From: Mathias Froehlich Date: Mon, 17 May 2010 21:13:59 +0000 (+0200) Subject: Add a tight and cheap method to represent a rotation. X-Git-Url: https://git.mxchange.org/?a=commitdiff_plain;h=f161f78a33b175ff0241688c276ba18c5ba9dd7b;p=simgear.git Add a tight and cheap method to represent a rotation. Adapt tests for that new method. --- diff --git a/simgear/math/SGMathTest.cxx b/simgear/math/SGMathTest.cxx index aeedc7a9..010f9995 100644 --- a/simgear/math/SGMathTest.cxx +++ b/simgear/math/SGMathTest.cxx @@ -79,6 +79,22 @@ Vec3Test(void) return true; } +template +bool +isSameRotation(const SGQuat& q1, const SGQuat& q2) +{ + const SGVec3 e1(1, 0, 0); + const SGVec3 e2(0, 1, 0); + const SGVec3 e3(0, 0, 1); + if (!equivalent(q1.transform(e1), q2.transform(e1))) + return false; + if (!equivalent(q1.transform(e2), q2.transform(e2))) + return false; + if (!equivalent(q1.transform(e3), q2.transform(e3))) + return false; + return true; +} + template bool QuatTest(void) @@ -94,7 +110,7 @@ QuatTest(void) v2 = SGVec3(1, -2, -3); if (!equivalent(q1.transform(v1), v2)) return false; - + // Check a rotation around the x axis q1 = SGQuat::fromAngleAxis(0.5*SGMisc::pi(), e1); v2 = SGVec3(1, 3, -2); @@ -106,7 +122,7 @@ QuatTest(void) v2 = SGVec3(-1, 2, -3); if (!equivalent(q1.transform(v1), v2)) return false; - + // Check a rotation around the y axis q1 = SGQuat::fromAngleAxis(0.5*SGMisc::pi(), e2); v2 = SGVec3(-3, 2, 1); @@ -153,15 +169,32 @@ QuatTest(void) SGVec3 angleAxis; q1.getAngleAxis(angleAxis); q4 = SGQuat::fromAngleAxis(angleAxis); - if (!equivalent(q1, q4)) + if (!isSameRotation(q1, q4)) return false; q2.getAngleAxis(angleAxis); q4 = SGQuat::fromAngleAxis(angleAxis); - if (!equivalent(q2, q4)) + if (!isSameRotation(q2, q4)) return false; q3.getAngleAxis(angleAxis); q4 = SGQuat::fromAngleAxis(angleAxis); - if (!equivalent(q3, q4)) + if (!isSameRotation(q3, q4)) + return false; + + /// Test angle axis forward and back transform + q1 = SGQuat::fromAngleAxis(0.2*SGMisc::pi(), e1); + q2 = SGQuat::fromAngleAxis(1.7*SGMisc::pi(), e2); + q3 = q1*q2; + SGVec3 positiveAngleAxis = q1.getPositiveRealImag(); + q4 = SGQuat::fromPositiveRealImag(positiveAngleAxis); + if (!isSameRotation(q1, q4)) + return false; + positiveAngleAxis = q2.getPositiveRealImag(); + q4 = SGQuat::fromPositiveRealImag(positiveAngleAxis); + if (!isSameRotation(q2, q4)) + return false; + positiveAngleAxis = q3.getPositiveRealImag(); + q4 = SGQuat::fromPositiveRealImag(positiveAngleAxis); + if (!isSameRotation(q3, q4)) return false; return true; @@ -204,7 +237,7 @@ MatrixTest(void) return false; if (!equivalent(m3*m0, SGMatrix::unit())) return false; - + return true; } @@ -241,105 +274,6 @@ GeodesyTest(void) return true; } - -bool -sgInterfaceTest(void) -{ - SGVec3f v3f = SGVec3f::e2(); - SGVec4f v4f = SGVec4f::e2(); - SGQuatf qf = SGQuatf::fromEulerRad(1.2, 1.3, -0.4); - SGMatrixf mf; - mf.postMultTranslate(v3f); - mf.postMultRotate(qf); - - // Copy to and from plibs types check if result is equal, - // test for exact equality - SGVec3f tv3f; - sgVec3 sv3f; - sgCopyVec3(sv3f, v3f.sg()); - sgCopyVec3(tv3f.sg(), sv3f); - if (tv3f != v3f) - return false; - - // Copy to and from plibs types check if result is equal, - // test for exact equality - SGVec4f tv4f; - sgVec4 sv4f; - sgCopyVec4(sv4f, v4f.sg()); - sgCopyVec4(tv4f.sg(), sv4f); - if (tv4f != v4f) - return false; - - // Copy to and from plibs types check if result is equal, - // test for exact equality - SGQuatf tqf; - sgQuat sqf; - sgCopyQuat(sqf, qf.sg()); - sgCopyQuat(tqf.sg(), sqf); - if (tqf != qf) - return false; - - // Copy to and from plibs types check if result is equal, - // test for exact equality - SGMatrixf tmf; - sgMat4 smf; - sgCopyMat4(smf, mf.sg()); - sgCopyMat4(tmf.sg(), smf); - if (tmf != mf) - return false; - - return true; -} - -bool -sgdInterfaceTest(void) -{ - SGVec3d v3d = SGVec3d::e2(); - SGVec4d v4d = SGVec4d::e2(); - SGQuatd qd = SGQuatd::fromEulerRad(1.2, 1.3, -0.4); - SGMatrixd md; - md.postMultTranslate(v3d); - md.postMultRotate(qd); - - // Copy to and from plibs types check if result is equal, - // test for exact equality - SGVec3d tv3d; - sgdVec3 sv3d; - sgdCopyVec3(sv3d, v3d.sg()); - sgdCopyVec3(tv3d.sg(), sv3d); - if (tv3d != v3d) - return false; - - // Copy to and from plibs types check if result is equal, - // test for exact equality - SGVec4d tv4d; - sgdVec4 sv4d; - sgdCopyVec4(sv4d, v4d.sg()); - sgdCopyVec4(tv4d.sg(), sv4d); - if (tv4d != v4d) - return false; - - // Copy to and from plibs types check if result is equal, - // test for exact equality - SGQuatd tqd; - sgdQuat sqd; - sgdCopyQuat(sqd, qd.sg()); - sgdCopyQuat(tqd.sg(), sqd); - if (tqd != qd) - return false; - - // Copy to and from plibs types check if result is equal, - // test for exact equality - SGMatrixd tmd; - sgdMat4 smd; - sgdCopyMat4(smd, md.sg()); - sgdCopyMat4(tmd.sg(), smd); - if (tmd != md) - return false; - - return true; -} - int main(void) { @@ -365,12 +299,6 @@ main(void) if (!GeodesyTest()) return EXIT_FAILURE; - // Check interaction with sg*/sgd* - if (!sgInterfaceTest()) - return EXIT_FAILURE; - if (!sgdInterfaceTest()) - return EXIT_FAILURE; - std::cout << "Successfully passed all tests!" << std::endl; return EXIT_SUCCESS; } diff --git a/simgear/math/SGQuat.hxx b/simgear/math/SGQuat.hxx index a48cbf1a..256ddb28 100644 --- a/simgear/math/SGQuat.hxx +++ b/simgear/math/SGQuat.hxx @@ -150,6 +150,17 @@ public: return fromRealImag(cos(angle2), T(sin(angle2)/nAxis)*axis); } + /// Create a normalized quaternion just from the imaginary part. + /// The imaginary part should point into that axis direction that results in + /// a quaternion with a positive real part. + /// This is the smallest numerically stable representation of an orientation + /// in space. See getPositiveRealImag() + static SGQuat fromPositiveRealImag(const SGVec3& imag) + { + T r = sqrt(SGMisc::max(T(0), T(1) - dot(imag, imag))); + return fromRealImag(r, imag); + } + /// Return a quaternion that rotates the from vector onto the to vector. static SGQuat fromRotateTo(const SGVec3& from, const SGVec3& to) { @@ -326,6 +337,19 @@ public: axis *= angle; } + /// Get the imaginary part of the quaternion. + /// The imaginary part should point into that axis direction that results in + /// a quaternion with a positive real part. + /// This is the smallest numerically stable representation of an orientation + /// in space. See fromPositiveRealImag() + SGVec3 getPositiveRealImag() const + { + if (real(*this) < T(0)) + return (T(-1)/norm(*this))*imag(*this); + else + return (T(1)/norm(*this))*imag(*this); + } + /// Access by index, the index is unchecked const T& operator()(unsigned i) const { return data()[i]; }