Adding upstream version 1.23.0.upstream/1.23.0upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1060 insertions, 0 deletions

diff --git a/src/preproc/grn/hgraph.cpp b/src/preproc/grn/hgraph.cpp
new file mode 100644
index 0000000..9ed81a4
--- /dev/null
+++ b/src/preproc/grn/hgraph.cpp
@@ -0,0 +1,1060 @@
+/* Last non-groff version: hgraph.c  1.14 (Berkeley) 84/11/27
+ *
+ * This file contains the graphics routines for converting gremlin
+ * pictures to troff input.
+ */
+
+#include "lib.h"
+
+#include "gprint.h"
+
+#define MAXVECT	40
+#define MAXPOINTS	200
+#define LINELENGTH	1
+#define PointsPerInterval 64
+#define pi		3.14159265358979324
+#define twopi		(2.0 * pi)
+#define len(a, b)	groff_hypot((double)(b.x-a.x), \
+			            (double)(b.y-a.y))
+
+
+extern int dotshifter;		/* for the length of dotted curves */
+
+extern int style[];		/* line and character styles */
+extern double thick[];
+extern char *tfont[];
+extern int tsize[];
+extern int stipple_index[];	/* stipple font idx for stipples 0-16 */
+extern char *stipple;		/* stipple type (cf or ug) */
+
+
+extern double troffscale;	/* imports from main.c */
+extern double linethickness;
+extern int linmod;
+extern int lastx;
+extern int lasty;
+extern int lastyline;
+extern int ytop;
+extern int ybottom;
+extern int xleft;
+extern int xright;
+extern enum E {
+  OUTLINE, FILL, BOTH
+} polyfill;
+
+extern double adj1;
+extern double adj2;
+extern double adj3;
+extern double adj4;
+extern int res;
+
+void HGSetFont(int font, int size);
+void HGPutText(int justify, POINT pnt, char *string);
+void HGSetBrush(int mode);
+void tmove2(int px, int py);
+void doarc(POINT cp, POINT sp, int angle);
+void tmove(POINT * ptr);
+void cr();
+void drawwig(POINT * ptr, int type);
+void HGtline(int x1, int y1);
+void deltax(double x);
+void deltay(double y);
+void HGArc(int cx, int cy, int px, int py, int angle);
+void picurve(int *x, int *y, int npts);
+void HGCurve(int *x, int *y, int numpoints);
+void Parameterize(int x[], int y[], double h[], int n);
+void PeriodicSpline(double h[], int z[],
+		    double dz[], double d2z[], double d3z[],
+		    int npoints);
+void NaturalEndSpline(double h[], int z[],
+		      double dz[], double d2z[], double d3z[],
+		      int npoints);
+
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	HGPrintElt (element_pointer, baseline)
+ |
+ | Results:	Examines a picture element and calls the appropriate
+ |		routine(s) to print them according to their type.  After
+ |		the picture is drawn, current position is (lastx,lasty).
+ *--------------------------------------------------------------------*/
+
+void
+HGPrintElt(ELT *element,
+	   int /* baseline */)
+{
+  POINT *p1;
+  POINT *p2;
+  int length;
+  int graylevel;
+
+  if (!DBNullelt(element) && !Nullpoint((p1 = element->ptlist))) {
+    /* p1 always has first point */
+    if (TEXT(element->type)) {
+      HGSetFont(element->brushf, element->size);
+      switch (element->size) {
+      case 1:
+	p1->y += adj1;
+	break;
+      case 2:
+	p1->y += adj2;
+	break;
+      case 3:
+	p1->y += adj3;
+	break;
+      case 4:
+	p1->y += adj4;
+	break;
+      default:
+	break;
+      }
+      HGPutText(element->type, *p1, element->textpt);
+    } else {
+      if (element->brushf)		/* if there is a brush, the */
+	HGSetBrush(element->brushf);	/* graphics need it set     */
+
+      switch (element->type) {
+
+      case ARC:
+	p2 = PTNextPoint(p1);
+	tmove(p2);
+	doarc(*p1, *p2, element->size);
+	cr();
+	break;
+
+      case CURVE:
+	length = 0;	/* keep track of line length */
+	drawwig(p1, CURVE);
+	cr();
+	break;
+
+      case BSPLINE:
+	length = 0;	/* keep track of line length */
+	drawwig(p1, BSPLINE);
+	cr();
+	break;
+
+      case VECTOR:
+	length = 0;		/* keep track of line length so */
+	tmove(p1);		/* single lines don't get long  */
+	while (!Nullpoint((p1 = PTNextPoint(p1)))) {
+	  HGtline((int) (p1->x * troffscale),
+		  (int) (p1->y * troffscale));
+	  if (length++ > LINELENGTH) {
+	    length = 0;
+	    printf("\\\n");
+	  }
+	}			/* end while */
+	cr();
+	break;
+
+      case POLYGON:
+	{
+	  /* brushf = style of outline; size = color of fill:
+	   * on first pass (polyfill=FILL), do the interior using 'P'
+	   *    unless size=0
+	   * on second pass (polyfill=OUTLINE), do the outline using a
+	   *    series of vectors. It might make more sense to use \D'p
+	   *    ...', but there is no uniform way to specify a 'fill
+	   *    character' that prints as 'no fill' on all output
+	   *    devices (and stipple fonts).
+	   * If polyfill=BOTH, just use the \D'p ...' command.
+	   */
+	  double firstx = p1->x;
+	  double firsty = p1->y;
+
+	  length = 0;		/* keep track of line length so */
+				/* single lines don't get long  */
+
+	  if (polyfill == FILL || polyfill == BOTH) {
+	    /* do the interior */
+	    char command = (polyfill == BOTH && element->brushf)
+			   ? 'p' : 'P';
+
+	    /* include outline, if there is one and */
+	    /* the -p flag was set                  */
+
+	    /* switch based on what gremlin gives */
+	    switch (element->size) {
+	    case 1:
+	      graylevel = 1;
+	      break;
+	    case 3:
+	      graylevel = 2;
+	      break;
+	    case 12:
+	      graylevel = 3;
+	      break;
+	    case 14:
+	      graylevel = 4;
+	      break;
+	    case 16:
+	      graylevel = 5;
+	      break;
+	    case 19:
+	      graylevel = 6;
+	      break;
+	    case 21:
+	      graylevel = 7;
+	      break;
+	    case 23:
+	      graylevel = 8;
+	      break;
+	    default:		/* who's giving something else? */
+	      graylevel = NSTIPPLES;
+	      break;
+	    }
+	    /* int graylevel = element->size; */
+
+	    if (graylevel < 0)
+	      break;
+	    if (graylevel > NSTIPPLES)
+	      graylevel = NSTIPPLES;
+	    printf("\\D'Fg %.3f'",
+		   double(1000 - stipple_index[graylevel]) / 1000.0);
+	    cr();
+	    tmove(p1);
+	    printf("\\D'%c", command);
+
+	    while (!Nullpoint((PTNextPoint(p1)))) {
+	      p1 = PTNextPoint(p1);
+	      deltax((double) p1->x);
+	      deltay((double) p1->y);
+	      if (length++ > LINELENGTH) {
+		length = 0;
+		printf("\\\n");
+	      }
+	    } /* end while */
+
+	    /* close polygon if not done so by user */
+	    if ((firstx != p1->x) || (firsty != p1->y)) {
+	      deltax((double) firstx);
+	      deltay((double) firsty);
+	    }
+	    putchar('\'');
+	    cr();
+	    break;
+	  }
+	  /* else polyfill == OUTLINE; only draw the outline */
+	  if (!(element->brushf))
+	    break;
+	  length = 0;		/* keep track of line length */
+	  tmove(p1);
+
+	  while (!Nullpoint((PTNextPoint(p1)))) {
+	    p1 = PTNextPoint(p1);
+	    HGtline((int) (p1->x * troffscale),
+		    (int) (p1->y * troffscale));
+	    if (length++ > LINELENGTH) {
+	      length = 0;
+	      printf("\\\n");
+	    }
+	  }			/* end while */
+
+	  /* close polygon if not done so by user */
+	  if ((firstx != p1->x) || (firsty != p1->y)) {
+	    HGtline((int) (firstx * troffscale),
+		    (int) (firsty * troffscale));
+	  }
+	  cr();
+	  break;
+	}			/* end case POLYGON */
+      }				/* end switch */
+    }				/* end else Text */
+  }				/* end if */
+}				/* end PrintElt */
+
+
+/*---------------------------------------------------------------------*
+ | Routine:	HGPutText (justification, position_point, string)
+ |
+ | Results:	Given the justification, a point to position with, and a
+ |		string to put, HGPutText first sends the string into a
+ |		diversion, moves to the positioning point, then outputs
+ |		local vertical and horizontal motions as needed to
+ |		justify the text.  After all motions are done, the
+ |		diversion is printed out.
+ *--------------------------------------------------------------------*/
+
+void
+HGPutText(int justify,
+	  POINT pnt,
+	  char *string)
+{
+  int savelasty = lasty;	/* vertical motion for text is to be */
+				/* ignored.  Save current y here     */
+
+  printf(".nr g8 \\n(.d\n");	/* save current vertical position. */
+  printf(".ds g9 \"");		/* define string containing the text. */
+  while (*string) {		/* put out the string */
+    if (*string == '\\' &&
+	*(string + 1) == '\\') {	/* one character at a */
+      printf("\\\\\\");			/* time replacing //  */
+      string++;				/* by //// to prevent */
+    }					/* interpretation at  */
+    printf("%c", *(string++));		/* printout time      */
+  }
+  printf("\n");
+
+  tmove(&pnt);			/* move to positioning point */
+
+  switch (justify) {
+    /* local vertical motions--the numbers here are used to be
+       somewhat compatible with gprint */
+  case CENTLEFT:
+  case CENTCENT:
+  case CENTRIGHT:
+    printf("\\v'0.85n'");	/* down half */
+    break;
+
+  case TOPLEFT:
+  case TOPCENT:
+  case TOPRIGHT:
+    printf("\\v'1.7n'");	/* down whole */
+  }
+
+  switch (justify) {
+    /* local horizontal motions */
+  case BOTCENT:
+  case CENTCENT:
+  case TOPCENT:
+    printf("\\h'-\\w'\\*(g9'u/2u'");	/* back half */
+    break;
+
+  case BOTRIGHT:
+  case CENTRIGHT:
+  case TOPRIGHT:
+    printf("\\h'-\\w'\\*(g9'u'");	/* back whole */
+  }
+
+  printf("\\&\\*(g9\n");	/* now print the text. */
+  printf(".sp |\\n(g8u\n");	/* restore vertical position */
+  lasty = savelasty;		/* vertical position restored to */
+  lastx = xleft;		/* where it was before text, also */
+				/* horizontal is at left */
+}				/* end HGPutText */
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	doarc (center_point, start_point, angle)
+ |
+ | Results:	Produces either drawarc command or a drawcircle command
+ |		depending on the angle needed to draw through.
+ *--------------------------------------------------------------------*/
+
+void
+doarc(POINT cp,
+      POINT sp,
+      int angle)
+{
+  if (angle)			/* arc with angle */
+    HGArc((int) (cp.x * troffscale), (int) (cp.y * troffscale),
+	  (int) (sp.x * troffscale), (int) (sp.y * troffscale), angle);
+  else				/* a full circle (angle == 0) */
+    HGArc((int) (cp.x * troffscale), (int) (cp.y * troffscale),
+	  (int) (sp.x * troffscale), (int) (sp.y * troffscale), 0);
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	HGSetFont (font_number, Point_size)
+ |
+ | Results:	ALWAYS outputs a .ft and .ps directive to troff.  This
+ |		is done because someone may change stuff inside a text
+ |		string.  Changes thickness back to default thickness.
+ |		Default thickness depends on font and point size.
+ *--------------------------------------------------------------------*/
+
+void
+HGSetFont(int font,
+	  int size)
+{
+  printf(".ft %s\n"
+	 ".ps %d\n", tfont[font - 1], tsize[size - 1]);
+  linethickness = DEFTHICK;
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	HGSetBrush (line_mode)
+ |
+ | Results:	Generates the troff commands to set up the line width
+ |		and style of subsequent lines.  Does nothing if no
+ |		change is needed.
+ |
+ | Side Efct:	Sets 'linmode' and 'linethickness'.
+ *--------------------------------------------------------------------*/
+
+void
+HGSetBrush(int mode)
+{
+  int printed = 0;
+
+  if (linmod != style[--mode]) {
+    /* Groff doesn't understand \Ds, so we take it out */
+    /* printf ("\\D's %du'", linmod = style[mode]); */
+    linmod = style[mode];
+    printed = 1;
+  }
+  if (linethickness != thick[mode]) {
+    linethickness = thick[mode];
+    printf("\\h'-%.2fp'\\D't %.2fp'", linethickness, linethickness);
+    printed = 1;
+  }
+  if (printed)
+    cr();
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	deltax (x_destination)
+ |
+ | Results:	Scales and outputs a number for delta x (with a leading
+ |		space) given 'lastx' and x_destination.
+ |
+ | Side Efct:	Resets 'lastx' to x_destination.
+ *--------------------------------------------------------------------*/
+
+void
+deltax(double x)
+{
+  int ix = (int) (x * troffscale);
+
+  printf(" %du", ix - lastx);
+  lastx = ix;
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	deltay (y_destination)
+ |
+ | Results:	Scales and outputs a number for delta y (with a leading
+ |		space) given 'lastyline' and y_destination.
+ |
+ | Side Efct:	Resets 'lastyline' to y_destination.  Since 'line'
+ |		vertical motions don't affect 'page' ones, 'lasty' isn't
+ |		updated.
+ *--------------------------------------------------------------------*/
+
+void
+deltay(double y)
+{
+  int iy = (int) (y * troffscale);
+
+  printf(" %du", iy - lastyline);
+  lastyline = iy;
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	tmove2 (px, py)
+ |
+ | Results:	Produces horizontal and vertical moves for troff given
+ |		the pair of points to move to and knowing the current
+ |		position.  Also puts out a horizontal move to start the
+ |		line.  This is a variation without the .sp command.
+ *--------------------------------------------------------------------*/
+
+void
+tmove2(int px,
+       int py)
+{
+  int dx;
+  int dy;
+
+  if ((dy = py - lasty)) {
+    printf("\\v'%du'", dy);
+  }
+  lastyline = lasty = py;	/* lasty is always set to current */
+  if ((dx = px - lastx)) {
+    printf("\\h'%du'", dx);
+    lastx = px;
+  }
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	tmove (point_pointer)
+ |
+ | Results:	Produces horizontal and vertical moves for troff given
+ |		the pointer of a point to move to and knowing the
+ |		current position.  Also puts out a horizontal move to
+ |		start the line.
+ *--------------------------------------------------------------------*/
+
+void
+tmove(POINT * ptr)
+{
+  int ix = (int) (ptr->x * troffscale);
+  int iy = (int) (ptr->y * troffscale);
+  int dx;
+  int dy;
+
+  if ((dy = iy - lasty)) {
+    printf(".sp %du\n", dy);
+  }
+  lastyline = lasty = iy;	/* lasty is always set to current */
+  if ((dx = ix - lastx)) {
+    printf("\\h'%du'", dx);
+    lastx = ix;
+  }
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	cr ( )
+ |
+ | Results:	Ends off an input line.  '.sp -1' is also added to
+ |		counteract the vertical move done at the end of text
+ |		lines.
+ |
+ | Side Efct:	Sets 'lastx' to 'xleft' for troff's return to left
+ |		margin.
+ *--------------------------------------------------------------------*/
+
+void
+cr()
+{
+  printf("\n.sp -1\n");
+  lastx = xleft;
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	line ( )
+ |
+ | Results:	Draws a single solid line to (x,y).
+ *--------------------------------------------------------------------*/
+
+void
+line(int px,
+     int py)
+{
+  printf("\\D'l");
+  printf(" %du", px - lastx);
+  printf(" %du'", py - lastyline);
+  lastx = px;
+  lastyline = lasty = py;
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	drawwig (ptr, type)
+ |
+ | Results:	The point sequence found in the structure pointed by ptr
+ |		is placed in integer arrays for further manipulation by
+ |		the existing routing.  With the corresponding type
+ |		parameter, either picurve or HGCurve are called.
+ *--------------------------------------------------------------------*/
+
+void
+drawwig(POINT * ptr,
+	int type)
+{
+  int npts;			/* point list index */
+  int x[MAXPOINTS], y[MAXPOINTS];	/* point list */
+
+  for (npts = 1; !Nullpoint(ptr); ptr = PTNextPoint(ptr), npts++) {
+    x[npts] = (int) (ptr->x * troffscale);
+    y[npts] = (int) (ptr->y * troffscale);
+  }
+  if (--npts) {
+    if (type == CURVE) /* Use the 2 different types of curves */
+      HGCurve(&x[0], &y[0], npts);
+    else
+      picurve(&x[0], &y[0], npts);
+  }
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	HGArc (xcenter, ycenter, xstart, ystart, angle)
+ |
+ | Results:	This routine plots an arc centered about (cx, cy)
+ |		counter-clockwise starting from the point (px, py)
+ |		through 'angle' degrees.  If angle is 0, a full circle
+ |		is drawn.  It does so by creating a draw-path around the
+ |		arc whose density of points depends on the size of the
+ |		arc.
+ *--------------------------------------------------------------------*/
+
+void
+HGArc(int cx,
+      int cy,
+      int px,
+      int py,
+      int angle)
+{
+  double xs, ys, resolution, fullcircle;
+  int m;
+  int mask;
+  int extent;
+  int nx;
+  int ny;
+  int length;
+  double epsilon;
+
+  xs = px - cx;
+  ys = py - cy;
+
+  length = 0;
+
+  resolution = (1.0 + groff_hypot(xs, ys) / res) * PointsPerInterval;
+  /* mask = (1 << (int) log10(resolution + 1.0)) - 1; */
+  (void) frexp(resolution, &m);		/* more elegant than log10 */
+  for (mask = 1; mask < m; mask = mask << 1);
+  mask -= 1;
+
+  epsilon = 1.0 / resolution;
+  fullcircle = (2.0 * pi) * resolution;
+  if (angle == 0)
+    extent = (int) fullcircle;
+  else
+    extent = (int) (angle * fullcircle / 360.0);
+
+  HGtline(px, py);
+  while (--extent >= 0) {
+    xs += epsilon * ys;
+    nx = cx + (int) (xs + 0.5);
+    ys -= epsilon * xs;
+    ny = cy + (int) (ys + 0.5);
+    if (!(extent & mask)) {
+      HGtline(nx, ny);		/* put out a point on circle */
+      if (length++ > LINELENGTH) {
+	length = 0;
+	printf("\\\n");
+      }
+    }
+  }				/* end for */
+}				/* end HGArc */
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	picurve (xpoints, ypoints, num_of_points)
+ |
+ | Results:	Draws a curve delimited by (not through) the line
+ |		segments traced by (xpoints, ypoints) point list.  This
+ |		is the 'Pic'-style curve.
+ *--------------------------------------------------------------------*/
+
+void
+picurve(int *x,
+	int *y,
+	int npts)
+{
+  int nseg;		/* effective resolution for each curve */
+  int xp;		/* current point (and temporary) */
+  int yp;
+  int pxp, pyp;		/* previous point (to make lines from) */
+  int i;		/* inner curve segment traverser */
+  int length = 0;
+  double w;			/* position factor */
+  double t1, t2, t3;		/* calculation temps */
+
+  if (x[1] == x[npts] && y[1] == y[npts]) {
+    x[0] = x[npts - 1];		/* if the lines' ends meet, make */
+    y[0] = y[npts - 1];		/* sure the curve meets          */
+    x[npts + 1] = x[2];
+    y[npts + 1] = y[2];
+  } else {			/* otherwise, make the ends of the  */
+    x[0] = x[1];		/* curve touch the ending points of */
+    y[0] = y[1];		/* the line segments                */
+    x[npts + 1] = x[npts];
+    y[npts + 1] = y[npts];
+  }
+
+  pxp = (x[0] + x[1]) / 2;	/* make the last point pointers       */
+  pyp = (y[0] + y[1]) / 2;	/* point to the start of the 1st line */
+  tmove2(pxp, pyp);
+
+  for (; npts--; x++, y++) {	/* traverse the line segments */
+    xp = x[0] - x[1];
+    yp = y[0] - y[1];
+    nseg = (int) groff_hypot((double) xp, (double) yp);
+    xp = x[1] - x[2];
+    yp = y[1] - y[2];
+				/* 'nseg' is the number of line    */
+				/* segments that will be drawn for */
+				/* each curve segment.             */
+    nseg = (int) ((double) (nseg + (int) groff_hypot((double) xp,
+						     (double) yp)) /
+		  res * PointsPerInterval);
+
+    for (i = 1; i < nseg; i++) {
+      w = (double) i / (double) nseg;
+      t1 = w * w;
+      t3 = t1 + 1.0 - (w + w);
+      t2 = 2.0 - (t3 + t1);
+      xp = (((int) (t1 * x[2] + t2 * x[1] + t3 * x[0])) + 1) / 2;
+      yp = (((int) (t1 * y[2] + t2 * y[1] + t3 * y[0])) + 1) / 2;
+
+      HGtline(xp, yp);
+      if (length++ > LINELENGTH) {
+	length = 0;
+	printf("\\\n");
+      }
+    }
+  }
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	HGCurve(xpoints, ypoints, num_points)
+ |
+ | Results:	This routine generates a smooth curve through a set of
+ |		points.  The method used is the parametric spline curve
+ |		on unit knot mesh described in 'Spline Curve Techniques'
+ |		by Patrick Baudelaire, Robert Flegal, and Robert Sproull
+ |		-- Xerox Parc.
+ *--------------------------------------------------------------------*/
+
+void
+HGCurve(int *x,
+	int *y,
+	int numpoints)
+{
+  double h[MAXPOINTS], dx[MAXPOINTS], dy[MAXPOINTS];
+  double d2x[MAXPOINTS], d2y[MAXPOINTS], d3x[MAXPOINTS], d3y[MAXPOINTS];
+  double t, t2, t3;
+  int j;
+  int k;
+  int nx;
+  int ny;
+  int lx, ly;
+  int length = 0;
+
+  lx = x[1];
+  ly = y[1];
+  tmove2(lx, ly);
+
+  /*
+   * Solve for derivatives of the curve at each point separately for x
+   * and y (parametric).
+   */
+  Parameterize(x, y, h, numpoints);
+
+  /* closed curve */
+  if ((x[1] == x[numpoints]) && (y[1] == y[numpoints])) {
+    PeriodicSpline(h, x, dx, d2x, d3x, numpoints);
+    PeriodicSpline(h, y, dy, d2y, d3y, numpoints);
+  } else {
+    NaturalEndSpline(h, x, dx, d2x, d3x, numpoints);
+    NaturalEndSpline(h, y, dy, d2y, d3y, numpoints);
+  }
+
+  /*
+   * Generate the curve using the above information and
+   * PointsPerInterval vectors between each specified knot.
+   */
+
+  for (j = 1; j < numpoints; ++j) {
+    if ((x[j] == x[j + 1]) && (y[j] == y[j + 1]))
+      continue;
+    for (k = 0; k <= PointsPerInterval; ++k) {
+      t = (double) k *h[j] / (double) PointsPerInterval;
+      t2 = t * t;
+      t3 = t * t * t;
+      nx = x[j] + (int) (t * dx[j] + t2 * d2x[j] / 2 + t3 * d3x[j] / 6);
+      ny = y[j] + (int) (t * dy[j] + t2 * d2y[j] / 2 + t3 * d3y[j] / 6);
+      HGtline(nx, ny);
+      if (length++ > LINELENGTH) {
+	length = 0;
+	printf("\\\n");
+      }
+    }				/* end for k */
+  }				/* end for j */
+}				/* end HGCurve */
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	Parameterize (xpoints, ypoints, hparams, num_points)
+ |
+ | Results:	This routine calculates parametric values for use in
+ |		calculating curves.  The parametric values are returned
+ |		in the array h.  The values are an approximation of
+ |		cumulative arc lengths of the curve (uses cord length).
+ |		For additional information, see paper cited below.
+ *--------------------------------------------------------------------*/
+
+void
+Parameterize(int x[],
+	     int y[],
+	     double h[],
+	     int n)
+{
+  int dx;
+  int dy;
+  int i;
+  int j;
+  double u[MAXPOINTS];
+
+  for (i = 1; i <= n; ++i) {
+    u[i] = 0;
+    for (j = 1; j < i; j++) {
+      dx = x[j + 1] - x[j];
+      dy = y[j + 1] - y[j];
+      /* Here was overflowing, so I changed it.       */
+      /* u[i] += sqrt ((double) (dx * dx + dy * dy)); */
+      u[i] += groff_hypot((double) dx, (double) dy);
+    }
+  }
+  for (i = 1; i < n; ++i)
+    h[i] = u[i + 1] - u[i];
+}				/* end Parameterize */
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	PeriodicSpline (h, z, dz, d2z, d3z, npoints)
+ |
+ | Results:	This routine solves for the cubic polynomial to fit a
+ |		spline curve to the points specified by the list of
+ |		values.  The curve generated is periodic.  The
+ |		algorithms for this curve are from the 'Spline Curve
+ |		Techniques' paper cited above.
+ *--------------------------------------------------------------------*/
+
+void
+PeriodicSpline(double h[],	/* parameterization  */
+	       int z[],		/* point list */
+	       double dz[],	/* to return the 1st derivative */
+	       double d2z[],	/* 2nd derivative */
+	       double d3z[],	/* 3rd derivative */
+	       int npoints)	/* number of valid points */
+{
+  double d[MAXPOINTS];
+  double deltaz[MAXPOINTS], a[MAXPOINTS], b[MAXPOINTS];
+  double c[MAXPOINTS], r[MAXPOINTS], s[MAXPOINTS];
+  int i;
+
+  /* step 1 */
+  for (i = 1; i < npoints; ++i) {
+    deltaz[i] = h[i] ? ((double) (z[i + 1] - z[i])) / h[i] : 0;
+  }
+  h[0] = h[npoints - 1];
+  deltaz[0] = deltaz[npoints - 1];
+
+  /* step 2 */
+  for (i = 1; i < npoints - 1; ++i) {
+    d[i] = deltaz[i + 1] - deltaz[i];
+  }
+  d[0] = deltaz[1] - deltaz[0];
+
+  /* step 3a */
+  a[1] = 2 * (h[0] + h[1]);
+  b[1] = d[0];
+  c[1] = h[0];
+  for (i = 2; i < npoints - 1; ++i) {
+    a[i] = 2 * (h[i - 1] + h[i]) -
+	   pow((double) h[i - 1], (double) 2.0) / a[i - 1];
+    b[i] = d[i - 1] - h[i - 1] * b[i - 1] / a[i - 1];
+    c[i] = -h[i - 1] * c[i - 1] / a[i - 1];
+  }
+
+  /* step 3b */
+  r[npoints - 1] = 1;
+  s[npoints - 1] = 0;
+  for (i = npoints - 2; i > 0; --i) {
+    r[i] = -(h[i] * r[i + 1] + c[i]) / a[i];
+    s[i] = (6 * b[i] - h[i] * s[i + 1]) / a[i];
+  }
+
+  /* step 4 */
+  d2z[npoints - 1] = (6 * d[npoints - 2] - h[0] * s[1]
+		      - h[npoints - 1] * s[npoints - 2])
+		     / (h[0] * r[1] + h[npoints - 1] * r[npoints - 2]
+		      + 2 * (h[npoints - 2] + h[0]));
+  for (i = 1; i < npoints - 1; ++i) {
+    d2z[i] = r[i] * d2z[npoints - 1] + s[i];
+  }
+  d2z[npoints] = d2z[1];
+
+  /* step 5 */
+  for (i = 1; i < npoints; ++i) {
+    dz[i] = deltaz[i] - h[i] * (2 * d2z[i] + d2z[i + 1]) / 6;
+    d3z[i] = h[i] ? (d2z[i + 1] - d2z[i]) / h[i] : 0;
+  }
+}				/* end PeriodicSpline */
+
+
+/*--------------------------------------------------------------------
+ | Routine:	NaturalEndSpline (h, z, dz, d2z, d3z, npoints)
+ |
+ | Results:	This routine solves for the cubic polynomial to fit a
+ |		spline curve the points specified by the list of values.
+ |		The algorithms for this curve are from the 'Spline Curve
+ |		Techniques' paper cited above.
+ *--------------------------------------------------------------------*/
+
+void
+NaturalEndSpline(double h[],	/* parameterization */
+		 int z[],	/* Point list */
+		 double dz[],	/* to return the 1st derivative */
+		 double d2z[],	/* 2nd derivative */
+		 double d3z[],	/* 3rd derivative */
+		 int npoints)	/* number of valid points */
+{
+  double d[MAXPOINTS];
+  double deltaz[MAXPOINTS], a[MAXPOINTS], b[MAXPOINTS];
+  int i;
+
+  /* step 1 */
+  for (i = 1; i < npoints; ++i) {
+    deltaz[i] = h[i] ? ((double) (z[i + 1] - z[i])) / h[i] : 0;
+  }
+  deltaz[0] = deltaz[npoints - 1];
+
+  /* step 2 */
+  for (i = 1; i < npoints - 1; ++i) {
+    d[i] = deltaz[i + 1] - deltaz[i];
+  }
+  d[0] = deltaz[1] - deltaz[0];
+
+  /* step 3 */
+  a[0] = 2 * (h[2] + h[1]);
+  b[0] = d[1];
+  for (i = 1; i < npoints - 2; ++i) {
+    a[i] = 2 * (h[i + 1] + h[i + 2]) -
+	    pow((double) h[i + 1], (double) 2.0) / a[i - 1];
+    b[i] = d[i + 1] - h[i + 1] * b[i - 1] / a[i - 1];
+  }
+
+  /* step 4 */
+  d2z[npoints] = d2z[1] = 0;
+  for (i = npoints - 1; i > 1; --i) {
+    d2z[i] = (6 * b[i - 2] - h[i] * d2z[i + 1]) / a[i - 2];
+  }
+
+  /* step 5 */
+  for (i = 1; i < npoints; ++i) {
+    dz[i] = deltaz[i] - h[i] * (2 * d2z[i] + d2z[i + 1]) / 6;
+    d3z[i] = h[i] ? (d2z[i + 1] - d2z[i]) / h[i] : 0;
+  }
+}				/* end NaturalEndSpline */
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	change (x_position, y_position, visible_flag)
+ |
+ | Results:	As HGtline passes from the invisible to visible (or vice
+ |		versa) portion of a line, change is called to either
+ |		draw the line, or initialize the beginning of the next
+ |		one.  Change calls line to draw segments if visible_flag
+ |		is set (which means we're leaving a visible area).
+ *--------------------------------------------------------------------*/
+
+void
+change(int x,
+       int y,
+       int vis)
+{
+  static int length = 0;
+
+  if (vis) {			/* leaving a visible area, draw it. */
+    line(x, y);
+    if (length++ > LINELENGTH) {
+      length = 0;
+      printf("\\\n");
+    }
+  } else {			/* otherwise entering one; remember */
+				/* beginning                        */
+    tmove2(x, y);
+  }
+}
+
+
+/*--------------------------------------------------------------------*
+ | Routine:	HGtline (xstart, ystart, xend, yend)
+ |
+ | Results:	Draws a line from current position to (x1,y1) using
+ |		line(x1, y1) to place individual segments of dotted or
+ |		dashed lines.
+ *--------------------------------------------------------------------*/
+
+void
+HGtline(int x_1,
+	int y_1)
+{
+  int x_0 = lastx;
+  int y_0 = lasty;
+  int dx;
+  int dy;
+  int oldcoord;
+  int res1;
+  int visible;
+  int res2;
+  int xinc;
+  int yinc;
+  int dotcounter;
+
+  if (linmod == SOLID) {
+    line(x_1, y_1);
+    return;
+  }
+
+  /* for handling different resolutions */
+  dotcounter = linmod << dotshifter;
+
+  xinc = 1;
+  yinc = 1;
+  if ((dx = x_1 - x_0) < 0) {
+    xinc = -xinc;
+    dx = -dx;
+  }
+  if ((dy = y_1 - y_0) < 0) {
+    yinc = -yinc;
+    dy = -dy;
+  }
+  res1 = 0;
+  res2 = 0;
+  visible = 0;
+  if (dx >= dy) {
+    oldcoord = y_0;
+    while (x_0 != x_1) {
+      if ((x_0 & dotcounter) && !visible) {
+	change(x_0, y_0, 0);
+	visible = 1;
+      } else if (visible && !(x_0 & dotcounter)) {
+	change(x_0 - xinc, oldcoord, 1);
+	visible = 0;
+      }
+      if (res1 > res2) {
+	oldcoord = y_0;
+	res2 += dx - res1;
+	res1 = 0;
+	y_0 += yinc;
+      }
+      res1 += dy;
+      x_0 += xinc;
+    }
+  } else {
+    oldcoord = x_0;
+    while (y_0 != y_1) {
+      if ((y_0 & dotcounter) && !visible) {
+	change(x_0, y_0, 0);
+	visible = 1;
+      } else if (visible && !(y_0 & dotcounter)) {
+	change(oldcoord, y_0 - yinc, 1);
+	visible = 0;
+      }
+      if (res1 > res2) {
+	oldcoord = x_0;
+	res2 += dy - res1;
+	res1 = 0;
+	x_0 += xinc;
+      }
+      res1 += dx;
+      y_0 += yinc;
+    }
+  }
+  if (visible)
+    change(x_1, y_1, 1);
+  else
+    change(x_1, y_1, 0);
+}
+
+// Local Variables:
+// fill-column: 72
+// mode: C++
+// End:
+// vim: set cindent noexpandtab shiftwidth=2 textwidth=72: