/* Copyright (C) 2001-2026 Artifex Software, Inc.

   All Rights Reserved.

   This software is provided AS-IS with no warranty, either express or

   implied.

   This software is distributed under license and may not be copied,

   modified or distributed except as expressly authorized under the terms

   of the license contained in the file LICENSE in this distribution.

   Refer to licensing information at http://www.artifex.com or contact

   Artifex Software, Inc.,  39 Mesa Street, Suite 108A, San Francisco,

   CA 94129, USA, for further information.

*/

/* Additional PostScript Level 1 path routines for Ghostscript library */

#include "math_.h"

#include "gx.h"

#include "gserrors.h"

#include "gsstruct.h"

#include "gxfixed.h"

#include "gxfarith.h"

#include "gxmatrix.h"

#include "gzstate.h"

#include "gspath.h"

#include "gzpath.h"

#include "gscoord.h"            /* gs_itransform prototype */

/* ------ Arcs ------ */

/* Conversion parameters */

#define degrees_to_radians (M_PI / 180.0)

typedef enum {

    arc_nothing,

    arc_moveto,

    arc_lineto

} arc_action;

typedef struct arc_curve_params_s {

    /* The following are set once. */

    gx_path *ppath;

    gs_gstate *pgs;

    gs_point center;            /* (not used by arc_add) */

    double radius;

    /* The following may be updated dynamically. */

    arc_action action;

    segment_notes notes;

    gs_point p0, p3, pt;

    gs_sincos_t sincos;         /* (not used by arc_add) */

    double angle;               /* (not used by arc_add) */

    int fast_quadrant;          /* 0 = not calculated, -1 = not fast, */

                                /* 1 = fast (only used for quadrants) */

    /* The following are set once iff fast_quadrant > 0. */

    fixed scaled_radius;        /* radius * CTM scale */

    fixed quadrant_delta;       /* scaled_radius * quarter_arc_fraction */

} arc_curve_params_t;

/* Forward declarations */

static int arc_add(const arc_curve_params_t *arc, bool is_quadrant);

static int gs_gstate_arc_add(gx_path * ppath, gs_gstate * pgs, bool clockwise,

            double axc, double ayc, double arad, double aang1, double aang2,

                  bool add_line, gs_point *p3);

int

gx_setcurrentpoint_from_path(gs_gstate *pgs, gx_path *path)

{

    gs_point pt;

    pt.x = fixed2float(path->position.x);

    pt.y = fixed2float(path->position.y);

    gx_setcurrentpoint(pgs, pt.x, pt.y);

    pgs->current_point_valid = true;

    return 0;

}

static inline int

gs_arc_add_inline(gs_gstate *pgs, bool cw, double xc, double yc, double rad,

                    double a1, double a2, bool add)

{

    gs_point p3;

    int code = gs_gstate_arc_add(pgs->path, pgs, cw, xc, yc, rad, a1, a2, add, &p3);

    if (code < 0)

        return code;

#if !PRECISE_CURRENTPOINT

    return gx_setcurrentpoint_from_path(pgs, pgs->path);

#else

    pgs->current_point_valid = true;

    return gs_point_transform(p3.x, p3.y, &ctm_only(pgs), &pgs->current_point);

#endif

}

int

gs_arc(gs_gstate * pgs,

       double xc, double yc, double r, double ang1, double ang2)

{

    return gs_arc_add_inline(pgs, false, xc, yc, r, ang1, ang2, true);

}

int

gs_arcn(gs_gstate * pgs,

        double xc, double yc, double r, double ang1, double ang2)

{

    return gs_arc_add_inline(pgs, true, xc, yc, r, ang1, ang2, true);

}

int

gs_arc_add(gs_gstate * pgs, bool clockwise, double axc, double ayc,

           double arad, double aang1, double aang2, bool add_line)

{

    return gs_arc_add_inline(pgs, clockwise, axc, ayc, arad,

                             aang1, aang2, add_line);

}

/* Compute the next curve as part of an arc. */

static int

next_arc_curve(arc_curve_params_t * arc, double anext)

{

    double x0 = arc->p0.x = arc->p3.x;

    double y0 = arc->p0.y = arc->p3.y;

    double trad = arc->radius *

        tan((anext - arc->angle) *

            (degrees_to_radians / 2));

    arc->pt.x = x0 - trad * arc->sincos.sin;

    arc->pt.y = y0 + trad * arc->sincos.cos;

    gs_sincos_degrees(anext, &arc->sincos);

    arc->p3.x = arc->center.x + arc->radius * arc->sincos.cos;

    arc->p3.y = arc->center.y + arc->radius * arc->sincos.sin;

    arc->angle = anext;

    return arc_add(arc, false);

}

/*

 * Use this when both arc.angle and anext are multiples of 90 degrees,

 * and anext = arc.angle +/- 90.

 */

static int

next_arc_quadrant(arc_curve_params_t * arc, double anext)

{

    double x0 = arc->p0.x = arc->p3.x;

    double y0 = arc->p0.y = arc->p3.y;

    if (!arc->fast_quadrant) {

        /*

         * If the CTM is well-behaved, we can pre-calculate the delta

         * from the arc points to the control points.

         */

        const gs_gstate *pgs = arc->pgs;

        double scale = 0; /* Quiet gcc warning. */

        if (is_fzero2(pgs->ctm.xy, pgs->ctm.yx) ?

            (scale = fabs(pgs->ctm.xx)) == fabs(pgs->ctm.yy) :

            is_fzero2(pgs->ctm.xx, pgs->ctm.yy) ?

            (scale = fabs(pgs->ctm.xy)) == fabs(pgs->ctm.yx) :

            0

            ) {

            double scaled_radius = arc->radius * scale;

            arc->scaled_radius = float2fixed(scaled_radius);

            arc->quadrant_delta =

                float2fixed(scaled_radius * quarter_arc_fraction);

            arc->fast_quadrant = 1;

        } else {

            arc->fast_quadrant = -1;

        }

    }

    /*

     * We know that anext is a multiple of 90 (as a fixed); we want

     * (anext / 90) & 3.  The following is much faster than a division.

     */

    switch (((int)anext >> 1) & 3) {

    case 0:

        arc->sincos.sin = 0, arc->sincos.cos = 1;

        arc->p3.x = x0 = arc->center.x + arc->radius;

        arc->p3.y = arc->center.y;

        break;

    case 1:

        arc->sincos.sin = 1, arc->sincos.cos = 0;

        arc->p3.x = arc->center.x;

        arc->p3.y = y0 = arc->center.y + arc->radius;

        break;

    case 2:

        arc->sincos.sin = 0, arc->sincos.cos = -1;

        arc->p3.x = x0 = arc->center.x - arc->radius;

        arc->p3.y = arc->center.y;

        break;

    case 3:

        arc->sincos.sin = -1, arc->sincos.cos = 0;

        arc->p3.x = arc->center.x;

        arc->p3.y = y0 = arc->center.y - arc->radius;

        break;

    }

    arc->pt.x = x0, arc->pt.y = y0;

    arc->angle = anext;

    return arc_add(arc, true);

}

static int

gs_gstate_arc_add(gx_path * ppath, gs_gstate * pgs, bool clockwise,

            double axc, double ayc, double arad, double aang1, double aang2,

                  bool add_line, gs_point *p3)

{

    double ar = arad;

    double ang1 = aang1, ang2 = aang2, anext;

    double ang1r;               /* reduced angle */

    arc_curve_params_t arc;

    int code;

    arc.ppath = ppath;

    arc.pgs = pgs;

    arc.center.x = axc;

    arc.center.y = ayc;

    if (ar < 0) {

        ang1 += 180;

        ang2 += 180;

        ar = -ar;

    }

    if (ang1 > (max_int - 360) || ang2 > (max_int - 360) ||

        ang1 < (min_int + 360) || ang2 < (min_int + 360))

        return_error(gs_error_limitcheck);

    arc.radius = ar;

    arc.action = (add_line ? arc_lineto : arc_moveto);

    arc.notes = sn_none;

    arc.fast_quadrant = 0;

    ang1r = fmod(ang1, 360);

    gs_sincos_degrees(ang1r, &arc.sincos);

    arc.p3.x = axc + ar * arc.sincos.cos;

    arc.p3.y = ayc + ar * arc.sincos.sin;

    if (clockwise) {

        if (ang1 < ang2) {

            ang2 -= ceil((ang2 - ang1) / 360) * 360;

        }

        if (ang2 < 0) {

            double adjust = ceil(-ang2 / 360) * 360;

            ang1 += adjust, ang2 += adjust;

        }

        arc.angle = ang1;

        if (ang1 == ang2)

            goto last;

        /* Do the first part, up to a multiple of 90 degrees. */

        if (!arc.sincos.orthogonal) {

            anext = floor(arc.angle / 90) * 90;

            if (anext < ang2)

                goto last;

            code = next_arc_curve(&arc, anext);

            if (code < 0)

                return code;

            arc.action = arc_nothing;

            arc.notes = sn_not_first;

        }

        /* Do multiples of 90 degrees.  Invariant: ang1 >= ang2 >= 0. */

        while ((anext = arc.angle - 90) >= ang2) {

            code = next_arc_quadrant(&arc, anext);

            if (code < 0)

                return code;

            arc.action = arc_nothing;

            arc.notes = sn_not_first;

        }

    } else {

        if (ang2 < ang1) {

            ang2 += ceil((ang1 - ang2) / 360) * 360;

        }

        if (ang1 < 0) {

            double adjust = ceil(-ang1 / 360) * 360;

            ang1 += adjust, ang2 += adjust;

        }

        arc.angle = ang1;

        if (ang1 == ang2) {

            code = next_arc_curve(&arc, ang2);

            if (code < 0)

                return code;

            *p3 = arc.p3;

        }

        /* Do the first part, up to a multiple of 90 degrees. */

        if (!arc.sincos.orthogonal) {

            anext = ceil(arc.angle / 90) * 90;

            if (anext > ang2)

                goto last;

            code = next_arc_curve(&arc, anext);

            if (code < 0)

                return code;

            arc.action = arc_nothing;

            arc.notes = sn_not_first;

        }

        /* Do multiples of 90 degrees.  Invariant: 0 <= ang1 <= ang2. */

        while ((anext = arc.angle + 90) <= ang2) {

            code = next_arc_quadrant(&arc, anext);

            if (code < 0)

                return code;

            arc.action = arc_nothing;

            arc.notes = sn_not_first;

        }

    }

    /*

     * Do the last curve of the arc, if any.

     */

    if (arc.angle == ang2) {

        *p3 = arc.p3;

        return 0;

    }

last:

    code = next_arc_curve(&arc, ang2);

    if (code < 0)

        return code;

    *p3 = arc.p3;

    return 0;

}

int

gs_arcto(gs_gstate * pgs,

double ax1, double ay1, double ax2, double ay2, double arad, float retxy[4])

{

    double xt0, yt0, xt2, yt2;

    gs_point up0;

#define ax0 up0.x

#define ay0 up0.y

    /* Transform the current point back into user coordinates. */

    int code = gs_currentpoint(pgs, &up0);

    if (code < 0)

        return code;

    {

        double dx0, dy0, dx2, dy2, sql0, sql2;

        /* Now we have to compute the tangent points. */

        /* Basically, the idea is to compute the tangent */

        /* of the bisector by using tan(x+y) and tan(z/2) */

        /* formulas, without ever using any trig. */

        dx0 = ax0 - ax1; dy0 = ay0 - ay1;

        dx2 = ax2 - ax1; dy2 = ay2 - ay1;

        /* Compute the squared lengths from p1 to p0 and p2. */

        sql0 = dx0 * dx0 + dy0 * dy0;

        sql2 = dx2 * dx2 + dy2 * dy2;

        if (sql0 == 0. || sql2 == 0.)

            return_error(gs_error_undefinedresult); /* for CET 11-04 */

        /* Check for collinear points. */

        if (dx0*dy2 == dy0*dx2) {

            code = gs_lineto(pgs, ax1, ay1);

            xt0 = xt2 = ax1;

            yt0 = yt2 = ay1;

        } else {                /* not collinear */

            /* Compute the distance from p1 to the tangent points. */

            /* This is the only messy part. */

            double num = dy0 * dx2 - dy2 * dx0;

            double denom = sqrt(sql0 * sql2) - (dx0 * dx2 + dy0 * dy2);

            double dist = fabs(arad * num / denom);

            double l0 = dist / sqrt(sql0), l2 = dist / sqrt(sql2);

            arc_curve_params_t arc;

            arc.ppath = pgs->path;

            arc.pgs = pgs;

            arc.radius = arad;

            arc.action = arc_lineto;

            arc.notes = sn_none;

            if (arad < 0)

                l0 = -l0, l2 = -l2;

            arc.p0.x = xt0 = ax1 + dx0 * l0;

            arc.p0.y = yt0 = ay1 + dy0 * l0;

            arc.p3.x = xt2 = ax1 + dx2 * l2;

            arc.p3.y = yt2 = ay1 + dy2 * l2;

            arc.pt.x = ax1;

            arc.pt.y = ay1;

            code = arc_add(&arc, false);

            if (code == 0)

                code = gx_setcurrentpoint_from_path(pgs, pgs->path);

        }

    }

    if (retxy != 0) {

        retxy[0] = xt0;

        retxy[1] = yt0;

        retxy[2] = xt2;

        retxy[3] = yt2;

    }

    return code;

}

/* Internal routine for adding an arc to the path. */

static int

arc_add(const arc_curve_params_t * arc, bool is_quadrant)

{

    gx_path *path = arc->ppath;

    gs_gstate *pgs = arc->pgs;

    double x0 = arc->p0.x, y0 = arc->p0.y;

    double xt = arc->pt.x, yt = arc->pt.y;

    double fraction;

    gs_fixed_point p0, p2, p3, pt;

    int code;

    if ((arc->action != arc_nothing &&

#if !PRECISE_CURRENTPOINT

         (code = gs_point_transform2fixed(&pgs->ctm, x0, y0, &p0)) < 0) ||

        (code = gs_point_transform2fixed(&pgs->ctm, xt, yt, &pt)) < 0 ||

        (code = gs_point_transform2fixed(&pgs->ctm, arc->p3.x, arc->p3.y, &p3)) < 0

#else

         (code = gs_point_transform2fixed_rounding(&pgs->ctm, x0, y0, &p0)) < 0) ||

        (code = gs_point_transform2fixed_rounding(&pgs->ctm, xt, yt, &pt)) < 0 ||

        (code = gs_point_transform2fixed_rounding(&pgs->ctm, arc->p3.x, arc->p3.y, &p3)) < 0

#endif

        )

        return code;

#if PRECISE_CURRENTPOINT

    if (!path_position_valid(path))

        gs_point_transform(arc->p0.x, arc->p0.y, &ctm_only(arc->pgs), &pgs->subpath_start);

#endif

    code = (arc->action == arc_nothing ?

          (p0.x = path->position.x, p0.y = path->position.y, 0) :

          arc->action == arc_lineto && path_position_valid(path) ?

          gx_path_add_line(path, p0.x, p0.y) :

          /* action == arc_moveto, or lineto with no current point */

          gx_path_add_point(path, p0.x, p0.y));

    if (code < 0)

        return code;

    /* Compute the fraction coefficient for the curve. */

    /* See gx_path_add_partial_arc for details. */

    if (is_quadrant) {

        /* one of |dx| and |dy| is r, the other is zero */

        fraction = quarter_arc_fraction;

        if (arc->fast_quadrant > 0) {

            /*

             * The CTM is well-behaved, and we have pre-calculated the delta

             * from the circumference points to the control points.

             */

            fixed delta = arc->quadrant_delta;

            if (pt.x != p0.x)

                p0.x = (pt.x > p0.x ? p0.x + delta : p0.x - delta);

            if (pt.y != p0.y)

                p0.y = (pt.y > p0.y ? p0.y + delta : p0.y - delta);

            p2.x = (pt.x == p3.x ? p3.x :

                    pt.x > p3.x ? p3.x + delta : p3.x - delta);

            p2.y = (pt.y == p3.y ? p3.y :

                    pt.y > p3.y ? p3.y + delta : p3.y - delta);

            goto add;

        }

    } else {

        double r = arc->radius;

        double dx = xt - x0, dy = yt - y0;

        double dist = dx * dx + dy * dy;

        double r2 = r * r;

        if (dist >= r2 * 1.0e8) /* almost zero radius; */

            /* the >= catches dist == r == 0 */

            fraction = 0.0;

        else

            fraction = (4.0 / 3.0) / (1 + sqrt(1 + dist / r2));

    }

    p0.x += (fixed)((pt.x - p0.x) * fraction);

    p0.y += (fixed)((pt.y - p0.y) * fraction);

    p2.x = p3.x + (fixed)((pt.x - p3.x) * fraction);

    p2.y = p3.y + (fixed)((pt.y - p3.y) * fraction);

add:

    if_debug8m('r', path->memory,

              "[r]Arc f=%f p0=(%f,%f) pt=(%f,%f) p3=(%f,%f) action=%d\n",

              fraction, x0, y0, xt, yt, arc->p3.x, arc->p3.y,

              (int)arc->action);

    /* Open-code gx_path_add_partial_arc_notes */

    return gx_path_add_curve_notes(path, p0.x, p0.y, p2.x, p2.y, p3.x, p3.y,

                                   arc->notes | sn_from_arc);

}

void

make_quadrant_arc(gs_point *p, const gs_point *c,

        const gs_point *p0, const gs_point *p1, double r)

{

    p[0].x = c->x + p0->x * r;

    p[0].y = c->y + p0->y * r;

    p[1].x = c->x + p0->x * r + p1->x * r * quarter_arc_fraction;

    p[1].y = c->y + p0->y * r + p1->y * r * quarter_arc_fraction;

    p[2].x = c->x + p0->x * r * quarter_arc_fraction + p1->x * r;

    p[2].y = c->y + p0->y * r * quarter_arc_fraction + p1->y * r;

    p[3].x = c->x + p1->x * r;

    p[3].y = c->y + p1->y * r;

}

/* ------ Path transformers ------ */

int

gs_dashpath(gs_gstate * pgs)

{

    gx_path *ppath;

    gx_path fpath;

    int code;

    if (gs_currentdash_length(pgs) == 0)

        return 0;               /* no dash pattern */

    code = gs_flattenpath(pgs);

    if (code < 0)

        return code;

    ppath = pgs->path;

    gx_path_init_local(&fpath, ppath->memory);

    code = gx_path_add_dash_expansion(ppath, &fpath, pgs);

    if (code < 0) {

        gx_path_free(&fpath, "gs_dashpath");

        return code;

    }

    gx_path_assign_free(pgs->path, &fpath);

    return 0;

}

int

gs_flattenpath(gs_gstate * pgs)

{

    gx_path *ppath = pgs->path;

    gx_path fpath;

    int code;

    if (!gx_path_has_curves(ppath))

        return 0;               /* nothing to do */

    gx_path_init_local(&fpath, ppath->memory);

    code = gx_path_add_flattened_accurate(ppath, &fpath, pgs->flatness,

                                          pgs->accurate_curves);

    if (code < 0) {

        gx_path_free(&fpath, "gs_flattenpath");

        return code;

    }

    gx_path_assign_free(ppath, &fpath);

    return 0;

}

int

gs_reversepath(gs_gstate * pgs)

{

    gx_path *ppath = pgs->path;

    gx_path rpath;

    int code;

    gx_path_init_local(&rpath, ppath->memory);

    code = gx_path_copy_reversed(ppath, &rpath);

    if (code < 0) {

        gx_path_free(&rpath, "gs_reversepath");

        return code;

    }

    if (pgs->current_point_valid) {

        /* Not empty. */

        gx_setcurrentpoint(pgs, fixed2float(rpath.position.x),

                                fixed2float(rpath.position.y));

        if (rpath.first_subpath != 0) {

            pgs->subpath_start.x = fixed2float(rpath.segments->contents.subpath_current->pt.x);

            pgs->subpath_start.y = fixed2float(rpath.segments->contents.subpath_current->pt.y);

        }

    }

    gx_path_assign_free(ppath, &rpath);

    return 0;

}

/* ------ Accessors ------ */

int

gs_upathbbox(gs_gstate * pgs, gs_rect * pbox, bool include_moveto)

{

    gs_fixed_rect fbox;         /* box in device coordinates */

    gs_rect dbox;

    int code = gx_path_bbox_set(pgs->path, &fbox);

    if (code < 0)

        return code;

    /* If the path ends with a moveto and include_moveto is true, */

    /* include the moveto in the bounding box. */

    if (path_last_is_moveto(pgs->path) && include_moveto) {

        gs_fixed_point pt;

        code = gx_path_current_point_inline(pgs, &pt);

        if (code < 0)

            return code;

        if (pt.x < fbox.p.x)

            fbox.p.x = pt.x;

        if (pt.y < fbox.p.y)

            fbox.p.y = pt.y;

        if (pt.x > fbox.q.x)

            fbox.q.x = pt.x;

        if (pt.y > fbox.q.y)

            fbox.q.y = pt.y;

    }

    /* Transform the result back to user coordinates. */

    dbox.p.x = fixed2float(fbox.p.x);

    dbox.p.y = fixed2float(fbox.p.y);

    dbox.q.x = fixed2float(fbox.q.x);

    dbox.q.y = fixed2float(fbox.q.y);

    return gs_bbox_transform_inverse(&dbox, &ctm_only(pgs), pbox);

}

/* ------ Enumerators ------ */

/* Start enumerating a path */

int

gs_path_enum_copy_init(gs_memory_t *mem, gs_path_enum * penum, const gs_gstate * pgs, bool copy)

{

    if (copy) {

        gx_path *copied_path =

        gx_path_alloc(mem, "gs_path_enum_init");

        int code;

        if (copied_path == 0)

            return_error(gs_error_VMerror);

        code = gx_path_copy(pgs->path, copied_path);

        if (code < 0) {

            gx_path_free(copied_path, "gs_path_enum_init");

            return code;

        }

        gx_path_enum_init(penum, copied_path);

        penum->copied_path = copied_path;

    } else {

        gx_path_enum_init(penum, pgs->path);

    }

    penum->memory = mem;

    gs_currentmatrix(pgs, &penum->mat);

    return 0;

}

/* Enumerate the next element of a path. */

/* If the path is finished, return 0; */

/* otherwise, return the element type. */

int

gs_path_enum_next(gs_path_enum * penum, gs_point ppts[3])

{

    gs_fixed_point fpts[3];

    int pe_op = gx_path_enum_next(penum, fpts);

    int code;

    switch (pe_op) {

        case 0:         /* all done */

        case gs_pe_closepath:

            break;

        case gs_pe_curveto:

            if ((code = gs_point_transform_inverse(

                                                      fixed2float(fpts[1].x),

                                                      fixed2float(fpts[1].y),

                                              &penum->mat, &ppts[1])) < 0 ||

                (code = gs_point_transform_inverse(

                                                      fixed2float(fpts[2].x),

                                                      fixed2float(fpts[2].y),

                                                &penum->mat, &ppts[2])) < 0)

                return code;

            /* falls through */

        case gs_pe_moveto:

        case gs_pe_lineto:

        case gs_pe_gapto:

            if ((code = gs_point_transform_inverse(

                                                      fixed2float(fpts[0].x),

                                                      fixed2float(fpts[0].y),

                                                &penum->mat, &ppts[0])) < 0)

                return code;

        default:                /* error */

            break;

    }

    return pe_op;

}

/* Clean up after a pathforall. */

void

gs_path_enum_cleanup(gs_path_enum * penum)

{

    if (penum->copied_path != 0) {

        gx_path_free(penum->copied_path, "gs_path_enum_cleanup");

        penum->path = 0;

        penum->copied_path = 0;

    }

}