Less X connections.

ui/gfx/gl/gl_surface_egl.cc

Index: ui/gfx/gl/gl_surface_egl.cc
diff --git a/ui/gfx/gl/gl_surface_egl.cc b/ui/gfx/gl/gl_surface_egl.cc
index f1d075048a45d2c5f97cb92cea7d668af3fd2b78..62e6c250f77ffc9803c6da1775da756207a46fbe 100644
--- a/ui/gfx/gl/gl_surface_egl.cc
+++ b/ui/gfx/gl/gl_surface_egl.cc
@@ -25,6 +25,7 @@
 extern "C" {
 #include <X11/Xlib.h>
 }
+#include "ui/base/x/x11_util.h"
 #endif
 
 #if defined(USE_WAYLAND)
@@ -36,7 +37,6 @@ namespace gfx {
 namespace {
 EGLConfig g_config;
 EGLDisplay g_display;
-EGLNativeDisplayType g_native_display;
 EGLConfig g_software_config;
 EGLDisplay g_software_display;
 EGLNativeDisplayType g_software_native_display;
@@ -48,19 +48,13 @@ GLSurfaceEGL::GLSurfaceEGL() : software_(false) {
 GLSurfaceEGL::~GLSurfaceEGL() {
 }
 
+// static
 bool GLSurfaceEGL::InitializeOneOff() {
   static bool initialized = false;
   if (initialized)
     return true;
 
-#if defined(USE_WAYLAND)
-  g_native_display = ui::WaylandDisplay::Connect(NULL)->display();
-#elif defined(USE_X11)
-  g_native_display = XOpenDisplay(NULL);
-#else
-  g_native_display = EGL_DEFAULT_DISPLAY;
-#endif
-  g_display = eglGetDisplay(g_native_display);
+  g_display = eglGetDisplay(GetNativeDisplay());
   if (!g_display) {
     LOG(ERROR) << "eglGetDisplay failed with error " << GetLastEGLErrorString();
     return false;
@@ -164,16 +158,28 @@ EGLConfig GLSurfaceEGL::GetConfig() {
   return software_ ? g_software_config : g_config;
 }
 
+// static
 EGLDisplay GLSurfaceEGL::GetHardwareDisplay() {
   return g_display;
 }
 
+// static
 EGLDisplay GLSurfaceEGL::GetSoftwareDisplay() {
   return g_software_display;
 }
 
+// static
 EGLNativeDisplayType GLSurfaceEGL::GetNativeDisplay() {
-  return g_native_display;
+#if defined(USE_WAYLAND)
+  static EGLNativeDisplayType native_display = NULL;
+  if (!native_display)
+    native_display = ui::WaylandDisplay::Connect(NULL)->display();
+  return native_display;
+#elif defined(USE_X11)
+  return ui::GetXDisplay();
+#else
+  return EGL_DEFAULT_DISPLAY;
+#endif
 }
 
 NativeViewGLSurfaceEGL::NativeViewGLSurfaceEGL(bool software,