Move out generic math parts out of the native barrier implementation

In order to reuse some vector math for pointer confinement, move out
those parts to its own file, introducing the types old types
"MetaVector2" and "MetaLine2" outside of meta-barrier-native.c, as well
as introducing MetaBorder which is a line, with a blocking direction.

https://bugzilla.gnome.org/show_bug.cgi?id=744104

src/core/meta-border.c

@@ -0,0 +1,154 @@
+/* -*- mode: C; c-file-style: "gnu"; indent-tabs-mode: nil; -*- */
+
+/*
+ * Copyright (C) 2015 Red Hat
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * This program 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
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
+ * 02111-1307, USA.
+ *
+ * Written by:
+ *     Jonas Ådahl <jadahl@gmail.com>
+ */
+
+#include "config.h"
+
+#include "core/meta-border.h"
+
+#include <math.h>
+
+static inline float
+meta_vector2_cross_product (const MetaVector2 a,
+                            const MetaVector2 b)
+{
+  return a.x * b.y - a.y * b.x;
+}
+
+static inline MetaVector2
+meta_vector2_add (const MetaVector2 a,
+                  const MetaVector2 b)
+{
+  return (MetaVector2) {
+    .x = a.x + b.x,
+    .y = a.y + b.y,
+  };
+}
+
+static inline MetaVector2
+meta_vector2_multiply_constant (const float       c,
+                                const MetaVector2 a)
+{
+  return (MetaVector2) {
+    .x = c * a.x,
+    .y = c * a.y,
+  };
+}
+
+gboolean
+meta_line2_intersects_with (const MetaLine2 *line1,
+                            const MetaLine2 *line2,
+                            MetaVector2     *intersection)
+{
+  MetaVector2 p = line1->a;
+  MetaVector2 r = meta_vector2_subtract (line1->b, line1->a);
+  MetaVector2 q = line2->a;
+  MetaVector2 s = meta_vector2_subtract (line2->b, line2->a);
+  float rxs;
+  float sxr;
+  float t;
+  float u;
+
+  /*
+   * The line (p, r) and (q, s) intersects where
+   *
+   *   p + t r = q + u s
+   *
+   * Calculate t:
+   *
+   *   (p + t r) × s = (q + u s) × s
+   *   p × s + t (r × s) = q × s + u (s × s)
+   *   p × s + t (r × s) = q × s
+   *   t (r × s) = q × s - p × s
+   *   t (r × s) = (q - p) × s
+   *   t = ((q - p) × s) / (r × s)
+   *
+   * Using the same method, for u we get:
+   *
+   *   u = ((p - q) × r) / (s × r)
+   */
+
+  rxs = meta_vector2_cross_product (r, s);
+  sxr = meta_vector2_cross_product (s, r);
+
+  /* If r × s = 0 then the lines are either parallel or collinear. */
+  if (fabs (rxs) < DBL_MIN)
+    return FALSE;
+
+  t = meta_vector2_cross_product (meta_vector2_subtract (q, p), s) / rxs;
+  u = meta_vector2_cross_product (meta_vector2_subtract (p, q), r) / sxr;
+
+  /* The lines only intersect if 0 ≤ t ≤ 1 and 0 ≤ u ≤ 1. */
+  if (t < 0.0 || t > 1.0 || u < 0.0 || u > 1.0)
+    return FALSE;
+
+  *intersection = meta_vector2_add (p, meta_vector2_multiply_constant (t, r));
+
+  return TRUE;
+}
+
+gboolean
+meta_border_is_horizontal (MetaBorder *border)
+{
+  return border->line.a.y == border->line.b.y;
+}
+
+gboolean
+meta_border_is_blocking_directions (MetaBorder               *border,
+                                    MetaBorderMotionDirection directions)
+{
+  if (meta_border_is_horizontal (border))
+    {
+      if ((directions & (META_BORDER_MOTION_DIRECTION_POSITIVE_Y |
+                         META_BORDER_MOTION_DIRECTION_NEGATIVE_Y)) == 0)
+        return FALSE;
+    }
+  else
+    {
+      if ((directions & (META_BORDER_MOTION_DIRECTION_POSITIVE_X |
+                         META_BORDER_MOTION_DIRECTION_NEGATIVE_X)) == 0)
+        return FALSE;
+    }
+
+  return (~border->blocking_directions & directions) != directions;
+}
+
+unsigned int
+meta_border_get_allows_directions (MetaBorder *border)
+{
+  return ~border->blocking_directions &
+    (META_BORDER_MOTION_DIRECTION_POSITIVE_X |
+     META_BORDER_MOTION_DIRECTION_POSITIVE_Y |
+     META_BORDER_MOTION_DIRECTION_NEGATIVE_X |
+     META_BORDER_MOTION_DIRECTION_NEGATIVE_Y);
+}
+
+void
+meta_border_set_allows_directions (MetaBorder *border, unsigned int directions)
+{
+  border->blocking_directions =
+    ~directions & (META_BORDER_MOTION_DIRECTION_POSITIVE_X |
+                   META_BORDER_MOTION_DIRECTION_POSITIVE_Y |
+                   META_BORDER_MOTION_DIRECTION_NEGATIVE_X |
+                   META_BORDER_MOTION_DIRECTION_NEGATIVE_Y);
+}