///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2007, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
//
// All rights reserved.
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///////////////////////////////////////////////////////////////////////////
#include <testQuat.h>
#include "ImathQuat.h"
#include "ImathMatrixAlgo.h"
#include "ImathFun.h"
#include "ImathLimits.h"
#include "ImathPlatform.h" /* [i_a] M_PI_2 */
#include <iostream>
#include <cassert>
#include <cmath>
using namespace std;
using namespace IMATH_INTERNAL_NAMESPACE;
namespace {
template <class T>
void
testQuatT ()
{
const T s = limits<T>::smallest();
const T e = 4 * limits<T>::epsilon();
//
// constructors, r(), v()
//
{
Quat<T> q = Quat<T>();
assert (q.r == 1 && q.v == Vec3<T> (0, 0, 0));
q = Quat<T> (2, 3, 4, 5);
assert (q.r == 2 && q.v == Vec3<T> (3, 4, 5));
q = Quat<T> (6, Vec3<T> (7, 8, 9));
assert (q.r == 6 && q.v == Vec3<T> (7, 8, 9));
Quat<T> q1 = Quat<T> (q);
assert (q1.r == 6 && q1.v == Vec3<T> (7, 8, 9));
}
//
// invert(), inverse()
//
{
Quat<T> q = Quat<T> (1, 0, 0, 1);
assert (q.inverse() == Quat<T> (0.5, 0, 0, -0.5));
q.invert();
assert (q == Quat<T> (0.5, 0, 0, -0.5));
}
//
// normalize(), normalized()
//
{
Quat<T> q = Quat<T> (2, Vec3<T> (0, 0, 0));
assert (q.normalized() == Quat<T> (1, 0, 0, 0));
q.normalize();
assert (q == Quat<T> (1, 0, 0, 0));
q = Quat<T> (0, Vec3<T> (0, 2, 0));
assert (q.normalized() == Quat<T> (0, 0, 1, 0));
q.normalize();
assert (q == Quat<T> (0, 0, 1, 0));
}
//
// length()
//
{
Quat<T> q = Quat<T> (3, 0, 4, 0);
assert (q.length() == 5);
}
//
// setAxisAngle(), angle(), axis()
//
{
Quat<T> q;
q.setAxisAngle (Vec3<T> (0, 0, 1), M_PI_2);
Vec3<T> v = q.axis();
T a = q.angle();
assert (v.equalWithAbsError (Vec3<T> (0, 0, 1), e));
assert (IMATH_INTERNAL_NAMESPACE::equal (a, T (M_PI_2), e));
}
//
// Accuracy of angle() for very small angles
// and when real part is slightly greater than 1.
//
{
T t = 10 * Math<T>::sqrt (s);
Quat<T> q;
q.setAxisAngle (Vec3<T> (0, 0, 1), t);
Vec3<T> v = q.axis();
T a = q.angle();
assert (v.equalWithAbsError (Vec3<T> (0, 0, 1), e));
assert (IMATH_INTERNAL_NAMESPACE::equal (a, t, t * e));
q.r *= 1.1;
q.v *= 1.1;
v = q.axis();
a = q.angle();
assert (v.equalWithAbsError (Vec3<T> (0, 0, 1), e));
assert (IMATH_INTERNAL_NAMESPACE::equal (a, t, t * e));
}
{
T t = 0.001 * Math<T>::sqrt (s);
Quat<T> q;
q.setAxisAngle (Vec3<T> (0, 0, 1), t);
Vec3<T> v = q.axis();
T a = q.angle();
assert (v.equalWithAbsError (Vec3<T> (0, 0, 1), e));
assert (IMATH_INTERNAL_NAMESPACE::equal (a, t, t * e));
q.r *= 1.1;
q.v *= 1.1;
v = q.axis();
a = q.angle();
assert (v.equalWithAbsError (Vec3<T> (0, 0, 1), e));
assert (IMATH_INTERNAL_NAMESPACE::equal (a, t, t * e));
}
//
// toMatrix33(), toMatrix44()
//
{
Quat<T> q;
q.setRotation (Vec3<T> (1, 0, 0), Vec3<T> (0, 1, 0));
Matrix33<T> m1 = q.toMatrix33();
assert (m1.equalWithAbsError (Matrix33<T> (0, 1, 0,
-1, 0, 0,
0, 0, 1),
e));
Matrix44<T> m2 = q.toMatrix44();
assert (m2.equalWithAbsError (Matrix44<T> (0, 1, 0, 0,
-1, 0, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1),
e));
}
//
// +, - (unary and binary), ~ *, /, ^
//
assert (Quat<T> (1, 2, 3, 4) + Quat<T> (5, 6, 7, 8) ==
Quat<T> (6, 8, 10, 12));
assert (Quat<T> (-1, -2, -3, -4) - Quat<T> (5, 6, 7, 8) ==
Quat<T> (-6, -8, -10, -12));
assert (-Quat<T> (1, 2, 3, 4) == Quat<T> (-1, -2, -3, -4));
assert (~Quat<T> (1, 2, 3, 4) == Quat<T> (1, -2, -3, -4));
assert (T (2) * Quat<T> (1, 2, 3, 4) == Quat<T> (2, 4, 6, 8));
assert (Quat<T> (1, 2, 3, 4) * T (2 )== Quat<T> (2, 4, 6, 8));
assert (Quat<T> (1, 0, 0, 1) * Quat<T> (1, 1, 0, 0) ==
Quat<T> (1, 1, 1, 1));
assert (Quat<T> (1, 1, 0, 0) * Quat<T> (1, 0, 0, 1) ==
Quat<T> (1, 1, -1, 1));
assert (Quat<T> (1, 0, 0, 1) / Quat<T> (0.5, -0.5, 0, 0) ==
Quat<T> (1, 1, 1, 1));
assert (Quat<T> (2, 4, 6, 8) / T (2) == Quat<T> (1, 2, 3, 4));
assert ((Quat<T> (1, 2, 3, 4) ^ Quat<T> (2, 2, 2, 2)) == 20);
//
// extract()
//
{
Vec3<T> vFrom (1, 0, 0);
Vec3<T> vTo (0, 1, 1);
Matrix44<T> m1 = rotationMatrix (vFrom, vTo);
Quat<T> q = extractQuat (m1);;
Matrix44<T> m2 = q.toMatrix44();
assert (m2.equalWithAbsError (m1, 2 * e));
}
}
void
testQuatConversions ()
{
{
Quatf q (1, V3f (2, 3, 4));
Quatd q1 = Quatd (q);
assert (q1.r == 1 && q1.v == V3d (2, 3, 4));
}
{
Quatd q (1, V3d (2, 3, 4));
Quatf q1 = Quatf (q);
assert (q1.r == 1 && q1.v == V3f (2, 3, 4));
}
}
} // namespace
void
testQuat ()
{
cout << "Testing basic quaternion operations" << endl;
testQuatT<float>();
testQuatT<double>();
testQuatConversions();
cout << "ok\n" << endl;
}