/* -*- Mode: c; tab-width: 8; c-basic-offset: 4; indent-tabs-mode: t; -*- */

/* cairo - a vector graphics library with display and print output

 *

 * Copyright © 2002 University of Southern California

 * Copyright © 2011 Intel Corporation

 *

 * This library is free software; you can redistribute it and/or

 * modify it either under the terms of the GNU Lesser General Public

 * License version 2.1 as published by the Free Software Foundation

 * (the "LGPL") or, at your option, under the terms of the Mozilla

 * Public License Version 1.1 (the "MPL"). If you do not alter this

 * notice, a recipient may use your version of this file under either

 * the MPL or the LGPL.

 *

 * You should have received a copy of the LGPL along with this library

 * in the file COPYING-LGPL-2.1; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA

 * You should have received a copy of the MPL along with this library

 * in the file COPYING-MPL-1.1

 *

 * The contents of this file are subject to the Mozilla Public License

 * Version 1.1 (the "License"); you may not use this file except in

 * compliance with the License. You may obtain a copy of the License at

 * http://www.mozilla.org/MPL/

 *

 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY

 * OF ANY KIND, either express or implied. See the LGPL or the MPL for

 * the specific language governing rights and limitations.

 *

 * The Original Code is the cairo graphics library.

 *

 * The Initial Developer of the Original Code is University of Southern

 * California.

 *

 * Contributor(s):

 *	Carl D. Worth <cworth@cworth.org>

 *	Chris Wilson <chris@chris-wilson.co.uk>

 */

#define _DEFAULT_SOURCE /* for hypot() */

#include "cairoint.h"

#include "cairo-box-inline.h"

#include "cairo-boxes-private.h"

#include "cairo-contour-inline.h"

#include "cairo-contour-private.h"

#include "cairo-error-private.h"

#include "cairo-path-fixed-private.h"

#include "cairo-slope-private.h"

#define DEBUG 0

struct stroker {

    cairo_stroke_style_t style;

#if DEBUG

    cairo_contour_t path;

#endif

    struct stroke_contour {

	/* Note that these are not strictly contours as they may intersect */

	cairo_contour_t contour;

    } cw, ccw;

    cairo_uint64_t contour_tolerance;

    cairo_polygon_t *polygon;

    const cairo_matrix_t *ctm;

    const cairo_matrix_t *ctm_inverse;

    double tolerance;

    double spline_cusp_tolerance;

    double half_line_width;

    cairo_bool_t ctm_det_positive;

    cairo_pen_t pen;

    cairo_point_t first_point;

    cairo_bool_t has_initial_sub_path;

    cairo_bool_t has_current_face;

    cairo_stroke_face_t current_face;

    cairo_bool_t has_first_face;

    cairo_stroke_face_t first_face;

    cairo_bool_t has_bounds;

    cairo_box_t bounds;

};

static inline double

normalize_slope (double *dx, double *dy);

static void

compute_face (const cairo_point_t *point,

	      const cairo_slope_t *dev_slope,

	      struct stroker *stroker,

	      cairo_stroke_face_t *face);

static cairo_uint64_t

			const cairo_point_t *p2)

{

}

static cairo_bool_t

	      const cairo_point_t *p2,

	      cairo_uint64_t tolerance)

{

    return _cairo_int64_lt (point_distance_sq (p1, p2), tolerance);

}

static void

		   struct stroke_contour *c,

		   const cairo_point_t *point)

{

			stroker->contour_tolerance))

    //*_cairo_contour_last_point (&c->contour) = *point;

static void

{

static int

{

}

/*

 * Construct a fan around the midpoint using the vertices from pen between

 * inpt and outpt.

 */

static void

	 const cairo_slope_t *in_vector,

	 const cairo_slope_t *out_vector,

	 const cairo_point_t *midpt,

	 cairo_bool_t clockwise,

	 struct stroke_contour *c)

{

    int start, stop;

					    in_vector, out_vector,

					    &start, &stop);

	}

    } else {

					     in_vector, out_vector,

					     &start, &stop);

	}

    }

}

static int

		   const cairo_stroke_face_t *out)

{

}

static void

	    const cairo_stroke_face_t *in,

	    const cairo_stroke_face_t *out,

	    int clockwise)

{

#if 0

    cairo_point_t last;

    const cairo_point_t *p, *outpt;

    struct stroke_contour *inner;

    cairo_int64_t d_p, d_last;

    cairo_int64_t half_line_width;

    cairo_bool_t negate;

    /* XXX line segments shorter than line-width */

    if (clockwise) {

	inner = &stroker->ccw;

	outpt = &out->ccw;

	negate = 1;

    } else {

	inner = &stroker->cw;

	outpt = &out->cw;

	negate = 0;

    }

    half_line_width = CAIRO_FIXED_ONE*CAIRO_FIXED_ONE/2 * stroker->style.line_width * out->length + .5;

    /* On the inside, the previous end-point is always

     * closer to the new face by definition.

     */

    last = *_cairo_contour_last_point (&inner->contour);

    d_last = distance_from_face (out, &last, negate);

    _cairo_contour_remove_last_point (&inner->contour);

prev:

    if (inner->contour.chain.num_points == 0) {

	contour_add_point (stroker, inner, outpt);

	return;

    }

    p = _cairo_contour_last_point (&inner->contour);

    d_p = distance_from_face (out, p, negate);

    if (_cairo_int64_lt (d_p, half_line_width) &&

	!_cairo_int64_negative (distance_along_face (out, p)))

    {

	last = *p;

	d_last = d_p;

	_cairo_contour_remove_last_point (&inner->contour);

	goto prev;

    }

    compute_inner_joint (&last, d_last, p, d_p, half_line_width);

    contour_add_point (stroker, inner, &last);

#else

    const cairo_point_t *outpt;

    struct stroke_contour *inner;

    } else {

    }

#endif

static void

	     const cairo_stroke_face_t *in,

	     cairo_stroke_face_t *out)

{

#if 0

    cairo_point_t last;

    const cairo_point_t *p, *outpt, *inpt;

    struct stroke_contour *inner;

    struct _cairo_contour_chain *chain;

    /* XXX line segments shorter than line-width */

    if (join_is_clockwise (in, out)) {

	inner = &stroker->ccw;

	outpt = &in->ccw;

	inpt = &out->ccw;

    } else {

	inner = &stroker->cw;

	outpt = &in->cw;

	inpt = &out->cw;

    }

    if (inner->contour.chain.num_points == 0) {

	contour_add_point (stroker, inner, &in->point);

	contour_add_point (stroker, inner, inpt);

	*_cairo_contour_first_point (&inner->contour) =

	    *_cairo_contour_last_point (&inner->contour);

	return;

    }

    line_width = stroker->style.line_width/2;

    line_width *= CAIRO_FIXED_ONE;

    d_last = sign * distance_from_face (out, outpt);

    last = *outpt;

    for (chain = &inner->contour.chain; chain; chain = chain->next) {

	for (i = 0; i < chain->num_points; i++) {

	    p = &chain->points[i];

	    if ((d_p = sign * distance_from_face (in, p)) >= line_width &&

		distance_from_edge (stroker, inpt, &last, p) < line_width)

	    {

		goto out;

	    }

	    if (p->x != last.x || p->y != last.y) {

		last = *p;

		d_last = d_p;

	    }

	}

    }

out:

    if (d_p != d_last) {

	double dot = (line_width - d_last) / (d_p - d_last);

	last.x += dot * (p->x - last.x);

	last.y += dot * (p->y - last.y);

    }

    *_cairo_contour_last_point (&inner->contour) = last;

    for (chain = &inner->contour.chain; chain; chain = chain->next) {

	for (i = 0; i < chain->num_points; i++) {

	    cairo_point_t *pp = &chain->points[i];

	    if (pp == p)

		return;

	    *pp = last;

	}

    }

#else

    const cairo_point_t *inpt;

    struct stroke_contour *inner;

    } else {

    }

#endif

static void

	     const cairo_stroke_face_t *in,

	     const cairo_stroke_face_t *out)

{

    const cairo_point_t	*inpt, *outpt;

    struct stroke_contour *outer;

    int	clockwise;

    {

    }

    } else {

    }

    }

	{

	    /* construct a fan around the common midpoint */

		     &in->dev_vector, &out->dev_vector, &in->point,

		     clockwise, outer);

	} /* else: bevel join */

    default: {

	/* dot product of incoming slope vector with outgoing slope vector */

	/* Check the miter limit -- lines meeting at an acute angle

	 * can generate long miters, the limit converts them to bevel

	 *

	 * Consider the miter join formed when two line segments

	 * meet at an angle psi:

	 *

	 *	   /.\

	 *	  /. .\

	 *	 /./ \.\

	 *	/./psi\.\

	 *

	 * We can zoom in on the right half of that to see:

	 *

	 *	    |\

	 *	    | \ psi/2

	 *	    |  \

	 *	    |   \

	 *	    |    \

	 *	    |     \

	 *	  miter    \

	 *	 length     \

	 *	    |        \

	 *	    |        .\

	 *	    |    .     \

	 *	    |.   line   \

	 *	     \    width  \

	 *	      \           \

	 *

	 *

	 * The right triangle in that figure, (the line-width side is

	 * shown faintly with three '.' characters), gives us the

	 * following expression relating miter length, angle and line

	 * width:

	 *

	 *	1 /sin (psi/2) = miter_length / line_width

	 *

	 * The right-hand side of this relationship is the same ratio

	 * in which the miter limit (ml) is expressed. We want to know

	 * when the miter length is within the miter limit. That is

	 * when the following condition holds:

	 *

	 *	1/sin(psi/2) <= ml

	 *	1 <= ml sin(psi/2)

	 *	1 <= ml² sin²(psi/2)

	 *	2 <= ml² 2 sin²(psi/2)

	 *				2·sin²(psi/2) = 1-cos(psi)

	 *	2 <= ml² (1-cos(psi))

	 *

	 *				in · out = |in| |out| cos (psi)

	 *

	 * in and out are both unit vectors, so:

	 *

	 *				in · out = cos (psi)

	 *

	 *	2 <= ml² (1 - in · out)

	 *

	 */

	    double		x1, y1, x2, y2;

	    double		mx, my;

	    double		dx1, dx2, dy1, dy2;

	    double		ix, iy;

	    double		fdx1, fdy1, fdx2, fdy2;

	    double		mdx, mdy;

	    /*

	     * we've got the points already transformed to device

	     * space, but need to do some computation with them and

	     * also need to transform the slope from user space to

	     * device space

	     */

	    /* outer point of incoming line face */

	    /* outer point of outgoing line face */

	    /*

	     * Compute the location of the outer corner of the miter.

	     * That's pretty easy -- just the intersection of the two

	     * outer edges.  We've got slopes and points on each

	     * of those edges.  Compute my directly, then compute

	     * mx by using the edge with the larger dy; that avoids

	     * dividing by values close to zero.

	     */

	    else

	    /*

	     * When the two outer edges are nearly parallel, slight

	     * perturbations in the position of the outer points of the lines

	     * caused by representing them in fixed point form can cause the

	     * intersection point of the miter to move a large amount. If

	     * that moves the miter intersection from between the two faces,

	     * then draw a bevel instead.

	     */

	    /* slope of one face */

	    /* slope of the other face */

	    /* slope from the intersection to the miter point */

	    /*

	     * Make sure the miter point line lies between the two

	     * faces by comparing the slopes

	     */

	    {

		cairo_point_t p;

	    }

	}

    }

    }

}

static void

	    const cairo_stroke_face_t *in,

	    const cairo_stroke_face_t *out,

	    int clockwise)

{

    const cairo_point_t	*inpt, *outpt;

    struct stroke_contour *outer;

    {

    }

    } else {

    }

	{

	    /* construct a fan around the common midpoint */

		     &in->dev_vector, &out->dev_vector, &in->point,

		     clockwise, outer);

	} /* else: bevel join */

    default: {

	/* dot product of incoming slope vector with outgoing slope vector */

	/* Check the miter limit -- lines meeting at an acute angle

	 * can generate long miters, the limit converts them to bevel

	 *

	 * Consider the miter join formed when two line segments

	 * meet at an angle psi:

	 *

	 *	   /.\

	 *	  /. .\

	 *	 /./ \.\

	 *	/./psi\.\

	 *

	 * We can zoom in on the right half of that to see:

	 *

	 *	    |\

	 *	    | \ psi/2

	 *	    |  \

	 *	    |   \

	 *	    |    \

	 *	    |     \

	 *	  miter    \

	 *	 length     \

	 *	    |        \

	 *	    |        .\

	 *	    |    .     \

	 *	    |.   line   \

	 *	     \    width  \

	 *	      \           \

	 *

	 *

	 * The right triangle in that figure, (the line-width side is

	 * shown faintly with three '.' characters), gives us the

	 * following expression relating miter length, angle and line

	 * width:

	 *

	 *	1 /sin (psi/2) = miter_length / line_width

	 *

	 * The right-hand side of this relationship is the same ratio

	 * in which the miter limit (ml) is expressed. We want to know

	 * when the miter length is within the miter limit. That is

	 * when the following condition holds:

	 *

	 *	1/sin(psi/2) <= ml

	 *	1 <= ml sin(psi/2)

	 *	1 <= ml² sin²(psi/2)

	 *	2 <= ml² 2 sin²(psi/2)

	 *				2·sin²(psi/2) = 1-cos(psi)

	 *	2 <= ml² (1-cos(psi))

	 *

	 *				in · out = |in| |out| cos (psi)

	 *

	 * in and out are both unit vectors, so:

	 *

	 *				in · out = cos (psi)

	 *

	 *	2 <= ml² (1 - in · out)

	 *

	 */

	    double		x1, y1, x2, y2;

	    double		mx, my;

	    double		dx1, dx2, dy1, dy2;

	    double		ix, iy;

	    double		fdx1, fdy1, fdx2, fdy2;

	    double		mdx, mdy;

	    /*

	     * we've got the points already transformed to device

	     * space, but need to do some computation with them and

	     * also need to transform the slope from user space to

	     * device space

	     */

	    /* outer point of incoming line face */

	    /* outer point of outgoing line face */

	    /*

	     * Compute the location of the outer corner of the miter.

	     * That's pretty easy -- just the intersection of the two

	     * outer edges.  We've got slopes and points on each

	     * of those edges.  Compute my directly, then compute

	     * mx by using the edge with the larger dy; that avoids

	     * dividing by values close to zero.

	     */

	    else

	    /*

	     * When the two outer edges are nearly parallel, slight

	     * perturbations in the position of the outer points of the lines

	     * caused by representing them in fixed point form can cause the

	     * intersection point of the miter to move a large amount. If

	     * that moves the miter intersection from between the two faces,

	     * then draw a bevel instead.

	     */

	    /* slope of one face */

	    /* slope of the other face */

	    /* slope from the intersection to the miter point */

	    /*

	     * Make sure the miter point line lies between the two

	     * faces by comparing the slopes

	     */

	    {

		cairo_point_t p;

	    }

	}

    }

    }

}

static void

	 const cairo_stroke_face_t *f,

	 struct stroke_contour *c)

{

	cairo_slope_t slope;

    }

	cairo_slope_t fvector;

	cairo_point_t p;

	double dx, dy;

    }

    default:

    }

static void

		 const cairo_stroke_face_t *face,

		 struct stroke_contour *c)

{

    cairo_stroke_face_t reversed;

    cairo_point_t t;

    /* The initial cap needs an outward facing vector. Reverse everything */

static void

		  const cairo_stroke_face_t *face,

		  struct stroke_contour *c)

{

static inline double

{

    double mag;

	} else {

	}

	} else {

	}

    } else {

    }

}

static void

	      const cairo_slope_t *dev_slope,

	      struct stroker *stroker,

	      cairo_stroke_face_t *face)

{

    double face_dx, face_dy;

    cairo_point_t offset_ccw, offset_cw;

    double slope_dx, slope_dy;

    /*

     * rotate to get a line_width/2 vector along the face, note that

     * the vector must be rotated the right direction in device space,

     * but by 90° in user space. So, the rotation depends on

     * whether the ctm reflects or not, and that can be determined

     * by looking at the determinant of the matrix.

     */

	/* Normalize the matrix! */

					 &slope_dx, &slope_dy);

	} else {

	}

	/* back to device space */

    } else {

    }

static void

{

    /* check for a degenerative sub_path */

	/* pick an arbitrary slope to use */

	cairo_stroke_face_t face;

	/* arbitrarily choose first_point */

	/* ensure the circle is complete */

    } else {

#if DEBUG

	{

	    FILE *file = fopen ("contours.txt", "a");

	    _cairo_debug_print_contour (file, &stroker->path);

	    _cairo_debug_print_contour (file, &stroker->cw.contour);

	    _cairo_debug_print_contour (file, &stroker->ccw.contour);

	    fclose (file);

	    _cairo_contour_reset (&stroker->path);

	}

#endif

#if DEBUG

	    {

		FILE *file = fopen ("contours.txt", "a");

		_cairo_debug_print_contour (file, &stroker->ccw.contour);

		fclose (file);

	    }

#endif

	}

    }

static cairo_status_t

close_path (void *closure);

static cairo_status_t

	 const cairo_point_t *point)

{

    /* Cap the start and end of the previous sub path as needed */

#if DEBUG

    _cairo_contour_add_point (&stroker->path, point);

#endif

}

static cairo_status_t

	 const cairo_point_t *point)

{

    cairo_stroke_face_t start;

    cairo_slope_t dev_slope;

#if DEBUG

    _cairo_contour_add_point (&stroker->path, point);

#endif

					      &start.dev_vector);

	    /* Join with final face from previous segment */

				    stroker->contour_tolerance))

	    {

	    }

	}

    } else {

	    /* Save sub path's first face in case needed for closing join */

	}

    }

}

static cairo_status_t

	   const cairo_point_t *point,

	   const cairo_slope_t *tangent)

{

    cairo_stroke_face_t face;

#if DEBUG

    _cairo_contour_add_point (&stroker->path, point);

#endif

	struct stroke_contour *outer;

	cairo_point_t t;

	int clockwise;

	} else {

	}

		 &face.dev_vector,

		 clockwise, outer);

    } else {

	{

	    struct stroke_contour *outer;

	    } else {

	    }

		     &face.dev_vector,

		     clockwise, outer);

	}

    }

}

static cairo_status_t

	  const cairo_point_t *b,

	  const cairo_point_t *c,

	  const cairo_point_t *d)

{

    cairo_spline_t spline;

    cairo_stroke_face_t face;

		  stroker, &face);

	/* Join with final face from previous segment */

    } else {

	    /* Save sub path's first face in case needed for closing join */

	}

    }

}

static cairo_status_t

{

    cairo_status_t status;

	/* Join first and final faces of sub path */

#if 0

	*_cairo_contour_first_point (&stroker->ccw.contour) =

	    *_cairo_contour_last_point (&stroker->ccw.contour);

	*_cairo_contour_first_point (&stroker->cw.contour) =

	    *_cairo_contour_last_point (&stroker->cw.contour);

#endif

#if DEBUG

	{

	    FILE *file = fopen ("contours.txt", "a");

	    _cairo_debug_print_contour (file, &stroker->path);

	    _cairo_debug_print_contour (file, &stroker->cw.contour);

	    _cairo_debug_print_contour (file, &stroker->ccw.contour);

	    fclose (file);

	    _cairo_contour_reset (&stroker->path);

	}

#endif

    } else {

	/* Cap the start and end of the sub path as needed */

    }

}

cairo_status_t

				     const cairo_stroke_style_t	*style,

				     const cairo_matrix_t	*ctm,

				     const cairo_matrix_t	*ctm_inverse,

				     double		 tolerance,

				     cairo_polygon_t *polygon)

{

    struct stroker stroker;

    cairo_status_t status;

							   style,

							   ctm,

							   ctm_inverse,

							   tolerance,

							   polygon);

    }

	/* Extend the bounds in each direction to account for the maximum area

	 * we might generate trapezoids, to capture line segments that are

	 * outside of the bounds but which might generate rendering that's

	 * within bounds.

	 */

	double dx, dy;

	cairo_fixed_t fdx, fdy;

	int i;

    }

    /* If `CAIRO_LINE_JOIN_ROUND` is selected and a joint's `arc height`

     * is greater than `tolerance` then two segments are joined with

     * round-join, otherwise bevel-join is used.

     *

     * (See https://gitlab.freedesktop.org/cairo/cairo/-/merge_requests/372#note_1698225

     *  for an illustration.)

     *

     * `Arc height` is the distance from the center of arc's chord to

     * the center of the arc. It is also the difference of arc's radius

     * and the "distance from a point where segments are joined to the

     * chord" (distance to the chord). Arc's radius is the half of a line

     * width and the "distance to the chord" is equal to "half of a line width"

     * times `cos(half the angle between segment vectors)`. So

     *

     *     arc_height = w/2 - w/2 * cos(phi/2),

     *

     * where `w/2` is the "half of a line width".

     *

     * Using the double angle cosine formula we can express the `cos(phi/2)`

     * with just `cos(phi)` which is also the dot product of segments'

     * unit vectors.

     *

     *     cos(phi/2) = sqrt ( (1 + cos(phi)) / 2 );

     *     cos(phi/2) is in [0; 1] range, cannot be negative;

     *

     *     cos(phi) = a . b  = (ax * bx + ay * by),

     *

     * where `a` and `b` are unit vectors of the segments to be joined.

     *

     * Since `arc height` should be greater than the `tolerance` to produce

     * a round-join we can write

     *

     *     w/2 * (1 - cos(phi/2))  >  tolerance;

     *     1 - tolerance / (w/2)  >  cos(phi/2);    [!]

     *

     * which can be rewritten with the above double angle formula to

     *

     *     cos(phi)  <  2 * ( 1 - tolerance / (w/2) )^2 - 1,

     *

     * [!] Note that `w/2` is in [tolerance; +inf] range, since `cos(phi/2)`

     * cannot be negative. The left part of the above inequality is the

     * dot product and the right part is the `spline_cusp_tolerance`:

     *

     *     (ax * bx + ay * by) < spline_cusp_tolerance.

     *