epfl-archive/cs440-acg/ext/openexr/IlmBase/ImathTest/testQuatSlerp.cpp

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#include <testQuatSlerp.h>
#include "ImathQuat.h"
#include "ImathRandom.h"
#include <iostream>
#include <math.h>
#include <assert.h>


using namespace std;
using namespace IMATH_INTERNAL_NAMESPACE;

namespace {

void
compareQuats (const Quatf &q1, const Quatf &q2, float e)
{
    assert (equalWithAbsError (q1.v.x, q2.v.x, e));
    assert (equalWithAbsError (q1.v.y, q2.v.y, e));
    assert (equalWithAbsError (q1.v.z, q2.v.z, e));
    assert (equalWithAbsError (q1.r,   q2.r,   e));
}


Quatd
pow (const Quatd q, int n)
{
    Quatd result;

    for (int i = 0; i < n; ++i)
	result *= q;

    return result;
}


void
testSlerp (const Quatf q1, const Quatf q2, int m, int n)
{
    //
    // For two quaternions, q1 and q2, and the identity quaternion, qi,
    //
    //     slerp (q1, q2, f) == q1 * slerp (qi, q1.inverse() * q2, f);  (1)
    //
    // In addition, for integers m and n, with m >= 0, n > 0,
    //
    //     pow (slerp (qi, q3, m/n), n) == pow (q3, m)                  (2)
    //
    // This allows us to test if slerp (q1, q2, m/n) works correctly.
    // Thanks to Dan Piponi for pointing this out.
    //
    // Note that e2, our upper bound for the numerical error in (2) is
    // fairly large.  The reason for this is that testSlerp() will be
    // called with m and n up to 16.  Taking quaternions to the 16th
    // power amplifies any inaccuracies.
    //

    Quatf qi;
    Quatf q3 = q1.inverse() * q2;
    Quatf q1q2 = slerp (q1, q2, float (m) / float (n));
    Quatf qiq3 = slerp (qi, q3, float (m) / float (n));
    float e1 = 60 * limits<float>::epsilon();
    float e2 = 600 * limits<float>::epsilon();

    compareQuats (q1q2, q1 * qiq3, e1);
    compareQuats (pow (qiq3, n), pow (q3, m), e2);
}


void
testSlerp (const Quatf q1, const Quatf q2)
{
    const int n = 16;

    for (int m = 0; m <= n; ++m)
	testSlerp (q1, q2, m, n);
}


void
specificRotations ()
{
    cout << "  combinations of 90-degree rotations around x, y and z" << endl;

    for (int x1 = 0; x1 < 3; ++x1)
    {
	V3f axis1 (0, 0, 0);
	axis1[x1] = 1;

	for (int n1 = 0; n1 < 4; ++n1)
	{
	    float angle1 = n1 * M_PI / 2;

	    Quatf q1;
	    q1.setAxisAngle (axis1, angle1);

	    for (int x2 = 0; x2 < 3; ++x2)
	    {
		V3f axis2 (0, 0, 0);
		axis2[x2] = 1;

		for (int n2 = 0; n2 < 4; ++n2)
		{
		    float angle2 = n2 * M_PI / 2;

		    Quatf q2;
		    q2.setAxisAngle (axis2, angle2);

		    testSlerp (q1, q2);
		    testSlerp (-q1, -q2);

		    if ((q1 ^ q2) < 0.99)
		    {
			testSlerp (q1, -q2);
			testSlerp (-q1, q2);
		    }
		}
	    }
	}
    }
}


void
randomRotations ()
{
    cout << "  random rotations" << endl;

    Rand48 rand (53);

    for (int i = 0; i < 10000; ++i)
    {
	V3f axis1 = hollowSphereRand<V3f> (rand);
	V3f axis2 = hollowSphereRand<V3f> (rand);
	float angle1 = rand.nextf (0, M_PI);
	float angle2 = rand.nextf (0, M_PI);

	Quatf q1, q2;
	q1.setAxisAngle (axis1, angle1);
	q2.setAxisAngle (axis2, angle2);

	testSlerp (q1, q2);
	testSlerp (-q1, -q2);

	if ((q1 ^ q2) < 0.99)
	{
	    testSlerp (q1, -q2);
	    testSlerp (-q1, q2);
	}
    }
}

} // namespace


void
testQuatSlerp ()
{
    cout << "Testing quaternion spherical linear interpolation" << endl;

    specificRotations();
    randomRotations();

    cout << "ok\n" << endl;
}