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nr-path.cpp

#define __NR_PATH_C__

/*
 * Pixel buffer rendering library
 *
 * Authors:
 *   Lauris Kaplinski <lauris@kaplinski.com>
 *
 * This code is in public domain
 */

#include "n-art-bpath.h"
#include "nr-matrix.h"
#include "nr-matrix-ops.h"
#include "nr-rect.h"
#include "nr-path.h"

static void nr_curve_bbox (NR::Coord x000, NR::Coord y000, NR::Coord x001, NR::Coord y001, NR::Coord x011, NR::Coord y011, NR::Coord x111, NR::Coord y111, NRRect *bbox);

static void nr_curve_bbox(NR::Point const p000, NR::Point const p001,
                    NR::Point const p011, NR::Point const p111,
                    NRRect *bbox);

NRBPath *nr_path_duplicate_transform(NRBPath *d, NRBPath *s, NRMatrix const *transform)
{
      int i;

      if (!s->path) {
            d->path = NULL;
            return d;
      }

      i = 0;
      while (s->path[i].code != NR_END) i += 1;

      d->path = nr_new (NArtBpath, i + 1);

      i = 0;
      while (s->path[i].code != NR_END) {
            d->path[i].code = s->path[i].code;
            if (s->path[i].code == NR_CURVETO) {
                  d->path[i].x1 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x1, s->path[i].y1);
                  d->path[i].y1 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x1, s->path[i].y1);
                  d->path[i].x2 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x2, s->path[i].y2);
                  d->path[i].y2 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x2, s->path[i].y2);
            }
            d->path[i].x3 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x3, s->path[i].y3);
            d->path[i].y3 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x3, s->path[i].y3);
            i += 1;
      }
      d->path[i].code = NR_END;

      return d;
}

NRBPath *nr_path_duplicate_transform(NRBPath *d, NRBPath *s, NR::Matrix const transform) {
      NRMatrix tr = transform;
      return nr_path_duplicate_transform(d, s, &tr);
}

NArtBpath* nr_artpath_affine(NArtBpath *s, NR::Matrix const &aff) {
      NRBPath bp, abp;
      bp.path = s;
      nr_path_duplicate_transform(&abp, &bp, aff);
      return abp.path;
}

static void
nr_line_wind_distance (NR::Coord x0, NR::Coord y0, NR::Coord x1, NR::Coord y1, NR::Point &pt, int *wind, NR::Coord *best)
{
      NR::Coord Ax, Ay, Bx, By, Dx, Dy, s;
      NR::Coord dist2;

      /* Find distance */
      Ax = x0;
      Ay = y0;
      Bx = x1;
      By = y1;
      Dx = x1 - x0;
      Dy = y1 - y0;
      const NR::Coord Px = pt[NR::X];
      const NR::Coord Py = pt[NR::Y];

      if (best) {
            s = ((Px - Ax) * Dx + (Py - Ay) * Dy) / (Dx * Dx + Dy * Dy);
            if (s <= 0.0) {
                  dist2 = (Px - Ax) * (Px - Ax) + (Py - Ay) * (Py - Ay);
            } else if (s >= 1.0) {
                  dist2 = (Px - Bx) * (Px - Bx) + (Py - By) * (Py - By);
            } else {
                  NR::Coord Qx, Qy;
                  Qx = Ax + s * Dx;
                  Qy = Ay + s * Dy;
                  dist2 = (Px - Qx) * (Px - Qx) + (Py - Qy) * (Py - Qy);
            }

            if (dist2 < (*best * *best)) *best = sqrt (dist2);
      }

      if (wind) {
            /* Find wind */
            if ((Ax >= Px) && (Bx >= Px)) return;
            if ((Ay >= Py) && (By >= Py)) return;
            if ((Ay < Py) && (By < Py)) return;
            if (Ay == By) return;
            /* Ctach upper y bound */
            if (Ay == Py) {
                  if (Ax < Px) *wind -= 1;
                  return;
            } else if (By == Py) {
                  if (Bx < Px) *wind += 1;
                  return;
            } else {
                  NR::Coord Qx;
                  /* Have to calculate intersection */
                  Qx = Ax + Dx * (Py - Ay) / Dy;
                  if (Qx < Px) {
                        *wind += (Dy > 0.0) ? 1 : -1;
                  }
            }
      }
}

static void
nr_curve_bbox_wind_distance (NR::Coord x000, NR::Coord y000,
                       NR::Coord x001, NR::Coord y001,
                       NR::Coord x011, NR::Coord y011,
                       NR::Coord x111, NR::Coord y111,
                       NR::Point &pt,
                       NRRect *bbox, int *wind, NR::Coord *best,
                       NR::Coord tolerance)
{
      NR::Coord x0, y0, x1, y1, len2;
      int needdist, needwind, needline;

      const NR::Coord Px = pt[NR::X];
      const NR::Coord Py = pt[NR::Y];

      needdist = 0;
      needwind = 0;
      needline = 0;

      if (bbox) nr_curve_bbox (x000, y000, x001, y001, x011, y011, x111, y111, bbox);

      x0 = MIN (x000, x001);
      x0 = MIN (x0, x011);
      x0 = MIN (x0, x111);
      y0 = MIN (y000, y001);
      y0 = MIN (y0, y011);
      y0 = MIN (y0, y111);
      x1 = MAX (x000, x001);
      x1 = MAX (x1, x011);
      x1 = MAX (x1, x111);
      y1 = MAX (y000, y001);
      y1 = MAX (y1, y011);
      y1 = MAX (y1, y111);

      if (best) {
            /* Quicly adjust to endpoints */
            len2 = (x000 - Px) * (x000 - Px) + (y000 - Py) * (y000 - Py);
            if (len2 < (*best * *best)) *best = (NR::Coord) sqrt (len2);
            len2 = (x111 - Px) * (x111 - Px) + (y111 - Py) * (y111 - Py);
            if (len2 < (*best * *best)) *best = (NR::Coord) sqrt (len2);

            if (((x0 - Px) < *best) && ((y0 - Py) < *best) && ((Px - x1) < *best) && ((Py - y1) < *best)) {
                  /* Point is inside sloppy bbox */
                  /* Now we have to decide, whether subdivide */
                  /* fixme: (Lauris) */
                  if (((y1 - y0) > 5.0) || ((x1 - x0) > 5.0)) {
                        needdist = 1;
                  } else {
                        needline = 1;
                  }
            }
      }
      if (!needdist && wind) {
            if ((y1 >= Py) && (y0 < Py) && (x0 < Px)) {
                  /* Possible intersection at the left */
                  /* Now we have to decide, whether subdivide */
                  /* fixme: (Lauris) */
                  if (((y1 - y0) > 5.0) || ((x1 - x0) > 5.0)) {
                        needwind = 1;
                  } else {
                        needline = 1;
                  }
            }
      }

      if (needdist || needwind) {
            NR::Coord x00t, x0tt, xttt, x1tt, x11t, x01t;
            NR::Coord y00t, y0tt, yttt, y1tt, y11t, y01t;
            NR::Coord s, t;

            t = 0.5;
            s = 1 - t;

            x00t = s * x000 + t * x001;
            x01t = s * x001 + t * x011;
            x11t = s * x011 + t * x111;
            x0tt = s * x00t + t * x01t;
            x1tt = s * x01t + t * x11t;
            xttt = s * x0tt + t * x1tt;

            y00t = s * y000 + t * y001;
            y01t = s * y001 + t * y011;
            y11t = s * y011 + t * y111;
            y0tt = s * y00t + t * y01t;
            y1tt = s * y01t + t * y11t;
            yttt = s * y0tt + t * y1tt;

            nr_curve_bbox_wind_distance (x000, y000, x00t, y00t, x0tt, y0tt, xttt, yttt, pt, NULL, wind, best, tolerance);
            nr_curve_bbox_wind_distance (xttt, yttt, x1tt, y1tt, x11t, y11t, x111, y111, pt, NULL, wind, best, tolerance);
      } else if (1 || needline) {
            nr_line_wind_distance (x000, y000, x111, y111, pt, wind, best);
      }
}

void
nr_path_matrix_point_bbox_wind_distance (NRBPath *bpath, NR::Matrix const &m, NR::Point &pt,
                                   NRRect *bbox, int *wind, NR::Coord *dist,
                                   NR::Coord tolerance)
{
      NR::Coord x0, y0, x3, y3;
      const NArtBpath *p;

      if (!bpath->path) {
            if (wind) *wind = 0;
            if (dist) *dist = NR_HUGE;
            return;
      }

      x0 = y0 = 0.0;
      x3 = y3 = 0.0;

      for (p = bpath->path; p->code != NR_END; p+= 1) {
            switch (p->code) {
            case NR_MOVETO_OPEN:
            case NR_MOVETO:
                  x0 = m[0] * p->x3 + m[2] * p->y3 + m[4];
                  y0 = m[1] * p->x3 + m[3] * p->y3 + m[5];
                  if (bbox) {
                        bbox->x0 = (NR::Coord) MIN (bbox->x0, x0);
                        bbox->y0 = (NR::Coord) MIN (bbox->y0, y0);
                        bbox->x1 = (NR::Coord) MAX (bbox->x1, x0);
                        bbox->y1 = (NR::Coord) MAX (bbox->y1, y0);
                  }
                  break;
            case NR_LINETO:
                  x3 = m[0] * p->x3 + m[2] * p->y3 + m[4];
                  y3 = m[1] * p->x3 + m[3] * p->y3 + m[5];
                  if (bbox) {
                        bbox->x0 = (NR::Coord) MIN (bbox->x0, x3);
                        bbox->y0 = (NR::Coord) MIN (bbox->y0, y3);
                        bbox->x1 = (NR::Coord) MAX (bbox->x1, x3);
                        bbox->y1 = (NR::Coord) MAX (bbox->y1, y3);
                  }
                  if (dist || wind) {
                        nr_line_wind_distance (x0, y0, x3, y3, pt, wind, dist);
                  }
                  x0 = x3;
                  y0 = y3;
                  break;
            case NR_CURVETO:
                  x3 = m[0] * p->x3 + m[2] * p->y3 + m[4];
                  y3 = m[1] * p->x3 + m[3] * p->y3 + m[5];
                  nr_curve_bbox_wind_distance (x0, y0,
                                         m[0] * p->x1 + m[2] * p->y1 + m[4],
                                         m[1] * p->x1 + m[3] * p->y1 + m[5],
                                         m[0] * p->x2 + m[2] * p->y2 + m[4],
                                         m[1] * p->x2 + m[3] * p->y2 + m[5],
                                         x3, y3,
                                         pt,
                                         bbox, wind, dist, tolerance);
                  x0 = x3;
                  y0 = y3;
                  break;
            default:
                  break;
            }
      }
}

static void
nr_curve_bbox(NR::Point const p000, NR::Point const p001,
            NR::Point const p011, NR::Point const p111,
            NRRect *bbox)
{
      using NR::X;
      using NR::Y;

      nr_curve_bbox(p000[X], p000[Y],
                  p001[X], p001[Y],
                  p011[X], p011[Y],
                  p111[X], p111[Y],
                  bbox);
}

/* Fast bbox calculation */
/* Thanks to Nathan Hurst for suggesting it */

static void
nr_curve_bbox (NR::Coord x000, NR::Coord y000, NR::Coord x001, NR::Coord y001, NR::Coord x011, NR::Coord y011, NR::Coord x111, NR::Coord y111, NRRect *bbox)
{
      NR::Coord a, b, c, D;

      bbox->x0 = (NR::Coord) MIN (bbox->x0, x111);
      bbox->y0 = (NR::Coord) MIN (bbox->y0, y111);
      bbox->x1 = (NR::Coord) MAX (bbox->x1, x111);
      bbox->y1 = (NR::Coord) MAX (bbox->y1, y111);

      /*
       * xttt = s * (s * (s * x000 + t * x001) + t * (s * x001 + t * x011)) + t * (s * (s * x001 + t * x011) + t * (s * x011 + t * x111))
       * xttt = s * (s2 * x000 + s * t * x001 + t * s * x001 + t2 * x011) + t * (s2 * x001 + s * t * x011 + t * s * x011 + t2 * x111)
       * xttt = s * (s2 * x000 + 2 * st * x001 + t2 * x011) + t * (s2 * x001 + 2 * st * x011 + t2 * x111)
       * xttt = s3 * x000 + 2 * s2t * x001 + st2 * x011 + s2t * x001 + 2st2 * x011 + t3 * x111
       * xttt = s3 * x000 + 3s2t * x001 + 3st2 * x011 + t3 * x111
       * xttt = s3 * x000 + (1 - s) 3s2 * x001 + (1 - s) * (1 - s) * 3s * x011 + (1 - s) * (1 - s) * (1 - s) * x111
       * xttt = s3 * x000 + (3s2 - 3s3) * x001 + (3s - 6s2 + 3s3) * x011 + (1 - 2s + s2 - s + 2s2 - s3) * x111
       * xttt = (x000 - 3 * x001 + 3 * x011 -     x111) * s3 +
       *        (       3 * x001 - 6 * x011 + 3 * x111) * s2 +
       *        (                  3 * x011 - 3 * x111) * s  +
       *        (                                 x111)
       * xttt' = (3 * x000 - 9 * x001 +  9 * x011 - 3 * x111) * s2 +
       *         (           6 * x001 - 12 * x011 + 6 * x111) * s  +
       *         (                       3 * x011 - 3 * x111)
       */

      a = 3 * x000 - 9 * x001 + 9 * x011 - 3 * x111;
      b = 6 * x001 - 12 * x011 + 6 * x111;
      c = 3 * x011 - 3 * x111;

      /*
       * s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a;
       */
      if (fabs (a) < NR_EPSILON) {
            /* s = -c / b */
            if (fabs (b) > NR_EPSILON) {
                  double s, t, xttt;
                  s = -c / b;
                  if ((s > 0.0) && (s < 1.0)) {
                        t = 1.0 - s;
                        xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
                        bbox->x0 = (float) MIN (bbox->x0, xttt);
                        bbox->x1 = (float) MAX (bbox->x1, xttt);
                  }
            }
      } else {
            /* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a; */
            D = b * b - 4 * a * c;
            if (D >= 0.0) {
                  NR::Coord d, s, t, xttt;
                  /* Have solution */
                  d = sqrt (D);
                  s = (-b + d) / (2 * a);
                  if ((s > 0.0) && (s < 1.0)) {
                        t = 1.0 - s;
                        xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
                        bbox->x0 = (NR::Coord) MIN (bbox->x0, xttt);
                        bbox->x1 = (NR::Coord) MAX (bbox->x1, xttt);
                  }
                  s = (-b - d) / (2 * a);
                  if ((s > 0.0) && (s < 1.0)) {
                        t = 1.0 - s;
                        xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
                        bbox->x0 = (NR::Coord) MIN (bbox->x0, xttt);
                        bbox->x1 = (NR::Coord) MAX (bbox->x1, xttt);
                  }
            }
      }

      a = 3 * y000 - 9 * y001 + 9 * y011 - 3 * y111;
      b = 6 * y001 - 12 * y011 + 6 * y111;
      c = 3 * y011 - 3 * y111;

      if (fabs (a) < NR_EPSILON) {
            /* s = -c / b */
            if (fabs (b) > NR_EPSILON) {
                  double s, t, yttt;
                  s = -c / b;
                  if ((s > 0.0) && (s < 1.0)) {
                        t = 1.0 - s;
                        yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
                        bbox->y0 = (float) MIN (bbox->y0, yttt);
                        bbox->y1 = (float) MAX (bbox->y1, yttt);
                  }
            }
      } else {
            /* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a; */
            D = b * b - 4 * a * c;
            if (D >= 0.0) {
                  NR::Coord d, s, t, yttt;
                  /* Have solution */
                  d = sqrt (D);
                  s = (-b + d) / (2 * a);
                  if ((s > 0.0) && (s < 1.0)) {
                        t = 1.0 - s;
                        yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
                        bbox->y0 = (NR::Coord) MIN (bbox->y0, yttt);
                        bbox->y1 = (NR::Coord) MAX (bbox->y1, yttt);
                  }
                  s = (-b - d) / (2 * a);
                  if ((s > 0.0) && (s < 1.0)) {
                        t = 1.0 - s;
                        yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
                        bbox->y0 = (NR::Coord) MIN (bbox->y0, yttt);
                        bbox->y1 = (NR::Coord) MAX (bbox->y1, yttt);
                  }
            }
      }
}

void
nr_path_matrix_bbox_union(NRBPath const *bpath, NR::Matrix const &m,
                    NRRect *bbox)
{
    using NR::X;
    using NR::Y;

    if (!bpath->path) {
      return;
    }

    NR::Point prev0(0, 0);
    for (NArtBpath const *p = bpath->path; p->code != NR_END; ++p) {
      switch (p->code) {
          case NR_MOVETO_OPEN:
          case NR_MOVETO: {
            NR::Point const c3(p->x3,
                           p->y3);
            prev0 = c3 * m;
            nr_rect_union_pt(bbox, prev0);
            break;
          }

          case NR_LINETO: {
            NR::Point const c3(p->x3,
                           p->y3);
            NR::Point const endPt( c3 * m );
            nr_rect_union_pt(bbox, endPt);
            prev0 = endPt;
            break;
          }

          case NR_CURVETO: {
            NR::Point const c1(p->x1, p->y1);
            NR::Point const c2(p->x2, p->y2);
            NR::Point const c3(p->x3, p->y3);
            NR::Point const endPt( c3 * m );
            nr_curve_bbox(prev0,
                        c1 * m,
                        c2 * m,
                        endPt,
                        bbox);
            prev0 = endPt;
            break;
          }

          default:
              break;
      }
    }
}


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