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diff --git a/libs/cairo-1.16.0/src/cairo-stroke-style.c b/libs/cairo-1.16.0/src/cairo-stroke-style.c
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+/* 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;
+}
+
+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;
+
+ 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];
+}
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