src/preproc/grn/hgraph.cc

   1 /* Last non-groff version: hgraph.c  1.14 (Berkeley) 84/11/27
   2  *
   3  * This file contains the graphics routines for converting gremlin pictures
   4  * to troff input.
   5  */
   6
   7 #include "lib.h"
   8
   9 #include "gprint.h"
  10
  11 #ifdef NEED_DECLARATION_HYPOT
  12 extern "C" {
  13   double hypot(double, double);
  14 }
  15 #endif /* NEED_DECLARATION_HYPOT */
  16
  17 #define MAXVECT 40
  18 #define MAXPOINTS       200
  19 #define LINELENGTH      1
  20 #define PointsPerInterval 64
  21 #define pi              3.14159265358979324
  22 #define twopi           (2.0 * pi)
  23 #define len(a, b)       hypot((double)(b.x-a.x), (double)(b.y-a.y))
  24
  25
  26 extern int dotshifter;          /* for the length of dotted curves */
  27
  28 extern int style[];             /* line and character styles */
  29 extern double thick[];
  30 extern char *tfont[];
  31 extern int tsize[];
  32 extern int stipple_index[];     /* stipple font index for stipples 0 - 16 */
  33 extern char *stipple;           /* stipple type (cf or ug) */
  34
  35
  36 extern double troffscale;       /* imports from main.c */
  37 extern double linethickness;
  38 extern int linmod;
  39 extern int lastx;
  40 extern int lasty;
  41 extern int lastyline;
  42 extern int ytop;
  43 extern int ybottom;
  44 extern int xleft;
  45 extern int xright;
  46 extern enum {
  47   OUTLINE, FILL, BOTH
  48 } polyfill;
  49
  50 extern double adj1;
  51 extern double adj2;
  52 extern double adj3;
  53 extern double adj4;
  54 extern int res;
  55
  56 void HGSetFont(int font, int size);
  57 void HGPutText(int justify, POINT pnt, register char *string);
  58 void HGSetBrush(int mode);
  59 void tmove2(int px, int py);
  60 void doarc(POINT cp, POINT sp, int angle);
  61 void tmove(POINT * ptr);
  62 void cr();
  63 void drawwig(POINT * ptr, int type);
  64 void HGtline(int x1, int y1);
  65 void dx(double x);
  66 void dy(double y);
  67 void HGArc(register int cx, register int cy, int px, int py, int angle);
  68 void picurve(register int *x, register int *y, int npts);
  69 void HGCurve(int *x, int *y, int numpoints);
  70 void Paramaterize(int x[], int y[], float h[], int n);
  71 void PeriodicSpline(float h[], int z[],
  72                     float dz[], float d2z[], float d3z[],
  73                     int npoints);
  74 void NaturalEndSpline(float h[], int z[],
  75                       float dz[], float d2z[], float d3z[],
  76                       int npoints);
  77
  78
  79
  80 /*----------------------------------------------------------------------------*
  81  | Routine:     HGPrintElt (element_pointer, baseline)
  82  |
  83  | Results:     Examines a picture element and calls the appropriate
  84  |              routine(s) to print them according to their type.  After the
  85  |              picture is drawn, current position is (lastx, lasty).
  86  *----------------------------------------------------------------------------*/
  87
  88 void
  89 HGPrintElt(ELT *element,
  90            int baseline)
  91 {
  92   register POINT *p1;
  93   register POINT *p2;
  94   register int length;
  95   register int graylevel;
  96
  97   if (!DBNullelt(element) && !Nullpoint((p1 = element->ptlist))) {
  98     /* p1 always has first point */
  99     if (TEXT(element->type)) {
 100       HGSetFont(element->brushf, element->size);
 101       switch (element->size) {
 102       case 1:
 103         p1->y += adj1;
 104         break;
 105       case 2:
 106         p1->y += adj2;
 107         break;
 108       case 3:
 109         p1->y += adj3;
 110         break;
 111       case 4:
 112         p1->y += adj4;
 113         break;
 114       default:
 115         break;
 116       }
 117       HGPutText(element->type, *p1, element->textpt);
 118     } else {
 119       if (element->brushf)              /* if there is a brush, the */
 120         HGSetBrush(element->brushf);    /* graphics need it set     */
 121
 122       switch (element->type) {
 123
 124       case ARC:
 125         p2 = PTNextPoint(p1);
 126         tmove(p2);
 127         doarc(*p1, *p2, element->size);
 128         cr();
 129         break;
 130
 131       case CURVE:
 132         length = 0;     /* keep track of line length */
 133         drawwig(p1, CURVE);
 134         cr();
 135         break;
 136
 137       case BSPLINE:
 138         length = 0;     /* keep track of line length */
 139         drawwig(p1, BSPLINE);
 140         cr();
 141         break;
 142
 143       case VECTOR:
 144         length = 0;             /* keep track of line length so */
 145         tmove(p1);              /* single lines don't get long  */
 146         while (!Nullpoint((p1 = PTNextPoint(p1)))) {
 147           HGtline((int) (p1->x * troffscale),
 148                   (int) (p1->y * troffscale));
 149           if (length++ > LINELENGTH) {
 150             length = 0;
 151             printf("\\\n");
 152           }
 153         }                       /* end while */
 154         cr();
 155         break;
 156
 157       case POLYGON:
 158         {
 159           /* brushf = style of outline; size = color of fill:
 160            * on first pass (polyfill=FILL), do the interior using 'P'
 161            *    unless size=0
 162            * on second pass (polyfill=OUTLINE), do the outline using a series
 163            *    of vectors. It might make more sense to use \D'p ...',
 164            *    but there is no uniform way to specify a 'fill character'
 165            *    that prints as 'no fill' on all output devices (and
 166            *    stipple fonts).
 167            * If polyfill=BOTH, just use the \D'p ...' command.
 168            */
 169           float firstx = p1->x;
 170           float firsty = p1->y;
 171
 172           length = 0;           /* keep track of line length so */
 173                                 /* single lines don't get long  */
 174
 175           if (polyfill == FILL || polyfill == BOTH) {
 176             /* do the interior */
 177             char command = (polyfill == BOTH && element->brushf) ? 'p' : 'P';
 178
 179             /* include outline, if there is one and */
 180             /* the -p flag was set                  */
 181
 182             /* switch based on what gremlin gives */
 183             switch (element->size) {
 184             case 1:
 185               graylevel = 1;
 186               break;
 187             case 3:
 188               graylevel = 2;
 189               break;
 190             case 12:
 191               graylevel = 3;
 192               break;
 193             case 14:
 194               graylevel = 4;
 195               break;
 196             case 16:
 197               graylevel = 5;
 198               break;
 199             case 19:
 200               graylevel = 6;
 201               break;
 202             case 21:
 203               graylevel = 7;
 204               break;
 205             case 23:
 206               graylevel = 8;
 207               break;
 208             default:            /* who's giving something else? */
 209               graylevel = NSTIPPLES;
 210               break;
 211             }
 212             /* int graylevel = element->size; */
 213
 214             if (graylevel < 0)
 215               break;
 216             if (graylevel > NSTIPPLES)
 217               graylevel = NSTIPPLES;
 218             printf("\\D'f %du'", stipple_index[graylevel])
 219             cr();
 220             tmove(p1);
 221             printf("\\D'%c", command);
 222
 223             while (!Nullpoint((PTNextPoint(p1)))) {
 224               p1 = PTNextPoint(p1);
 225               dx((double) p1->x);
 226               dy((double) p1->y);
 227               if (length++ > LINELENGTH) {
 228                 length = 0;
 229                 printf("\\\n");
 230               }
 231             } /* end while */
 232
 233             /* close polygon if not done so by user */
 234             if ((firstx != p1->x) || (firsty != p1->y)) {
 235               dx((double) firstx);
 236               dy((double) firsty);
 237             }
 238             putchar('\'');
 239             cr();
 240             break;
 241           }
 242           /* else polyfill == OUTLINE; only draw the outline */
 243           if (!(element->brushf))
 244             break;
 245           length = 0;           /* keep track of line length */
 246           tmove(p1);
 247
 248           while (!Nullpoint((PTNextPoint(p1)))) {
 249             p1 = PTNextPoint(p1);
 250             HGtline((int) (p1->x * troffscale),
 251                     (int) (p1->y * troffscale));
 252             if (length++ > LINELENGTH) {
 253               length = 0;
 254               printf("\\\n");
 255             }
 256           }                     /* end while */
 257
 258           /* close polygon if not done so by user */
 259           if ((firstx != p1->x) || (firsty != p1->y)) {
 260             HGtline((int) (firstx * troffscale),
 261                     (int) (firsty * troffscale));
 262           }
 263           cr();
 264           break;
 265         }                       /* end case POLYGON */
 266       }                         /* end switch */
 267     }                           /* end else Text */
 268   }                             /* end if */
 269 }                               /* end PrintElt */
 270
 271
 272 /*----------------------------------------------------------------------------*
 273  | Routine:     HGPutText (justification, position_point, string)
 274  |
 275  | Results:     Given the justification, a point to position with, and a
 276  |              string to put, HGPutText first sends the string into a
 277  |              diversion, moves to the positioning point, then outputs
 278  |              local vertical and horizontal motions as needed to justify
 279  |              the text.  After all motions are done, the diversion is
 280  |              printed out.
 281  *----------------------------------------------------------------------------*/
 282
 283 void
 284 HGPutText(int justify,
 285           POINT pnt,
 286           register char *string)
 287 {
 288   int savelasty = lasty;        /* vertical motion for text is to be */
 289                                 /* ignored.  Save current y here     */
 290
 291   printf(".nr g8 \\n(.d\n");    /* save current vertical position. */
 292   printf(".ds g9 \"");          /* define string containing the text. */
 293   while (*string) {             /* put out the string */
 294     if (*string == '\\' &&
 295         *(string + 1) == '\\') {        /* one character at a */
 296       printf("\\\\\\");                 /* time replacing //  */
 297       string++;                         /* by //// to prevent */
 298     }                                   /* interpretation at  */
 299     printf("%c", *(string++));          /* printout time      */
 300   }
 301   printf("\n");
 302
 303   tmove(&pnt);                  /* move to positioning point */
 304
 305   switch (justify) {
 306     /* local vertical motions                                            */
 307     /* (the numbers here are used to be somewhat compatible with gprint) */
 308   case CENTLEFT:
 309   case CENTCENT:
 310   case CENTRIGHT:
 311     printf("\\v'0.85n'");       /* down half */
 312     break;
 313
 314   case TOPLEFT:
 315   case TOPCENT:
 316   case TOPRIGHT:
 317     printf("\\v'1.7n'");        /* down whole */
 318   }
 319
 320   switch (justify) {
 321     /* local horizontal motions */
 322   case BOTCENT:
 323   case CENTCENT:
 324   case TOPCENT:
 325     printf("\\h'-\\w'\\*(g9'u/2u'");    /* back half */
 326     break;
 327
 328   case BOTRIGHT:
 329   case CENTRIGHT:
 330   case TOPRIGHT:
 331     printf("\\h'-\\w'\\*(g9'u'");       /* back whole */
 332   }
 333
 334   printf("\\&\\*(g9\n");        /* now print the text. */
 335   printf(".sp |\\n(g8u\n");     /* restore vertical position */
 336   lasty = savelasty;            /* vertical position restored to where it */
 337   lastx = xleft;                /* was before text, also horizontal is at */
 338                                 /* left                                   */
 339 }                               /* end HGPutText */
 340
 341
 342 /*----------------------------------------------------------------------------*
 343  | Routine:     doarc (center_point, start_point, angle)
 344  |
 345  | Results:     Produces either drawarc command or a drawcircle command
 346  |              depending on the angle needed to draw through.
 347  *----------------------------------------------------------------------------*/
 348
 349 void
 350 doarc(POINT cp,
 351       POINT sp,
 352       int angle)
 353 {
 354   if (angle)                    /* arc with angle */
 355     HGArc((int) (cp.x * troffscale), (int) (cp.y * troffscale),
 356           (int) (sp.x * troffscale), (int) (sp.y * troffscale), angle);
 357   else                          /* a full circle (angle == 0) */
 358     HGArc((int) (cp.x * troffscale), (int) (cp.y * troffscale),
 359           (int) (sp.x * troffscale), (int) (sp.y * troffscale), 0);
 360 }
 361
 362
 363 /*----------------------------------------------------------------------------*
 364  | Routine:     HGSetFont (font_number, Point_size)
 365  |
 366  | Results:     ALWAYS outputs a .ft and .ps directive to troff.  This is
 367  |              done because someone may change stuff inside a text string.
 368  |              Changes thickness back to default thickness.  Default
 369  |              thickness depends on font and pointsize.
 370  *----------------------------------------------------------------------------*/
 371
 372 void
 373 HGSetFont(int font,
 374           int size)
 375 {
 376   printf(".ft %s\n"
 377          ".ps %d\n", tfont[font - 1], tsize[size - 1]);
 378   linethickness = DEFTHICK;
 379 }
 380
 381
 382 /*----------------------------------------------------------------------------*
 383  | Routine:     HGSetBrush (line_mode)
 384  |
 385  | Results:     Generates the troff commands to set up the line width and
 386  |              style of subsequent lines.  Does nothing if no change is
 387  |              needed.
 388  |
 389  | Side Efct:   Sets `linmode' and `linethicknes'.
 390  *----------------------------------------------------------------------------*/
 391
 392 void
 393 HGSetBrush(int mode)
 394 {
 395   register int printed = 0;
 396
 397   if (linmod != style[--mode]) {
 398     /* Groff doesn't understand \Ds, so we take it out */
 399     /* printf ("\\D's %du'", linmod = style[mode]); */
 400     linmod = style[mode];
 401     printed = 1;
 402   }
 403   if (linethickness != thick[mode]) {
 404     linethickness = thick[mode];
 405     printf("\\h'-%.2fp'\\D't %.2fp'", linethickness, linethickness);
 406     printed = 1;
 407   }
 408   if (printed)
 409     cr();
 410 }
 411
 412
 413 /*----------------------------------------------------------------------------*
 414  | Routine:     dx (x_destination)
 415  |
 416  | Results:     Scales and outputs a number for delta x (with a leading
 417  |              space) given `lastx' and x_destination.
 418  |
 419  | Side Efct:   Resets `lastx' to x_destination.
 420  *----------------------------------------------------------------------------*/
 421
 422 void
 423 dx(double x)
 424 {
 425   register int ix = (int) (x * troffscale);
 426
 427   printf(" %du", ix - lastx);
 428   lastx = ix;
 429 }
 430
 431
 432 /*----------------------------------------------------------------------------*
 433  | Routine:     dy (y_destination)
 434  |
 435  | Results:     Scales and outputs a number for delta y (with a leading
 436  |              space) given `lastyline' and y_destination.
 437  |
 438  | Side Efct:   Resets `lastyline' to y_destination.  Since `line' vertical
 439  |              motions don't affect `page' ones, `lasty' isn't updated.
 440  *----------------------------------------------------------------------------*/
 441
 442 void
 443 dy(double y)
 444 {
 445   register int iy = (int) (y * troffscale);
 446
 447   printf(" %du", iy - lastyline);
 448   lastyline = iy;
 449 }
 450
 451
 452 /*----------------------------------------------------------------------------*
 453  | Routine:     tmove2 (px, py)
 454  |
 455  | Results:     Produces horizontal and vertical moves for troff given the
 456  |              pair of points to move to and knowing the current position.
 457  |              Also puts out a horizontal move to start the line.  This is
 458  |              a variation without the .sp command.
 459  *----------------------------------------------------------------------------*/
 460
 461 void
 462 tmove2(int px,
 463        int py)
 464 {
 465   register int dx;
 466   register int dy;
 467
 468   if ((dy = py - lasty)) {
 469     printf("\\v'%du'", dy);
 470   }
 471   lastyline = lasty = py;       /* lasty is always set to current */
 472   if ((dx = px - lastx)) {
 473     printf("\\h'%du'", dx);
 474     lastx = px;
 475   }
 476 }
 477
 478
 479 /*----------------------------------------------------------------------------*
 480  | Routine:     tmove (point_pointer)
 481  |
 482  | Results:     Produces horizontal and vertical moves for troff given the
 483  |              pointer of a point to move to and knowing the current
 484  |              position.  Also puts out a horizontal move to start the
 485  |              line.
 486  *----------------------------------------------------------------------------*/
 487
 488 void
 489 tmove(POINT * ptr)
 490 {
 491   register int ix = (int) (ptr->x * troffscale);
 492   register int iy = (int) (ptr->y * troffscale);
 493   register int dx;
 494   register int dy;
 495
 496   if ((dy = iy - lasty)) {
 497     printf(".sp %du\n", dy);
 498   }
 499   lastyline = lasty = iy;       /* lasty is always set to current */
 500   if ((dx = ix - lastx)) {
 501     printf("\\h'%du'", dx);
 502     lastx = ix;
 503   }
 504 }
 505
 506
 507 /*----------------------------------------------------------------------------*
 508  | Routine:     cr ( )
 509  |
 510  | Results:     Ends off an input line.  `.sp -1' is also added to counteract
 511  |              the vertical move done at the end of text lines.
 512  |
 513  | Side Efct:   Sets `lastx' to `xleft' for troff's return to left margin.
 514  *----------------------------------------------------------------------------*/
 515
 516 void
 517 cr()
 518 {
 519   printf("\n.sp -1\n");
 520   lastx = xleft;
 521 }
 522
 523
 524 /*----------------------------------------------------------------------------*
 525  | Routine:     line ( )
 526  |
 527  | Results:     Draws a single solid line to (x,y).
 528  *----------------------------------------------------------------------------*/
 529
 530 void
 531 line(int px,
 532      int py)
 533 {
 534   printf("\\D'l");
 535   printf(" %du", px - lastx);
 536   printf(" %du'", py - lastyline);
 537   lastx = px;
 538   lastyline = lasty = py;
 539 }
 540
 541
 542 /*----------------------------------------------------------------------------
 543  | Routine:     drawwig (ptr, type)
 544  |
 545  | Results:     The point sequence found in the structure pointed by ptr is
 546  |              placed in integer arrays for further manipulation by the
 547  |              existing routing.  With the corresponding type parameter,
 548  |              either picurve or HGCurve are called.
 549  *----------------------------------------------------------------------------*/
 550
 551 void
 552 drawwig(POINT * ptr,
 553         int type)
 554 {
 555   register int npts;                    /* point list index */
 556   int x[MAXPOINTS], y[MAXPOINTS];       /* point list */
 557
 558   for (npts = 1; !Nullpoint(ptr); ptr = PTNextPoint(ptr), npts++) {
 559     x[npts] = (int) (ptr->x * troffscale);
 560     y[npts] = (int) (ptr->y * troffscale);
 561   }
 562   if (--npts) {
 563     if (type == CURVE) /* Use the 2 different types of curves */
 564       HGCurve(&x[0], &y[0], npts);
 565     else
 566       picurve(&x[0], &y[0], npts);
 567   }
 568 }
 569
 570
 571 /*----------------------------------------------------------------------------
 572  | Routine:     HGArc (xcenter, ycenter, xstart, ystart, angle)
 573  |
 574  | Results:     This routine plots an arc centered about (cx, cy) counter
 575  |              clockwise starting from the point (px, py) through `angle'
 576  |              degrees.  If angle is 0, a full circle is drawn.  It does so
 577  |              by creating a draw-path around the arc whose density of
 578  |              points depends on the size of the arc.
 579  *----------------------------------------------------------------------------*/
 580
 581 void
 582 HGArc(register int cx,
 583       register int cy,
 584       int px,
 585       int py,
 586       int angle)
 587 {
 588   double xs, ys, resolution, fullcircle;
 589   int m;
 590   register int mask;
 591   register int extent;
 592   register int nx;
 593   register int ny;
 594   register int length;
 595   register double epsilon;
 596
 597   xs = px - cx;
 598   ys = py - cy;
 599
 600   length = 0;
 601
 602   resolution = (1.0 + hypot(xs, ys) / res) * PointsPerInterval;
 603   /* mask = (1 << (int) log10(resolution + 1.0)) - 1; */
 604   (void) frexp(resolution, &m);         /* A bit more elegant than log10 */
 605   for (mask = 1; mask < m; mask = mask << 1);
 606   mask -= 1;
 607
 608   epsilon = 1.0 / resolution;
 609   fullcircle = (2.0 * pi) * resolution;
 610   if (angle == 0)
 611     extent = (int) fullcircle;
 612   else
 613     extent = (int) (angle * fullcircle / 360.0);
 614
 615   HGtline(px, py);
 616   while (--extent >= 0) {
 617     xs += epsilon * ys;
 618     nx = cx + (int) (xs + 0.5);
 619     ys -= epsilon * xs;
 620     ny = cy + (int) (ys + 0.5);
 621     if (!(extent & mask)) {
 622       HGtline(nx, ny);          /* put out a point on circle */
 623       if (length++ > LINELENGTH) {
 624         length = 0;
 625         printf("\\\n");
 626       }
 627     }
 628   }                             /* end for */
 629 }                               /* end HGArc */
 630
 631
 632 /*----------------------------------------------------------------------------
 633  | Routine:     picurve (xpoints, ypoints, num_of_points)
 634  |
 635  | Results:     Draws a curve delimited by (not through) the line segments
 636  |              traced by (xpoints, ypoints) point list.  This is the `Pic'
 637  |              style curve.
 638  *----------------------------------------------------------------------------*/
 639
 640 void
 641 picurve(register int *x,
 642         register int *y,
 643         int npts)
 644 {
 645   register int nseg;            /* effective resolution for each curve */
 646   register int xp;              /* current point (and temporary) */
 647   register int yp;
 648   int pxp, pyp;                 /* previous point (to make lines from) */
 649   int i;                        /* inner curve segment traverser */
 650   int length = 0;
 651   double w;                     /* position factor */
 652   double t1, t2, t3;            /* calculation temps */
 653
 654   if (x[1] == x[npts] && y[1] == y[npts]) {
 655     x[0] = x[npts - 1];         /* if the lines' ends meet, make */
 656     y[0] = y[npts - 1];         /* sure the curve meets          */
 657     x[npts + 1] = x[2];
 658     y[npts + 1] = y[2];
 659   } else {                      /* otherwise, make the ends of the  */
 660     x[0] = x[1];                /* curve touch the ending points of */
 661     y[0] = y[1];                /* the line segments                */
 662     x[npts + 1] = x[npts];
 663     y[npts + 1] = y[npts];
 664   }
 665
 666   pxp = (x[0] + x[1]) / 2;      /* make the last point pointers       */
 667   pyp = (y[0] + y[1]) / 2;      /* point to the start of the 1st line */
 668   tmove2(pxp, pyp);
 669
 670   for (; npts--; x++, y++) {    /* traverse the line segments */
 671     xp = x[0] - x[1];
 672     yp = y[0] - y[1];
 673     nseg = (int) hypot((double) xp, (double) yp);
 674     xp = x[1] - x[2];
 675     yp = y[1] - y[2];
 676                                 /* `nseg' is the number of line    */
 677                                 /* segments that will be drawn for */
 678                                 /* each curve segment.             */
 679     nseg = (int) ((double) (nseg + (int) hypot((double) xp, (double) yp)) /
 680                   res * PointsPerInterval);
 681
 682     for (i = 1; i < nseg; i++) {
 683       w = (double) i / (double) nseg;
 684       t1 = w * w;
 685       t3 = t1 + 1.0 - (w + w);
 686       t2 = 2.0 - (t3 + t1);
 687       xp = (((int) (t1 * x[2] + t2 * x[1] + t3 * x[0])) + 1) / 2;
 688       yp = (((int) (t1 * y[2] + t2 * y[1] + t3 * y[0])) + 1) / 2;
 689
 690       HGtline(xp, yp);
 691       if (length++ > LINELENGTH) {
 692         length = 0;
 693         printf("\\\n");
 694       }
 695     }
 696   }
 697 }
 698
 699
 700 /*----------------------------------------------------------------------------
 701  | Routine:     HGCurve(xpoints, ypoints, num_points)
 702  |
 703  | Results:     This routine generates a smooth curve through a set of
 704  |              points.  The method used is the parametric spline curve on
 705  |              unit knot mesh described in `Spline Curve Techniques' by
 706  |              Patrick Baudelaire, Robert Flegal, and Robert Sproull --
 707  |              Xerox Parc.
 708  *----------------------------------------------------------------------------*/
 709
 710 void
 711 HGCurve(int *x,
 712         int *y,
 713         int numpoints)
 714 {
 715   float h[MAXPOINTS], dx[MAXPOINTS], dy[MAXPOINTS];
 716   float d2x[MAXPOINTS], d2y[MAXPOINTS], d3x[MAXPOINTS], d3y[MAXPOINTS];
 717   float t, t2, t3;
 718   register int j;
 719   register int k;
 720   register int nx;
 721   register int ny;
 722   int lx, ly;
 723   int length = 0;
 724
 725   lx = x[1];
 726   ly = y[1];
 727   tmove2(lx, ly);
 728
 729   /*
 730    * Solve for derivatives of the curve at each point separately for x and y
 731    * (parametric).
 732    */
 733   Paramaterize(x, y, h, numpoints);
 734
 735   /* closed curve */
 736   if ((x[1] == x[numpoints]) && (y[1] == y[numpoints])) {
 737     PeriodicSpline(h, x, dx, d2x, d3x, numpoints);
 738     PeriodicSpline(h, y, dy, d2y, d3y, numpoints);
 739   } else {
 740     NaturalEndSpline(h, x, dx, d2x, d3x, numpoints);
 741     NaturalEndSpline(h, y, dy, d2y, d3y, numpoints);
 742   }
 743
 744   /*
 745    * generate the curve using the above information and PointsPerInterval
 746    * vectors between each specified knot.
 747    */
 748
 749   for (j = 1; j < numpoints; ++j) {
 750     if ((x[j] == x[j + 1]) && (y[j] == y[j + 1]))
 751       continue;
 752     for (k = 0; k <= PointsPerInterval; ++k) {
 753       t = (float) k *h[j] / (float) PointsPerInterval;
 754       t2 = t * t;
 755       t3 = t * t * t;
 756       nx = x[j] + (int) (t * dx[j] + t2 * d2x[j] / 2 + t3 * d3x[j] / 6);
 757       ny = y[j] + (int) (t * dy[j] + t2 * d2y[j] / 2 + t3 * d3y[j] / 6);
 758       HGtline(nx, ny);
 759       if (length++ > LINELENGTH) {
 760         length = 0;
 761         printf("\\\n");
 762       }
 763     }                           /* end for k */
 764   }                             /* end for j */
 765 }                               /* end HGCurve */
 766
 767
 768 /*----------------------------------------------------------------------------
 769  | Routine:     Paramaterize (xpoints, ypoints, hparams, num_points)
 770  |
 771  | Results:     This routine calculates parameteric values for use in
 772  |              calculating curves.  The parametric values are returned
 773  |              in the array h.  The values are an approximation of
 774  |              cumulative arc lengths of the curve (uses cord length).
 775  |              For additional information, see paper cited below.
 776  *----------------------------------------------------------------------------*/
 777
 778 void
 779 Paramaterize(int x[],
 780              int y[],
 781              float h[],
 782              int n)
 783 {
 784   register int dx;
 785   register int dy;
 786   register int i;
 787   register int j;
 788   float u[MAXPOINTS];
 789
 790   for (i = 1; i <= n; ++i) {
 791     u[i] = 0;
 792     for (j = 1; j < i; j++) {
 793       dx = x[j + 1] - x[j];
 794       dy = y[j + 1] - y[j];
 795       /* Here was overflowing, so I changed it.       */
 796       /* u[i] += sqrt ((double) (dx * dx + dy * dy)); */
 797       u[i] += hypot((double) dx, (double) dy);
 798     }
 799   }
 800   for (i = 1; i < n; ++i)
 801     h[i] = u[i + 1] - u[i];
 802 }                               /* end Paramaterize */
 803
 804
 805 /*----------------------------------------------------------------------------
 806  | Routine:     PeriodicSpline (h, z, dz, d2z, d3z, npoints)
 807  |
 808  | Results:     This routine solves for the cubic polynomial to fit a spline
 809  |              curve to the the points specified by the list of values.
 810  |              The Curve generated is periodic.  The algorithms for this
 811  |              curve are from the `Spline Curve Techniques' paper cited
 812  |              above.
 813  *----------------------------------------------------------------------------*/
 814
 815 void
 816 PeriodicSpline(float h[],       /* paramaterization  */
 817                int z[],         /* point list */
 818                float dz[],      /* to return the 1st derivative */
 819                float d2z[],     /* 2nd derivative */
 820                float d3z[],     /* 3rd derivative */
 821                int npoints)     /* number of valid points */
 822 {
 823   float d[MAXPOINTS];
 824   float deltaz[MAXPOINTS], a[MAXPOINTS], b[MAXPOINTS];
 825   float c[MAXPOINTS], r[MAXPOINTS], s[MAXPOINTS];
 826   int i;
 827
 828   /* step 1 */
 829   for (i = 1; i < npoints; ++i) {
 830     deltaz[i] = h[i] ? ((double) (z[i + 1] - z[i])) / h[i] : 0;
 831   }
 832   h[0] = h[npoints - 1];
 833   deltaz[0] = deltaz[npoints - 1];
 834
 835   /* step 2 */
 836   for (i = 1; i < npoints - 1; ++i) {
 837     d[i] = deltaz[i + 1] - deltaz[i];
 838   }
 839   d[0] = deltaz[1] - deltaz[0];
 840
 841   /* step 3a */
 842   a[1] = 2 * (h[0] + h[1]);
 843   b[1] = d[0];
 844   c[1] = h[0];
 845   for (i = 2; i < npoints - 1; ++i) {
 846     a[i] = 2 * (h[i - 1] + h[i]) -
 847            pow((double) h[i - 1], (double) 2.0) / a[i - 1];
 848     b[i] = d[i - 1] - h[i - 1] * b[i - 1] / a[i - 1];
 849     c[i] = -h[i - 1] * c[i - 1] / a[i - 1];
 850   }
 851
 852   /* step 3b */
 853   r[npoints - 1] = 1;
 854   s[npoints - 1] = 0;
 855   for (i = npoints - 2; i > 0; --i) {
 856     r[i] = -(h[i] * r[i + 1] + c[i]) / a[i];
 857     s[i] = (6 * b[i] - h[i] * s[i + 1]) / a[i];
 858   }
 859
 860   /* step 4 */
 861   d2z[npoints - 1] = (6 * d[npoints - 2] - h[0] * s[1]
 862                       - h[npoints - 1] * s[npoints - 2])
 863                      / (h[0] * r[1] + h[npoints - 1] * r[npoints - 2]
 864                       + 2 * (h[npoints - 2] + h[0]));
 865   for (i = 1; i < npoints - 1; ++i) {
 866     d2z[i] = r[i] * d2z[npoints - 1] + s[i];
 867   }
 868   d2z[npoints] = d2z[1];
 869
 870   /* step 5 */
 871   for (i = 1; i < npoints; ++i) {
 872     dz[i] = deltaz[i] - h[i] * (2 * d2z[i] + d2z[i + 1]) / 6;
 873     d3z[i] = h[i] ? (d2z[i + 1] - d2z[i]) / h[i] : 0;
 874   }
 875 }                               /* end PeriodicSpline */
 876
 877
 878 /*----------------------------------------------------------------------------
 879  | Routine:     NaturalEndSpline (h, z, dz, d2z, d3z, npoints)
 880  |
 881  | Results:     This routine solves for the cubic polynomial to fit a spline
 882  |              curve the the points specified by the list of values.  The
 883  |              alogrithms for this curve are from the `Spline Curve
 884  |              Techniques' paper cited above.
 885  *----------------------------------------------------------------------------*/
 886
 887 void
 888 NaturalEndSpline(float h[],     /* parameterization */
 889                  int z[],       /* Point list */
 890                  float dz[],    /* to return the 1st derivative */
 891                  float d2z[],   /* 2nd derivative */
 892                  float d3z[],   /* 3rd derivative */
 893                  int npoints)   /* number of valid points */
 894 {
 895   float d[MAXPOINTS];
 896   float deltaz[MAXPOINTS], a[MAXPOINTS], b[MAXPOINTS];
 897   int i;
 898
 899   /* step 1 */
 900   for (i = 1; i < npoints; ++i) {
 901     deltaz[i] = h[i] ? ((double) (z[i + 1] - z[i])) / h[i] : 0;
 902   }
 903   deltaz[0] = deltaz[npoints - 1];
 904
 905   /* step 2 */
 906   for (i = 1; i < npoints - 1; ++i) {
 907     d[i] = deltaz[i + 1] - deltaz[i];
 908   }
 909   d[0] = deltaz[1] - deltaz[0];
 910
 911   /* step 3 */
 912   a[0] = 2 * (h[2] + h[1]);
 913   b[0] = d[1];
 914   for (i = 1; i < npoints - 2; ++i) {
 915     a[i] = 2 * (h[i + 1] + h[i + 2]) -
 916             pow((double) h[i + 1], (double) 2.0) / a[i - 1];
 917     b[i] = d[i + 1] - h[i + 1] * b[i - 1] / a[i - 1];
 918   }
 919
 920   /* step 4 */
 921   d2z[npoints] = d2z[1] = 0;
 922   for (i = npoints - 1; i > 1; --i) {
 923     d2z[i] = (6 * b[i - 2] - h[i] * d2z[i + 1]) / a[i - 2];
 924   }
 925
 926   /* step 5 */
 927   for (i = 1; i < npoints; ++i) {
 928     dz[i] = deltaz[i] - h[i] * (2 * d2z[i] + d2z[i + 1]) / 6;
 929     d3z[i] = h[i] ? (d2z[i + 1] - d2z[i]) / h[i] : 0;
 930   }
 931 }                               /* end NaturalEndSpline */
 932
 933
 934 /*----------------------------------------------------------------------------*
 935  | Routine:     change (x_position, y_position, visible_flag)
 936  |
 937  | Results:     As HGtline passes from the invisible to visible (or vice
 938  |              versa) portion of a line, change is called to either draw
 939  |              the line, or initialize the beginning of the next one.
 940  |              Change calls line to draw segments if visible_flag is set
 941  |              (which means we're leaving a visible area).
 942  *----------------------------------------------------------------------------*/
 943
 944 void
 945 change(register int x,
 946        register int y,
 947        register int vis)
 948 {
 949   static int length = 0;
 950
 951   if (vis) {                    /* leaving a visible area, draw it. */
 952     line(x, y);
 953     if (length++ > LINELENGTH) {
 954       length = 0;
 955       printf("\\\n");
 956     }
 957   } else {                      /* otherwise, we're entering one, remember */
 958                                 /* beginning                               */
 959     tmove2(x, y);
 960   }
 961 }
 962
 963
 964 /*----------------------------------------------------------------------------
 965  | Routine:     HGtline (xstart, ystart, xend, yend)
 966  |
 967  | Results:     Draws a line from current position to (x1,y1) using line(x1,
 968  |              y1) to place individual segments of dotted or dashed lines.
 969  *----------------------------------------------------------------------------*/
 970
 971 void
 972 HGtline(int x1,
 973         int y1)
 974 {
 975   register int x0 = lastx;
 976   register int y0 = lasty;
 977   register int dx;
 978   register int dy;
 979   register int oldcoord;
 980   register int res1;
 981   register int visible;
 982   register int res2;
 983   register int xinc;
 984   register int yinc;
 985   register int dotcounter;
 986
 987   if (linmod == SOLID) {
 988     line(x1, y1);
 989     return;
 990   }
 991
 992   /* for handling different resolutions */
 993   dotcounter = linmod << dotshifter;
 994
 995   xinc = 1;
 996   yinc = 1;
 997   if ((dx = x1 - x0) < 0) {
 998     xinc = -xinc;
 999     dx = -dx;
1000   }
1001   if ((dy = y1 - y0) < 0) {
1002     yinc = -yinc;
1003     dy = -dy;
1004   }
1005   res1 = 0;
1006   res2 = 0;
1007   visible = 0;
1008   if (dx >= dy) {
1009     oldcoord = y0;
1010     while (x0 != x1) {
1011       if ((x0 & dotcounter) && !visible) {
1012         change(x0, y0, 0);
1013         visible = 1;
1014       } else if (visible && !(x0 & dotcounter)) {
1015         change(x0 - xinc, oldcoord, 1);
1016         visible = 0;
1017       }
1018       if (res1 > res2) {
1019         oldcoord = y0;
1020         res2 += dx - res1;
1021         res1 = 0;
1022         y0 += yinc;
1023       }
1024       res1 += dy;
1025       x0 += xinc;
1026     }
1027   } else {
1028     oldcoord = x0;
1029     while (y0 != y1) {
1030       if ((y0 & dotcounter) && !visible) {
1031         change(x0, y0, 0);
1032         visible = 1;
1033       } else if (visible && !(y0 & dotcounter)) {
1034         change(oldcoord, y0 - yinc, 1);
1035         visible = 0;
1036       }
1037       if (res1 > res2) {
1038         oldcoord = x0;
1039         res2 += dy - res1;
1040         res1 = 0;
1041         x0 += xinc;
1042       }
1043       res1 += dx;
1044       y0 += yinc;
1045     }
1046   }
1047   if (visible)
1048     change(x1, y1, 1);
1049   else
1050     change(x1, y1, 0);
1051 }
1052
1053 /* EOF */