         * -- but not for double start case */
        if (!two_starts)
        {
            /* final start point marked by ALL_DONE marker */
            int first = (edge0 == 0 && !pass2);
            long e0 = edge0;
            if (data[edge0] & ALL_DONE)
                return 0;
            while (!(data[edge0] & START_ROW))
                edge0 += imax;
            if (e0 == edge0)
                edge0++;        /* two starts handled specially */
            if (first)
                /* if this is the very first start point, we want to remove
                 * the START_ROW marker placed by data_init */
                data[edge0 - edge0 % imax] &= ~START_ROW;
        }

    }
    else
    {
        /* first pass ends when all potential start points visited */
        if (site->count <= 0)
        {
            /* place ALL_DONE marker for second pass */
            data[edge00] |= ALL_DONE;
            /* reset initial site for second pass */
            site->edge0 = site->edge00 = site->left0 = 0;
            return 0;
        }
        if (!two_starts)
            edge0++;
    }

    if (two_starts)
    {
        /* trace second curve with this start immediately */
        if (left0 == 1 && (data[edge0] & I0_START))
        {
            left0 = -1;
            level = (data[edge0] & I_BNDY) ? 2 : 0;
        }
        else if ((left0 == 1 || left0 == -1) && (data[edge0] & J1_START))
        {
            left0 = imax;
            level = 2;
        }
        else
        {
            left0 = -imax;
            level = 2;
        }

    }
    else
    {
        /* usual case is to scan for next start marker
         * -- on second pass, this is at most one row of mesh, but first
         *    pass hits nearly every point of the mesh, since it can't
         *    know in advance which potential start marks removed */
        while (!(data[edge0] & ANY_START))
            edge0++;

        if (data[edge0] & I1_START)
            left0 = 1;
        else if (data[edge0] & I0_START)
            left0 = -1;
        else if (data[edge0] & J1_START)
            left0 = imax;
        else                    /*data[edge0]&J0_START */
            left0 = -imax;

        if (data[edge0] & (I1_START | I0_START))
            level = (data[edge0] & I_BNDY) ? 2 : 0;
        else
            level = 2;
    }

    /* this start marker will not be unmarked, but it has been visited */
    if (!pass2)
        site->count--;

    /* if this curve starts on a non-boundary i-edge, we need to
     * determine the level */
    if (!level && two_levels)
        level = left0 > 0 ?
            ((data[edge0 - imax] & Z_VALUE) !=
             0) : ((data[edge0] & Z_VALUE) != 0);

    /* initialize site for this curve */
    site->edge = site->edge0 = edge0;
    site->left = site->left0 = left0;
    site->level0 = level0 = level;      /* for open curve detection only */

    /* single level case just uses zone_crosser */
    if (!two_levels)
        level = 0;

    /* to generate the curve, alternate between zone_crosser and
     * edge_walker until closure or first call to edge_walker in
     * single level case */
    site->n = 0;
    for (;;)
    {
        if (level < 2)
            level = zone_crosser (site, level, pass2);
        else if (level < 3)
            level = edge_walker (site, pass2);
        else
            break;
    }
    n = site->n;

    /* single level case may have ended at a boundary rather than closing
     * -- need to recognize this case here in order to place the
     *    OPEN_END mark for zone_crosser, remove this start marker,
     *    and be sure not to make a START_ROW mark for this case
     * two level case may close with slit_cutter, in which case start
     *    must also be removed and no START_ROW mark made
     * -- change sign of return n to inform caller */
    if (!pass2 && level > 3 && (two_levels || level0 == 0))
    {
        if (!two_levels)
            data[edge0] |= OPEN_END;
        data[edge0] &= ~(left0 > 0 ? I1_START : I0_START);
        mark_row = 0;           /* do not mark START_ROW */
        n = -n;
    }
    else
    {
        if (two_levels)
            mark_row = !two_starts;
        else
            mark_row = 1;
    }

    /* on first pass, must apply START_ROW mark in column above previous
     * start marker
     * -- but skip if we just did second of two start case */
    if (!pass2 && mark_row)
    {
        data[edge0 - (edge0 - edge00) % imax] |= START_ROW;
        site->edge00 = edge0;
    }

    return n;
}

/* ------------------------------------------------------------------------ */

static void
data_init (Csite * site)
{
    Cdata * data = site->data;
    long imax = site->imax;
    long jmax = site->jmax;
    long ijmax = imax * jmax;
    const double *z = site->z;
    double zlev0 = site->zlevel[0];
    double zlev1 = site->zlevel[1];
    int two_levels = zlev1 > zlev0;
    char *reg = site->reg;
    long count = 0;
    int started = 0;
    int ibndy, jbndy, i_was_chunk;

    long ichunk, jchunk, i, j, ij;
    long i_chunk_size = site->i_chunk_size;
    long j_chunk_size = site->j_chunk_size;

    if (!two_levels)
    {
        /* Chunking not used for lines as start points are not correct. */
        i_chunk_size = imax - 1;
        j_chunk_size = jmax - 1;
    }

    /* do everything in a single pass through the data array to
     * minimize cache faulting (z, reg, and data are potentially
     * very large arrays)
     * access to the z and reg arrays is strictly sequential,
     * but we need two rows (+-imax) of the data array at a time */
    if (z[0] > zlev0)
        data[0] = (two_levels && z[0] > zlev1) ? 2 : 1;
    else
        data[0] = 0;
    jchunk = 0;
    for (j = ij = 0; j < jmax; j++)
    {
        ichunk = i_was_chunk = 0;
        for (i = 0; i < imax; i++, ij++)
        {
            /* transfer zonal existence from reg to data array
             * -- get these for next row so we can figure existence of
             *    points and j-edges for this row */
            data[ij + imax + 1] = 0;
            if (reg)
            {
                if (reg[ij + imax + 1] != 0)
                    data[ij + imax + 1] = ZONE_EX;
            }
            else
            {
                if (i < imax - 1 && j < jmax - 1)
                    data[ij + imax + 1] = ZONE_EX;
            }

            /* translate z values to 0, 1, 2 flags */
            if (ij < imax)
                data[ij + 1] = 0;
            if (ij < ijmax - 1 && z[ij + 1] > zlev0)
                data[ij + 1] |= (two_levels && z[ij + 1] > zlev1) ? 2 : 1;

            /* apply edge boundary marks */
            ibndy = i == ichunk
                || (data[ij] & ZONE_EX) != (data[ij + 1] & ZONE_EX);
            jbndy = j == jchunk
                || (data[ij] & ZONE_EX) != (data[ij + imax] & ZONE_EX);
            if (ibndy)
                data[ij] |= I_BNDY;
            if (jbndy)
                data[ij] |= J_BNDY;

            /* apply i-edge start marks
             * -- i-edges are only marked when actually cut
             * -- no mark is necessary if one of the j-edges which share
             *    the lower endpoint is also cut
             * -- no I0 mark necessary unless filled region below some cut,
             *    no I1 mark necessary unless filled region above some cut */
            if (j)
            {
                int v0 = (data[ij] & Z_VALUE);
                int vb = (data[ij - imax] & Z_VALUE);
                if (v0 != vb)
                {               /* i-edge is cut */
                    if (ibndy)
                    {
                        if (data[ij] & ZONE_EX)
                        {
                            data[ij] |= I0_START;
                            count++;
                        }
                        if (data[ij + 1] & ZONE_EX)
                        {
                            data[ij] |= I1_START;
                            count++;
                        }
                    }
                    else
                    {
                        int va = (data[ij - 1] & Z_VALUE);
                        int vc = (data[ij + 1] & Z_VALUE);
                        int vd = (data[ij - imax + 1] & Z_VALUE);
                        if (v0 != 1 && va != v0
                            && (vc != v0 || vd != v0) && (data[ij] & ZONE_EX))
                        {
                            data[ij] |= I0_START;
                            count++;
                        }
                        if (vb != 1 && va == vb
                            && (vc == vb || vd == vb)
                            && (data[ij + 1] & ZONE_EX))
                        {
                            data[ij] |= I1_START;
                            count++;
                        }
                    }
                }
            }

            /* apply j-edge start marks
             * -- j-edges are only marked when they are boundaries
             * -- all cut boundary edges marked
             * -- for two level case, a few uncut edges must be marked
             */
            if (i && jbndy)
            {
                int v0 = (data[ij] & Z_VALUE);
                int vb = (data[ij - 1] & Z_VALUE);
                if (v0 != vb)
                {
                    if (data[ij] & ZONE_EX)
                    {
                        data[ij] |= J0_START;
                        count++;
                    }
                    if (data[ij + imax] & ZONE_EX)
                    {
                        data[ij] |= J1_START;
                        count++;
                    }
                }
                else if (two_levels && v0 == 1)
                {
                    if (data[ij + imax] & ZONE_EX)
                    {
                        if (i_was_chunk || !(data[ij + imax - 1] & ZONE_EX))
                        {
                            /* lower left is a drawn part of boundary */
                            data[ij] |= J1_START;
                            count++;
                        }
                    }
                    else if (data[ij] & ZONE_EX)
                    {
                        if (data[ij + imax - 1] & ZONE_EX)
                        {
                            /* weird case of open hole at lower left */
                            data[ij] |= J0_START;
                            count++;
                        }
                    }
                }
            }

            i_was_chunk = (i == ichunk);
            if (i_was_chunk)
                ichunk += i_chunk_size;
        }

        if (j == jchunk)
            jchunk += j_chunk_size;

        /* place first START_ROW marker */
        if (count && !started)
        {
            data[ij - imax] |= START_ROW;
            started = 1;
        }
    }

    /* place immediate stop mark if nothing found */
    if (!count)
        data[0] |= ALL_DONE;
    else
        for (i = 0; i < ijmax; ++i) site->saddle[i] = 0;

    /* initialize site */
    site->edge0 = site->edge00 = site->edge = 0;
    site->left0 = site->left = 0;
    site->n = 0;
    site->count = count;
}

/* ------------------------------------------------------------------------
   Original (slightly modified) core contour generation routines are above;
   below are new routines for interfacing to mpl.

 ------------------------------------------------------------------------ */

/* Note: index order gets switched in the Python interface;
   python Z[i,j] -> C z[j,i]
   so if the array has shape Mi, Nj in python,
   we have iMax = Nj, jMax = Mi in gcntr.c.
   On the Python side:  Ny, Nx = shape(z),
   so in C, the x-dimension is the first index, the y-dimension
   the second.
*/

/* reg should have the same dimensions as data, which
   has an extra iMax + 1 points relative to Z.
   It differs from mask in being the opposite (True
   where a region exists, versus the mask, which is True
   where a data point is bad), and in that it marks
   zones, not points.  All four zones sharing a bad
   point must be marked as not existing.
*/
static void
mask_zones (long iMax, long jMax, const bool *mask, char *reg)
{
    long i, j, ij;
    long nreg = iMax * jMax + iMax + 1;

    for (ij = iMax+1; ij < iMax*jMax; ij++)
    {
        reg[ij] = 1;
    }

    ij = 0;
    for (j = 0; j < jMax; j++)
    {
        for (i = 0; i < iMax; i++, ij++)
        {
            if (i == 0 || j == 0) reg[ij] = 0;
            if (mask[ij])
            {
                reg[ij] = 0;
                reg[ij + 1] = 0;
                reg[ij + iMax] = 0;
                reg[ij + iMax + 1] = 0;
            }
        }
    }
    for (; ij < nreg; ij++)
    {
        reg[ij] = 0;
    }
}

Csite *
cntr_new()
{
    Csite *site = new Csite;
    if (site == nullptr) return nullptr;
    site->data = nullptr;
    site->reg = nullptr;
    site->saddle = nullptr;
    site->xcp = nullptr;
    site->ycp = nullptr;
    site->kcp = nullptr;
    site->x = nullptr;
    site->y = nullptr;
    site->z = nullptr;
    return site;
}

void
cntr_init(Csite *site, long iMax, long jMax, const double *x, const double *y,
          const double *z, const bool *mask, long i_chunk_size, long j_chunk_size)
{
    long ijmax = iMax * jMax;
    long nreg = iMax * jMax + iMax + 1;

    site->imax = iMax;
    site->jmax = jMax;
    site->data = new Cdata[nreg];
    site->saddle = new Saddle[ijmax];
    if (mask != nullptr)
    {
        site->reg = new char[nreg];
        mask_zones(iMax, jMax, mask, site->reg);
    }
    /* I don't think we need to initialize site->data. */
    site->x = x;
    site->y = y;
    site->z = z;
    site->xcp = nullptr;
    site->ycp = nullptr;
    site->kcp = nullptr;

    /* Store correct chunk sizes for filled contours.  Chunking not used for
       line contours. */
    if (i_chunk_size <= 0 || i_chunk_size > iMax - 1)
        i_chunk_size = iMax - 1;
    site->i_chunk_size = i_chunk_size;

    if (j_chunk_size <= 0 || j_chunk_size > jMax - 1)
        j_chunk_size = jMax - 1;
    site->j_chunk_size = j_chunk_size;
}

void cntr_del(Csite *site)
{
    delete [] site->saddle;
    delete [] site->reg;
    delete [] site->data;
    delete site;
    site = nullptr;
}

static int
reorder(double *xpp, double *ypp, short *kpp, double *xy, unsigned char *c, int npts, int nlevels)
{
    std::vector<int> subp;
    int isp, nsp;
    int iseg, nsegs;
    int isegplus;
    int i;
    int k;
    int started;
    int maxnsegs = npts/2 + 1;
    /* allocate maximum possible size--gross overkill */
    std::vector<int> i0(maxnsegs);
    std::vector<int> i1(maxnsegs);

    /* Find the segments. */
    iseg = 0;
    started = 0;
    for (i=0; i<npts; i++)
    {
        if (started)
        {
            if ((kpp[i] >= kind_slit_up) || (i == npts-1))
            {
                i1[iseg] = i;
                started = 0;
                iseg++;
                if (iseg == maxnsegs)
                {
                    k = -1;
                    return k;
                }
            }
        }
        else if ((kpp[i] < kind_slit_up) && (i < npts-1))
        {
            i0[iseg] = i;
            started = 1;
        }
    }

    nsegs = iseg;

    /* Find the subpaths as sets of connected segments. */

    subp.resize(nsegs, false);
    for (i=0; i<nsegs; i++) subp[i] = -1;

    nsp = 0;
    for (iseg=0; iseg<nsegs; iseg++)
    {
        /* For each segment, if it is not closed, look ahead for
           the next connected segment.
        */
        double xend, yend;
        xend = xpp[i1[iseg]];
        yend = ypp[i1[iseg]];
        if (subp[iseg] >= 0) continue;
        subp[iseg] = nsp;
        nsp++;
        if (iseg == nsegs-1) continue;
        for (isegplus = iseg+1; isegplus < nsegs; isegplus++)
        {
            if (subp[isegplus] >= 0) continue;

            if (xend == xpp[i0[isegplus]] && yend == ypp[i0[isegplus]])
            {
                subp[isegplus] = subp[iseg];
                xend = xpp[i1[isegplus]];
                yend = ypp[i1[isegplus]];
            }
        }
    }

    /* Generate the verts and codes from the subpaths. */
    k = 0;
    for (isp=0; isp<nsp; isp++)
    {
        int first = 1;
        int kstart = k;
        for (iseg=0; iseg<nsegs; iseg++)
        {
            int istart, iend;
            if (subp[iseg] != isp) continue;
            iend = i1[iseg];
            if (first)
            {
                istart = i0[iseg];
            }
            else
            {
                istart = i0[iseg]+1; /* skip duplicate */
            }
            for (i=istart; i<=iend; i++)
            {
                xy[2*k] = xpp[i];
                xy[2*k+1] = ypp[i];
                if (first) c[k] = MOVETO;
                else       c[k] = LINETO;
                first = 0;
                k++;
                if (k > npts)  /* should never happen */
                {
                    k = -1;
                    return k;
                }
            }
        }
        if (nlevels == 2 ||
            (xy[2*kstart] == xy[2*k-2] && xy[2*kstart+1] == xy[2*k-1]))
        {
            c[k-1] = CLOSEPOLY;
        }
    }

    return k;
}

/* Build a list of XY 2-D arrays, shape (N,2), to which a list of path
        code arrays is concatenated.
*/
static py::tuple
build_cntr_list_v2(long *np, double *xp, double *yp, short *kp,
                   int nparts, long ntotal, int nlevels)
{
    int i;
    long k;
    py::ssize_t dims[2];
    py::ssize_t kdims[1];

    py::list all_verts(nparts);
    py::list all_codes(nparts);

    for (i=0, k=0; i < nparts; k+= np[i], i++)
    {
        double *xpp = xp+k;
        double *ypp = yp+k;
        short *kpp = kp+k;
        int n;

        dims[0] = np[i];
        dims[1] = 2;
        kdims[0] = np[i];
        PointArray xyv(dims);
        CodeArray kv(kdims);

        n = reorder(xpp, ypp, kpp, xyv.mutable_data(), kv.mutable_data(), np[i], nlevels);
        if (n == -1)
        {
            throw std::runtime_error("Error reordering vertices");
        }

        dims[0] = n;
        xyv.resize(dims, false);
        all_verts[i] = xyv;

        kdims[0] = n;
        kv.resize(kdims, false);
        all_codes[i] = kv;
    }

    return py::make_tuple(all_verts, all_codes);
}

/* cntr_trace is called once per contour level or level pair.
   If nlevels is 1, a set of contour lines will be returned; if nlevels
   is 2, the set of polygons bounded by the levels will be returned.
   If points is True, the lines will be returned as a list of list
   of points; otherwise, as a list of tuples of vectors.
*/

py::tuple
cntr_trace(Csite *site, double levels[], int nlevels)
{
    int iseg;

    long n;
    long nparts = 0;
    long ntotal = 0;
    long ntotal2 = 0;

    site->zlevel[0] = levels[0];
    site->zlevel[1] = levels[0];
    if (nlevels == 2)
    {
        site->zlevel[1] = levels[1];
    }
    site->n = site->count = 0;
    data_init (site);

    /* make first pass to compute required sizes for second pass */
    for (;;)
    {
        n = curve_tracer (site, 0);

        if (!n)
            break;
        if (n > 0)
        {
            nparts++;
            ntotal += n;
        }
        else
        {
            ntotal -= n;
        }
    }
    std::vector<double> xp0(ntotal);
    std::vector<double> yp0(ntotal);
    std::vector<short> kp0(ntotal);
    std::vector<long> nseg0(nparts);

    /* second pass */
    site->xcp = xp0.data();
    site->ycp = yp0.data();
    site->kcp = kp0.data();
    iseg = 0;
    for (;;iseg++)
    {
        n = curve_tracer (site, 1);
        if (ntotal2 + n > ntotal)
        {
            throw std::runtime_error("curve_tracer: ntotal2, pass 2 exceeds ntotal, pass 1");
        }
        if (n == 0)
            break;
        if (n > 0)
        {
            /* could add array bounds checking */
            nseg0[iseg] = n;
            site->xcp += n;
            site->ycp += n;
            site->kcp += n;
            ntotal2 += n;
        }
        else
        {
            throw std::runtime_error("Negative n from curve_tracer in pass 2");
        }
    }

    site->xcp = nullptr;
    site->ycp = nullptr;
    site->kcp = nullptr;

    return build_cntr_list_v2(
        nseg0.data(), xp0.data(), yp0.data(), kp0.data(), nparts, ntotal, nlevels);
}

} // namespace contourpy