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cs440-acg/ext/openexr/IlmBase/ImathTest/testQuatSetRotation.cpp

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+///////////////////////////////////////////////////////////////////////////
+//
+// Copyright (c) 2006, Industrial Light & Magic, a division of Lucas
+// Digital Ltd. LLC
+// 
+// All rights reserved.
+// 
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+// *       Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+// *       Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+// *       Neither the name of Industrial Light & Magic nor the names of
+// its contributors may be used to endorse or promote products derived
+// from this software without specific prior written permission. 
+// 
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+///////////////////////////////////////////////////////////////////////////
+
+
+#include <testQuatSetRotation.h>
+#include "ImathQuat.h"
+#include "ImathRandom.h"
+#include <iostream>
+#include <assert.h>
+
+
+using namespace std;
+using namespace IMATH_INTERNAL_NAMESPACE;
+
+namespace {
+
+void
+testRotation (const V3f &from, const V3f &to)
+{
+    //
+    // Build a quaternion.
+    //
+
+    Quatf Q;
+    Q.setRotation (from, to);
+    M44f M = Q.toMatrix44();
+
+    //
+    // Verify that the quaternion rotates vector from into vector to.
+    //
+
+    float e = 20 * limits<float>::epsilon();
+
+    V3f fromM = from * M;
+    V3f fromQ = from * Q;
+    V3f t0 = to.normalized();
+    V3f fM0 = fromM.normalized();
+    V3f fQ0 = fromQ.normalized();
+
+    assert (t0.equalWithAbsError (fM0, e));
+    assert (t0.equalWithAbsError (fQ0, e));
+
+    //
+    // Verify that the rotation axis is the cross product of from and to.
+    //
+
+    V3f f0 = from.normalized();
+
+    if (abs (f0 ^ t0) < 0.9)
+    {
+	V3f n0 = (from % to).normalized();
+	V3f n0M = n0 * M;
+
+	assert (n0.equalWithAbsError (n0M, e));
+    }
+}
+
+
+void
+specificVectors ()
+{
+    cout << "  exact 90-degree rotations" << endl;
+
+    testRotation (V3f (1, 0, 0), V3f (0, 1, 0));
+    testRotation (V3f (1, 0, 0), V3f (0, 0, 1));
+    testRotation (V3f (0, 1, 0), V3f (1, 0, 0));
+    testRotation (V3f (0, 1, 0), V3f (0, 0, 1));
+    testRotation (V3f (0, 0, 1), V3f (1, 0, 0));
+    testRotation (V3f (0, 0, 1), V3f (0, 1, 0));
+
+    cout << "  exact zero-degree rotations" << endl;
+
+    testRotation (V3f (1, 0, 0), V3f (1, 0, 0));
+    testRotation (V3f (0, 1, 0), V3f (0, 1, 0));
+    testRotation (V3f (0, 0, 1), V3f (0, 0, 1));
+    testRotation (V3f (1, 2, 3), V3f (2, 4, 6));
+
+    cout << "  exact 180-degree rotations" << endl;
+
+    testRotation (V3f (1, 0, 0), V3f (-1, 0, 0));
+    testRotation (V3f (0, 1, 0), V3f (0, -1, 0));
+    testRotation (V3f (0, 0, 1), V3f (0, 0, -1));
+    testRotation (V3f (1, 2, 3), V3f (-2, -4, -6));
+    testRotation (V3f (1, 3, 2), V3f (-2, -6, -4));
+    testRotation (V3f (2, 1, 3), V3f (-4, -2, -6));
+    testRotation (V3f (3, 1, 2), V3f (-6, -2, -4));
+    testRotation (V3f (2, 3, 1), V3f (-4, -6, -2));
+    testRotation (V3f (3, 2, 1), V3f (-6, -4, -2));
+
+    cout << "  other angles" << endl;
+
+    testRotation (V3f (1, 2, 3), V3f (4, 5, 6));
+    testRotation (V3f (1, 2, 3), V3f (4, 6, 5));
+    testRotation (V3f (1, 2, 3), V3f (5, 4, 6));
+    testRotation (V3f (1, 2, 3), V3f (6, 4, 5));
+    testRotation (V3f (1, 2, 3), V3f (5, 6, 4));
+    testRotation (V3f (1, 2, 3), V3f (6, 5, 4));
+    testRotation (V3f (1, 2, 3), V3f (-4, -5, -6));
+    testRotation (V3f (1, 2, 3), V3f (-4, -6, -5));
+    testRotation (V3f (1, 2, 3), V3f (-5, -4, -6));
+    testRotation (V3f (1, 2, 3), V3f (-6, -4, -5));
+    testRotation (V3f (1, 2, 3), V3f (-5, -6, -4));
+    testRotation (V3f (1, 2, 3), V3f (-6, -5, -4));
+}
+
+
+void
+randomVectors ()
+{
+    cout << "  random from and to vectors" << endl;
+
+    Rand48 rand (17);
+
+    for (int i = 0; i < 500000; ++i)
+    {
+	V3f from = hollowSphereRand<V3f> (rand) * rand.nextf (0.1, 10.0);
+	V3f to = hollowSphereRand<V3f> (rand) * rand.nextf (0.1, 10.0);
+	testRotation (from, to);
+    }
+}
+
+
+void
+nearlyEqualVectors ()
+{
+    cout << "  nearly equal from and to vectors" << endl;
+
+    Rand48 rand (19);
+    float e = 100 * limits<float>::epsilon();
+
+    for (int i = 0; i < 500000; ++i)
+    {
+	V3f from = hollowSphereRand<V3f> (rand);
+	V3f to = from + e * hollowSphereRand<V3f> (rand);
+	testRotation (from, to);
+    }
+}
+
+
+void
+nearlyOppositeVectors ()
+{
+    cout << "  nearly opposite from and to vectors" << endl;
+
+    Rand48 rand (19);
+    float e = 100 * limits<float>::epsilon();
+
+    for (int i = 0; i < 500000; ++i)
+    {
+	V3f from = hollowSphereRand<V3f> (rand);
+	V3f to = -from + e * hollowSphereRand<V3f> (rand);
+	testRotation (from, to);
+    }
+}
+
+
+
+} // namespace
+
+
+void
+testQuatSetRotation ()
+{
+    cout << "Testing quaternion rotations" << endl;
+
+    specificVectors();
+    randomVectors();
+    nearlyEqualVectors();
+    nearlyOppositeVectors();
+
+    cout << "ok\n" << endl;
+}