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

 *

 * Copyright © 2005 Red Hat, Inc

 *

 * 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 Red Hat, Inc.

 *

 * Contributor(s):

 *  Carl Worth <cworth@cworth.org>

 */

#include "cairoint.h"

#include "cairo-error-private.h"

void

_cairo_stroke_style_init (cairo_stroke_style_t *style)

{

    VG (VALGRIND_MAKE_MEM_UNDEFINED (style, sizeof (cairo_stroke_style_t)));

    style->line_width = CAIRO_GSTATE_LINE_WIDTH_DEFAULT;

    style->line_cap = CAIRO_GSTATE_LINE_CAP_DEFAULT;

    style->line_join = CAIRO_GSTATE_LINE_JOIN_DEFAULT;

    style->miter_limit = CAIRO_GSTATE_MITER_LIMIT_DEFAULT;

    style->dash = NULL;

    style->num_dashes = 0;

    style->dash_offset = 0.0;

    style->is_hairline = FALSE;

}

cairo_status_t

_cairo_stroke_style_init_copy (cairo_stroke_style_t *style,

             const cairo_stroke_style_t *other)

{

    if (CAIRO_INJECT_FAULT ())

  return _cairo_error (CAIRO_STATUS_NO_MEMORY);

    VG (VALGRIND_MAKE_MEM_UNDEFINED (style, sizeof (cairo_stroke_style_t)));

    style->line_width = other->line_width;

    style->line_cap = other->line_cap;

    style->line_join = other->line_join;

    style->miter_limit = other->miter_limit;

    style->num_dashes = other->num_dashes;

    if (other->dash == NULL) {

  style->dash = NULL;

    } else {

  style->dash = _cairo_malloc_ab (style->num_dashes, sizeof (double));

  if (unlikely (style->dash == NULL))

      return _cairo_error (CAIRO_STATUS_NO_MEMORY);

  memcpy (style->dash, other->dash,

    style->num_dashes * sizeof (double));

    }

    style->dash_offset = other->dash_offset;

    style->is_hairline = other->is_hairline;

    return CAIRO_STATUS_SUCCESS;

}

void

_cairo_stroke_style_fini (cairo_stroke_style_t *style)

{

    free (style->dash);

    style->dash = NULL;

    style->num_dashes = 0;

    VG (VALGRIND_MAKE_MEM_UNDEFINED (style, sizeof (cairo_stroke_style_t)));

}

/*

 * For a stroke in the given style, compute the maximum distance

 * from the path that vertices could be generated.  In the case

 * of rotation in the ctm, the distance will not be exact.

 */

void

_cairo_stroke_style_max_distance_from_path (const cairo_stroke_style_t *style,

              const cairo_path_fixed_t *path,

                                            const cairo_matrix_t *ctm,

                                            double *dx, double *dy)

{

    double style_expansion = 0.5;

    if (style->line_cap == CAIRO_LINE_CAP_SQUARE)

  style_expansion = M_SQRT1_2;

    if (style->line_join == CAIRO_LINE_JOIN_MITER &&

  ! path->stroke_is_rectilinear &&

  style_expansion < M_SQRT2 * style->miter_limit)

    {

  style_expansion = M_SQRT2 * style->miter_limit;

    }

    style_expansion *= style->line_width;

    if (_cairo_matrix_has_unity_scale (ctm)) {

  *dx = *dy = style_expansion;

    } else {

  *dx = style_expansion * hypot (ctm->xx, ctm->xy);

  *dy = style_expansion * hypot (ctm->yy, ctm->yx);

    }

}

void

_cairo_stroke_style_max_line_distance_from_path (const cairo_stroke_style_t *style,

             const cairo_path_fixed_t *path,

             const cairo_matrix_t *ctm,

             double *dx, double *dy)

{

    double style_expansion = 0.5 * style->line_width;

    if (_cairo_matrix_has_unity_scale (ctm)) {

  *dx = *dy = style_expansion;

    } else {

  *dx = style_expansion * hypot (ctm->xx, ctm->xy);

  *dy = style_expansion * hypot (ctm->yy, ctm->yx);

    }

}

void

_cairo_stroke_style_max_join_distance_from_path (const cairo_stroke_style_t *style,

             const cairo_path_fixed_t *path,

             const cairo_matrix_t *ctm,

             double *dx, double *dy)

{

    double style_expansion = 0.5;

    if (style->line_join == CAIRO_LINE_JOIN_MITER &&

  ! path->stroke_is_rectilinear &&

  style_expansion < M_SQRT2 * style->miter_limit)

    {

  style_expansion = M_SQRT2 * style->miter_limit;

    }

    style_expansion *= style->line_width;

    if (_cairo_matrix_has_unity_scale (ctm)) {

  *dx = *dy = style_expansion;

    } else {

  *dx = style_expansion * hypot (ctm->xx, ctm->xy);

  *dy = style_expansion * hypot (ctm->yy, ctm->yx);

    }

}

/*

 * Computes the period of a dashed stroke style.

 * Returns 0 for non-dashed styles.

 */

double

_cairo_stroke_style_dash_period (const cairo_stroke_style_t *style)

{

    double period;

    unsigned int i;

    period = 0.0;

    for (i = 0; i < style->num_dashes; i++)

  period += style->dash[i];

    if (style->num_dashes & 1)

  period *= 2.0;

    return period;

}

/*

 * Coefficient of the linear approximation (minimizing square difference)

 * of the surface covered by round caps

 *

 * This can be computed in the following way:

 * the area inside the circle with radius w/2 and the region -d/2 <= x <= d/2 is:

 *   f(w,d) = 2 * integrate (sqrt (w*w/4 - x*x), x, -d/2, d/2)

 * The square difference to a generic linear approximation (c*d) in the range (0,w) would be:

 *   integrate ((f(w,d) - c*d)^2, d, 0, w)

 * To minimize this difference it is sufficient to find a solution of the differential with

 * respect to c:

 *   solve ( diff (integrate ((f(w,d) - c*d)^2, d, 0, w), c), c)

 * Which leads to c = 9/32*pi*w

 * Since we're not interested in the true area, but just in a coverage extimate,

 * we always divide the real area by the line width (w).

 * The same computation for square caps would be

 *   f(w,d) = 2 * integrate(w/2, x, -d/2, d/2)

 *   c = 1*w

 * but in this case it would not be an approximation, since f is already linear in d.

 */

#define ROUND_MINSQ_APPROXIMATION (9*M_PI/32)

/*

 * Computes the length of the "on" part of a dashed stroke style,

 * taking into account also line caps.

 * Returns 0 for non-dashed styles.

 */

double

_cairo_stroke_style_dash_stroked (const cairo_stroke_style_t *style)

{

    double stroked, cap_scale;

    unsigned int i;

    switch (style->line_cap) {

    default: ASSERT_NOT_REACHED;

    case CAIRO_LINE_CAP_BUTT:   cap_scale = 0.0; break;

    case CAIRO_LINE_CAP_ROUND:  cap_scale = ROUND_MINSQ_APPROXIMATION; break;

    case CAIRO_LINE_CAP_SQUARE: cap_scale = 1.0; break;

    }

    stroked = 0.0;

    if (style->num_dashes & 1) {

        /* Each dash element is used both as on and as off. The order in which they are summed is

   * irrelevant, so sum the coverage of one dash element, taken both on and off at each iteration */

  for (i = 0; i < style->num_dashes; i++)

      stroked += style->dash[i] + cap_scale * MIN (style->dash[i], style->line_width);

    } else {

        /* Even (0, 2, ...) dashes are on and simply counted for the coverage, odd dashes are off, thus

   * their coverage is approximated based on the area covered by the caps of adjacent on dases. */

  for (i = 0; i + 1 < style->num_dashes; i += 2)

      stroked += style->dash[i] + cap_scale * MIN (style->dash[i+1], style->line_width);

    }

    return stroked;

}

/*

 * Verifies if _cairo_stroke_style_dash_approximate should be used to generate

 * an approximation of the dash pattern in the specified style, when used for

 * stroking a path with the given CTM and tolerance.

 * Always %FALSE for non-dashed styles.

 */

cairo_bool_t

_cairo_stroke_style_dash_can_approximate (const cairo_stroke_style_t *style,

            const cairo_matrix_t *ctm,

            double tolerance)

{

    double period;

    if (! style->num_dashes)

        return FALSE;

    period = _cairo_stroke_style_dash_period (style);

    return _cairo_matrix_transformed_circle_major_axis (ctm, period) < tolerance;

}

/*

 * Create a 2-dashes approximation of a dashed style, by making the "on" and "off"

 * parts respect the original ratio.

 */

void

_cairo_stroke_style_dash_approximate (const cairo_stroke_style_t *style,

              const cairo_matrix_t *ctm,

              double tolerance,

              double *dash_offset,

              double *dashes,

              unsigned int *num_dashes)

{

    double coverage, scale, offset;

    cairo_bool_t on = TRUE;

    unsigned int i = 0;

    coverage = _cairo_stroke_style_dash_stroked (style) / _cairo_stroke_style_dash_period (style);

    coverage = MIN (coverage, 1.0);

    scale = tolerance / _cairo_matrix_transformed_circle_major_axis (ctm, 1.0);

    /* We stop searching for a starting point as soon as the

     * offset reaches zero.  Otherwise when an initial dash

     * segment shrinks to zero it will be skipped over. */

    offset = style->dash_offset;

    while (offset > 0.0 && offset >= style->dash[i]) {

  offset -= style->dash[i];

  on = !on;

  if (++i == style->num_dashes)

      i = 0;

    }

    *num_dashes = 2;

    /*

     * We want to create a new dash pattern with the same relative coverage,

     * but composed of just 2 elements with total length equal to scale.

     * Based on the formula in _cairo_stroke_style_dash_stroked:

     * scale * coverage = dashes[0] + cap_scale * MIN (dashes[1], line_width)

     *                  = MIN (dashes[0] + cap_scale * (scale - dashes[0]),

     *                         dashes[0] + cap_scale * line_width) = 

     *                  = MIN (dashes[0] * (1 - cap_scale) + cap_scale * scale,

     *                         dashes[0] + cap_scale * line_width)

     *

     * Solving both cases we get:

     *   dashes[0] = scale * (coverage - cap_scale) / (1 - cap_scale)

     *    when scale - dashes[0] <= line_width

     *  dashes[0] = scale * coverage - cap_scale * line_width

     *    when scale - dashes[0] > line_width.

     *

     * Comparing the two cases we get:

     *   second > first

     *   second > scale * (coverage - cap_scale) / (1 - cap_scale)

     *   second - cap_scale * second - scale * coverage + scale * cap_scale > 0

     *   (scale * coverage - cap_scale * line_width) - cap_scale * second - scale * coverage + scale * cap_scale > 0

     *   - line_width - second + scale > 0

     *   scale - second > line_width

     * which is the condition for the second solution to be the valid one.

     * So when second > first, the second solution is the correct one (i.e.

     * the solution is always MAX (first, second).

     */

    switch (style->line_cap) {

    default:

        ASSERT_NOT_REACHED;

  dashes[0] = 0.0;

  break;

    case CAIRO_LINE_CAP_BUTT:

        /* Simplified formula (substituting 0 for cap_scale): */

        dashes[0] = scale * coverage;

  break;

    case CAIRO_LINE_CAP_ROUND:

        dashes[0] = MAX(scale * (coverage - ROUND_MINSQ_APPROXIMATION) / (1.0 - ROUND_MINSQ_APPROXIMATION),

      scale * coverage - ROUND_MINSQ_APPROXIMATION * style->line_width);

  break;

    case CAIRO_LINE_CAP_SQUARE:

        /*

   * Special attention is needed to handle the case cap_scale == 1 (since the first solution

   * is either indeterminate or -inf in this case). Since dash lengths are always >=0, using

   * 0 as first solution always leads to the correct solution.

   */

        dashes[0] = MAX(0.0, scale * coverage - style->line_width);

  break;

    }

    dashes[1] = scale - dashes[0];

    *dash_offset = on ? 0.0 : dashes[0];

}