tools: Add more commands to gtk4-path-tool

Add pathops.

demos/gtk-demo/demo.gresource.xml

@@ -295,6 +295,7 @@
     <file>gears.c</file>
     <file>gestures.c</file>
     <file>glarea.c</file>
+    <file>glyphs.c</file>
     <file>gltransition.c</file>
     <file>headerbar.c</file>
     <file>hypertext.c</file>
@@ -339,6 +340,7 @@
     <file>path_fill.c</file>
     <file>path_maze.c</file>
     <file>path_spinner.c</file>
+    <file>path_sweep.c</file>
     <file>path_walk.c</file>
     <file>path_text.c</file>
     <file>peg_solitaire.c</file>
@@ -426,6 +428,10 @@
   <gresource prefix="/fontrendering">
     <file>fontrendering.ui</file>
   </gresource>
+  <gresource prefix="/path_sweep">
+    <file>path_sweep.ui</file>
+    <file compressed="true">path_world.txt</file>
+  </gresource>
   <gresource prefix="/path_walk">
     <file>path_walk.ui</file>
     <file compressed="true">path_world.txt</file>

demos/gtk-demo/meson.build

@@ -34,6 +34,7 @@ demos = files([
   'gestures.c',
   'glarea.c',
   'gltransition.c',
+  'glyphs.c',
   'headerbar.c',
   'hypertext.c',
   'iconscroll.c',
@@ -75,6 +76,7 @@ demos = files([
   'path_fill.c',
   'path_maze.c',
   'path_spinner.c',
+  'path_sweep.c',
   'path_walk.c',
   'path_text.c',
   'peg_solitaire.c',

demos/gtk-demo/path_sweep.c

@@ -0,0 +1,319 @@
+/* Path/Sweep
+ *
+ * This demo shows how path intersections can be used.
+ *
+ * The world map that is used here is a path with 211 lines and 1569 cubic
+ * Bėzier segments in 121 contours.
+ */
+
+#include <glib/gi18n.h>
+#include <gtk/gtk.h>
+
+#define GTK_TYPE_PATH_SWEEP (gtk_path_sweep_get_type ())
+G_DECLARE_FINAL_TYPE (GtkPathSweep, gtk_path_sweep, GTK, PATH_SWEEP, GtkWidget)
+
+#define POINT_SIZE 8
+
+enum {
+  PROP_0,
+  PROP_PATH,
+  N_PROPS
+};
+
+struct _GtkPathSweep
+{
+  GtkWidget parent_instance;
+
+  GskPath *path;
+  graphene_rect_t bounds;
+  float y_pos;
+  gboolean in;
+};
+
+struct _GtkPathSweepClass
+{
+  GtkWidgetClass parent_class;
+};
+
+static GParamSpec *properties[N_PROPS] = { NULL, };
+
+G_DEFINE_TYPE (GtkPathSweep, gtk_path_sweep, GTK_TYPE_WIDGET)
+
+static gboolean
+intersection_cb (GskPath             *path1,
+                 const GskPathPoint  *point1,
+                 GskPath             *path2,
+                 const GskPathPoint  *point2,
+                 GskPathIntersection  kind,
+                 gpointer             data)
+{
+  GskPathBuilder *builder = data;
+  graphene_point_t p;
+
+  gsk_path_point_get_position (point1, path1, &p);
+  gsk_path_builder_add_circle (builder, &p, 4);
+
+  return TRUE;
+}
+
+static GskPath *
+get_intersection_path (GskPath *path1,
+                       GskPath *path2)
+{
+  GskPathBuilder *builder = gsk_path_builder_new ();
+
+  gsk_path_foreach_intersection (path1, path2, intersection_cb, builder);
+
+  return gsk_path_builder_to_path (builder);
+}
+
+static void
+gtk_path_sweep_snapshot (GtkWidget   *widget,
+                        GtkSnapshot *snapshot)
+{
+  GtkPathSweep *self = GTK_PATH_SWEEP (widget);
+  GskStroke *stroke;
+
+  if (self->path == NULL)
+    return;
+
+  gtk_snapshot_save (snapshot);
+
+  stroke = gsk_stroke_new (2.0);
+
+  gtk_snapshot_append_stroke (snapshot, self->path, stroke, &(GdkRGBA) { 0, 0, 0, 1 });
+
+  if (self->in)
+    {
+      graphene_rect_t bounds;
+      GskPathBuilder *builder;
+      GskPath *line, *isecs;
+
+      gsk_path_get_stroke_bounds (self->path, stroke, &bounds);
+
+      builder = gsk_path_builder_new ();
+      gsk_path_builder_move_to (builder, bounds.origin.x, bounds.origin.y + self->y_pos);
+      gsk_path_builder_line_to (builder, bounds.origin.x + bounds.size.width, bounds.origin.y + self->y_pos);
+      line = gsk_path_builder_free_to_path (builder);
+
+      gtk_snapshot_append_stroke (snapshot, line, stroke, &(GdkRGBA) { 0, 0, 0, 1 });
+
+      isecs = get_intersection_path (self->path, line);
+
+      gtk_snapshot_append_fill (snapshot, isecs, GSK_FILL_RULE_WINDING, &(GdkRGBA) { 1, 0, 0, 1 });
+      gtk_snapshot_append_stroke (snapshot, isecs, stroke, &(GdkRGBA) { 0, 0, 0, 1 });
+
+      gsk_path_unref (isecs);
+      gsk_path_unref (line);
+    }
+
+  gsk_stroke_free (stroke);
+
+  gtk_snapshot_restore (snapshot);
+}
+
+static void
+gtk_path_sweep_measure (GtkWidget      *widget,
+                        GtkOrientation  orientation,
+                        int             for_size,
+                        int            *minimum,
+                        int            *natural,
+                        int            *minimum_baseline,
+                        int            *natural_baseline)
+{
+  GtkPathSweep *self = GTK_PATH_SWEEP (widget);
+
+  if (orientation == GTK_ORIENTATION_HORIZONTAL)
+    *minimum = *natural = (int) ceilf (self->bounds.size.width);
+  else
+    *minimum = *natural = (int) ceilf (self->bounds.size.height);
+}
+
+static void
+gtk_path_sweep_set_path (GtkPathSweep *self,
+                        GskPath     *path)
+{
+  if (self->path == path)
+    return;
+
+  g_clear_pointer (&self->path, gsk_path_unref);
+  graphene_rect_init (&self->bounds, 0, 0, 0, 0);
+  if (path)
+    {
+      GskStroke *stroke;
+
+      self->path = gsk_path_ref (path);
+      stroke = gsk_stroke_new (2.0);
+      gsk_path_get_stroke_bounds (path, stroke, &self->bounds);
+      gsk_stroke_free (stroke);
+    }
+
+  gtk_widget_queue_resize (GTK_WIDGET (self));
+
+  g_object_notify_by_pspec (G_OBJECT (self), properties[PROP_PATH]);
+}
+
+static void
+gtk_path_sweep_set_property (GObject      *object,
+                            guint         prop_id,
+                            const GValue *value,
+                            GParamSpec   *pspec)
+
+{
+  GtkPathSweep *self = GTK_PATH_SWEEP (object);
+
+  switch (prop_id)
+    {
+    case PROP_PATH:
+      gtk_path_sweep_set_path (self, g_value_get_boxed (value));
+      break;
+
+    default:
+      G_OBJECT_WARN_INVALID_PROPERTY_ID (object, prop_id, pspec);
+      break;
+    }
+}
+
+static void
+gtk_path_sweep_get_property (GObject    *object,
+                            guint       prop_id,
+                            GValue     *value,
+                            GParamSpec *pspec)
+{
+  GtkPathSweep *self = GTK_PATH_SWEEP (object);
+
+  switch (prop_id)
+    {
+    case PROP_PATH:
+      g_value_set_boxed (value, self->path);
+      break;
+
+    default:
+      G_OBJECT_WARN_INVALID_PROPERTY_ID (object, prop_id, pspec);
+      break;
+    }
+}
+
+static void
+gtk_path_sweep_dispose (GObject *object)
+{
+  GtkPathSweep *self = GTK_PATH_SWEEP (object);
+
+  g_clear_pointer (&self->path, gsk_path_unref);
+
+  G_OBJECT_CLASS (gtk_path_sweep_parent_class)->dispose (object);
+}
+
+static void
+gtk_path_sweep_class_init (GtkPathSweepClass *klass)
+{
+  GtkWidgetClass *widget_class = GTK_WIDGET_CLASS (klass);
+  GObjectClass *object_class = G_OBJECT_CLASS (klass);
+
+  object_class->dispose = gtk_path_sweep_dispose;
+  object_class->set_property = gtk_path_sweep_set_property;
+  object_class->get_property = gtk_path_sweep_get_property;
+
+  widget_class->snapshot = gtk_path_sweep_snapshot;
+  widget_class->measure = gtk_path_sweep_measure;
+
+  properties[PROP_PATH] =
+    g_param_spec_boxed ("path", NULL, NULL,
+                        GSK_TYPE_PATH,
+                        G_PARAM_READWRITE | G_PARAM_EXPLICIT_NOTIFY | G_PARAM_STATIC_STRINGS);
+
+  g_object_class_install_properties (object_class, N_PROPS, properties);
+}
+
+static void
+motion_cb (GtkEventControllerMotion *controller,
+           double                    x,
+           double                    y,
+           gpointer                  data)
+{
+  GtkPathSweep *self = data;
+
+  self->y_pos = y;
+  gtk_widget_queue_draw (GTK_WIDGET (self));
+}
+
+static void
+enter_cb (GtkEventControllerMotion *controller,
+          double                    x,
+          double                    y,
+          gpointer                  data)
+{
+  GtkPathSweep *self = data;
+
+  self->in = TRUE;
+  self->y_pos = y;
+  gtk_widget_queue_draw (GTK_WIDGET (self));
+}
+
+static void
+leave_cb (GtkEventControllerMotion *controller,
+          gpointer                  data)
+{
+  GtkPathSweep *self = data;
+
+  self->in = FALSE;
+  gtk_widget_queue_draw (GTK_WIDGET (self));
+}
+
+static void
+gtk_path_sweep_init (GtkPathSweep *self)
+{
+  GtkEventController *controller;
+
+  /* Data taken from
+   * https://commons.wikimedia.org/wiki/Maps_of_the_world#/media/File:Simplified_blank_world_map_without_Antartica_(no_borders).svg
+   */
+  GBytes *data = g_resources_lookup_data ("/path_sweep/path_world.txt", 0, NULL);
+  GskPath *path = gsk_path_parse (g_bytes_get_data (data, NULL));
+  g_bytes_unref (data);
+  gtk_path_sweep_set_path (self, path);
+  gsk_path_unref (path);
+
+  controller = gtk_event_controller_motion_new ();
+  g_signal_connect (controller, "motion", G_CALLBACK (motion_cb), self);
+  g_signal_connect (controller, "enter", G_CALLBACK (enter_cb), self);
+  g_signal_connect (controller, "leave", G_CALLBACK (leave_cb), self);
+  gtk_widget_add_controller (GTK_WIDGET (self), controller);
+}
+
+GtkWidget *
+gtk_path_sweep_new (void)
+{
+  GtkPathSweep *self;
+
+  self = g_object_new (GTK_TYPE_PATH_SWEEP, NULL);
+
+  return GTK_WIDGET (self);
+}
+
+GtkWidget *
+do_path_sweep (GtkWidget *do_widget)
+{
+  static GtkWidget *window = NULL;
+
+  if (!window)
+    {
+      GtkBuilder *builder;
+
+      g_type_ensure (GTK_TYPE_PATH_SWEEP);
+
+      builder = gtk_builder_new_from_resource ("/path_sweep/path_sweep.ui");
+      window = GTK_WIDGET (gtk_builder_get_object (builder, "window"));
+      gtk_window_set_display (GTK_WINDOW (window),
+                              gtk_widget_get_display (do_widget));
+      g_object_add_weak_pointer (G_OBJECT (window), (gpointer *) &window);
+      g_object_unref (builder);
+    }
+
+  if (!gtk_widget_get_visible (window))
+    gtk_window_present (GTK_WINDOW (window));
+  else
+    gtk_window_destroy (GTK_WINDOW (window));
+
+  return window;
+}

demos/gtk-demo/path_sweep.ui

@@ -0,0 +1,17 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<interface>
+  <object class="GtkWindow" id="window">
+    <property name="title" translatable="yes">World Map</property>
+    <property name="child">
+      <object class="GtkBox">
+        <property name="orientation">vertical</property>
+        <child>
+          <object class="GtkPathSweep" id="view">
+            <property name="hexpand">true</property>
+            <property name="vexpand">true</property>
+          </object>
+        </child>
+      </object>
+    </property>
+  </object>
+</interface>

docs/reference/gtk/gtk4-path-tool.rst

@@ -12,6 +12,11 @@ SYNOPSIS
 --------
 |   **gtk4-path-tool** <COMMAND> [OPTIONS...] <PATH>
 |
+|   **gtk4-path-tool** simplify [OPTIONS...] <PATH>
+|   **gtk4-path-tool** intersection [OPTIONS...] <PATH> <PATH>
+|   **gtk4-path-tool** union [OPTIONS...] <PATH> <PATH>
+|   **gtk4-path-tool** difference [OPTIONS...] <PATH> <PATH>
+|   **gtk4-path-tool** symmetric-difference [OPTIONS...] <PATH> <PATH>
 |   **gtk4-path-tool** decompose [OPTIONS...] <PATH>
 |   **gtk4-path-tool** show [OPTIONS...] <PATH>
 |   **gtk4-path-tool** render [OPTIONS...] <PATH>
@@ -195,6 +200,7 @@ The interior of the path is filled.
 
   The limit at which to clip miters at line joins. The default value is 4.
 
+<<<<<<< HEAD
 ``--dashes=VALUE``
 
   The dash pattern to use for this stroke. A dash pattern is specified by
@@ -208,6 +214,21 @@ The interior of the path is filled.
   The offset into the dash pattern where dashing should begin.
   The default value is 0.
 
+Boolean Operations
+^^^^^^^^^^^^^^^^^^
+
+The ``intersection``, ``union``, ``difference`` and ``symmetric-difference`` commands
+perform boolean operations on paths. Given two paths, they create a new path which
+encircles the area that is the intersection, union, difference or symmetric difference
+of the areas encircled by the paths.
+
+Simplification
+^^^^^^^^^^^^^^
+
+The ``simplify`` command removes areas of overlap from a path such that the resulting
+path encircles the same area, but every edge in the resulting path is a boundary between
+the inside and the outside.
+
 Reversing
 ^^^^^^^^^
 

gsk/gskcontour.c

@@ -1749,6 +1749,19 @@ gsk_circle_contour_new (const graphene_point_t *center,
   return (GskContour *) self;
 }
 
+void
+gsk_circle_contour_get_params (const GskContour *contour,
+                               graphene_point_t *center,
+                               float            *radius,
+                               gboolean         *ccw)
+{
+  const GskCircleContour *self = (const GskCircleContour *) contour;
+
+  *center = self->center;
+  *radius = self->radius;
+  *ccw = self->ccw;
+}
+
 /* }}} */
 /* {{{ Rectangle */
 

gsk/gskcontourprivate.h

@@ -36,6 +36,10 @@ GskContour *            gsk_standard_contour_new                (GskPathFlags
 
 GskContour *            gsk_circle_contour_new                  (const graphene_point_t *center,
                                                                  float                   radius);
+void                    gsk_circle_contour_get_params           (const GskContour       *contour,
+                                                                 graphene_point_t       *center,
+                                                                 float                  *radius,
+                                                                 gboolean               *ccw);
 GskContour *            gsk_rect_contour_new                    (const graphene_rect_t  *rect);
 GskContour *            gsk_rounded_rect_contour_new            (const GskRoundedRect   *rounded_rect);
 

gsk/gskcurve.c

@@ -2330,6 +2330,30 @@ gsk_curve_get_crossing (const GskCurve         *curve,
   return get_class (curve->op)->get_crossing (curve, point);
 }
 
+float
+gsk_curve_get_length_to (const GskCurve *curve,
+                         float           t)
+{
+  return get_class (curve->op)->get_length_to (curve, t);
+}
+
+float
+gsk_curve_get_length (const GskCurve *curve)
+{
+  return gsk_curve_get_length_to (curve, 1);
+}
+
+float
+gsk_curve_at_length (const GskCurve *curve,
+                     float           length,
+                     float           epsilon)
+{
+  return get_class (curve->op)->get_at_length (curve, length, epsilon);
+}
+
+/* }}} */
+/* {{{ Closest point */
+
 static gboolean
 project_point_onto_line (const GskCurve         *curve,
                          const graphene_point_t *point,
@@ -2451,187 +2475,6 @@ gsk_curve_get_closest_point (const GskCurve         *curve,
     return find_closest_point (curve, point, threshold, 0, 1, out_dist, out_t);
 }
 
-float
-gsk_curve_get_length_to (const GskCurve *curve,
-                         float           t)
-{
-  return get_class (curve->op)->get_length_to (curve, t);
-}
-
-float
-gsk_curve_get_length (const GskCurve *curve)
-{
-  return gsk_curve_get_length_to (curve, 1);
-}
-
-/* Compute the inverse of the arclength using bisection,
- * to a given precision
- */
-float
-gsk_curve_at_length (const GskCurve *curve,
-                     float           length,
-                     float           epsilon)
-{
-  return get_class (curve->op)->get_at_length (curve, length, epsilon);
-}
-
-static inline void
-_sincosf (float  angle,
-          float *out_s,
-          float *out_c)
-{
-#ifdef HAVE_SINCOSF
-      sincosf (angle, out_s, out_c);
-#else
-      *out_s = sinf (angle);
-      *out_c = cosf (angle);
-#endif
-}
-
-static void
-align_points (const graphene_point_t *p,
-              const graphene_point_t *a,
-              const graphene_point_t *b,
-              graphene_point_t       *q,
-              int                     n)
-{
-  graphene_vec2_t n1;
-  float angle;
-  float s, c;
-
-  get_tangent (a, b, &n1);
-  angle = - atan2f (graphene_vec2_get_y (&n1), graphene_vec2_get_x (&n1));
-  _sincosf (angle, &s, &c);
-
-  for (int i = 0; i < n; i++)
-    {
-      q[i].x = (p[i].x - a->x) * c - (p[i].y - a->y) * s;
-      q[i].y = (p[i].x - a->x) * s + (p[i].y - a->y) * c;
-    }
-}
-
-static int
-filter_allowable (float t[3],
-                  int   n)
-{
-  float g[3];
-  int j = 0;
-
-  for (int i = 0; i < n; i++)
-    if (0 < t[i] && t[i] < 1)
-      g[j++] = t[i];
-  for (int i = 0; i < j; i++)
-    t[i] = g[i];
-  return j;
-}
-
-/* find solutions for at^2 + bt + c = 0 */
-static int
-solve_quadratic (float a, float b, float c, float t[2])
-{
-  float d;
-  int n = 0;
-
-  if (fabsf (a) > 0.0001)
-    {
-      if (b*b > 4*a*c)
-        {
-          d = sqrtf (b*b - 4*a*c);
-          t[n++] = (-b + d)/(2*a);
-          t[n++] = (-b - d)/(2*a);
-        }
-      else
-        {
-          t[n++] = -b / (2*a);
-        }
-    }
-  else if (fabsf (b) > 0.0001)
-    {
-      t[n++] = -c / b;
-    }
-
-  return n;
-}
-
-int
-gsk_curve_get_curvature_points (const GskCurve *curve,
-                                float           t[3])
-{
-  const graphene_point_t *pts = curve->cubic.points;
-  graphene_point_t p[4];
-  float a, b, c, d;
-  float x, y, z;
-  int n;
-
-  if (curve->op != GSK_PATH_CUBIC)
-    return 0; /* FIXME */
-
-  align_points (pts, &pts[0], &pts[3], p, 4);
-
-  a = p[2].x * p[1].y;
-  b = p[3].x * p[1].y;
-  c = p[1].x * p[2].y;
-  d = p[3].x * p[2].y;
-
-  x = - 3*a + 2*b + 3*c - d;
-  y = 3*a - b - 3*c;
-  z = c - a;
-
-  n = solve_quadratic (x, y, z, t);
-  return filter_allowable (t, n);
-}
-
-/* Find cusps inside the open interval from 0 to 1.
- *
- * According to Stone & deRose, A Geometric Characterization
- * of Parametric Cubic curves, a necessary and sufficient
- * condition is that the first derivative vanishes.
- */
-int
-gsk_curve_get_cusps (const GskCurve *curve,
-                     float           t[2])
-{
-  const graphene_point_t *pts = curve->cubic.points;
-  graphene_point_t p[3];
-  float ax, bx, cx;
-  float ay, by, cy;
-  float tx[3];
-  int nx;
-  int n = 0;
-
-  if (curve->op != GSK_PATH_CUBIC)
-    return 0;
-
-  p[0].x = 3 * (pts[1].x - pts[0].x);
-  p[0].y = 3 * (pts[1].y - pts[0].y);
-  p[1].x = 3 * (pts[2].x - pts[1].x);
-  p[1].y = 3 * (pts[2].y - pts[1].y);
-  p[2].x = 3 * (pts[3].x - pts[2].x);
-  p[2].y = 3 * (pts[3].y - pts[2].y);
-
-  ax = p[0].x - 2 * p[1].x + p[2].x;
-  bx = - 2 * p[0].x + 2 * p[1].x;
-  cx = p[0].x;
-
-  nx = solve_quadratic (ax, bx, cx, tx);
-  nx = filter_allowable (tx, nx);
-
-  ay = p[0].y - 2 * p[1].y + p[2].y;
-  by = - 2 * p[0].y + 2 * p[1].y;
-  cy = p[0].y;
-
-  for (int i = 0; i < nx; i++)
-    {
-      float ti = tx[i];
-
-      if (0 < ti && ti < 1 &&
-          fabsf (ay * ti * ti + by * ti + cy) < 0.001)
-        t[n++] = ti;
-    }
-
-  return n;
-}
-
 /* }}} */
 
 /* vim:set foldmethod=marker expandtab: */

gsk/gskcurveprivate.h

@@ -187,6 +187,19 @@ int                    gsk_curve_get_curvature_points           (const GskCurve
 int                    gsk_curve_get_cusps                      (const GskCurve         *curve,
                                                                  float                   t[2]);
 
+int                    gsk_curve_intersect                      (const GskCurve         *curve1,
+                                                                 const GskCurve         *curve2,
+                                                                 float                  *t1,
+                                                                 float                  *t2,
+                                                                 graphene_point_t       *p,
+                                                                 GskPathIntersection    *kind,
+                                                                 int                     n);
+
+int                    gsk_curve_self_intersect                 (const GskCurve         *curve,
+                                                                 float                  *t1,
+                                                                 graphene_point_t       *p,
+                                                                 int                     n);
+
 
 G_END_DECLS
 

gsk/gskpath.h

@@ -144,6 +144,79 @@ gboolean                gsk_path_foreach                        (GskPath
                                                                  GskPathForeachFunc      func,
                                                                  gpointer                user_data);
 
+/**
+ * GskPathIntersection:
+ * @GSK_PATH_INTERSECTION_NONE: No intersection
+ * @GSK_PATH_INTERSECTION_NORMAL: A normal intersection, where the two paths
+ *   cross each other
+ * @GSK_PATH_INTERSECTION_START: The start of a segment where the two paths coincide
+ * @GSK_PATH_INTERSECTION_END: The end of a segment where the two paths coincide
+ *
+ * The values of this enumeration classify intersections
+ * between paths.
+ */
+typedef enum
+{
+  GSK_PATH_INTERSECTION_NONE,
+  GSK_PATH_INTERSECTION_NORMAL,
+  GSK_PATH_INTERSECTION_START,
+  GSK_PATH_INTERSECTION_END,
+} GskPathIntersection;
+
+/**
+ * GskPathIntersectionFunc:
+ * @path1: the first path
+ * @point1: the intersection as point on @path1
+ * @path2: the second path
+ * @point2: the intersection as point on @path2
+ * @kind: specify the nature of the intersection
+ * @user_data: user data
+ *
+ * Prototype of the callback to iterate through the
+ * intersections of two paths.
+ *
+ * Returns: %TRUE to continue iterating, %FALSE to
+ *   immediately abort and not call the function again
+ *
+ * Since: 4.14
+ */
+typedef gboolean (* GskPathIntersectionFunc)                    (GskPath                *path1,
+                                                                 const GskPathPoint     *point1,
+                                                                 GskPath                *path2,
+                                                                 const GskPathPoint     *point2,
+                                                                 GskPathIntersection     kind,
+                                                                 gpointer                user_data);
+
+GDK_AVAILABLE_IN_4_14
+gboolean                gsk_path_foreach_intersection           (GskPath                *path1,
+                                                                 GskPath                *path2,
+                                                                 GskPathIntersectionFunc func,
+                                                                 gpointer                user_data);
+
+GDK_AVAILABLE_IN_4_14
+GskPath *               gsk_path_union                          (GskPath                *first,
+                                                                 GskPath                *second,
+                                                                 GskFillRule             fill_rule);
+
+GDK_AVAILABLE_IN_4_14
+GskPath *               gsk_path_intersection                   (GskPath                *first,
+                                                                 GskPath                *second,
+                                                                 GskFillRule             fill_rule);
+
+GDK_AVAILABLE_IN_4_14
+GskPath *               gsk_path_difference                     (GskPath                *first,
+                                                                 GskPath                *second,
+                                                                 GskFillRule             fill_rule);
+
+GDK_AVAILABLE_IN_4_14
+GskPath *               gsk_path_symmetric_difference           (GskPath                *first,
+                                                                 GskPath                *second,
+                                                                 GskFillRule             fill_rule);
+
+GDK_AVAILABLE_IN_4_14
+GskPath *               gsk_path_simplify                       (GskPath                *self,
+                                                                 GskFillRule             fill_rule);
+
 G_DEFINE_AUTOPTR_CLEANUP_FUNC(GskPath, gsk_path_unref)
 
 G_END_DECLS

gsk/gskpathintersect.c

@@ -0,0 +1,705 @@
+/*
+ * Copyright © 2020 Benjamin Otte
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library 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
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library. If not, see <http://www.gnu.org/licenses/>.
+ *
+ * Authors: Benjamin Otte <otte@gnome.org>
+ */
+
+#include "config.h"
+
+#include "gskpathprivate.h"
+
+#include "gskcurveprivate.h"
+#include "gskpathbuilder.h"
+#include "gskpathpoint.h"
+#include "gskcontourprivate.h"
+
+typedef struct
+{
+  gsize count;
+  gboolean closed;
+  gboolean z_is_empty;
+} CountCurveData;
+
+static gboolean
+count_cb (GskPathOperation        op,
+          const graphene_point_t *pts,
+          gsize                   n_pts,
+          float                   weight,
+          gpointer                data)
+{
+  CountCurveData *ccd = data;
+
+  (ccd->count)++;
+
+  if (op ==GSK_PATH_CLOSE)
+    {
+      ccd->closed = TRUE;
+      ccd->z_is_empty = graphene_point_equal (&pts[0], &pts[1]);
+    }
+
+  return TRUE;
+}
+
+static gsize
+count_curves (const GskContour *contour,
+              gboolean         *closed,
+              gboolean         *z_is_empty)
+{
+  CountCurveData data;
+
+  data.count = 0;
+  data.closed = FALSE;
+  data.z_is_empty = FALSE;
+
+  gsk_contour_foreach (contour, count_cb, &data);
+
+  *closed = data.closed;
+  *z_is_empty = data.z_is_empty;
+
+  return data.count;
+}
+
+typedef struct
+{
+  GskPathPoint point1;
+  GskPathPoint point2;
+  GskPathIntersection kind;
+} Intersection;
+
+typedef struct
+{
+  GskPath *path1;
+  GskPath *path2;
+  GskPathIntersectionFunc func;
+  gpointer data;
+
+  gsize contour1;
+  gsize contour2;
+  gsize idx1;
+  gsize idx2;
+
+  const GskContour *c1;
+  const GskContour *c2;
+  GskCurve curve1;
+  GskCurve curve2;
+
+  gboolean c1_closed;
+  gboolean c2_closed;
+  gboolean c1_z_is_empty;
+  gboolean c2_z_is_empty;
+
+  gsize c1_count;
+  gsize c2_count;
+
+  GArray *points;
+  GArray *all_points;
+} PathIntersectData;
+
+static gboolean
+intersect_curve2 (GskPathOperation        op,
+                  const graphene_point_t *pts,
+                  gsize                   n_pts,
+                  float                   weight,
+                  gpointer                data)
+{
+  PathIntersectData *pd = data;
+  float t1[10], t2[10];
+  graphene_point_t p[10];
+  GskPathIntersection kind[10];
+  int n;
+
+  if (op == GSK_PATH_MOVE)
+    {
+      if (gsk_contour_get_n_ops (pd->c2) == 1)
+        {
+          float dist, tt;
+
+          if (gsk_curve_get_closest_point (&pd->curve1, &pts[0], 1, &dist, &tt) && dist == 0)
+            {
+              Intersection is;
+
+              is.kind = GSK_PATH_INTERSECTION_NORMAL;
+              is.point1.contour = pd->contour1;
+              is.point1.idx = pd->idx1;
+              is.point1.t = tt;
+              is.point2.contour = pd->contour2;
+              is.point2.idx = 0;
+              is.point2.t = 1;
+
+              g_array_append_val (pd->points, is);
+            }
+        }
+
+      return TRUE;
+    }
+
+  if (op == GSK_PATH_CLOSE)
+    {
+      if (graphene_point_equal (&pts[0], &pts[1]))
+        return TRUE;
+    }
+
+  pd->idx2++;
+
+  gsk_curve_init_foreach (&pd->curve2, op, pts, n_pts, weight);
+
+  n = gsk_curve_intersect (&pd->curve1, &pd->curve2, t1, t2, p, kind, 19);
+
+  for (int i = 0; i < n; i++)
+    {
+      Intersection is;
+
+      is.point1.contour = pd->contour1;
+      is.point2.contour = pd->contour2;
+      is.point1.idx = pd->idx1;
+      is.point2.idx = pd->idx2;
+      is.point1.t = t1[i];
+      is.point2.t = t2[i];
+      is.kind = kind[i];
+
+#if 0
+      g_print ("append p1 { %lu %lu %f } p2 { %lu %lu %f } %s\n",
+               is.point1.contour, is.point1.idx, is.point1.t,
+               is.point2.contour, is.point2.idx, is.point2.t,
+               kn[is.kind]);
+#endif
+      g_array_append_val (pd->points, is);
+    }
+
+  return TRUE;
+}
+
+static gboolean
+intersect_curve (GskPathOperation        op,
+                 const graphene_point_t *pts,
+                 gsize                   n_pts,
+                 float                   weight,
+                 gpointer                data)
+{
+  PathIntersectData *pd = data;
+  GskBoundingBox b1, b2;
+
+  if (op == GSK_PATH_MOVE)
+    {
+      if (gsk_contour_get_n_ops (pd->c1) == 1)
+        {
+          GskPathPoint point;
+          float dist;
+
+          if (gsk_contour_get_closest_point (pd->c2, &pts[0], 1, &point, &dist) && dist == 0)
+            {
+              Intersection is;
+
+              is.kind = GSK_PATH_INTERSECTION_NORMAL;
+              is.point1.contour = pd->contour1;
+              is.point1.idx = 0;
+              is.point1.t = 1;
+              is.point2.contour = pd->contour2;
+              is.point2.idx = point.idx;
+              is.point2.t = point.t;
+
+              g_array_append_val (pd->points, is);
+            }
+        }
+
+      return TRUE;
+    }
+
+  if (op == GSK_PATH_CLOSE)
+    {
+      if (graphene_point_equal (&pts[0], &pts[1]))
+        return TRUE;
+    }
+
+  pd->idx1++;
+
+  gsk_curve_init_foreach (&pd->curve1, op, pts, n_pts, weight);
+  gsk_curve_get_bounds (&pd->curve1, &b1);
+
+  gsk_contour_get_bounds (pd->c2, &b2);
+
+  if (gsk_bounding_box_intersection (&b1, &b2, NULL))
+    {
+      pd->idx2 = 0;
+
+      if (!gsk_contour_foreach (pd->c2, intersect_curve2, pd))
+        return FALSE;
+    }
+
+  return TRUE;
+}
+
+static gboolean
+gsk_path_point_near (const GskPathPoint *p1,
+                     const GskPathPoint *p2,
+                     gboolean            closed,
+                     gsize               count,
+                     gboolean            z_is_empty,
+                     float               epsilon)
+{
+  if (p1->idx == p2->idx && fabsf (p1->t - p2->t) < epsilon)
+    return TRUE;
+
+  if (p1->idx + 1 == p2->idx && (1 - p1->t + p2->t < epsilon))
+    return TRUE;
+
+  if (p2->idx + 1 == p1->idx && (1 - p2->t + p1->t < epsilon))
+    return TRUE;
+
+  if (closed)
+    {
+      if (p1->idx == 1 && p2->idx == count - 1 && (1 - p2->t + p1->t < epsilon))
+        return TRUE;
+
+      if (p2->idx == 1 && p1->idx == count - 1 && (1 - p1->t + p2->t < epsilon))
+        return TRUE;
+    }
+
+  if (closed && z_is_empty)
+    {
+      if (p1->idx == 1 && p2->idx == count - 2 && (1 - p2->t + p1->t < epsilon))
+        return TRUE;
+
+      if (p2->idx == 1 && p1->idx == count - 2 && (1 - p1->t + p2->t < epsilon))
+        return TRUE;
+    }
+
+  return FALSE;
+}
+
+static int cmp_path1 (gconstpointer p1, gconstpointer p2);
+
+static void
+default_contour_collect_intersections (const GskContour  *contour1,
+                                       const GskContour  *contour2,
+                                       PathIntersectData *pd)
+{
+  pd->idx1 = 0;
+
+  g_array_set_size (pd->points, 0);
+
+  gsk_contour_foreach (contour1, intersect_curve, pd);
+
+  g_array_sort (pd->points, cmp_path1);
+
+#if 0
+  g_print ("after sorting\n");
+  for (gsize i = 0; i < pd->points->len; i++)
+    {
+      Intersection *is = &g_array_index (pd->points, Intersection, i);
+      const char *kn[] = { "none", "normal", "start", "end" };
+
+      g_print ("p1 { %lu %lu %f } p2 { %lu %lu %f } %s\n",
+               is->point1.contour, is->point1.idx, is->point1.t,
+               is->point2.contour, is->point2.idx, is->point2.t,
+               kn[is->kind]);
+    }
+#endif
+
+  for (gsize i = 0; i < pd->points->len; i++)
+    {
+      Intersection *is1 = &g_array_index (pd->points, Intersection, i);
+
+      for (gsize j = i + 1; j < pd->points->len; j++)
+        {
+          Intersection *is2 = &g_array_index (pd->points, Intersection, j);
+
+          if (!gsk_path_point_near (&is1->point1, &is2->point1,
+                                    pd->c1_closed, pd->c1_count, pd->c1_z_is_empty,
+                                    0.001))
+            continue;
+
+          if (!gsk_path_point_near (&is1->point2, &is2->point2,
+                                    pd->c2_closed, pd->c2_count, pd->c2_z_is_empty,
+                                    0.001))
+            continue;
+
+          if (is1->kind == GSK_PATH_INTERSECTION_NORMAL && is2->kind != GSK_PATH_INTERSECTION_NONE)
+            is1->kind = GSK_PATH_INTERSECTION_NONE;
+          else if (is2->kind == GSK_PATH_INTERSECTION_NORMAL && is1->kind != GSK_PATH_INTERSECTION_NONE)
+            is2->kind = GSK_PATH_INTERSECTION_NONE;
+        }
+    }
+
+#if 0
+  g_print ("after collapsing\n");
+  for (gsize i = 0; i < pd->points->len; i++)
+    {
+      Intersection *is = &g_array_index (pd->points, Intersection, i);
+      const char *kn[] = { "none", "normal", "start", "end" };
+
+      g_print ("p1 { %lu %lu %f } p2 { %lu %lu %f } %s\n",
+               is->point1.contour, is->point1.idx, is->point1.t,
+               is->point2.contour, is->point2.idx, is->point2.t,
+               kn[is->kind]);
+    }
+#endif
+
+  for (gsize i = 0; i < pd->points->len; i++)
+    {
+      Intersection *is1 = &g_array_index (pd->points, Intersection, i);
+
+      for (gsize j = i + 1; j < pd->points->len; j++)
+        {
+          Intersection *is2 = &g_array_index (pd->points, Intersection, j);
+
+          if (!gsk_path_point_near (&is1->point1, &is2->point1, FALSE, 0, FALSE, 0.001))
+            break;
+
+          if (!gsk_path_point_near (&is1->point2, &is2->point2,
+                                    pd->c2_closed, pd->c2_count, pd->c2_z_is_empty,
+                                    0.001))
+            break;
+
+          if ((is1->kind == GSK_PATH_INTERSECTION_END &&
+               is2->kind == GSK_PATH_INTERSECTION_START) ||
+              (is1->kind == GSK_PATH_INTERSECTION_START &&
+               is2->kind == GSK_PATH_INTERSECTION_END))
+            {
+              is1->kind = GSK_PATH_INTERSECTION_NONE;
+              is2->kind = GSK_PATH_INTERSECTION_NONE;
+            }
+        }
+    }
+
+#if 0
+  g_print ("after merging segments\n");
+  for (gsize i = 0; i < pd->points->len; i++)
+    {
+      Intersection *is = &g_array_index (pd->points, Intersection, i);
+      const char *kn[] = { "none", "normal", "start", "end" };
+
+      g_print ("p1 { %lu %lu %f } p2 { %lu %lu %f } %s\n",
+               is->point1.contour, is->point1.idx, is->point1.t,
+               is->point2.contour, is->point2.idx, is->point2.t,
+               kn[is->kind]);
+    }
+#endif
+
+  for (gsize j = 0; j < pd->points->len; j++)
+    {
+      Intersection *is = &g_array_index (pd->points, Intersection, j);
+
+      if (is->kind != GSK_PATH_INTERSECTION_NONE)
+        g_array_append_val (pd->all_points, *is);
+    }
+}
+
+static int
+circle_intersect (const graphene_point_t *center1,
+                  float                   radius1,
+                  const graphene_point_t *center2,
+                  float                   radius2,
+                  graphene_point_t        points[2])
+{
+  float d;
+  float a, h;
+  graphene_point_t m;
+  graphene_vec2_t n;
+
+  g_assert (radius1 >= 0);
+  g_assert (radius2 >= 0);
+
+  d = graphene_point_distance (center1, center2, NULL, NULL);
+
+  if (d < fabsf (radius1 - radius2))
+    return 0;
+
+  if (d > radius1 + radius2)
+    return 0;
+
+  if (d == radius1 + radius2)
+    {
+      graphene_point_interpolate (center1, center2, radius1 / (radius1 + radius2), &points[0]);
+      return 1;
+    }
+
+  a = (radius1*radius1 - radius2*radius2 + d*d)/(2*d);
+  h = sqrtf (radius1*radius1 - a*a);
+
+  graphene_point_interpolate (center1, center2, a/d, &m);
+  graphene_vec2_init (&n, center2->y - center1->y, center1->x - center2->x);
+  graphene_vec2_normalize (&n, &n);
+
+  graphene_point_init (&points[0], m.x + graphene_vec2_get_x (&n) * h,
+                                   m.y + graphene_vec2_get_y (&n) * h);
+  graphene_point_init (&points[1], m.x - graphene_vec2_get_x (&n) * h,
+                                   m.y - graphene_vec2_get_y (&n) * h);
+
+  return 2;
+}
+
+static void
+circle_contour_collect_intersections (const GskContour  *contour1,
+                                      const GskContour  *contour2,
+                                      PathIntersectData *pd)
+{
+  graphene_point_t center1, center2;
+  float radius1, radius2;
+  gboolean ccw1, ccw2;
+  graphene_point_t p[2];
+  int n;
+  Intersection is[2];
+
+  gsk_circle_contour_get_params (contour1, &center1, &radius1, &ccw1);
+  gsk_circle_contour_get_params (contour2, &center2, &radius2, &ccw2);
+
+  if (graphene_point_equal (&center1, &center2) && radius1 == radius2)
+    {
+      is[0].kind = GSK_PATH_INTERSECTION_START;
+      is[0].point1.contour = pd->contour1;
+      is[0].point1.idx = 1;
+      is[0].point1.t = 0;
+      is[0].point2.contour = pd->contour2;
+      is[0].point2.idx = 1;
+      is[0].point2.t = 0;
+
+      is[1].kind = GSK_PATH_INTERSECTION_END;
+      is[1].point1.contour = pd->contour1;
+      is[1].point1.idx = 1;
+      is[1].point1.t = 1;
+      is[1].point2.contour = pd->contour2;
+      is[1].point2.idx = 1;
+      is[1].point2.t = 1;
+
+      if (ccw1 != ccw2)
+        {
+          is[0].point2.t = 1;
+          is[1].point2.t = 0;
+        }
+
+      g_array_append_val (pd->all_points, is[0]);
+      g_array_append_val (pd->all_points, is[1]);
+
+      return;
+    }
+
+  n = circle_intersect (&center1, radius1, &center2, radius2, p);
+
+  for (int i = 0; i < n; i++)
+    {
+      float d;
+
+      is[i].kind = GSK_PATH_INTERSECTION_NORMAL;
+      is[i].point1.contour = pd->contour1;
+      is[i].point2.contour = pd->contour2;
+
+      gsk_contour_get_closest_point (contour1, &p[i], 1, &is[i].point1, &d);
+      gsk_contour_get_closest_point (contour2, &p[i], 1, &is[i].point2, &d);
+    }
+
+  if (n == 1)
+    {
+      g_array_append_val (pd->all_points, is[0]);
+    }
+  else if (n == 2)
+    {
+      if (gsk_path_point_compare (&is[0].point1, &is[1].point1) < 0)
+        {
+          g_array_append_val (pd->all_points, is[0]);
+          g_array_append_val (pd->all_points, is[1]);
+        }
+      else
+        {
+          g_array_append_val (pd->all_points, is[1]);
+          g_array_append_val (pd->all_points, is[0]);
+        }
+    }
+}
+
+static void
+contour_collect_intersections (const GskContour  *contour1,
+                               const GskContour  *contour2,
+                               PathIntersectData *pd)
+{
+  if (strcmp (gsk_contour_get_type_name (contour1), "GskCircleContour") == 0 &&
+      strcmp (gsk_contour_get_type_name (contour2), "GskCircleContour") == 0)
+    circle_contour_collect_intersections (contour1, contour2, pd);
+  else
+    default_contour_collect_intersections (contour1, contour2, pd);
+}
+
+static int
+cmp_path1 (gconstpointer p1,
+           gconstpointer p2)
+{
+  const Intersection *i1 = p1;
+  const Intersection *i2 = p2;
+  int i;
+
+  i = gsk_path_point_compare (&i1->point1, &i2->point1);
+  if (i != 0)
+    return i;
+
+  return gsk_path_point_compare (&i1->point2, &i2->point2);
+}
+
+static gboolean
+contour_foreach_intersection (const GskContour  *contour1,
+                              PathIntersectData *pd)
+{
+  GskBoundingBox b1, b2;
+
+  gsk_contour_get_bounds (contour1, &b1);
+
+  g_array_set_size (pd->all_points, 0);
+
+  for (gsize i = 0; i < gsk_path_get_n_contours (pd->path2); i++)
+    {
+      const GskContour *contour2 = gsk_path_get_contour (pd->path2, i);
+
+      gsk_contour_get_bounds (contour1, &b2);
+
+      if (gsk_bounding_box_intersection (&b1, &b2, NULL))
+        {
+          pd->contour2 = i;
+          pd->c2 = contour2;
+          pd->c2_count = count_curves (contour2, &pd->c2_closed, &pd->c2_z_is_empty);
+
+          contour_collect_intersections (contour1, contour2, pd);
+        }
+    }
+
+  g_array_sort (pd->all_points, cmp_path1);
+
+#if 0
+  g_print ("after sorting\n");
+  for (gsize i = 0; i < pd->all_points->len; i++)
+    {
+      Intersection *is = &g_array_index (pd->all_points, Intersection, i);
+      const char *kn[] = { "none", "normal", "start", "end" };
+
+      g_print ("p1 { %lu %lu %f } p2 { %lu %lu %f } %s\n",
+               is->point1.contour, is->point1.idx, is->point1.t,
+               is->point2.contour, is->point2.idx, is->point2.t,
+               kn[is->kind]);
+    }
+
+  for (gsize i = 0; i + 1 < pd->all_points->len; i++)
+    {
+      Intersection *is1 = &g_array_index (pd->all_points, Intersection, i);
+      Intersection *is2 = &g_array_index (pd->all_points, Intersection, i + 1);
+
+      if (gsk_path_point_equal (&is1->point1, &is2->point1) &&
+          gsk_path_point_equal (&is1->point2, &is2->point2))
+        {
+          if (is1->kind == GSK_PATH_INTERSECTION_END &&
+              is2->kind == GSK_PATH_INTERSECTION_START)
+            {
+              is1->kind = GSK_PATH_INTERSECTION_NONE;
+              is2->kind = GSK_PATH_INTERSECTION_NONE;
+            }
+          else
+            {
+              is2->kind = MAX (is1->kind, is2->kind);
+              is1->kind = GSK_PATH_INTERSECTION_NONE;
+            }
+        }
+    }
+
+  g_print ("emitting\n");
+  for (gsize i = 0; i < pd->all_points->len; i++)
+    {
+      Intersection *is = &g_array_index (pd->all_points, Intersection, i);
+      const char *kn[] = { "none", "normal", "start", "end" };
+
+      g_print ("p1 { %lu %lu %f } p2 { %lu %lu %f } %s\n",
+               is->point1.contour, is->point1.idx, is->point1.t,
+               is->point2.contour, is->point2.idx, is->point2.t,
+               kn[is->kind]);
+    }
+#endif
+
+  for (gsize i = 0; i < pd->all_points->len; i++)
+    {
+      Intersection *is = &g_array_index (pd->all_points, Intersection, i);
+
+      if (is->kind != GSK_PATH_INTERSECTION_NONE)
+        {
+
+          if (!pd->func (pd->path1, &is->point1, pd->path2, &is->point2, is->kind, pd->data))
+            return FALSE;
+        }
+    }
+
+  return TRUE;
+}
+
+/**
+ * gsk_path_foreach_intersection:
+ * @path1: the first path
+ * @path2: the second path
+ * @func: (scope call) (closure user_data): the function to call for intersections
+ * @user_data: (nullable): user data passed to @func
+ *
+ * Finds intersections between two paths.
+ *
+ * This function finds intersections between @path1 and @path2,
+ * and calls @func for each of them, in increasing order for @path1.
+ *
+ * When segments of the paths coincide, the callback is called once
+ * for the start of the segment, with @GSK_PATH_INTERSECTION_START, and
+ * once for the end of the segment, with @GSK_PATH_INTERSECTION_END.
+ * Note that other intersections may occur between the start and end
+ * of such a segment.
+ *
+ * If @func returns `FALSE`, the iteration is stopped.
+ *
+ * Returns: `FALSE` if @func returned FALSE`, `TRUE` otherwise.
+ *
+ * Since: 4.14
+ */
+gboolean
+gsk_path_foreach_intersection (GskPath                 *path1,
+                               GskPath                 *path2,
+                               GskPathIntersectionFunc  func,
+                               gpointer                 data)
+{
+  PathIntersectData pd = {
+    .path1 = path1,
+    .path2 = path2,
+    .func = func,
+    .data = data,
+  };
+  gboolean ret;
+
+  pd.points = g_array_new (FALSE, FALSE, sizeof (Intersection));
+  pd.all_points = g_array_new (FALSE, FALSE, sizeof (Intersection));
+
+  ret = TRUE;
+  for (gsize i = 0; i < gsk_path_get_n_contours (path1); i++)
+    {
+      const GskContour *contour1 = gsk_path_get_contour (path1, i);
+
+      pd.contour1 = i;
+      pd.c1 = contour1;
+      pd.c1_count = count_curves (contour1, &pd.c1_closed, &pd.c1_z_is_empty);
+      pd.idx1 = 0;
+
+      if (!contour_foreach_intersection (contour1, &pd))
+        {
+          ret = FALSE;
+          break;
+        }
+    }
+
+  g_array_unref (pd.points);
+  g_array_unref (pd.all_points);
+
+  return ret;
+}
+
+/* vim:set foldmethod=marker expandtab: */

gsk/gskpathprivate.h

@@ -56,5 +56,19 @@ gboolean                gsk_path_foreach_with_tolerance         (GskPath
 void                    gsk_path_builder_add_contour            (GskPathBuilder         *builder,
                                                                  GskContour             *contour);
 
+typedef enum
+{
+  GSK_PATH_OP_SIMPLIFY,
+  GSK_PATH_OP_UNION,
+  GSK_PATH_OP_INTERSECTION,
+  GSK_PATH_OP_DIFFERENCE,
+  GSK_PATH_OP_XOR
+} GskPathOp;
+
+GskPath *               gsk_path_op                             (GskPathOp               operation,
+                                                                 GskFillRule             fill_rule,
+                                                                 GskPath                *first,
+                                                                 GskPath                *second);
+
 G_END_DECLS
 

gsk/meson.build

@@ -28,7 +28,9 @@ gsk_public_sources = files([
   'gskglshader.c',
   'gskpath.c',
   'gskpathbuilder.c',
+  'gskpathintersect.c',
   'gskpathmeasure.c',
+  'gskpathops.c',
   'gskpathparser.c',
   'gskpathpoint.c',
   'gskrenderer.c',
@@ -45,6 +47,7 @@ gsk_private_sources = files([
   'gskcairoblur.c',
   'gskcontour.c',
   'gskcurve.c',
+  'gskcurveintersect.c',
   'gskdebug.c',
   'gskprivate.c',
   'gskprofiler.c',

testsuite/gsk/curve-intersect.c

@@ -0,0 +1,551 @@
+#include <gtk/gtk.h>
+#include "gsk/gskcurveprivate.h"
+
+static void
+test_line_line_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[2], p2[2];
+  float t1, t2;
+  graphene_point_t p;
+  GskPathIntersection kind;
+  int n;
+
+  graphene_point_init (&p1[0], 10, 0);
+  graphene_point_init (&p1[1], 10, 100);
+  graphene_point_init (&p2[0], 0, 10);
+  graphene_point_init (&p2[1], 100, 10);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_LINE, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, &t1, &t2, &p, &kind, 1);
+
+  g_assert_cmpint (n, ==, 1);
+  g_assert_cmpfloat_with_epsilon (t1, 0.1, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2, 0.1, 0.0001);
+  g_assert_true (graphene_point_near (&p, &GRAPHENE_POINT_INIT (10, 10), 0.0001));
+}
+
+static void
+test_line_line_end_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[2], p2[2];
+  float t1, t2;
+  graphene_point_t p;
+  GskPathIntersection kind;
+  int n;
+
+  graphene_point_init (&p1[0], 10, 0);
+  graphene_point_init (&p1[1], 10, 100);
+  graphene_point_init (&p2[0], 10, 100);
+  graphene_point_init (&p2[1], 100, 10);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_LINE, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, &t1, &t2, &p, &kind, 1);
+
+  g_assert_cmpint (n, ==, 1);
+  g_assert_cmpfloat_with_epsilon (t1, 1, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2, 0, 0.0001);
+  g_assert_true (graphene_point_near (&p, &GRAPHENE_POINT_INIT (10, 100), 0.0001));
+}
+
+static void
+test_line_line_none_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[2], p2[2];
+  float t1, t2;
+  graphene_point_t p;
+  GskPathIntersection kind;
+  int n;
+
+  graphene_point_init (&p1[0], 0, 0);
+  graphene_point_init (&p1[1], 10, 0);
+  graphene_point_init (&p2[0], 20, 0);
+  graphene_point_init (&p2[1], 30, 0);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_LINE, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, &t1, &t2, &p, &kind, 1);
+
+  g_assert_cmpint (n, ==, 0);
+
+  graphene_point_init (&p1[0], 247.103424, 95.7965317);
+  graphene_point_init (&p1[1], 205.463974, 266.758484);
+  graphene_point_init (&p2[0], 183.735962, 355.968689);
+  graphene_point_init (&p2[1], 121.553253, 611.27655);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_LINE, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, &t1, &t2, &p, &kind, 1);
+
+  g_assert_cmpint (n, ==, 0);
+}
+
+static void
+test_line_line_parallel (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[2], p2[2];
+  float t1[2], t2[2];
+  graphene_point_t p[2];
+  GskPathIntersection kind[2];
+  int n;
+
+  graphene_point_init (&p1[0], 10, 10);
+  graphene_point_init (&p1[1], 110, 10);
+  graphene_point_init (&p2[0], 20, 10);
+  graphene_point_init (&p2[1], 120, 10);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_LINE, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 2);
+
+  g_assert_cmpint (n, ==, 2);
+  g_assert_cmpfloat_with_epsilon (t1[0], 0.1f, 0.01);
+  g_assert_cmpfloat_with_epsilon (t1[1], 1.f, 0.01);
+  g_assert_cmpfloat_with_epsilon (t2[0], 0.f, 0.01);
+  g_assert_cmpfloat_with_epsilon (t2[1], 0.9f, 0.01);
+}
+
+static void
+test_line_line_same (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[2], p2[2];
+  float t1[2], t2[2];
+  graphene_point_t p[2];
+  GskPathIntersection kind[2];
+  int n;
+
+  graphene_point_init (&p1[0], 10, 10);
+  graphene_point_init (&p1[1], 100, 10);
+  graphene_point_init (&p2[0], 10, 10);
+  graphene_point_init (&p2[1], 100, 10);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_LINE, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 2);
+
+  g_assert_cmpint (n, ==, 2);
+  g_assert_cmpfloat_with_epsilon (t1[0], 0.f, 0.01);
+  g_assert_cmpfloat_with_epsilon (t1[1], 1.f, 0.01);
+  g_assert_cmpfloat_with_epsilon (t2[0], 0.f, 0.01);
+  g_assert_cmpfloat_with_epsilon (t2[1], 1.f, 0.01);
+}
+
+static void
+test_line_curve_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[4], p2[2];
+  float t1[9], t2[9];
+  graphene_point_t p[9];
+  GskPathIntersection kind[9];
+  int n;
+  GskBoundingBox b;
+
+  graphene_point_init (&p1[0], 0, 100);
+  graphene_point_init (&p1[1], 50, 100);
+  graphene_point_init (&p1[2], 50, 0);
+  graphene_point_init (&p1[3], 100, 0);
+  graphene_point_init (&p2[0], 0, 0);
+  graphene_point_init (&p2[1], 100, 100);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 1);
+
+  g_assert_cmpint (n, ==, 1);
+  g_assert_cmpfloat_with_epsilon (t1[0], 0.5, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[0], 0.5, 0.0001);
+  g_assert_true (graphene_point_near (&p[0], &GRAPHENE_POINT_INIT (50, 50), 0.0001));
+
+  gsk_curve_get_tight_bounds (&c1, &b);
+  gsk_bounding_box_contains_point (&b, &p[0]);
+
+  gsk_curve_get_tight_bounds (&c2, &b);
+  gsk_bounding_box_contains_point (&b, &p[0]);
+}
+
+static void
+test_line_curve_multiple_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[4], p2[2];
+  float t1[9], t2[9];
+  graphene_point_t p[9];
+  GskPathIntersection kind[9];
+  graphene_point_t pp;
+  int n;
+  GskBoundingBox b1, b2;
+
+  graphene_point_init (&p1[0], 100, 200);
+  graphene_point_init (&p1[1], 350, 100);
+  graphene_point_init (&p1[2], 100, 350);
+  graphene_point_init (&p1[3], 400, 300);
+
+  graphene_point_init (&p2[0], 0, 0);
+  graphene_point_init (&p2[1], 100, 100);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 3);
+
+  g_assert_cmpint (n, ==, 0);
+
+  graphene_point_init (&p2[0], 0, 0);
+  graphene_point_init (&p2[1], 200, 200);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 3);
+
+  g_assert_cmpint (n, ==, 1);
+
+  g_assert_cmpfloat_with_epsilon (t1[0], 0.136196628, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[0], 0.88487947, 0.0001);
+  g_assert_true (graphene_point_near (&p[0], &GRAPHENE_POINT_INIT (176.975891, 176.975891), 0.001));
+
+  gsk_curve_get_point (&c1, t1[0], &pp);
+  g_assert_true (graphene_point_near (&p[0], &pp, 0.001));
+
+  gsk_curve_get_point (&c2, t2[0], &pp);
+  g_assert_true (graphene_point_near (&p[0], &pp, 0.001));
+
+  gsk_curve_get_tight_bounds (&c1, &b1);
+  gsk_curve_get_tight_bounds (&c2, &b2);
+
+  gsk_bounding_box_contains_point (&b1, &p[0]);
+  gsk_bounding_box_contains_point (&b2, &p[0]);
+
+  graphene_point_init (&p2[0], 0, 0);
+  graphene_point_init (&p2[1], 280, 280);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 3);
+
+  g_assert_cmpint (n, ==, 2);
+
+  g_assert_cmpfloat_with_epsilon (t1[0], 0.136196628, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[0], 0.632056773, 0.0001);
+  g_assert_true (graphene_point_near (&p[0], &GRAPHENE_POINT_INIT (176.975891, 176.975891), 0.001));
+
+  gsk_curve_get_point (&c1, t1[0], &pp);
+  g_assert_true (graphene_point_near (&p[0], &pp, 0.001));
+
+  gsk_curve_get_point (&c2, t2[0], &pp);
+  g_assert_true (graphene_point_near (&p[0], &pp, 0.001));
+
+  g_assert_cmpfloat_with_epsilon (t1[1], 0.499999911, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[1], 0.825892806, 0.0001);
+  g_assert_true (graphene_point_near (&p[1], &GRAPHENE_POINT_INIT (231.25, 231.25), 0.001));
+
+  gsk_curve_get_point (&c1, t1[1], &pp);
+  g_assert_true (graphene_point_near (&p[1], &pp, 0.001));
+
+  gsk_curve_get_point (&c2, t2[1], &pp);
+  g_assert_true (graphene_point_near (&p[1], &pp, 0.001));
+
+  gsk_curve_get_tight_bounds (&c1, &b1);
+  gsk_curve_get_tight_bounds (&c2, &b2);
+
+  gsk_bounding_box_contains_point (&b1, &p[0]);
+  gsk_bounding_box_contains_point (&b1, &p[1]);
+  gsk_bounding_box_contains_point (&b2, &p[0]);
+  gsk_bounding_box_contains_point (&b2, &p[1]);
+
+  graphene_point_init (&p2[0], 0, 0);
+  graphene_point_init (&p2[1], 1000, 1000);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 3);
+
+  g_assert_cmpint (n, ==, 3);
+
+  g_assert_cmpfloat_with_epsilon (t1[0], 0.863803446, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[0], 0.305377066, 0.0001);
+  g_assert_true (graphene_point_near (&p[0], &GRAPHENE_POINT_INIT (305.377075, 305.377075), 0.001));
+
+  gsk_curve_get_point (&c1, t1[0], &pp);
+  g_assert_true (graphene_point_near (&p[0], &pp, 0.001));
+
+  gsk_curve_get_point (&c2, t2[0], &pp);
+  g_assert_true (graphene_point_near (&p[0], &pp, 0.001));
+
+  g_assert_cmpfloat_with_epsilon (t1[1], 0.136196628, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[1], 0.176975891, 0.0001);
+  g_assert_true (graphene_point_near (&p[1], &GRAPHENE_POINT_INIT (176.975891, 176.975891), 0.001));
+
+  gsk_curve_get_point (&c1, t1[1], &pp);
+  g_assert_true (graphene_point_near (&p[1], &pp, 0.001));
+
+  gsk_curve_get_point (&c2, t2[1], &pp);
+  g_assert_true (graphene_point_near (&p[1], &pp, 0.001));
+
+  g_assert_cmpfloat_with_epsilon (t1[2], 0.5, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[2], 0.231249988, 0.0001);
+  g_assert_true (graphene_point_near (&p[2], &GRAPHENE_POINT_INIT (231.249985, 231.249985), 0.001));
+
+  gsk_curve_get_point (&c1, t1[2], &pp);
+  g_assert_true (graphene_point_near (&p[2], &pp, 0.001));
+
+  gsk_curve_get_point (&c2, t2[2], &pp);
+  g_assert_true (graphene_point_near (&p[2], &pp, 0.001));
+
+  gsk_curve_get_tight_bounds (&c1, &b1);
+  gsk_curve_get_tight_bounds (&c2, &b2);
+
+  gsk_bounding_box_contains_point (&b1, &p[0]);
+  gsk_bounding_box_contains_point (&b1, &p[1]);
+  gsk_bounding_box_contains_point (&b1, &p[2]);
+  gsk_bounding_box_contains_point (&b2, &p[0]);
+  gsk_bounding_box_contains_point (&b2, &p[1]);
+  gsk_bounding_box_contains_point (&b2, &p[2]);
+}
+
+static void
+test_line_curve_end_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[4], p2[2];
+  float t1[9], t2[9];
+  graphene_point_t p[9];
+  GskPathIntersection kind[9];
+  int n;
+
+  graphene_point_init (&p1[0], 0, 100);
+  graphene_point_init (&p1[1], 50, 100);
+  graphene_point_init (&p1[2], 50, 0);
+  graphene_point_init (&p1[3], 100, 0);
+  graphene_point_init (&p2[0], 100, 0);
+  graphene_point_init (&p2[1], 100, 100);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 1);
+
+  g_assert_cmpint (n, ==, 1);
+  g_assert_cmpfloat_with_epsilon (t1[0], 1, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[0], 0, 0.0001);
+  g_assert_true (graphene_point_near (&p[0], &GRAPHENE_POINT_INIT (100, 0), 0.0001));
+}
+
+static void
+test_line_curve_none_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[4], p2[2];
+  float t1[9], t2[9];
+  graphene_point_t p[9];
+  GskPathIntersection kind[9];
+  int n;
+
+  graphene_point_init (&p1[0], 333, 78);
+  graphene_point_init (&p1[1], 415, 78);
+  graphene_point_init (&p1[2], 463, 131);
+  graphene_point_init (&p1[3], 463, 223);
+
+  graphene_point_init (&p2[0], 520, 476);
+  graphene_point_init (&p2[1], 502, 418);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_LINE, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 1);
+
+  g_assert_cmpint (n, ==, 0);
+}
+
+static void
+test_curve_curve_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[4], p2[4];
+  float t1[9], t2[9];
+  graphene_point_t p[9];
+  GskPathIntersection kind[9];
+  int n;
+  GskBoundingBox b;
+
+  graphene_point_init (&p1[0], 0, 0);
+  graphene_point_init (&p1[1], 33.333, 100);
+  graphene_point_init (&p1[2], 66.667, 0);
+  graphene_point_init (&p1[3], 100, 100);
+  graphene_point_init (&p2[0], 0, 50);
+  graphene_point_init (&p2[1], 100, 0);
+  graphene_point_init (&p2[2], 20, 0); // weight 20
+  graphene_point_init (&p2[3], 50, 100);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_CONIC, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 9);
+
+  g_assert_cmpint (n, ==, 2);
+  g_assert_cmpfloat (t1[0], <, 0.5);
+  g_assert_cmpfloat (t1[1], >, 0.5);
+  g_assert_cmpfloat (t2[0], <, 0.5);
+  g_assert_cmpfloat (t2[1], >, 0.5);
+
+  gsk_curve_get_tight_bounds (&c1, &b);
+  gsk_bounding_box_contains_point (&b, &p[0]);
+
+  gsk_curve_get_tight_bounds (&c2, &b);
+  gsk_bounding_box_contains_point (&b, &p[0]);
+}
+
+static void
+test_curve_curve_end_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[4], p2[4];
+  float t1[9], t2[9];
+  graphene_point_t p[9];
+  GskPathIntersection kind[9];
+  int n;
+
+  graphene_point_init (&p1[0], 0, 0);
+  graphene_point_init (&p1[1], 33.333, 100);
+  graphene_point_init (&p1[2], 66.667, 0);
+  graphene_point_init (&p1[3], 100, 100);
+  graphene_point_init (&p2[0], 100, 100);
+  graphene_point_init (&p2[1], 100, 0);
+  graphene_point_init (&p2[2], 20, 0);
+  graphene_point_init (&p2[3], 10, 0);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_CONIC, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 9);
+
+  g_assert_cmpint (n, ==, 1);
+  g_assert_cmpfloat_with_epsilon (t1[0], 1, 0.0001);
+  g_assert_cmpfloat_with_epsilon (t2[0], 0, 0.0001);
+}
+
+static void
+test_curve_curve_end_intersection2 (void)
+{
+  GskCurve c, c1, c2;
+  graphene_point_t p1[4];
+  float t1[9], t2[9];
+  graphene_point_t p[9];
+  GskPathIntersection kind[9];
+  int n;
+
+  graphene_point_init (&p1[0], 200, 100);
+  graphene_point_init (&p1[1], 300, 300);
+  graphene_point_init (&p1[2], 100, 300);
+  graphene_point_init (&p1[3], 300, 100);
+
+  gsk_curve_init (&c, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+
+  gsk_curve_split (&c, 0.5, &c1, &c2);
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 9);
+
+  g_assert_cmpint (n, ==, 2);
+}
+
+static void
+test_curve_curve_max_intersection (void)
+{
+  GskCurve c1, c2;
+  graphene_point_t p1[4], p2[4];
+  float t1[9], t2[9];
+  graphene_point_t p[9];
+  GskPathIntersection kind[9];
+  int n;
+
+  graphene_point_init (&p1[0], 106, 100);
+  graphene_point_init (&p1[1], 118, 264);
+  graphene_point_init (&p1[2], 129,   4);
+  graphene_point_init (&p1[3], 128, 182);
+
+  graphene_point_init (&p2[0],  54, 135);
+  graphene_point_init (&p2[1], 263, 136);
+  graphene_point_init (&p2[2],   2, 143);
+  graphene_point_init (&p2[3], 141, 150);
+
+  gsk_curve_init (&c1, gsk_pathop_encode (GSK_PATH_CUBIC, p1));
+  gsk_curve_init (&c2, gsk_pathop_encode (GSK_PATH_CUBIC, p2));
+
+  n = gsk_curve_intersect (&c1, &c2, t1, t2, p, kind, 9);
+
+  g_assert_cmpint (n, ==, 9);
+}
+
+/* This showed up as artifacts in the stroker when our
+ * intersection code failed to find intersections with
+ * horizontal lines
+ */
+static void
+test_curve_intersection_horizontal_line (void)
+{
+  GskCurve c1, c2;
+  float t1, t2;
+  graphene_point_t p;
+  GskPathIntersection kind;
+  int n;
+
+  gsk_curve_init (&c1,
+                  gsk_pathop_encode (GSK_PATH_CONIC,
+                          (const graphene_point_t[4]) {
+                            GRAPHENE_POINT_INIT (200.000, 165.000),
+                            GRAPHENE_POINT_INIT (220.858, 165.000),
+                            GRAPHENE_POINT_INIT (1.4142, 0),
+                            GRAPHENE_POINT_INIT (292.929, 92.929),
+                          }));
+  gsk_curve_init_foreach (&c2,
+                          GSK_PATH_LINE,
+                          (const graphene_point_t[2]) {
+                            GRAPHENE_POINT_INIT (300, 110),
+                            GRAPHENE_POINT_INIT (100, 110),
+                          },
+                          2,
+                          0);
+
+  n = gsk_curve_intersect (&c1, &c2, &t1, &t2, &p, &kind, 1);
+
+  g_assert_true (n == 1);
+}
+
+int
+main (int argc, char *argv[])
+{
+  (g_test_init) (&argc, &argv, NULL);
+
+  g_test_add_func ("/curve/intersection/line-line", test_line_line_intersection);
+  g_test_add_func ("/curve/intersection/line-line-none", test_line_line_none_intersection);
+  g_test_add_func ("/curve/intersection/line-line-end", test_line_line_end_intersection);
+  g_test_add_func ("/curve/intersection/line-line-parallel", test_line_line_parallel);
+  g_test_add_func ("/curve/intersection/line-line-same", test_line_line_same);
+  g_test_add_func ("/curve/intersection/line-curve", test_line_curve_intersection);
+  g_test_add_func ("/curve/intersection/line-curve-end", test_line_curve_end_intersection);
+  g_test_add_func ("/curve/intersection/line-curve-none", test_line_curve_none_intersection);
+  g_test_add_func ("/curve/intersection/line-curve-multiple", test_line_curve_multiple_intersection);
+  g_test_add_func ("/curve/intersection/curve-curve", test_curve_curve_intersection);
+  g_test_add_func ("/curve/intersection/curve-curve-end", test_curve_curve_end_intersection);
+  g_test_add_func ("/curve/intersection/curve-curve-end2", test_curve_curve_end_intersection2);
+  g_test_add_func ("/curve/intersection/curve-curve-max", test_curve_curve_max_intersection);
+  g_test_add_func ("/curve/intersection/horizontal-line", test_curve_intersection_horizontal_line);
+
+  return g_test_run ();
+}

testsuite/gsk/meson.build

@@ -374,6 +374,8 @@ tests = [
   ['shader'],
   ['path', [ 'path-utils.c' ] ],
   ['path-special-cases'],
+  ['path-intersect'],
+  ['path-ops', [ 'path-utils.c' ] ],
 ]
 
 test_cargs = []
@@ -406,6 +408,7 @@ endforeach
 internal_tests = [
   [ 'curve' ],
   [ 'curve-special-cases' ],
+  [ 'curve-intersect' ],
   [ 'path-private' ],
   [ 'diff' ],
   [ 'half-float' ],

testsuite/gsk/path-intersect.c

@@ -0,0 +1,806 @@
+#include <gtk/gtk.h>
+
+#define assert_path_point_equal(point,_contour,_idx,_t) \
+  g_assert_cmpint ((point)->contour, ==, (_contour)); \
+  g_assert_cmpint ((point)->idx, ==, (_idx)); \
+  g_assert_cmpfloat_with_epsilon ((point)->t, (_t), 0.0001);
+
+typedef struct
+{
+  GskPathPoint point1[20];
+  GskPathPoint point2[20];
+  GskPathIntersection kind[20];
+  int found;
+} CollectData;
+
+static gboolean
+collect_cb (GskPath             *path1,
+            const GskPathPoint  *point1,
+            GskPath             *path2,
+            const GskPathPoint  *point2,
+            GskPathIntersection  kind,
+            gpointer             data)
+{
+  CollectData *res = data;
+#if 0
+  const char *kn[] = { "none", "normal", "start", "end" };
+
+  g_print ("%s idx1 %lu t1 %f idx2 %lu t2 %f\n",
+           kn[kind],
+           point1->idx, point1->t, point2->idx, point2->t);
+#endif
+
+  g_assert_true (res->found < 20);
+
+  res->point1[res->found] = *point1;
+  res->point2[res->found] = *point2;
+  res->kind[res->found] = kind;
+  res->found++;
+
+  return TRUE;
+}
+
+static void
+test_intersect_simple (void)
+{
+  GskPath *path1, *path2;
+  graphene_point_t p1, p2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+  path2 = gsk_path_parse ("M 150 150 h 200 v 100 h -200 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+  assert_path_point_equal (&res.point1[0], 0, 2, 0.5);
+  assert_path_point_equal (&res.point1[1], 0, 3, 0.75);
+  assert_path_point_equal (&res.point2[0], 0, 1, 0.75);
+  assert_path_point_equal (&res.point2[1], 0, 4, 0.5);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_NORMAL);
+
+  gsk_path_point_get_position (&res.point1[0], path1, &p1);
+  gsk_path_point_get_position (&res.point2[0], path2, &p2);
+  g_assert_true (graphene_point_equal (&p1, &p2));
+
+  gsk_path_point_get_position (&res.point1[1], path1, &p1);
+  gsk_path_point_get_position (&res.point2[1], path2, &p2);
+  g_assert_true (graphene_point_equal (&p1, &p2));
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_simple2 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+  path2 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_END);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_simple3 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+  path2 = gsk_path_parse ("M 300 100 h -200 v 100 h 200 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_END);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_reverse (void)
+{
+  GskPath *path1, *path2;
+  graphene_point_t p1, p2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+  path2 = gsk_path_parse ("M 150 150 v 100 h 200 v -100 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+  assert_path_point_equal (&res.point1[0], 0, 2, 0.5);
+  assert_path_point_equal (&res.point1[1], 0, 3, 0.75);
+  assert_path_point_equal (&res.point2[0], 0, 4, 0.25);
+  assert_path_point_equal (&res.point2[1], 0, 1, 0.5);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_NORMAL);
+
+  gsk_path_point_get_position (&res.point1[0], path1, &p1);
+  gsk_path_point_get_position (&res.point2[0], path2, &p2);
+  g_assert_true (graphene_point_equal (&p1, &p2));
+
+  gsk_path_point_get_position (&res.point1[1], path1, &p1);
+  gsk_path_point_get_position (&res.point2[1], path2, &p2);
+  g_assert_true (graphene_point_equal (&p1, &p2));
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_line_box (void)
+{
+  GskPath *path1, *path2;
+  graphene_point_t p1, p2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 50 150 l 300 0");
+  path2 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+  assert_path_point_equal (&res.point1[0], 0, 1, 50.f/300.f);
+  assert_path_point_equal (&res.point1[1], 0, 1, 250.f/300.f);
+  assert_path_point_equal (&res.point2[0], 0, 4, 0.5);
+  assert_path_point_equal (&res.point2[1], 0, 2, 0.5);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_NORMAL);
+
+  gsk_path_point_get_position (&res.point1[0], path1, &p1);
+  gsk_path_point_get_position (&res.point2[0], path2, &p2);
+  g_assert_true (graphene_point_equal (&p1, &p2));
+
+  gsk_path_point_get_position (&res.point1[1], path1, &p1);
+  gsk_path_point_get_position (&res.point2[1], path2, &p2);
+  g_assert_true (graphene_point_equal (&p1, &p2));
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_xplus (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 0 0 L 100 100 M 0 100 L 100 0");
+  path2 = gsk_path_parse ("M 0 50 L 100 50 M 50 0 L 50 100");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 4);
+  assert_path_point_equal (&res.point1[0], 0, 1, 0.5);
+  assert_path_point_equal (&res.point1[1], 0, 1, 0.5);
+  assert_path_point_equal (&res.point1[2], 1, 1, 0.5);
+  assert_path_point_equal (&res.point1[3], 1, 1, 0.5);
+
+  assert_path_point_equal (&res.point2[0], 0, 1, 0.5);
+  assert_path_point_equal (&res.point2[1], 1, 1, 0.5);
+  assert_path_point_equal (&res.point2[2], 0, 1, 0.5);
+  assert_path_point_equal (&res.point2[3], 1, 1, 0.5);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_point (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 0 50");
+  path2 = gsk_path_parse ("M 0 0 L 0 100");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+
+  g_assert_true (res.found == 1);
+  assert_path_point_equal (&res.point1[0], 0, 0, 1);
+  assert_path_point_equal (&res.point2[0], 0, 1, 0.5);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path2, path1, collect_cb, &res);
+
+  g_assert_true (res.found == 1);
+  assert_path_point_equal (&res.point1[0], 0, 1, 0.5);
+  assert_path_point_equal (&res.point2[0], 0, 0, 1);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path1, collect_cb, &res);
+
+  g_assert_true (res.found == 1);
+  assert_path_point_equal (&res.point1[0], 0, 0, 1);
+  assert_path_point_equal (&res.point2[0], 0, 0, 1);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_contours (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 0 100 L 200 100");
+  path2 = gsk_path_parse ("M 150 0 150 200 M 50 0 50 200");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+  assert_path_point_equal (&res.point1[0], 0, 1, 0.25f);
+  assert_path_point_equal (&res.point1[1], 0, 1, 0.75f);
+  assert_path_point_equal (&res.point2[0], 1, 1, 0.5f);
+  assert_path_point_equal (&res.point2[1], 0, 1, 0.5f);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_NORMAL);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_contours2 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 0 100 L 200 100");
+  path2 = gsk_path_parse ("M 150 0 L 150 200 M 50 0 L 50 200 M 60 100 L 140 100");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 4);
+  assert_path_point_equal (&res.point1[0], 0, 1, 0.25f);
+  assert_path_point_equal (&res.point1[1], 0, 1, 0.3f);
+  assert_path_point_equal (&res.point2[0], 1, 1, 0.5f);
+  assert_path_point_equal (&res.point2[1], 2, 1, 0.f);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[2] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[3] == GSK_PATH_INTERSECTION_NORMAL);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_contours3 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 150 0 L 150 200 M 50 0 L 50 200 M 60 100 L 140 100");
+  path2 = gsk_path_parse ("M 0 100 L 200 100");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 4);
+  assert_path_point_equal (&res.point1[0], 0, 1, 0.5f);
+  assert_path_point_equal (&res.point1[1], 1, 1, 0.5f);
+  assert_path_point_equal (&res.point2[0], 0, 1, 0.75f);
+  assert_path_point_equal (&res.point2[1], 0, 1, 0.25f);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[2] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[3] == GSK_PATH_INTERSECTION_END);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_coincide (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+  path2 = gsk_path_parse ("M 150 100 h 100 v 50 h -100 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+  assert_path_point_equal (&res.point1[0], 0, 1, 0.25);
+  assert_path_point_equal (&res.point1[1], 0, 1, 0.75);
+  assert_path_point_equal (&res.point2[0], 0, 1, 0);
+  assert_path_point_equal (&res.point2[1], 0, 1, 1);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_END);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_coincide2 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 150 100 h 100 v 50 h -100 z");
+  path2 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+  assert_path_point_equal (&res.point1[0], 0, 1, 0);
+  assert_path_point_equal (&res.point1[1], 0, 1, 1);
+  assert_path_point_equal (&res.point2[0], 0, 1, 0.25);
+  assert_path_point_equal (&res.point2[1], 0, 1, 0.75);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_END);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_coincide3 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+  path2 = gsk_path_parse ("M 150 100 h 100 v 50 h -25 v -50 h -50 v 50 h -25 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 4);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[2] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[3] == GSK_PATH_INTERSECTION_END);
+
+  assert_path_point_equal (&res.point1[0], 0, 1, 0.25);
+  assert_path_point_equal (&res.point1[1], 0, 1, 0.375);
+  assert_path_point_equal (&res.point1[2], 0, 1, 0.625);
+  assert_path_point_equal (&res.point1[3], 0, 1, 0.75);
+
+  assert_path_point_equal (&res.point2[0], 0, 1, 0);
+  assert_path_point_equal (&res.point2[1], 0, 5, 1);
+  assert_path_point_equal (&res.point2[2], 0, 5, 0);
+  assert_path_point_equal (&res.point2[3], 0, 1, 1);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_coincide4 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 100 100 h 200 v 100 h -200 z");
+  path2 = gsk_path_parse ("M 150 100 h 100 v 50 h -25 v -100 h -50 v 100 h -25 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 4);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[2] == GSK_PATH_INTERSECTION_NORMAL);
+  g_assert_true (res.kind[3] == GSK_PATH_INTERSECTION_END);
+
+  assert_path_point_equal (&res.point1[0], 0, 1, 0.25);
+  assert_path_point_equal (&res.point1[1], 0, 1, 0.375);
+  assert_path_point_equal (&res.point1[2], 0, 1, 0.625);
+  assert_path_point_equal (&res.point1[3], 0, 1, 0.75);
+
+  assert_path_point_equal (&res.point2[0], 0, 1, 0);
+  assert_path_point_equal (&res.point2[1], 0, 6, 0.5);
+  assert_path_point_equal (&res.point2[2], 0, 4, 0.5);
+  assert_path_point_equal (&res.point2[3], 0, 1, 1);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+/* the next few tests explore overlapping segments */
+static void
+test_intersect_coincide5 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 150 100 h 100 v 100 h -100 z");
+  path2 = gsk_path_parse ("M 100 100 h 200 v 50 h -100 v -50 h 25 v -50 h -100 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 5);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[2] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[3] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[4] == GSK_PATH_INTERSECTION_NORMAL);
+
+  assert_path_point_equal (&res.point1[0], 0, 1, 0);
+  assert_path_point_equal (&res.point1[1], 0, 1, 0.5);
+  assert_path_point_equal (&res.point1[2], 0, 1, 0.75);
+  assert_path_point_equal (&res.point1[3], 0, 1, 1);
+  assert_path_point_equal (&res.point1[4], 0, 2, 0.5);
+
+  assert_path_point_equal (&res.point2[0], 0, 1, 0.25);
+  assert_path_point_equal (&res.point2[1], 0, 5, 0);
+  assert_path_point_equal (&res.point2[2], 0, 5, 1);
+  assert_path_point_equal (&res.point2[3], 0, 1, 0.75);
+  assert_path_point_equal (&res.point2[4], 0, 3, 0.5);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_coincide6 (void)
+{
+  GskPath *path1, *path2;
+  CollectData res;
+
+  path1 = gsk_path_parse ("M 150 100 h 75 l 25 50 v 50 h -100 z");
+  path2 = gsk_path_parse ("M 100 100 h 200 v 50 h -100 v -50 h 50 v -50 h -125 z");
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 5);
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[2] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[3] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[4] == GSK_PATH_INTERSECTION_NORMAL);
+
+  assert_path_point_equal (&res.point1[0], 0, 1, 0);
+  assert_path_point_equal (&res.point1[1], 0, 1, 2./3.);
+  assert_path_point_equal (&res.point1[2], 0, 1, 1);
+  assert_path_point_equal (&res.point1[3], 0, 1, 1);
+  assert_path_point_equal (&res.point1[4], 0, 3, 0);
+
+  assert_path_point_equal (&res.point2[0], 0, 1, 0.25);
+  assert_path_point_equal (&res.point2[1], 0, 5, 0);
+  assert_path_point_equal (&res.point2[2], 0, 1, 0.625);
+  assert_path_point_equal (&res.point2[3], 0, 5, 0.5);
+  assert_path_point_equal (&res.point2[4], 0, 3, 0.5);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static int
+circle_intersect (const graphene_point_t *center1,
+                  float                   radius1,
+                  const graphene_point_t *center2,
+                  float                   radius2,
+                  graphene_point_t        points[2])
+{
+  float d;
+  float a, h;
+  graphene_point_t m;
+  graphene_vec2_t n;
+
+  g_assert (radius1 >= 0);
+  g_assert (radius2 >= 0);
+
+  d = graphene_point_distance (center1, center2, NULL, NULL);
+
+  if (d < fabsf (radius1 - radius2))
+    return 0;
+
+  if (d > radius1 + radius2)
+    return 0;
+
+  if (d == radius1 + radius2)
+    {
+      graphene_point_interpolate (center1, center2, radius1 / (radius1 + radius2), &points[0]);
+      return 1;
+    }
+
+  /*
+  a + b = d;
+
+  a^2 + h^2 = r1^2
+  b^2 + h^2 = r2^2
+
+  a^2 - (d - a)^2 = r1^2 - r2^2
+  a^2 - (d^2 - 2ad + a2) = r1^2 - r2^2
+
+  2ad -d^2 = r1^2 - r2^2
+  2ad = r1^2 - r2^2 + d^2
+  a = (r1^2 - r2^2 + d^2) / (2d)
+
+  p1/2 = c1 + a/d * (c2 - c1) +/- h * n(c1,c2);
+  */
+
+  a = (radius1*radius1 - radius2*radius2 + d*d)/(2*d);
+  h = sqrtf (radius1*radius1 - a*a);
+
+  graphene_point_interpolate (center1, center2, a/d, &m);
+  graphene_vec2_init (&n, center2->y - center1->y, center1->x - center2->x);
+  graphene_vec2_normalize (&n, &n);
+
+  graphene_point_init (&points[0], m.x + graphene_vec2_get_x (&n) * h,
+                                   m.y + graphene_vec2_get_y (&n) * h);
+  graphene_point_init (&points[1], m.x - graphene_vec2_get_x (&n) * h,
+                                   m.y - graphene_vec2_get_y (&n) * h);
+
+  return 2;
+}
+
+static void
+test_intersect_circle (void)
+{
+  GskPathBuilder *builder;
+  GskPath *path1, *path2;
+  CollectData res;
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (0, 0), 12);
+  path1 = gsk_path_builder_free_to_path (builder);
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (1, 1), 10);
+  path2 = gsk_path_builder_free_to_path (builder);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 0);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_circle2 (void)
+{
+  GskPathBuilder *builder;
+  GskPath *path1, *path2;
+  CollectData res;
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (0, 0), 12);
+  path1 = gsk_path_builder_free_to_path (builder);
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (0, 25), 10);
+  path2 = gsk_path_builder_free_to_path (builder);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 0);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_circle3 (void)
+{
+  GskPathBuilder *builder;
+  GskPath *path1, *path2;
+  CollectData res;
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (0, 0), 12);
+  path1 = gsk_path_builder_free_to_path (builder);
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (0, 22), 10);
+  path2 = gsk_path_builder_free_to_path (builder);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 1);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_circle4 (void)
+{
+  GskPathBuilder *builder;
+  GskPath *path1, *path2;
+  CollectData res;
+  graphene_point_t p[2], pos;
+  int n;
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (0, 0), 12);
+  path1 = gsk_path_builder_free_to_path (builder);
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (0, 18), 10);
+  path2 = gsk_path_builder_free_to_path (builder);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+
+  n = circle_intersect (&GRAPHENE_POINT_INIT (0, 0), 12,
+                        &GRAPHENE_POINT_INIT (0, 18), 10,
+                        p);
+
+  g_assert_true (n == 2);
+  gsk_path_point_get_position (&res.point1[0], path1, &pos);
+  g_assert_true (graphene_point_near (&p[0], &pos, 0.01));
+  gsk_path_point_get_position (&res.point1[1], path1, &pos);
+  g_assert_true (graphene_point_near (&p[1], &pos, 0.01));
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_circle5 (void)
+{
+  GskPathBuilder *builder;
+  GskPath *path1, *path2;
+  CollectData res;
+  graphene_point_t p[2], pos;
+  int n;
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (0, 0), 12);
+  path1 = gsk_path_builder_free_to_path (builder);
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (10, 10), 10);
+  path2 = gsk_path_builder_free_to_path (builder);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+
+  n = circle_intersect (&GRAPHENE_POINT_INIT (0, 0), 12,
+                        &GRAPHENE_POINT_INIT (10, 10), 10,
+                        p);
+
+  g_assert_true (n == 2);
+  gsk_path_point_get_position (&res.point1[0], path1, &pos);
+  g_assert_true (graphene_point_near (&p[0], &pos, 0.01));
+  gsk_path_point_get_position (&res.point1[1], path1, &pos);
+  g_assert_true (graphene_point_near (&p[1], &pos, 0.01));
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_circle6 (void)
+{
+  GskPathBuilder *builder;
+  GskPath *path1;
+  CollectData res;
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (100, 100), 12);
+  path1 = gsk_path_builder_free_to_path (builder);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path1, collect_cb, &res);
+  g_assert_true (res.found == 2);
+
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_END);
+
+  gsk_path_unref (path1);
+}
+
+static void
+test_intersect_circle7 (void)
+{
+  GskPathBuilder *builder;
+  GskPath *path1, *path2;
+  CollectData res;
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (100, 100), 12);
+  path1 = gsk_path_builder_free_to_path (builder);
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_reverse_path (builder, path1);
+  path2 = gsk_path_builder_free_to_path (builder);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 2);
+
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_END);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+static void
+test_intersect_circle_rounded_rect (void)
+{
+  GskRoundedRect rr;
+  GskPathBuilder *builder;
+  GskPath *path1, *path2;
+  CollectData res;
+
+  rr.bounds = GRAPHENE_RECT_INIT (10, 10, 100, 100);
+  rr.corner[GSK_CORNER_TOP_LEFT] = GRAPHENE_SIZE_INIT (20, 20);
+  rr.corner[GSK_CORNER_TOP_RIGHT] = GRAPHENE_SIZE_INIT (20, 20);
+  rr.corner[GSK_CORNER_BOTTOM_RIGHT] = GRAPHENE_SIZE_INIT (20, 20);
+  rr.corner[GSK_CORNER_BOTTOM_LEFT] = GRAPHENE_SIZE_INIT (20, 20);
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_rounded_rect (builder, &rr);
+  path1 = gsk_path_builder_free_to_path (builder);
+
+  builder = gsk_path_builder_new ();
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (30, 30), 20);
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (90, 30), 20);
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (90, 90), 20);
+  gsk_path_builder_add_circle (builder, &GRAPHENE_POINT_INIT (30, 90), 20);
+  path2 = gsk_path_builder_free_to_path (builder);
+
+  res.found = 0;
+  gsk_path_foreach_intersection (path1, path2, collect_cb, &res);
+  g_assert_true (res.found == 8);
+
+  g_assert_true (res.kind[0] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[1] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[2] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[3] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[4] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[5] == GSK_PATH_INTERSECTION_END);
+  g_assert_true (res.kind[6] == GSK_PATH_INTERSECTION_START);
+  g_assert_true (res.kind[7] == GSK_PATH_INTERSECTION_END);
+
+  gsk_path_unref (path1);
+  gsk_path_unref (path2);
+}
+
+int
+main (int argc, char *argv[])
+{
+  (g_test_init) (&argc, &argv, NULL);
+
+  g_test_add_func ("/path/intersect/simple", test_intersect_simple);
+  g_test_add_func ("/path/intersect/simple2", test_intersect_simple2);
+  g_test_add_func ("/path/intersect/simple3", test_intersect_simple3);
+  g_test_add_func ("/path/intersect/reverse", test_intersect_reverse);
+  g_test_add_func ("/path/intersect/line-box", test_intersect_line_box);
+  g_test_add_func ("/path/intersect/xplus", test_intersect_xplus);
+  g_test_add_func ("/path/intersect/point", test_intersect_point);
+  g_test_add_func ("/path/intersect/contours", test_intersect_contours);
+  g_test_add_func ("/path/intersect/contours2", test_intersect_contours2);
+  g_test_add_func ("/path/intersect/contours3", test_intersect_contours3);
+  g_test_add_func ("/path/intersect/coincide", test_intersect_coincide);
+  g_test_add_func ("/path/intersect/coincide2", test_intersect_coincide2);
+  g_test_add_func ("/path/intersect/coincide3", test_intersect_coincide3);
+  g_test_add_func ("/path/intersect/coincide4", test_intersect_coincide4);
+  g_test_add_func ("/path/intersect/coincide5", test_intersect_coincide5);
+  g_test_add_func ("/path/intersect/coincide6", test_intersect_coincide6);
+  g_test_add_func ("/path/intersect/circle", test_intersect_circle);
+  g_test_add_func ("/path/intersect/circle2", test_intersect_circle2);
+  g_test_add_func ("/path/intersect/circle3", test_intersect_circle3);
+  g_test_add_func ("/path/intersect/circle4", test_intersect_circle4);
+  g_test_add_func ("/path/intersect/circle5", test_intersect_circle5);
+  g_test_add_func ("/path/intersect/circle6", test_intersect_circle6);
+  g_test_add_func ("/path/intersect/circle7", test_intersect_circle7);
+  g_test_add_func ("/path/intersect/circle-rounded-rect", test_intersect_circle_rounded_rect);
+
+  return g_test_run ();
+}

testsuite/gsk/path-ops.c

@@ -0,0 +1,381 @@
+/*
+ * Copyright © 2022 Red Hat, Inc.
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library 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
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library. If not, see <http://www.gnu.org/licenses/>.
+ *
+ * Authors: Matthias Clasen <mclasen@redhat.com>
+ */
+
+#include <gtk/gtk.h>
+
+#include "path-utils.h"
+
+typedef enum
+{
+  OP_UNION,
+  OP_INTERSECTION,
+  OP_DIFFERENCE,
+  OP_SYMMETRIC_DIFFERENCE,
+} Op;
+
+static void
+test_ops_simple (void)
+{
+  struct {
+    const char *in1;
+    const char *in2;
+    Op op;
+    const char *out;
+  } tests[] = {
+    /* partially overlapping edge */
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 150 150 L 150 250 L 250 250 Z",
+      OP_UNION,
+      "M 100 100 L 100 200 L 150 200 L 150 250 L 250 250 L 200 200 L 150 150 L 100 100 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 150 150 L 150 250 L 250 250 Z",
+      OP_INTERSECTION,
+      "M 150 200 L 200 200 L 150 150 L 150 200 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 150 150 L 150 250 L 250 250 Z",
+      OP_DIFFERENCE,
+      "M 100 100 L 100 200 L 150 200 L 150 150 L 100 100 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 150 150 L 150 250 L 250 250 Z",
+      OP_SYMMETRIC_DIFFERENCE,
+      "M 100 100 L 100 200 L 150 200 L 150 150 L 100 100 Z M 200 200 L 150 200 L 150 250 "
+      "L 250 250 L 200 200 Z" },
+    /* two triangles in general position */
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 170 120 L 100 240 L 170 240 Z",
+      OP_UNION,
+      "M 100 100 L 100 200 L 123.33333587646484 200 L 100 240 L 170 240 L 170 200 L 200 200 "
+      "L 170 170 L 170 120 L 151.57894897460938 151.57894897460938 L 100 100 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 170 120 L 100 240 L 170 240 Z",
+      OP_INTERSECTION,
+      "M 123.33333587646484 200 L 170 200 L 170 170 L 151.57894897460938 151.57894897460938 "
+      "L 123.33332824707031 200 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 170 120 L 100 240 L 170 240 Z",
+      OP_DIFFERENCE,
+      "M 100 100 L 100 200 L 123.33333587646484 200 L 151.57894897460938 151.57894897460938 "
+      "L 100 100 Z M 170 200 L 200 200 L 170 170 L 170 200 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 170 120 L 100 240 L 170 240 Z",
+      OP_SYMMETRIC_DIFFERENCE,
+      "M 100 100 L 100 200 L 123.33333587646484 200 L 151.57894897460938 151.57894897460938 "
+      "L 100 100 Z M 170 200 L 123.33333587646484 200 L 100 240 L 170 240 L 170 200 Z "
+      "M 170 200 L 200 200 L 170 170 L 170 200 Z M 151.57894897460938 151.57894897460938 "
+      "L 170 170 L 170 120 L 151.57894897460938 151.57894897460938 Z" },
+    /* nested contours, oriented in opposite direction */
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 120 140 L 170 190 L 120 190 Z",
+      OP_UNION,
+      "M 100 100 L 100 200 L 200 200 L 100 100 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 120 140 L 170 190 L 120 190 Z",
+      OP_INTERSECTION,
+      "M 170 190 L 120 140 L 120 190 L 170 190 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 120 140 L 170 190 L 120 190 Z",
+      OP_DIFFERENCE,
+      "M 100 100 L 100 200 L 200 200 L 100 100 Z M 120 140 L 170 190 L 120 190 L 120 140 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 120 140 L 170 190 L 120 190 Z",
+      OP_SYMMETRIC_DIFFERENCE,
+      "M 100 100 L 100 200 L 200 200 L 100 100 Z M 120 140 L 170 190 L 120 190 L 120 140 Z" },
+    /* nested contours, oriented in opposite direction, other way around */
+    { "M 100 100 L 200 200 L 100 200 Z",
+      "M 120 140 L 120 190 L 170 190 Z",
+      OP_UNION,
+      "M 200 200 L 100 100 L 100 200 L 200 200 Z" },
+    { "M 100 100 L 200 200 L 100 200 Z",
+      "M 120 140 L 120 190 L 170 190 Z",
+      OP_INTERSECTION,
+      "M 120 140 L 120 190 L 170 190 L 120 140 Z" },
+    { "M 100 100 L 200 200 L 100 200 Z",
+      "M 120 140 L 120 190 L 170 190 Z",
+      OP_DIFFERENCE,
+      "M 200 200 L 100 100 L 100 200 L 200 200 Z M 120 190 L 120 140 L 170 190 L 120 190 Z" },
+    { "M 100 100 L 200 200 L 100 200 Z",
+      "M 120 140 L 120 190 L 170 190 Z",
+      OP_SYMMETRIC_DIFFERENCE,
+      "M 200 200 L 100 100 L 100 200 L 200 200 Z M 120 190 L 120 140 L 170 190 L 120 190 Z" },
+    /* nested contours, oriented in the same direction */
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 120 140 L 120 190 L 170 190 Z",
+      OP_UNION,
+      "M 100 100 L 100 200 L 200 200 L 100 100 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 120 140 L 120 190 L 170 190 Z",
+      OP_INTERSECTION,
+      "M 120 140 L 120 190 L 170 190 L 120 140 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 120 140 L 120 190 L 170 190 Z",
+      OP_DIFFERENCE,
+      "M 100 100 L 100 200 L 200 200 L 100 100 Z M 120 190 L 120 140 L 170 190 L 120 190 Z" },
+    { "M 100 100 L 100 200 L 200 200 Z",
+      "M 120 140 L 120 190 L 170 190 Z",
+      OP_SYMMETRIC_DIFFERENCE,
+      "M 100 100 L 100 200 L 200 200 L 100 100 Z M 120 190 L 120 140 L 170 190 L 120 190 Z" },
+    /* a 3-way intersection */
+    { "M 100 200 L 150 104 L 145 104 L 200 200 Z",
+      "M 100 108.571 L 200 108.571 L 200 50 L 100 50 Z",
+      OP_UNION,
+      "M 147.61904907226562 108.57142639160156 L 100 200 L 200 200 "
+      "L 147.61904907226562 108.57142639160156 Z M 100 108.57099914550781 "
+      "L 147.61927795410156 108.57099914550781 L 200 108.57099914550781 L 200 50 "
+      "L 100 50 L 100 108.57099914550781 Z" },
+    { "M 100 200 L 150 104 L 145 104 L 200 200 Z",
+      "M 100 108.571 L 200 108.571 L 200 50 L 100 50 Z",
+      OP_INTERSECTION,
+      "M 147.61904907226562 108.57142639160156 L 150 104 L 145 104 "
+      "L 147.61904907226562 108.57142639160156 Z" },
+    { "M 100 200 L 150 104 L 145 104 L 200 200 Z",
+      "M 100 108.571 L 200 108.571 L 200 50 L 100 50 Z",
+      OP_DIFFERENCE,
+      "M 147.61904907226562 108.57142639160156 L 100 200 L 200 200 "
+      "L 147.61904907226562 108.57142639160156 Z" },
+    { "M 100 200 L 150 104 L 145 104 L 200 200 Z",
+      "M 100 108.571 L 200 108.571 L 200 50 L 100 50 Z",
+      OP_SYMMETRIC_DIFFERENCE,
+      "M 147.61904907226562 108.57142639160156 L 100 200 L 200 200 "
+      "L 147.61904907226562 108.57142639160156 Z M 150 104 "
+      "L 147.61904907226562 108.57142639160156 L 200 108.57099914550781 "
+      "L 200 50 L 100 50 L 100 108.57099914550781 L 147.61927795410156 108.57099914550781 "
+      "L 145 104 L 150 104 Z" },
+     /* touching quadratics */
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 200 Q 150 100 200 200 Z",
+       OP_UNION,
+       "M 100 100 "
+       "Q 124.987984 149.975967, 149.975967 149.999985 "
+       "Q 174.987976 150.024033, 200 100 "
+       "L 100 100 "
+       "Z "
+       "M 149.975967 150 "
+       "Q 124.987984 150.024033, 100 200 "
+       "L 200 200 "
+       "Q 174.987976 149.975967, 149.975967 150.000015 "
+       "Z" },
+     /* overlapping quadratics, two intersections, different orientations */
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 180 Q 150 80 200 180 Z",
+       OP_UNION,
+       "M 100 100 "
+       "Q 113.819313 127.638626, 127.638626 139.999374 "
+       "Q 113.819695 152.360611, 100 180 "
+       "L 200 180 "
+       "Q 186.180313 152.360611, 172.360611 139.999939 "
+       "Q 186.180298 127.639389, 200 100 "
+       "L 100 100 "
+       "Z" },
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 180 Q 150 80 200 180 Z",
+       OP_INTERSECTION,
+       "M 127.638626 139.99939 "
+       "Q 149.999619 160.000275, 172.360611 140.000061 "
+       "Q 150 120.000061, 127.639389 139.999939 "
+       "Z" },
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 180 Q 150 80 200 180 Z",
+       OP_DIFFERENCE,
+       "M 100 100 "
+       "Q 113.819313 127.638626, 127.638626 139.999374 "
+       "Q 150 120.000061, 172.360611 139.999939 "
+       "Q 186.180298 127.639389, 200 100 "
+       "L 100 100 "
+       "Z" },
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 180 Q 150 80 200 180 Z",
+       OP_SYMMETRIC_DIFFERENCE,
+       "M 100 100 "
+       "Q 113.819313 127.638626, 127.638626 139.999374 "
+       "Q 150 120.000061, 172.360611 139.999939 "
+       "Q 186.180298 127.639389, 200 100 "
+       "L 100 100 "
+       "Z "
+       "M 172.360611 140.000061 "
+       "Q 149.999619 160.000275, 127.638626 139.999374 "
+       "Q 113.819695 152.360611, 100 180 "
+       "L 200 180 "
+       "Q 186.180313 152.360611, 172.360611 139.999939 "
+       "Z" },
+     /* overlapping quadratics, two intersections, same orientation */
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 180 L 200 180 Q 150 80 100 180 Z",
+       OP_UNION,
+       "M 100 100 "
+       "Q 113.819313 127.638626, 127.638626 139.999374 "
+       "Q 113.819695 152.360611, 100 180 "
+       "L 200 180 "
+       "Q 186.180695 152.361374, 172.361389 140.000626 "
+       "Q 186.180298 127.639389, 200 100 "
+       "L 100 100 "
+       "Z" },
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 180 L 200 180 Q 150 80 100 180 Z",
+       OP_INTERSECTION,
+       "M 127.638626 139.99939 "
+       "Q 149.999619 160.000275, 172.360611 140.000061 "
+       "Q 150.000397 119.999725, 127.639397 139.999939 "
+       "Z" },
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 180 L 200 180 Q 150 80 100 180 Z",
+       OP_DIFFERENCE,
+       "M 100 100 "
+       "Q 113.819313 127.638626, 127.638626 139.999374 "
+       "Q 150.000397 119.999725, 172.361389 140.000626 "
+       "Q 186.180298 127.639389, 200 100 "
+       "L 100 100 "
+       "Z" },
+     { "M 100 100 Q 150 200 200 100 Z",
+       "M 100 180 L 200 180 Q 150 80 100 180 Z",
+       OP_SYMMETRIC_DIFFERENCE,
+       "M 100 100 "
+       "Q 113.819313 127.638626, 127.638626 139.999374 "
+       "Q 150.000397 119.999725, 172.361389 140.000626 "
+       "Q 186.180298 127.639389, 200 100 "
+       "L 100 100 "
+       "Z "
+       "M 172.360611 140.000061 "
+       "Q 149.999619 160.000275, 127.638626 139.999374 "
+       "Q 113.819695 152.360611, 100 180 "
+       "L 200 180 "
+       "Q 186.180695 152.361374, 172.361389 140.000626 "
+       "Z" },
+     /* two polygons with near edges */
+     { "M 100 100 L 100 200 L 400 200 L 400 100 Z",
+       "M 150 103 L 250 100 L 300 103 L 250 180 Z",
+       OP_UNION,
+       "M 100 100 L 100 200 L 400 200 L 400 100 L 250 100 L 100 100 Z" },
+     { "M 100 100 L 100 200 L 400 200 L 400 100 Z",
+       "M 150 103 L 250 100 L 300 103 L 250 180 Z",
+       OP_INTERSECTION,
+      "M 250 100 L 150 103 L 250 180 L 300 103 L 250 100 Z" },
+     { "M 100 100 L 100 200 L 400 200 L 400 100 Z",
+       "M 150 103 L 250 100 L 300 103 L 250 180 Z",
+       OP_DIFFERENCE,
+       "M 100 100 L 100 200 L 400 200 L 400 100 L 250 100 L 300 103 L 250 180 L 150 103 L 250 100 L 100 100 Z" },
+     { "M 100 100 L 100 200 L 400 200 L 400 100 Z",
+       "M 150 103 L 250 100 L 300 103 L 250 180 Z",
+       OP_SYMMETRIC_DIFFERENCE,
+       "M 100 100 L 100 200 L 400 200 L 400 100 L 250 100 L 300 103 L 250 180 L 150 103 L 250 100 L 100 100 Z" },
+     /* Collinear line segments */
+     { "M 100 100 L 200 100 L 250 100 L 100 200 Z",
+       "M 150 100 L 300 100 L 300 200 Z",
+       OP_UNION,
+       "M 150 100 "
+       "L 100 100 "
+       "L 100 200 "
+       "L 200 133.333328 "
+       "L 300 200 "
+       "L 300 100 "
+       "L 250 100 "
+       "L 200 100 "
+       "L 150 100 "
+       "Z" },
+     { "M 100 100 L 200 100 L 250 100 L 100 200 Z",
+       "M 150 100 L 300 100 L 300 200 Z",
+       OP_INTERSECTION,
+       "M 200 100 "
+       "L 150 100 "
+       "L 200 133.333328 "
+       "L 250 100 "
+       "L 200 100 "
+       "Z" },
+     { "M 100 100 L 200 100 L 250 100 L 100 200 Z",
+       "M 150 100 L 300 100 L 300 200 Z",
+       OP_DIFFERENCE,
+       "M 150 100 L 100 100 L 100 200 L 200 133.33332824707031 L 150 100 Z" },
+     { "M 100 100 L 200 100 L 250 100 L 100 200 Z",
+       "M 150 100 L 300 100 L 300 200 Z",
+       OP_SYMMETRIC_DIFFERENCE,
+       "M 150 100 L 100 100 L 100 200 L 200 133.33332824707031 L 150 100 Z "
+       "M 250 100 L 200 133.33332824707031 L 300 200 L 300 100 L 250 100 Z" },
+     /* a complicated union */
+     { "M 175 100 L 175 400 L 300 400 L 300 100 z",
+       "M 100 100 C 200 200 200 300 100 400 L 0 400 C 233.3333334 300 233.3333334 200 0 100 Z",
+       OP_UNION,
+       "M 175 100 "
+       "L 175 250 "
+       "L 175 400 "
+       "L 300 400 "
+       "L 300 100 "
+       "L 175 100 "
+       "Z "
+       "M 175 250 "
+       "Q 175 175, 100 100 "
+       "L 0 100 "
+       "Q 174.955811 174.981064, 174.999985 249.962112 "
+       "Z "
+       "M 100 400 "
+       "Q 175 325, 175 250 "
+       "Q 175.044189 324.981049, 0 400 "
+       "L 100 400 "
+       "Z" },
+ };
+
+  for (int i = 0; i < G_N_ELEMENTS (tests); i++)
+    {
+      GskPath *p1, *p2, *p3, *p;
+
+      if (g_test_verbose ())
+        {
+          const char *opname[] = { "union", "intersection", "difference", "symmetric-difference" };
+          g_test_message ("testcase %d op %s \"%s\" \"%s\"", i, opname[tests[i].op], tests[i].in1, tests[i].in2);
+        }
+
+      p1 = gsk_path_parse (tests[i].in1);
+      p2 = gsk_path_parse (tests[i].in2);
+      switch (tests[i].op)
+        {
+        case OP_UNION:
+          p = gsk_path_union (p1, p2, GSK_FILL_RULE_WINDING);
+          break;
+        case OP_INTERSECTION:
+          p = gsk_path_intersection (p1, p2, GSK_FILL_RULE_WINDING);
+          break;
+        case OP_DIFFERENCE:
+          p = gsk_path_difference (p1, p2, GSK_FILL_RULE_WINDING);
+          break;
+        case OP_SYMMETRIC_DIFFERENCE:
+          p = gsk_path_symmetric_difference (p1, p2, GSK_FILL_RULE_WINDING);
+          break;
+        default:
+          g_assert_not_reached ();
+        }
+
+      g_assert_nonnull (p);
+      p3 = gsk_path_parse (tests[i].out);
+      assert_path_equal_with_epsilon (p, p3, 0.0001);
+
+      gsk_path_unref (p);
+      gsk_path_unref (p1);
+      gsk_path_unref (p2);
+      gsk_path_unref (p3);
+    }
+}
+
+int
+main (int   argc,
+      char *argv[])
+{
+  gtk_test_init (&argc, &argv, NULL);
+
+  g_test_add_func ("/ops/simple", test_ops_simple);
+
+  return g_test_run ();
+}

tools/gtk-path-tool-pathops.c

@@ -0,0 +1,104 @@
+/*  Copyright 2023 Red Hat, Inc.
+ *
+ * GTK+ is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU Lesser General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * GLib 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
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with GTK+; see the file COPYING.  If not,
+ * see <http://www.gnu.org/licenses/>.
+ *
+ * Author: Matthias Clasen
+ */
+
+#include "config.h"
+
+#include <gtk/gtk.h>
+#include "gtk-path-tool.h"
+
+#include <glib/gi18n-lib.h>
+
+void
+do_pathop (const char *op, int *argc, const char ***argv)
+{
+  GError *error = NULL;
+  const char *fill = "winding";
+  char **args = NULL;
+  GOptionContext *context;
+  GOptionEntry entries[] = {
+    { "fill-rule", 0, 0, G_OPTION_ARG_STRING, &fill, N_("Fill rule"), N_("RULE") },
+    { G_OPTION_REMAINING, 0, 0, G_OPTION_ARG_STRING_ARRAY, &args, NULL, N_("PATH…") },
+    { NULL, },
+  };
+  GskPath *path1, *path2, *result;
+  GskFillRule fill_rule;
+  char *prgname;
+  char *summary;
+
+  prgname = g_strconcat ("gtk4-path-tool ", op, NULL);
+  summary = g_strdup_printf (_("Apply the %s path operation."), op);
+  g_set_prgname (prgname);
+
+  context = g_option_context_new (NULL);
+  g_option_context_set_translation_domain (context, GETTEXT_PACKAGE);
+  g_option_context_add_main_entries (context, entries, NULL);
+  g_option_context_set_summary (context, summary);
+
+  if (!g_option_context_parse (context, argc, (char ***)argv, &error))
+    {
+      g_printerr ("%s\n", error->message);
+      g_error_free (error);
+      exit (1);
+    }
+
+  g_option_context_free (context);
+
+  if (args == NULL)
+    {
+      g_printerr ("%s\n", _("No paths given."));
+      exit (1);
+    }
+
+  path1 = get_path (args[0]);
+  if (args[1] != NULL)
+    path2 = get_path (args[1]);
+  else
+    path2 = NULL;
+
+  fill_rule = get_enum_value (GSK_TYPE_FILL_RULE, _("fill rule"), fill);
+
+  if (strcmp (op, "simplify") == 0)
+    result = gsk_path_simplify (path1, fill_rule);
+  else if (strcmp (op, "union") == 0)
+    result = gsk_path_union (path1, path2, fill_rule);
+  else if (strcmp (op, "intersection") == 0)
+    result = gsk_path_intersection (path1, path2, fill_rule);
+  else if (strcmp (op, "difference") == 0)
+    result = gsk_path_difference (path1, path2, fill_rule);
+  else if (strcmp (op, "symmetric-difference") == 0)
+    result = gsk_path_symmetric_difference (path1, path2, fill_rule);
+  else
+    {
+      char *msg = g_strdup_printf (_("'%s' is not a supported operation."), op);
+      g_printerr ("%s\n", msg);
+      exit (1);
+    }
+
+  if (result)
+    {
+      char *str = gsk_path_to_string (result);
+      g_print ("%s\n", str);
+      g_free (str);
+    }
+  else
+    {
+      g_printerr ("%s\n", _("That didn't work out."));
+      exit (1);
+    }
+}

tools/gtk-path-tool-show.c

@@ -32,12 +32,14 @@
 #include "path-view.h"
 
 static void
-show_path_fill (GskPath       *path,
+show_path_fill (GskPath       *path1,
+                GskPath       *path2,
                 GskFillRule    fill_rule,
                 const GdkRGBA *fg_color,
                 const GdkRGBA *bg_color,
                 gboolean       show_points,
                 gboolean       show_controls,
+                gboolean       show_intersections,
                 const GdkRGBA *point_color)
 {
   GtkWidget *window, *sw, *child;
@@ -52,14 +54,17 @@ show_path_fill (GskPath       *path,
   gtk_scrolled_window_set_propagate_natural_height (GTK_SCROLLED_WINDOW (sw), TRUE);
   gtk_window_set_child (GTK_WINDOW (window), sw);
 
-  child = path_view_new (path);
+  child = g_object_new (PATH_TYPE_VIEW, NULL);
   g_object_set (child,
+                "path1", path1,
+                "path2", path2,
                 "do-fill", TRUE,
                 "fill-rule", fill_rule,
                 "fg-color", fg_color,
                 "bg-color", bg_color,
                 "show-points", show_points,
                 "show-controls", show_controls,
+                "show-intersections", show_intersections,
                 "point-color", point_color,
                 NULL);
 
@@ -74,12 +79,14 @@ show_path_fill (GskPath       *path,
 }
 
 static void
-show_path_stroke (GskPath       *path,
+show_path_stroke (GskPath       *path1,
+                  GskPath       *path2,
                   GskStroke     *stroke,
                   const GdkRGBA *fg_color,
                   const GdkRGBA *bg_color,
                   gboolean       show_points,
                   gboolean       show_controls,
+                  gboolean       show_intersections,
                   const GdkRGBA *point_color)
 {
   GtkWidget *window, *sw, *child;
@@ -94,14 +101,17 @@ show_path_stroke (GskPath       *path,
   gtk_scrolled_window_set_propagate_natural_height (GTK_SCROLLED_WINDOW (sw), TRUE);
   gtk_window_set_child (GTK_WINDOW (window), sw);
 
-  child = path_view_new (path);
+  child = g_object_new (PATH_TYPE_VIEW, NULL);
   g_object_set (child,
+                "path1", path1,
+                "path2", path2,
                 "do-fill", FALSE,
                 "stroke", stroke,
                 "fg-color", fg_color,
                 "bg-color", bg_color,
                 "show-points", show_points,
                 "show-controls", show_controls,
+                "show-intersections", show_intersections,
                 "point-color", point_color,
                 NULL);
 
@@ -123,6 +133,7 @@ do_show (int          *argc,
   gboolean do_stroke = FALSE;
   gboolean show_points = FALSE;
   gboolean show_controls = FALSE;
+  gboolean show_intersections = FALSE;
   const char *fill = "winding";
   const char *fg_color = "black";
   const char *bg_color = "white";
@@ -141,6 +152,7 @@ do_show (int          *argc,
     { "stroke", 0, 0, G_OPTION_ARG_NONE, &do_stroke, N_("Stroke the path"), NULL },
     { "points", 0, 0, G_OPTION_ARG_NONE, &show_points, N_("Show path points"), NULL },
     { "controls", 0, 0, G_OPTION_ARG_NONE, &show_controls, N_("Show control points"), NULL },
+    { "intersections", 0, 0, G_OPTION_ARG_NONE, &show_intersections, N_("Show intersections"), NULL },
     { "fg-color", 0, 0, G_OPTION_ARG_STRING, &fg_color, N_("Foreground color"), N_("COLOR") },
     { "bg-color", 0, 0, G_OPTION_ARG_STRING, &bg_color, N_("Background color"), N_("COLOR") },
     { "point-color", 0, 0, G_OPTION_ARG_STRING, &point_color, N_("Point color"), N_("COLOR") },
@@ -160,7 +172,8 @@ do_show (int          *argc,
     { "dash-offset", 0, 0, G_OPTION_ARG_DOUBLE, &dash_offset, N_("Dash offset (number)"), N_("VALUE") },
     { NULL, }
   };
-  GskPath *path;
+  GskPath *path1;
+  GskPath *path2;
   GskFillRule fill_rule;
   GdkRGBA fg, bg, pc;
   GskLineCap line_cap;
@@ -210,13 +223,17 @@ do_show (int          *argc,
       exit (1);
     }
 
-  if (g_strv_length (args) > 1)
+  if (g_strv_length (args) > 2)
     {
-      g_printerr ("%s\n", _("Can only show a single path"));
+      g_printerr ("%s\n", _("Can only show one or two paths"));
       exit (1);
     }
 
-  path = get_path (args[0]);
+  path1 = get_path (args[0]);
+  if (g_strv_length (args) > 1)
+    path2 = get_path (args[1]);
+  else
+    path2 = NULL;
 
   fill_rule = get_enum_value (GSK_TYPE_FILL_RULE, _("fill rule"), fill);
   get_color (&fg, fg_color);
@@ -234,11 +251,12 @@ do_show (int          *argc,
   _gsk_stroke_set_dashes (stroke, dashes);
 
   if (do_stroke)
-    show_path_stroke (path, stroke, &fg, &bg, show_points, show_controls, &pc);
+    show_path_stroke (path1, path2, stroke, &fg, &bg, show_points, show_controls, show_intersections, &pc);
   else
-    show_path_fill (path, fill_rule, &fg, &bg, show_points, show_controls, &pc);
+    show_path_fill (path1, path2, fill_rule, &fg, &bg, show_points, show_controls, show_intersections, &pc);
 
-  gsk_path_unref (path);
+  g_clear_pointer (&path1, gsk_path_unref);
+  g_clear_pointer (&path2, gsk_path_unref);
 
   g_strfreev (args);
 }

tools/gtk-path-tool.c

@@ -38,6 +38,12 @@ usage (void)
              "Perform various tasks on paths.\n"
              "\n"
              "Commands:\n"
+             "  simplify     Simplify the path\n"
+             "  intersection Intersect two paths\n"
+             "  union        Create the union of two paths\n"
+             "  difference   Create the difference of two paths\n"
+             "  symmetric-difference\n"
+             "               Create the symmetric difference of two paths\n"
              "  decompose    Decompose the path\n"
              "  reverse      Reverse the path\n"
              "  restrict     Restrict the path to a segment\n"
@@ -128,8 +134,12 @@ main (int argc, const char *argv[])
 
   if (strcmp (argv[0], "decompose") == 0)
     do_decompose (&argc, &argv);
+  else if (strcmp (argv[0], "difference") == 0)
+    do_pathop (argv[0], &argc, &argv);
   else if (strcmp (argv[0], "info") == 0)
     do_info (&argc, &argv);
+  else if (strcmp (argv[0], "intersection") == 0)
+    do_pathop (argv[0], &argc, &argv);
   else if (strcmp (argv[0], "render") == 0)
     do_render (&argc, &argv);
   else if (strcmp (argv[0], "restrict") == 0)
@@ -138,6 +148,12 @@ main (int argc, const char *argv[])
     do_reverse (&argc, &argv);
   else if (strcmp (argv[0], "show") == 0)
     do_show (&argc, &argv);
+  else if (strcmp (argv[0], "simplify") == 0)
+    do_pathop (argv[0], &argc, &argv);
+  else if (strcmp (argv[0], "symmetric-difference") == 0)
+    do_pathop (argv[0], &argc, &argv);
+  else if (strcmp (argv[0], "union") == 0)
+    do_pathop (argv[0], &argc, &argv);
   else
     usage ();
 

tools/gtk-path-tool.h

@@ -6,6 +6,7 @@ void do_restrict  (int *argc, const char ***argv);
 void do_reverse   (int *argc, const char ***argv);
 void do_render    (int *argc, const char ***argv);
 void do_show      (int *argc, const char ***argv);
+void do_pathop    (const char *op, int *argc, const char ***argv);
 
 GskPath *get_path       (const char *arg);
 int      get_enum_value (GType       type,

tools/meson.build

@@ -26,6 +26,7 @@ gtk_tools = [
   ['gtk4-path-tool', ['gtk-path-tool.c',
                       'gtk-path-tool-decompose.c',
                       'gtk-path-tool-info.c',
+                      'gtk-path-tool-pathops.c',
                       'gtk-path-tool-render.c',
                       'gtk-path-tool-restrict.c',
                       'gtk-path-tool-reverse.c',

tools/path-view.c

@@ -25,6 +25,8 @@ struct _PathView
 {
   GtkWidget parent_instance;
 
+  GskPath *path1;
+  GskPath *path2;
   GskPath *path;
   GskStroke *stroke;
   graphene_rect_t bounds;
@@ -35,13 +37,17 @@ struct _PathView
   gboolean do_fill;
   gboolean show_points;
   gboolean show_controls;
+  gboolean show_intersections;
   GskPath *line_path;
   GskPath *point_path;
   GdkRGBA point_color;
+  GskPath *intersection_line_path;
+  GskPath *intersection_point_path;
 };
 
 enum {
-  PROP_PATH = 1,
+  PROP_PATH1 = 1,
+  PROP_PATH2,
   PROP_DO_FILL,
   PROP_STROKE,
   PROP_FILL_RULE,
@@ -50,6 +56,7 @@ enum {
   PROP_POINT_COLOR,
   PROP_SHOW_POINTS,
   PROP_SHOW_CONTROLS,
+  PROP_SHOW_INTERSECTIONS,
   N_PROPERTIES
 };
 
@@ -79,10 +86,14 @@ path_view_dispose (GObject *object)
 {
   PathView *self = PATH_VIEW (object);
 
+  g_clear_pointer (&self->path1, gsk_path_unref);
+  g_clear_pointer (&self->path2, gsk_path_unref);
   g_clear_pointer (&self->path, gsk_path_unref);
   g_clear_pointer (&self->stroke, gsk_stroke_free);
   g_clear_pointer (&self->line_path, gsk_path_unref);
   g_clear_pointer (&self->point_path, gsk_path_unref);
+  g_clear_pointer (&self->intersection_line_path, gsk_path_unref);
+  g_clear_pointer (&self->intersection_point_path, gsk_path_unref);
 
   G_OBJECT_CLASS (path_view_parent_class)->dispose (object);
 }
@@ -97,8 +108,12 @@ path_view_get_property (GObject    *object,
 
   switch (prop_id)
     {
-    case PROP_PATH:
+    case PROP_PATH1:
-      g_value_set_boxed (value, self->path);
+      g_value_set_boxed (value, self->path1);
+      break;
+
+    case PROP_PATH2:
+      g_value_set_boxed (value, self->path2);
       break;
 
     case PROP_DO_FILL:
@@ -129,6 +144,10 @@ path_view_get_property (GObject    *object,
       g_value_set_boolean (value, self->show_controls);
       break;
 
+    case PROP_SHOW_INTERSECTIONS:
+      g_value_set_boolean (value, self->show_intersections);
+      break;
+
     case PROP_POINT_COLOR:
       g_value_set_boxed (value, &self->point_color);
       break;
@@ -268,6 +287,93 @@ update_controls (PathView *self)
   update_bounds (self);
 }
 
+typedef struct {
+  GskPathBuilder *line_builder;
+  GskPathBuilder *point_builder;
+  GskPathPoint start;
+  int segment;
+} IntersectionData;
+
+static gboolean
+intersection_cb (GskPath             *path1,
+                 const GskPathPoint  *point1,
+                 GskPath             *path2,
+                 const GskPathPoint  *point2,
+                 GskPathIntersection  kind,
+                 gpointer             data)
+{
+  IntersectionData *id = data;
+  graphene_point_t pos;
+
+  switch (kind)
+    {
+    case GSK_PATH_INTERSECTION_NORMAL:
+      gsk_path_point_get_position (point1, path1, &pos);
+      gsk_path_builder_add_circle (id->point_builder, &pos, 3);
+      break;
+
+    case GSK_PATH_INTERSECTION_START:
+      if (id->segment == 0)
+        id->start = *point1;
+      id->segment++;
+      break;
+
+    case GSK_PATH_INTERSECTION_END:
+      id->segment--;
+      if (id->segment == 0)
+        gsk_path_builder_add_segment (id->line_builder, path1, &id->start, point1);
+      break;
+
+    case GSK_PATH_INTERSECTION_NONE:
+    default:
+      g_assert_not_reached ();
+    }
+
+  return TRUE;
+}
+
+static void
+update_intersections (PathView *self)
+{
+  IntersectionData id;
+
+  g_clear_pointer (&self->intersection_line_path, gsk_path_unref);
+  g_clear_pointer (&self->intersection_point_path, gsk_path_unref);
+
+  if (!self->show_intersections || !self->path1 || !self->path2)
+    return;
+
+  id.line_builder = gsk_path_builder_new ();
+  id.point_builder = gsk_path_builder_new ();
+  id.segment = 0;
+
+  gsk_path_foreach_intersection (self->path1, self->path2, intersection_cb, &id);
+
+  self->intersection_line_path = gsk_path_builder_free_to_path (id.line_builder);
+  self->intersection_point_path = gsk_path_builder_free_to_path (id.point_builder);
+  gtk_widget_queue_draw (GTK_WIDGET (self));
+}
+
+static void
+update_path (PathView *self)
+{
+  GskPathBuilder *builder;
+
+  g_clear_pointer (&self->path, gsk_path_unref);
+
+  builder = gsk_path_builder_new ();
+  if (self->path1)
+    gsk_path_builder_add_path (builder, self->path1);
+
+  if (self->path2)
+    gsk_path_builder_add_path (builder, self->path2);
+
+  self->path = gsk_path_builder_free_to_path (builder);
+
+  update_intersections (self);
+  update_controls (self);
+}
+
 static void
 path_view_set_property (GObject      *object,
                         guint         prop_id,
@@ -278,11 +384,16 @@ path_view_set_property (GObject      *object,
 
   switch (prop_id)
     {
+    case PROP_PATH1:
+      g_clear_pointer (&self->path1, gsk_path_unref);
+      self->path1 = g_value_dup_boxed (value);
+      update_path (self);
+      break;
 
-    case PROP_PATH:
+    case PROP_PATH2:
-      g_clear_pointer (&self->path, gsk_path_unref);
+      g_clear_pointer (&self->path2, gsk_path_unref);
-      self->path = g_value_dup_boxed (value);
+      self->path2 = g_value_dup_boxed (value);
-      update_controls (self);
+      update_path (self);
       break;
 
     case PROP_DO_FILL:
@@ -321,6 +432,11 @@ path_view_set_property (GObject      *object,
       update_controls (self);
       break;
 
+    case PROP_SHOW_INTERSECTIONS:
+      self->show_intersections = g_value_get_boolean (value);
+      update_intersections (self);
+      break;
+
     case PROP_POINT_COLOR:
       self->point_color = *(GdkRGBA *) g_value_get_boxed (value);
       gtk_widget_queue_draw (GTK_WIDGET (self));
@@ -344,9 +460,9 @@ path_view_measure (GtkWidget      *widget,
   PathView *self = PATH_VIEW (widget);
 
   if (orientation == GTK_ORIENTATION_HORIZONTAL)
-    *minimum = *natural = (int) ceilf (self->bounds.size.width) + 2 * self->padding;
+    *minimum = *natural = (int) ceilf (self->bounds.origin.x + self->bounds.size.width) + 2 * self->padding;
   else
-    *minimum = *natural = (int) ceilf (self->bounds.size.height) + 2 * self->padding;
+    *minimum = *natural = (int) ceilf (self->bounds.origin.y + self->bounds.size.height) + 2 * self->padding;
 }
 
 static void
@@ -383,6 +499,18 @@ path_view_snapshot (GtkWidget   *widget,
       gtk_snapshot_append_stroke (snapshot, self->point_path, stroke, &self->fg);
     }
 
+  if (self->intersection_line_path)
+    {
+      GskStroke *stroke = gsk_stroke_new (gsk_stroke_get_line_width (self->stroke));
+
+      gtk_snapshot_append_stroke (snapshot, self->intersection_line_path, stroke, &self->point_color);
+    }
+
+  if (self->intersection_point_path)
+    {
+      gtk_snapshot_append_fill (snapshot, self->intersection_point_path, GSK_FILL_RULE_WINDING, &self->point_color);
+    }
+
   gtk_snapshot_restore (snapshot);
 }
 
@@ -399,8 +527,13 @@ path_view_class_init (PathViewClass *class)
   widget_class->measure = path_view_measure;
   widget_class->snapshot = path_view_snapshot;
 
-  properties[PROP_PATH]
+  properties[PROP_PATH1]
-      = g_param_spec_boxed ("path", NULL, NULL,
+      = g_param_spec_boxed ("path1", NULL, NULL,
+                            GSK_TYPE_PATH,
+                            G_PARAM_READWRITE|G_PARAM_EXPLICIT_NOTIFY);
+
+  properties[PROP_PATH2]
+      = g_param_spec_boxed ("path2", NULL, NULL,
                             GSK_TYPE_PATH,
                             G_PARAM_READWRITE|G_PARAM_EXPLICIT_NOTIFY);
 
@@ -440,6 +573,11 @@ path_view_class_init (PathViewClass *class)
                               FALSE,
                               G_PARAM_READWRITE|G_PARAM_EXPLICIT_NOTIFY);
 
+  properties[PROP_SHOW_INTERSECTIONS]
+      = g_param_spec_boolean ("show-intersections", NULL, NULL,
+                              FALSE,
+                              G_PARAM_READWRITE|G_PARAM_EXPLICIT_NOTIFY);
+
   properties[PROP_POINT_COLOR]
       = g_param_spec_boxed ("point-color", NULL, NULL,
                             GDK_TYPE_RGBA,
@@ -452,6 +590,6 @@ GtkWidget *
 path_view_new (GskPath *path)
 {
   return g_object_new (PATH_TYPE_VIEW,
-                       "path", path,
+                       "path1", path,
                        NULL);
 }