Squashed 'third_party/eigen/' content from commit 61d72f6

Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/demos/opengl/trackball.cpp b/demos/opengl/trackball.cpp
new file mode 100644
index 0000000..77ac790
--- /dev/null
+++ b/demos/opengl/trackball.cpp
@@ -0,0 +1,59 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "trackball.h"
+#include "camera.h"
+
+using namespace Eigen;
+
+void Trackball::track(const Vector2i& point2D)
+{
+  if (mpCamera==0)
+    return;
+  Vector3f newPoint3D;
+  bool newPointOk = mapToSphere(point2D, newPoint3D);
+
+  if (mLastPointOk && newPointOk)
+  {
+    Vector3f axis = mLastPoint3D.cross(newPoint3D).normalized();
+    float cos_angle = mLastPoint3D.dot(newPoint3D);
+    if ( internal::abs(cos_angle) < 1.0 )
+    {
+      float angle = 2. * acos(cos_angle);
+      if (mMode==Around)
+        mpCamera->rotateAroundTarget(Quaternionf(AngleAxisf(angle, axis)));
+      else
+        mpCamera->localRotate(Quaternionf(AngleAxisf(-angle, axis)));
+    }
+  }
+
+  mLastPoint3D = newPoint3D;
+  mLastPointOk = newPointOk;
+}
+
+bool Trackball::mapToSphere(const Vector2i& p2, Vector3f& v3)
+{
+  if ((p2.x() >= 0) && (p2.x() <= int(mpCamera->vpWidth())) &&
+      (p2.y() >= 0) && (p2.y() <= int(mpCamera->vpHeight())) )
+  {
+    double x  = (double)(p2.x() - 0.5*mpCamera->vpWidth())  / (double)mpCamera->vpWidth();
+    double y  = (double)(0.5*mpCamera->vpHeight() - p2.y()) / (double)mpCamera->vpHeight();
+    double sinx         = sin(M_PI * x * 0.5);
+    double siny         = sin(M_PI * y * 0.5);
+    double sinx2siny2   = sinx * sinx + siny * siny;
+
+    v3.x() = sinx;
+    v3.y() = siny;
+    v3.z() = sinx2siny2 < 1.0 ? sqrt(1.0 - sinx2siny2) : 0.0;
+
+    return true;
+  }
+  else
+    return false;
+}