rsvg-path.c

/* -*- Mode: C; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/* vim: set sw=4 sts=4 ts=4 expandtab: */
/* 
   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 Library 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
   Library General Public License for more details.
  
   You should have received a copy of the GNU Library 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>
           F. Wang <fred.wang@free.fr> - fix drawing of arc
*/

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

#include "config.h"
#include "rsvg-path.h"

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

#include "rsvg-private.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.
*/

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 x1, y1, x2, y2, x3, y3;
    double t;
    double th_half;
    double f, sinf, cosf;

    f = x_axis_rotation * M_PI / 180.0;
    sinf = sin(f);
    cosf = cos(f);

    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 = rx*(cos (th0) - t * sin (th0));
    y1 = ry*(sin (th0) + t * cos (th0));
    x3 = rx*cos (th1);
    y3 = ry*sin (th1);
    x2 = x3 + rx*(t * sin (th1));
    y2 = y3 + ry*(-t * cos (th1));

    rsvg_bpath_def_curveto (ctx->bpath,
                            xc + cosf*x1 - sinf*y1,
                            yc + sinf*x1 + cosf*y1,
                            xc + cosf*x2 - sinf*y2,
                            yc + sinf*x2 + cosf*y2,
                            xc + cosf*x3 - sinf*y3,
                            yc + sinf*x3 + cosf*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)
{

    /* See Appendix F.6 Elliptical arc implementation notes
       http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes */

    double f, sinf, cosf;
    double x1, y1, x2, y2;
    double x1_, y1_;
    double cx_, cy_, cx, cy;
    double gamma;
    double theta1, delta_theta;
    double k1, k2, k3, k4, k5;

    int i, n_segs;

    /* Start and end of path segment */
    x1 = ctx->cpx;
    y1 = ctx->cpy;

    x2 = x;
    y2 = y;

    if(x1 == x2 && y1 == y2)
        return;

    /* X-axis */
    f = x_axis_rotation * M_PI / 180.0;
    sinf = sin(f);
    cosf = cos(f);

    /* Check the radius against floading point underflow.
       See http://bugs.debian.org/508443 */
    if ((fabs(rx) < DBL_EPSILON) || (fabs(ry) < DBL_EPSILON)) {
        rsvg_bpath_def_lineto (ctx->bpath, x, y);
        return;
    }

    if(rx < 0)rx = -rx;
    if(ry < 0)ry = -ry;

    k1 = (x1 - x2)/2;
    k2 = (y1 - y2)/2;

    x1_ = cosf * k1 + sinf * k2;
    y1_ = -sinf * k1 + cosf * k2;

    gamma = (x1_*x1_)/(rx*rx) + (y1_*y1_)/(ry*ry);
    if (gamma > 1) {
        rx *= sqrt(gamma);
        ry *= sqrt(gamma);
    }

    /* Compute the center */

    k1 = rx*rx*y1_*y1_ + ry*ry*x1_*x1_;
    if(k1 == 0)    
        return;

    k1 = sqrt(fabs((rx*rx*ry*ry)/k1 - 1));
    if(sweep_flag == large_arc_flag)
        k1 = -k1;

    cx_ = k1*rx*y1_/ry;
    cy_ = -k1*ry*x1_/rx;
    
    cx = cosf*cx_ - sinf*cy_ + (x1+x2)/2;
    cy = sinf*cx_ + cosf*cy_ + (y1+y2)/2;

    /* Compute start angle */

    k1 = (x1_ - cx_)/rx;
    k2 = (y1_ - cy_)/ry;
    k3 = (-x1_ - cx_)/rx;
    k4 = (-y1_ - cy_)/ry;

    k5 = sqrt(fabs(k1*k1 + k2*k2));
    if(k5 == 0)return;

    k5 = k1/k5;
    if(k5 < -1)k5 = -1;
    else if(k5 > 1)k5 = 1;
    theta1 = acos(k5);
    if(k2 < 0)theta1 = -theta1;

    /* Compute delta_theta */

    k5 = sqrt(fabs((k1*k1 + k2*k2)*(k3*k3 + k4*k4)));
    if(k5 == 0)return;

    k5 = (k1*k3 + k2*k4)/k5;
    if(k5 < -1)k5 = -1;
    else if(k5 > 1)k5 = 1;
    delta_theta = acos(k5);
    if(k1*k4 - k3*k2 < 0)delta_theta = -delta_theta;

    if(sweep_flag && delta_theta < 0)
        delta_theta += M_PI*2;
    else if(!sweep_flag && delta_theta > 0)
        delta_theta -= M_PI*2;
   
    /* Now draw the arc */

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

    for (i = 0; i < n_segs; i++)
        rsvg_path_arc_segment (ctx, cx, cy,
			                   theta1 + i * delta_theta / n_segs,
                               theta1 + (i + 1) * delta_theta / 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;

    switch (ctx->cmd) {
    case 'm':
        /* moveto */
        if (ctx->param == 2 || final) {
            rsvg_parse_path_default_xy (ctx, 2);
            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;
	    ctx->cmd = 'l'; /* implicit linetos after a moveto */
        }
        break;
    case 'l':
        /* lineto */
        if (ctx->param == 2 || final) {
            rsvg_parse_path_default_xy (ctx, 2);
            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];
            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];
            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) {
            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) {
            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);
            rsvg_bpath_def_curveto (ctx->bpath, x1, y1, x2, y2, x3, y3);
            ctx->rpx = ctx->params[0];
            ctx->rpy = ctx->params[1];
            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);
            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);
                rsvg_bpath_def_curveto (ctx->bpath, x1, y1, x2, y2, x3, y3);
                ctx->rpx = ctx->params[0];
                ctx->rpy = ctx->params[1];
                ctx->cpx = x3;
                ctx->cpy = y3;
            } else {
                rsvg_parse_path_default_xy (ctx, 2);
                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_path_end_of_number (RSVGParsePathCtx * ctx, double val, int sign, int exp_sign, int exp)
{
    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':
            /* 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;
        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);    
}

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_frac = TRUE;
                val = 0;
            }
            else if (in_frac) {
                rsvg_path_end_of_number(ctx, val, sign, exp_sign, exp);
                in_frac = FALSE;
                in_exp = FALSE;
                exp = 0;
                exp_sign = 1;
                exp_wait_sign = FALSE;
                val = 0;
                sign = 1;
            }
            else {
                in_frac = TRUE;
            }
            in_num = 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 */
            rsvg_path_end_of_number(ctx, val, sign, exp_sign, exp);
            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);
            rsvg_bpath_def_closepath (ctx->bpath);

            ctx->cpx = ctx->rpx = ctx->bpath->bpath[ctx->bpath->n_bpath - 1].x3;
            ctx->cpy = ctx->rpy = ctx->bpath->bpath[ctx->bpath->n_bpath - 1].y3;
        } 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;
}