xlabels.c

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/*************************************************************************
 * Copyright (c) 2011 AT&T Intellectual Property
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * https://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors: Details at https://graphviz.org
 *************************************************************************/
 
#include <assert.h>
#include <errno.h>
#include <limits.h>
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define XLABEL_INT
#include <label/xlabels.h>
#include <util/alloc.h>
#include <util/exit.h>
 
static int icompare(void *, void *);
 
Dtdisc_t Hdisc = {offsetof(HDict_t, key), sizeof(int), -1, 0, 0, icompare};
 
static int icompare(void *v1, void *v2) {
  const int k1 = *(int *)v1;
  const int k2 = *(int *)v2;
  if (k1 < k2) {
    return -1;
  }
  if (k1 > k2) {
    return 1;
  }
  return 0;
}
 
static XLabels_t *xlnew(object_t *objs, size_t n_objs, xlabel_t *lbls,
                        size_t n_lbls, label_params_t *params) {
  XLabels_t *xlp = gv_alloc(sizeof(XLabels_t));
 
  /* used to load the rtree in hilbert space filling curve order */
  if (!(xlp->hdx = dtopen(&Hdisc, Dtobag))) {
    fprintf(stderr, "out of memory\n");
    graphviz_exit(EXIT_FAILURE);
  }
 
  /* for querying intersection candidates */
  xlp->spdx = RTreeOpen();
  /* save arg pointers in the handle */
  xlp->objs = objs;
  xlp->n_objs = n_objs;
  xlp->lbls = lbls;
  xlp->n_lbls = n_lbls;
  xlp->params = params;
 
  return xlp;
}
 
static void xlfree(XLabels_t *xlp) {
  RTreeClose(xlp->spdx);
  free(xlp);
}
 
/***************************************************************************/
 
/*
 * determine the order(depth) of the hilbert sfc so that we satisfy the
 * precondition of hd_hil_s_from_xy()
 */
static unsigned int xlhorder(XLabels_t *xlp) {
  double maxx = xlp->params->bb.UR.x, maxy = xlp->params->bb.UR.y;
  return (unsigned)floor(log2(round(fmax(maxx, maxy)))) + 1;
}
 
/* from http://www.hackersdelight.org/ site for the book by Henry S Warren */
/*
 * precondition
 * pow(2, n) >= max(p.x, p.y)
 */
/* adapted from lams1.c
Given the "order" n of a Hilbert curve and coordinates x and y, this
program computes the length s of the curve from the origin to (x, y).
The square that the Hilbert curve traverses is of size 2**n by 2**n.
   The method is that given in [Lam&Shap], described by the following
table.  Here i = n-1 for the most significant bit of x and y, and i = 0
for the least significant bits.
 
                    x[i]  y[i] | s[2i+1:2i]   x   y
                    -----------|-------------------
                     0     0   |     00       y   x
                     0     1   |     01       x   y
                     1     0   |     11      ~y  ~x
                     1     1   |     10       x   y
 
To use this table, start at the most significant bits of x and y
(i = n - 1).  If they are both 0 (first row), set the most significant
two bits of s to 00 and interchange x and y.  (Actually, it is only
necessary to interchange the remaining bits of x and y.)  If the most
significant bits of x and y are 10 (third row), output 11, interchange x
and y, and complement x and y.
   Then, consider the next most significant bits of x and y (which may
have been changed by this process), and select the appropriate row of
the table to determine the next two bits of s, and how to change x and
y.  Continue until the least significant bits of x and y have been
processed. */
 
static unsigned int hd_hil_s_from_xy(point p, int n) {
  int x = p.x, y = p.y;
 
  unsigned s = 0; /* Initialize. */
  for (int i = n - 1; i >= 0; i--) {
    int xi = (x >> i) & 1; /* Get bit i of x. */
    int yi = (y >> i) & 1; /* Get bit i of y. */
    s = 4 * s + 2 * (unsigned)xi +
        ((unsigned)xi ^ (unsigned)yi); // Append two bits to s.
 
    x = x ^ y;              /* These 3 lines swap */
    y = y ^ (x & (yi - 1)); /* x and y if yi = 0. */
    x = x ^ y;
    x = x ^ (-xi & (yi - 1)); /* Complement x and y if */
    y = y ^ (-xi & (yi - 1)); /* xi = 1 and yi = 0. */
  }
  return s;
}
 
/* intersection test from
 * from Real-Time Collision Detection 4.2.1 by Christer Ericson
 * intersection area from
 * http://stackoverflow.com/questions/4549544/total-area-of-intersecting-rectangles
 */
static double aabbaabb(Rect_t r, Rect_t s) {
  if (!Overlap(r, s))
    return 0;
 
  /* if we get here we have an intersection */
 
  /* rightmost left edge of the 2 rectangles */
  double iminx = fmax(r.boundary[0], s.boundary[0]);
  /* upmost bottom edge */
  double iminy = fmax(r.boundary[1], s.boundary[1]);
  /* leftmost right edge */
  double imaxx = fmin(r.boundary[2], s.boundary[2]);
  /* downmost top edge */
  double imaxy = fmin(r.boundary[3], s.boundary[3]);
  return (imaxx - iminx) * (imaxy - iminy);
}
 
/*
 * test if objp1, a size 0 object is enclosed in the xlabel
 * associated with objp
 */
static bool lblenclosing(object_t *objp, object_t *objp1) {
  xlabel_t *xlp = objp->lbl;
  ;
 
  assert(objp1->sz.x == 0 && objp1->sz.y == 0);
 
  if (!xlp)
    return false;
 
  return objp1->pos.x > xlp->pos.x && objp1->pos.x < xlp->pos.x + xlp->sz.x &&
         objp1->pos.y > xlp->pos.y && objp1->pos.y < xlp->pos.y + xlp->sz.y;
}
 
/*fill in rectangle from the object */
static Rect_t objp2rect(const object_t *op) {
  Rect_t r = {0};
  r.boundary[0] = round(op->pos.x);
  r.boundary[1] = round(op->pos.y);
  r.boundary[2] = round(op->pos.x + op->sz.x);
  r.boundary[3] = round(op->pos.y + op->sz.y);
  return r;
}
 
/*fill in rectangle from the objects xlabel */
static Rect_t objplp2rect(const object_t *objp) {
  Rect_t r = {0};
  const xlabel_t *lp = objp->lbl;
  r.boundary[0] = round(lp->pos.x);
  r.boundary[1] = round(lp->pos.y);
  r.boundary[2] = round(lp->pos.x + lp->sz.x);
  r.boundary[3] = round(lp->pos.y + lp->sz.y);
  return r;
}
 
/* compute boundary that encloses all possible label boundaries */
static Rect_t objplpmks(object_t *objp) {
  Rect_t rect;
  pointf p = {0};
 
  if (objp->lbl)
    p = objp->lbl->sz;
 
  rect.boundary[0] = floor(objp->pos.x - p.x);
  rect.boundary[1] = floor(objp->pos.y - p.y);
 
  rect.boundary[2] = ceil(objp->pos.x + objp->sz.x + p.x);
  rect.boundary[3] = ceil(objp->pos.y + objp->sz.y + p.y);
 
  return rect;
}
 
/* determine the position clp will occupy in intrsx[] */
static int getintrsxi(object_t *op, object_t *cp) {
  xlabel_t *lp = op->lbl, *clp = cp->lbl;
  assert(lp != clp);
 
  if (lp->set == 0 || clp->set == 0)
    return -1;
  if ((op->pos.x == 0.0 && op->pos.y == 0.0) ||
      (cp->pos.x == 0.0 && cp->pos.y == 0.0))
    return -1;
 
  if (cp->pos.y < op->pos.y) {
    if (cp->pos.x < op->pos.x)
      return XLPXPY;
    if (cp->pos.x > op->pos.x)
      return XLNXPY;
    return XLCXPY;
  }
  if (cp->pos.y > op->pos.y) {
    if (cp->pos.x < op->pos.x)
      return XLPXNY;
    if (cp->pos.x > op->pos.x)
      return XLNXNY;
    return XLCXNY;
  }
  if (cp->pos.x < op->pos.x)
    return XLPXCY;
  if (cp->pos.x > op->pos.x)
    return XLNXCY;
 
  return -1;
}
 
/* record the intersecting objects label */
static double recordointrsx(object_t *op, object_t *cp, Rect_t rp, double a,
                            object_t *intrsx[XLNBR]) {
  int i = getintrsxi(op, cp);
  if (i < 0)
    i = 5;
  if (intrsx[i] != NULL) {
    double sa, maxa = 0.0;
    /* keep maximally overlapping object */
    Rect_t srect = objp2rect(intrsx[i]);
    sa = aabbaabb(rp, srect);
    if (sa > a)
      maxa = sa;
    /*keep maximally overlapping label */
    if (intrsx[i]->lbl) {
      srect = objplp2rect(intrsx[i]);
      sa = aabbaabb(rp, srect);
      if (sa > a)
        maxa = fmax(sa, maxa);
    }
    if (maxa > 0.0)
      return maxa;
    /*replace overlapping label/object pair */
    intrsx[i] = cp;
    return a;
  }
  intrsx[i] = cp;
  return a;
}
 
/* record the intersecting label */
static double recordlintrsx(object_t *op, object_t *cp, Rect_t *rp, double a,
                            object_t *intrsx[XLNBR]) {
  int i = getintrsxi(op, cp);
  if (i < 0)
    i = 5;
  if (intrsx[i] != NULL) {
    double sa, maxa = 0.0;
    /* keep maximally overlapping object */
    Rect_t srect = objp2rect(intrsx[i]);
    sa = aabbaabb(*rp, srect);
    if (sa > a)
      maxa = sa;
    /*keep maximally overlapping label */
    if (intrsx[i]->lbl) {
      srect = objplp2rect(intrsx[i]);
      sa = aabbaabb(*rp, srect);
      if (sa > a)
        maxa = fmax(sa, maxa);
    }
    if (maxa > 0.0)
      return maxa;
    /*replace overlapping label/object pair */
    intrsx[i] = cp;
    return a;
  }
  intrsx[i] = cp;
  return a;
}
 
/* find the objects and labels intersecting lp */
static BestPos_t xlintersections(XLabels_t *xlp, object_t *objp,
                                 object_t *intrsx[XLNBR]) {
  assert(objp->lbl);
 
  BestPos_t bp = {.pos = objp->lbl->pos};
 
  for (size_t i = 0; i < xlp->n_objs; i++) {
    if (objp == &xlp->objs[i])
      continue;
    if (xlp->objs[i].sz.x > 0 && xlp->objs[i].sz.y > 0)
      continue;
    if (lblenclosing(objp, &xlp->objs[i])) {
      bp.n++;
    }
  }
 
  Rect_t rect = objplp2rect(objp);
 
  LeafList_t *llp = RTreeSearch(xlp->spdx, xlp->spdx->root, rect);
  if (!llp)
    return bp;
 
  for (LeafList_t *ilp = llp; ilp; ilp = ilp->next) {
    double a;
    object_t *cp = ilp->leaf->data;
 
    if (cp == objp)
      continue;
 
    /*label-object intersect */
    Rect_t srect = objp2rect(cp);
    a = aabbaabb(rect, srect);
    if (a > 0.0) {
      const double ra = recordointrsx(objp, cp, rect, a, intrsx);
      bp.n++;
      bp.area += ra;
    }
    /*label-label intersect */
    if (!cp->lbl || !cp->lbl->set)
      continue;
    srect = objplp2rect(cp);
    a = aabbaabb(rect, srect);
    if (a > 0.0) {
      const double ra = recordlintrsx(objp, cp, &rect, a, intrsx);
      bp.n++;
      bp.area += ra;
    }
  }
  RTreeLeafListFree(llp);
  return bp;
}
 
/*
 * xladjust - find a label position
 * the individual tests at the top are intended to place a preference order
 * on the position
 */
static BestPos_t xladjust(XLabels_t *xlp, object_t *objp) {
  xlabel_t *lp = objp->lbl;
  double xincr = (2 * lp->sz.x + objp->sz.x) / XLXDENOM;
  double yincr = (2 * lp->sz.y + objp->sz.y) / XLYDENOM;
  object_t *intrsx[XLNBR] = {0};
 
  assert(objp->lbl);
 
  /*x left */
  lp->pos.x = objp->pos.x - lp->sz.x;
  /*top */
  lp->pos.y = objp->pos.y + objp->sz.y;
  BestPos_t bp = xlintersections(xlp, objp, intrsx);
  if (bp.n == 0)
    return bp;
  /*mid */
  lp->pos.y = objp->pos.y;
  BestPos_t nbp = xlintersections(xlp, objp, intrsx);
  if (nbp.n == 0)
    return nbp;
  if (nbp.area < bp.area)
    bp = nbp;
  /*bottom */
  lp->pos.y = objp->pos.y - lp->sz.y;
  nbp = xlintersections(xlp, objp, intrsx);
  if (nbp.n == 0)
    return nbp;
  if (nbp.area < bp.area)
    bp = nbp;
 
  /*x mid */
  lp->pos.x = objp->pos.x;
  /*top */
  lp->pos.y = objp->pos.y + objp->sz.y;
  nbp = xlintersections(xlp, objp, intrsx);
  if (nbp.n == 0)
    return nbp;
  if (nbp.area < bp.area)
    bp = nbp;
  /*bottom */
  lp->pos.y = objp->pos.y - lp->sz.y;
  nbp = xlintersections(xlp, objp, intrsx);
  if (nbp.n == 0)
    return nbp;
  if (nbp.area < bp.area)
    bp = nbp;
 
  /*x right */
  lp->pos.x = objp->pos.x + objp->sz.x;
  /*top */
  lp->pos.y = objp->pos.y + objp->sz.y;
  nbp = xlintersections(xlp, objp, intrsx);
  if (nbp.n == 0)
    return nbp;
  if (nbp.area < bp.area)
    bp = nbp;
  /*mid */
  lp->pos.y = objp->pos.y;
  nbp = xlintersections(xlp, objp, intrsx);
  if (nbp.n == 0)
    return nbp;
  if (nbp.area < bp.area)
    bp = nbp;
  /*bottom */
  lp->pos.y = objp->pos.y - lp->sz.y;
  nbp = xlintersections(xlp, objp, intrsx);
  if (nbp.n == 0)
    return nbp;
  if (nbp.area < bp.area)
    bp = nbp;
 
  /*sliding from top left */
  if (intrsx[XLPXNY] || intrsx[XLCXNY] || intrsx[XLNXNY] || intrsx[XLPXCY] ||
      intrsx[XLPXPY]) {                       /* have to move */
    if (!intrsx[XLCXNY] && !intrsx[XLNXNY]) { /* some room right? */
      /* slide along upper edge */
      for (lp->pos.x = objp->pos.x - lp->sz.x,
          lp->pos.y = objp->pos.y + objp->sz.y;
           lp->pos.x <= (objp->pos.x + objp->sz.x); lp->pos.x += xincr) {
        nbp = xlintersections(xlp, objp, intrsx);
        if (nbp.n == 0)
          return nbp;
        if (nbp.area < bp.area)
          bp = nbp;
      }
    }
    if (!intrsx[XLPXCY] && !intrsx[XLPXPY]) { /* some room down? */
      /* slide down left edge */
      for (lp->pos.x = objp->pos.x - lp->sz.x,
          lp->pos.y = objp->pos.y + objp->sz.y;
           lp->pos.y >= (objp->pos.y - lp->sz.y); lp->pos.y -= yincr) {
        nbp = xlintersections(xlp, objp, intrsx);
        if (nbp.n == 0)
          return nbp;
        if (nbp.area < bp.area)
          bp = nbp;
      }
    }
  }
 
  /*sliding from bottom right */
  lp->pos.x = objp->pos.x + objp->sz.x;
  lp->pos.y = objp->pos.y - lp->sz.y;
  if (intrsx[XLNXPY] || intrsx[XLCXPY] || intrsx[XLPXPY] || intrsx[XLNXCY] ||
      intrsx[XLNXNY]) {                       /* have to move */
    if (!intrsx[XLCXPY] && !intrsx[XLPXPY]) { /* some room left? */
      /* slide along lower edge */
      for (lp->pos.x = objp->pos.x + objp->sz.x,
          lp->pos.y = objp->pos.y - lp->sz.y;
           lp->pos.x >= (objp->pos.x - lp->sz.x); lp->pos.x -= xincr) {
        nbp = xlintersections(xlp, objp, intrsx);
        if (nbp.n == 0)
          return nbp;
        if (nbp.area < bp.area)
          bp = nbp;
      }
    }
    if (!intrsx[XLNXCY] && !intrsx[XLNXNY]) { /* some room up? */
      /* slide up right edge */
      for (lp->pos.x = objp->pos.x + objp->sz.x,
          lp->pos.y = objp->pos.y - lp->sz.y;
           lp->pos.y <= (objp->pos.y + objp->sz.y); lp->pos.y += yincr) {
        nbp = xlintersections(xlp, objp, intrsx);
        if (nbp.n == 0)
          return nbp;
        if (nbp.area < bp.area)
          bp = nbp;
      }
    }
  }
  return bp;
}
 
/* load the hilbert sfc keyed tree */
static int xlhdxload(XLabels_t *xlp) {
  int order = xlhorder(xlp);
 
  for (size_t i = 0; i < xlp->n_objs; i++) {
    HDict_t *hp = gv_alloc(sizeof(HDict_t));
 
    hp->d.data = &xlp->objs[i];
    hp->d.rect = objplpmks(&xlp->objs[i]);
    /* center of the labeling area */
    const double x = hp->d.rect.boundary[0] +
                     (hp->d.rect.boundary[2] - hp->d.rect.boundary[0]) / 2;
    const double y = hp->d.rect.boundary[1] +
                     (hp->d.rect.boundary[3] - hp->d.rect.boundary[1]) / 2;
    assert(x >= INT_MIN && x <= INT_MAX);
    assert(y >= INT_MIN && y <= INT_MAX);
    const point pi = {.x = (int)x, .y = (int)y};
 
    hp->key = hd_hil_s_from_xy(pi, order);
 
    if (!dtinsert(xlp->hdx, hp))
      return -1;
  }
  return 0;
}
 
static void xlhdxunload(XLabels_t *xlp) {
  int size = dtsize(xlp->hdx), freed = 0;
  while (dtsize(xlp->hdx)) {
    void *vp = dtfinger(xlp->hdx);
    assert(vp);
    if (vp) {
      dtdetach(xlp->hdx, vp);
      free(vp);
      freed++;
    }
  }
  assert(size == freed);
  (void)size;
}
 
static void xlspdxload(XLabels_t *xlp) {
  for (HDict_t *op = dtfirst(xlp->hdx); op; op = dtnext(xlp->hdx, op)) {
    //          tree       rectangle    data        node
    RTreeInsert(xlp->spdx, op->d.rect, op->d.data, &xlp->spdx->root);
  }
}
 
static int xlinitialize(XLabels_t *xlp) {
  int r = 0;
  if ((r = xlhdxload(xlp)) < 0)
    return r;
  xlspdxload(xlp);
  xlhdxunload(xlp);
  return dtclose(xlp->hdx);
}
 
int placeLabels(object_t *objs, size_t n_objs, xlabel_t *lbls, size_t n_lbls,
                label_params_t *params) {
  int r;
  XLabels_t *xlp = xlnew(objs, n_objs, lbls, n_lbls, params);
  if ((r = xlinitialize(xlp)) < 0)
    return r;
 
  /* Place xlabel_t* lp near lp->obj so that the rectangle whose lower-left
   * corner is lp->pos, and size is lp->sz does not intersect any object
   * in objs (by convention, an object consisting of a single point
   * intersects nothing) nor any other label, if possible. On input,
   * lp->set is 0.
   *
   * On output, any label with a position should have this stored in
   * lp->pos and have lp->set non-zero.
   *
   * If params->force is true, all labels must be positioned, even if
   * overlaps are necessary.
   *
   * Return 0 if all labels could be placed without overlap;
   * non-zero otherwise.
   */
  r = 0;
  for (size_t i = 0; i < n_objs; i++) {
    if (objs[i].lbl == 0)
      continue;
    const BestPos_t bp = xladjust(xlp, &objs[i]);
    if (bp.n == 0) {
      objs[i].lbl->set = 1;
    } else if (bp.area == 0) {
      objs[i].lbl->pos = bp.pos;
      objs[i].lbl->set = 1;
    } else if (params->force) {
      objs[i].lbl->pos = bp.pos;
      objs[i].lbl->set = 1;
    } else {
      r = 1;
    }
  }
  xlfree(xlp);
  return r;
}