path: root/librsvg/rsvg-path.c

/* 
   rsvg-path.c: Parse SVG path element data into bezier path.
 
   Copyright (C) 2000 Eazel, Inc.
  
   This program is free software; you can redistribute it and/or
   modify it under the terms of the GNU General Public License as
   published by the Free Software Foundation; either version 2 of the
   License, or (at your option) any later version.
  
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   General Public License for more details.
  
   You should have received a copy of the GNU General Public
   License along with this program; if not, write to the
   Free Software Foundation, Inc., 59 Temple Place - Suite 330,
   Boston, MA 02111-1307, USA.
  
   Author: Raph Levien <raph@artofcode.com>
*/

/* This is adapted from svg-path in Gill. */

#include <string.h>
#include <stdlib.h>
#include <math.h>

#include <glib.h>

#include "rsvg-bpath-util.h"
#include "rsvg-path.h"

/* This module parses an SVG path element into an RsvgBpathDef.

   At present, there is no support for <marker> or any other contextual
   information from the SVG file. The API will need to change rather
   significantly to support these.

   Reference: SVG working draft 3 March 2000, section 8.
*/

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif  /*  M_PI  */

typedef struct _RSVGParsePathCtx RSVGParsePathCtx;

struct _RSVGParsePathCtx {
  RsvgBpathDef *bpath;
  double cpx, cpy;  /* current point */
  double rpx, rpy;  /* reflection point (for 's' and 't' commands) */
  char cmd;         /* current command (lowercase) */
  int param;        /* parameter number */
  gboolean rel;     /* true if relative coords */
  double params[7]; /* parameters that have been parsed */
};

static void
rsvg_path_arc_segment (RSVGParsePathCtx *ctx,
		      double xc, double yc,
		      double th0, double th1,
		      double rx, double ry, double x_axis_rotation)
{
  double sin_th, cos_th;
  double a00, a01, a10, a11;
  double x1, y1, x2, y2, x3, y3;
  double t;
  double th_half;

  sin_th = sin (x_axis_rotation * (M_PI / 180.0));
  cos_th = cos (x_axis_rotation * (M_PI / 180.0)); 
  /* inverse transform compared with rsvg_path_arc */
  a00 = cos_th * rx;
  a01 = -sin_th * ry;
  a10 = sin_th * rx;
  a11 = cos_th * ry;

  th_half = 0.5 * (th1 - th0);
  t = (8.0 / 3.0) * sin (th_half * 0.5) * sin (th_half * 0.5) / sin (th_half);
  x1 = xc + cos (th0) - t * sin (th0);
  y1 = yc + sin (th0) + t * cos (th0);
  x3 = xc + cos (th1);
  y3 = yc + sin (th1);
  x2 = x3 + t * sin (th1);
  y2 = y3 - t * cos (th1);
  rsvg_bpath_def_curveto (ctx->bpath,
				  a00 * x1 + a01 * y1, a10 * x1 + a11 * y1,
				  a00 * x2 + a01 * y2, a10 * x2 + a11 * y2,
				  a00 * x3 + a01 * y3, a10 * x3 + a11 * y3);
}

/**
 * rsvg_path_arc: Add an RSVG arc to the path context.
 * @ctx: Path context.
 * @rx: Radius in x direction (before rotation).
 * @ry: Radius in y direction (before rotation).
 * @x_axis_rotation: Rotation angle for axes.
 * @large_arc_flag: 0 for arc length <= 180, 1 for arc >= 180.
 * @sweep: 0 for "negative angle", 1 for "positive angle".
 * @x: New x coordinate.
 * @y: New y coordinate.
 *
 **/
static void
rsvg_path_arc (RSVGParsePathCtx *ctx,
	      double rx, double ry, double x_axis_rotation,
	      int large_arc_flag, int sweep_flag,
	      double x, double y)
{
  double sin_th, cos_th;
  double a00, a01, a10, a11;
  double x0, y0, x1, y1, xc, yc;
  double d, sfactor, sfactor_sq;
  double th0, th1, th_arc;
  int i, n_segs;

  sin_th = sin (x_axis_rotation * (M_PI / 180.0));
  cos_th = cos (x_axis_rotation * (M_PI / 180.0));
  a00 = cos_th / rx;
  a01 = sin_th / rx;
  a10 = -sin_th / ry;
  a11 = cos_th / ry;
  x0 = a00 * ctx->cpx + a01 * ctx->cpy;
  y0 = a10 * ctx->cpx + a11 * ctx->cpy;
  x1 = a00 * x + a01 * y;
  y1 = a10 * x + a11 * y;
  /* (x0, y0) is current point in transformed coordinate space.
     (x1, y1) is new point in transformed coordinate space.

     The arc fits a unit-radius circle in this space.
  */
  d = (x1 - x0) * (x1 - x0) + (y1 - y0) * (y1 - y0);
  sfactor_sq = 1.0 / d - 0.25;
  if (sfactor_sq < 0) sfactor_sq = 0;
  sfactor = sqrt (sfactor_sq);
  if (sweep_flag == large_arc_flag) sfactor = -sfactor;
  xc = 0.5 * (x0 + x1) - sfactor * (y1 - y0);
  yc = 0.5 * (y0 + y1) + sfactor * (x1 - x0);
  /* (xc, yc) is center of the circle. */

  th0 = atan2 (y0 - yc, x0 - xc);
  th1 = atan2 (y1 - yc, x1 - xc);

  th_arc = th1 - th0;
  if (th_arc < 0 && sweep_flag)
    th_arc += 2 * M_PI;
  else if (th_arc > 0 && !sweep_flag)
    th_arc -= 2 * M_PI;

  n_segs = ceil (fabs (th_arc / (M_PI * 0.5 + 0.001)));

  for (i = 0; i < n_segs; i++)
    rsvg_path_arc_segment (ctx, xc, yc,
			  th0 + i * th_arc / n_segs,
			  th0 + (i + 1) * th_arc / n_segs,
			  rx, ry, x_axis_rotation);

  ctx->cpx = x;
  ctx->cpy = y;
}


/* supply defaults for missing parameters, assuming relative coordinates
   are to be interpreted as x,y */
static void
rsvg_parse_path_default_xy (RSVGParsePathCtx *ctx, int n_params)
{
  int i;

  if (ctx->rel)
    {
      for (i = ctx->param; i < n_params; i++)
	{
	  if (i > 2)
	    ctx->params[i] = ctx->params[i - 2];
	  else if (i == 1)
	    ctx->params[i] = ctx->cpy;
	  else if (i == 0)
	    /* we shouldn't get here (usually ctx->param > 0 as
               precondition) */
	    ctx->params[i] = ctx->cpx;
	}
    }
  else
    {
      for (i = ctx->param; i < n_params; i++)
	ctx->params[i] = 0.0;
    }
}

static void
rsvg_parse_path_do_cmd (RSVGParsePathCtx *ctx, gboolean final)
{
  double x1, y1, x2, y2, x3, y3;

#ifdef VERBOSE
  int i;

  g_print ("parse_path %c:", ctx->cmd);
  for (i = 0; i < ctx->param; i++)
    g_print (" %f", ctx->params[i]);
  g_print (final ? ".\n" : "\n");
#endif

  switch (ctx->cmd)
    {
    case 'm':
      /* moveto */
      if (ctx->param == 2 || final)
	{
	  rsvg_parse_path_default_xy (ctx, 2);
#ifdef VERBOSE
	  g_print ("'m' moveto %g,%g\n",
		   ctx->params[0], ctx->params[1]);
#endif
	  rsvg_bpath_def_moveto (ctx->bpath,
					 ctx->params[0], ctx->params[1]);
	  ctx->cpx = ctx->rpx = ctx->params[0];
	  ctx->cpy = ctx->rpy = ctx->params[1];
	  ctx->param = 0;
	}
      break;
    case 'l':
      /* lineto */
      if (ctx->param == 2 || final)
	{
	  rsvg_parse_path_default_xy (ctx, 2);
#ifdef VERBOSE
	  g_print ("'l' lineto %g,%g\n",
		   ctx->params[0], ctx->params[1]);
#endif
	  rsvg_bpath_def_lineto (ctx->bpath,
					 ctx->params[0], ctx->params[1]);
	  ctx->cpx = ctx->rpx = ctx->params[0];
	  ctx->cpy = ctx->rpy = ctx->params[1];
	  ctx->param = 0;
	}
      break;
    case 'c':
      /* curveto */
      if (ctx->param == 6 || final)
	{
	  rsvg_parse_path_default_xy (ctx, 6);
	  x1 = ctx->params[0];
	  y1 = ctx->params[1];
	  x2 = ctx->params[2];
	  y2 = ctx->params[3];
	  x3 = ctx->params[4];
	  y3 = ctx->params[5];
#ifdef VERBOSE
	  g_print ("'c' curveto %g,%g %g,%g, %g,%g\n",
		   x1, y1, x2, y2, x3, y3);
#endif
	  rsvg_bpath_def_curveto (ctx->bpath,
					  x1, y1, x2, y2, x3, y3);
	  ctx->rpx = x2;
	  ctx->rpy = y2;
	  ctx->cpx = x3;
	  ctx->cpy = y3;
	  ctx->param = 0;
	}
      break;
    case 's':
      /* smooth curveto */
      if (ctx->param == 4 || final)
	{
	  rsvg_parse_path_default_xy (ctx, 4);
	  x1 = 2 * ctx->cpx - ctx->rpx;
	  y1 = 2 * ctx->cpy - ctx->rpy;
	  x2 = ctx->params[0];
	  y2 = ctx->params[1];
	  x3 = ctx->params[2];
	  y3 = ctx->params[3];
#ifdef VERBOSE
	  g_print ("'s' curveto %g,%g %g,%g, %g,%g\n",
		   x1, y1, x2, y2, x3, y3);
#endif
	  rsvg_bpath_def_curveto (ctx->bpath,
					  x1, y1, x2, y2, x3, y3);
	  ctx->rpx = x2;
	  ctx->rpy = y2;
	  ctx->cpx = x3;
	  ctx->cpy = y3;
	  ctx->param = 0;
	}
      break;
    case 'h':
      /* horizontal lineto */
      if (ctx->param == 1)
	{
#ifdef VERBOSE
	  g_print ("'h' lineto %g,%g\n",
		   ctx->params[0], ctx->cpy);
#endif
	  rsvg_bpath_def_lineto (ctx->bpath,
					 ctx->params[0], ctx->cpy);
	  ctx->cpx = ctx->rpx = ctx->params[0];
	  ctx->param = 0;
	}
      break;
    case 'v':
      /* vertical lineto */
      if (ctx->param == 1)
	{
#ifdef VERBOSE
	  g_print ("'v' lineto %g,%g\n",
		   ctx->cpx, ctx->params[0]);
#endif
	  rsvg_bpath_def_lineto (ctx->bpath,
					 ctx->cpx, ctx->params[0]);
	  ctx->cpy = ctx->rpy = ctx->params[0];
	  ctx->param = 0;
	}
      break;
    case 'q':
      /* quadratic bezier curveto */

      /* non-normative reference:
	 http://www.icce.rug.nl/erikjan/bluefuzz/beziers/beziers/beziers.html
      */
      if (ctx->param == 4 || final)
	{
	  rsvg_parse_path_default_xy (ctx, 4);
	  /* raise quadratic bezier to cubic */
	  x1 = (ctx->cpx + 2 * ctx->params[0]) * (1.0 / 3.0);
	  y1 = (ctx->cpy + 2 * ctx->params[1]) * (1.0 / 3.0);
	  x3 = ctx->params[2];
	  y3 = ctx->params[3];
	  x2 = (x3 + 2 * ctx->params[0]) * (1.0 / 3.0);
	  y2 = (y3 + 2 * ctx->params[1]) * (1.0 / 3.0);
#ifdef VERBOSE
	  g_print ("'q' curveto %g,%g %g,%g, %g,%g\n",
		   x1, y1, x2, y2, x3, y3);
#endif
	  rsvg_bpath_def_curveto (ctx->bpath,
					  x1, y1, x2, y2, x3, y3);
	  ctx->rpx = x2;
	  ctx->rpy = y2;
	  ctx->cpx = x3;
	  ctx->cpy = y3;
	  ctx->param = 0;
	}
      break;
    case 't':
      /* Truetype quadratic bezier curveto */
      if (ctx->param == 2 || final)
	{
	  double xc, yc; /* quadratic control point */

	  xc = 2 * ctx->cpx - ctx->rpx;
	  yc = 2 * ctx->cpy - ctx->rpy;
	  /* generate a quadratic bezier with control point = xc, yc */
	  x1 = (ctx->cpx + 2 * xc) * (1.0 / 3.0);
	  y1 = (ctx->cpy + 2 * yc) * (1.0 / 3.0);
	  x3 = ctx->params[0];
	  y3 = ctx->params[1];
	  x2 = (x3 + 2 * xc) * (1.0 / 3.0);
	  y2 = (y3 + 2 * yc) * (1.0 / 3.0);
#ifdef VERBOSE
	  g_print ("'t' curveto %g,%g %g,%g, %g,%g\n",
		   x1, y1, x2, y2, x3, y3);
#endif
	  rsvg_bpath_def_curveto (ctx->bpath,
					  x1, y1, x2, y2, x3, y3);
	  ctx->rpx = xc;
	  ctx->rpy = yc;
	  ctx->cpx = x3;
	  ctx->cpy = y3;
	  ctx->param = 0;
	}
      else if (final)
	{
	  if (ctx->param > 2)
	    {
	      rsvg_parse_path_default_xy (ctx, 4);
	      /* raise quadratic bezier to cubic */
	      x1 = (ctx->cpx + 2 * ctx->params[0]) * (1.0 / 3.0);
	      y1 = (ctx->cpy + 2 * ctx->params[1]) * (1.0 / 3.0);
	      x3 = ctx->params[2];
	      y3 = ctx->params[3];
	      x2 = (x3 + 2 * ctx->params[0]) * (1.0 / 3.0);
	      y2 = (y3 + 2 * ctx->params[1]) * (1.0 / 3.0);
#ifdef VERBOSE
	      g_print ("'t' curveto %g,%g %g,%g, %g,%g\n",
		       x1, y1, x2, y2, x3, y3);
#endif
	      rsvg_bpath_def_curveto (ctx->bpath,
					      x1, y1, x2, y2, x3, y3);
	      ctx->rpx = x2;
	      ctx->rpy = y2;
	      ctx->cpx = x3;
	      ctx->cpy = y3;
	    }
	  else
	    {
	      rsvg_parse_path_default_xy (ctx, 2);
#ifdef VERBOSE
	      g_print ("'t' lineto %g,%g\n",
		       ctx->params[0], ctx->params[1]);
#endif
	      rsvg_bpath_def_lineto (ctx->bpath,
					     ctx->params[0], ctx->params[1]);
	      ctx->cpx = ctx->rpx = ctx->params[0];
	      ctx->cpy = ctx->rpy = ctx->params[1];
	    }
	  ctx->param = 0;
	}
      break;
    case 'a':
      if (ctx->param == 7 || final)
	{
	  rsvg_path_arc (ctx,
			ctx->params[0], ctx->params[1], ctx->params[2],
			ctx->params[3], ctx->params[4],
			ctx->params[5], ctx->params[6]);
	  ctx->param = 0;
	}
      break;
    default:
      ctx->param = 0;
    }
}

static void
rsvg_parse_path_data (RSVGParsePathCtx *ctx, const char *data)
{
  int i = 0;
  double val = 0;
  char c = 0;
  gboolean in_num = FALSE;
  gboolean in_frac = FALSE;
  gboolean in_exp = FALSE;
  gboolean exp_wait_sign = FALSE;
  int sign = 0;
  int exp = 0;
  int exp_sign = 0;
  double frac = 0.0;

  in_num = FALSE;
  for (i = 0; ; i++)
    {
      c = data[i];
      if (c >= '0' && c <= '9')
	{
	  /* digit */
	  if (in_num)
	    {
	      if (in_exp)
		{
		  exp = (exp * 10) + c - '0';
		  exp_wait_sign = FALSE;
		}
	      else if (in_frac)
		val += (frac *= 0.1) * (c - '0');
	      else
		val = (val * 10) + c - '0';
	    }
	  else
	    {
	      in_num = TRUE;
	      in_frac = FALSE;
	      in_exp = FALSE;
	      exp = 0;
	      exp_sign = 1;
	      exp_wait_sign = FALSE;
	      val = c - '0';
	      sign = 1;
	    }
	}
      else if (c == '.')
	{
	  if (!in_num)
	    {
	      in_num = TRUE;
	      val = 0;
	    }
	  in_frac = TRUE;
	  frac = 1;
	}
      else if ((c == 'E' || c == 'e') && in_num)
	{
	  in_exp = TRUE;
	  exp_wait_sign = TRUE;
	  exp = 0;
	  exp_sign = 1;
	}
      else if ((c == '+' || c == '-') && in_exp)
	{
	  exp_sign = c == '+' ? 1 : -1;
	}
      else if (in_num)
	{
	  /* end of number */

	  val *= sign * pow (10, exp_sign * exp);
	  if (ctx->rel)
	    {
	      /* Handle relative coordinates. This switch statement attempts
		 to determine _what_ the coords are relative to. This is
		 underspecified in the 12 Apr working draft. */
	      switch (ctx->cmd)
		{
		case 'l':
		case 'm':
		case 'c':
		case 's':
		case 'q':
		case 't':
#ifndef RSVGV_RELATIVE
		  /* rule: even-numbered params are x-relative, odd-numbered
		     are y-relative */
		  if ((ctx->param & 1) == 0)
		    val += ctx->cpx;
		  else if ((ctx->param & 1) == 1)
		    val += ctx->cpy;
		  break;
#else
		  /* rule: even-numbered params are x-relative, odd-numbered
		     are y-relative */
		  if (ctx->param == 0 || (ctx->param % 2 ==0))
		    val += ctx->cpx;
		  else 
		    val += ctx->cpy;
		  break;
#endif
		case 'a':
		  /* rule: sixth and seventh are x and y, rest are not
		     relative */
		  if (ctx->param == 5)
		    val += ctx->cpx;
		  else if (ctx->param == 6)
		    val += ctx->cpy;
		  break;
		case 'h':
		  /* rule: x-relative */
		  val += ctx->cpx;
		  break;
		case 'v':
		  /* rule: y-relative */
		  val += ctx->cpy;
		  break;
		}
	    }
	  ctx->params[ctx->param++] = val;
	  rsvg_parse_path_do_cmd (ctx, FALSE);
	  in_num = FALSE;
	}

      if (c == '\0')
	break;
      else if ((c == '+' || c == '-') && !exp_wait_sign)
	{
	  sign = c == '+' ? 1 : -1;;
	  val = 0;
	  in_num = TRUE;
	  in_frac = FALSE;
	  in_exp = FALSE;
	  exp = 0;
	  exp_sign = 1;
	  exp_wait_sign = FALSE;
	}
      else if (c == 'z' || c == 'Z')
	{
	  if (ctx->param)
	    rsvg_parse_path_do_cmd (ctx, TRUE);
#ifdef VERBOSE
	  g_print ("'z' closepath\n");
#endif
	  rsvg_bpath_def_closepath (ctx->bpath);
	}
      else if (c >= 'A' && c <= 'Z' && c != 'E')
	{
	  if (ctx->param)
	    rsvg_parse_path_do_cmd (ctx, TRUE);
	  ctx->cmd = c + 'a' - 'A';
	  ctx->rel = FALSE;
	}
      else if (c >= 'a' && c <= 'z' && c != 'e')
	{
	  if (ctx->param)
	    rsvg_parse_path_do_cmd (ctx, TRUE);
	  ctx->cmd = c;
	  ctx->rel = TRUE;
	}
      /* else c _should_ be whitespace or , */
    }
}

RsvgBpathDef *
rsvg_parse_path (const char *path_str)
{
  RSVGParsePathCtx ctx;

  ctx.bpath = rsvg_bpath_def_new ();
  ctx.cpx = 0.0;
  ctx.cpy = 0.0;
  ctx.cmd = 0;
  ctx.param = 0;

  rsvg_parse_path_data (&ctx, path_str);

  if (ctx.param)
    rsvg_parse_path_do_cmd (&ctx, TRUE);

  return ctx.bpath;
}