# How to convert DirectX Quaternion to Euler Angles?

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I have a question about Quaternion.

My Direct 3D animation system is using Quaternion as rotation data. and sampling method of rotation is Slerp that quaternion optimized algorithm. but sometimes Slerp is not best way so I needed to convert Quaternion to Euler Angles for to perform Lerp. Thus I was searched many algorithms that to convert Quaternion to Euler Angles but they were all wrong. so now I'm posting here.

I'm using DirectX 11 and XNA Math library (June 2010). The algorithm that assemble an quaternion with euler angles in XNA Math is like below.

XMFINLINE XMVECTOR XMQuaternionRotationRollPitchYawFromVector
(
FXMVECTOR Angles // <Pitch, Yaw, Roll, 0>
)
{
#if defined(_XM_NO_INTRINSICS_)

XMVECTOR                Q, Q0, Q1;
XMVECTOR                P0, P1, Y0, Y1, R0, R1;
XMVECTOR                HalfAngles;
XMVECTOR                SinAngles, CosAngles;
static CONST XMVECTORU32 ControlPitch = {XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1X, XM_PERMUTE_1X};
static CONST XMVECTORU32 ControlYaw = {XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Y};
static CONST XMVECTORU32 ControlRoll = {XM_PERMUTE_1Z, XM_PERMUTE_1Z, XM_PERMUTE_0Z, XM_PERMUTE_1Z};
static CONST XMVECTOR   Sign = {1.0f, -1.0f, -1.0f, 1.0f};

HalfAngles = XMVectorMultiply(Angles, g_XMOneHalf.v);
XMVectorSinCos(&SinAngles, &CosAngles, HalfAngles);

P0 = XMVectorPermute(SinAngles, CosAngles, ControlPitch.v);
Y0 = XMVectorPermute(SinAngles, CosAngles, ControlYaw.v);
R0 = XMVectorPermute(SinAngles, CosAngles, ControlRoll.v);
P1 = XMVectorPermute(CosAngles, SinAngles, ControlPitch.v);
Y1 = XMVectorPermute(CosAngles, SinAngles, ControlYaw.v);
R1 = XMVectorPermute(CosAngles, SinAngles, ControlRoll.v);

Q1 = XMVectorMultiply(P1, Sign);
Q0 = XMVectorMultiply(P0, Y0);
Q1 = XMVectorMultiply(Q1, Y1);
Q0 = XMVectorMultiply(Q0, R0);

return Q;

#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR                Q, Q0, Q1;
XMVECTOR                P0, P1, Y0, Y1, R0, R1;
XMVECTOR                HalfAngles;
XMVECTOR                SinAngles, CosAngles;
static CONST XMVECTORI32 ControlPitch = {XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1X, XM_PERMUTE_1X};
static CONST XMVECTORI32 ControlYaw = {XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Y};
static CONST XMVECTORI32 ControlRoll = {XM_PERMUTE_1Z, XM_PERMUTE_1Z, XM_PERMUTE_0Z, XM_PERMUTE_1Z};
static CONST XMVECTORF32 Sign = {1.0f, -1.0f, -1.0f, 1.0f};

HalfAngles = _mm_mul_ps(Angles, g_XMOneHalf);
XMVectorSinCos(&SinAngles, &CosAngles, HalfAngles);

P0 = XMVectorPermute(SinAngles, CosAngles, ControlPitch);
Y0 = XMVectorPermute(SinAngles, CosAngles, ControlYaw);
R0 = XMVectorPermute(SinAngles, CosAngles, ControlRoll);
P1 = XMVectorPermute(CosAngles, SinAngles, ControlPitch);
Y1 = XMVectorPermute(CosAngles, SinAngles, ControlYaw);
R1 = XMVectorPermute(CosAngles, SinAngles, ControlRoll);

Q1 = _mm_mul_ps(P1, Sign);
Q0 = _mm_mul_ps(P0, Y0);
Q1 = _mm_mul_ps(Q1, Y1);
Q0 = _mm_mul_ps(Q0, R0);
Q = _mm_mul_ps(Q1, R1);
return Q;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}



Final result is

x = cos(Pitch/2) sin(Yaw/2) sin(Roll/2) + sin(Pitch/2) cos(Yaw/2) cos(Roll/2)
y = cos(Pitch/2) sin(Yaw/2) cos(Roll/2) - sin(Pitch/2) cos(Yaw/2) sin(Roll/2)
z = cos(Pitch/2) cos(Yaw/2) sin(Roll/2) - sin(Pitch/2) sin(Yaw/2) cos(Roll/2)
w = cos(Pitch/2) cos(Yaw/2) cos(Roll/2) + sin(Pitch/2) sin(Yaw/2) sin(Roll/2)



I tried many codes but did not work.

pitchYawRoll.y = atan2(2.0f * x * w + 2.0f * y * z, 1.0f - 2.0f * (sqz + sqw));
pitchYawRoll.x = asin(2.0f * (x * z - w * y));
pitchYawRoll.z = atan2(2.0f * x * y + 2.0f * z * w, 1.0f - 2.0f * (sqy + sqz));

pitchYawRoll.x = atan2(2.0f * (y * z + x * w), (-sqx - sqy + sqz + sqw));
pitchYawRoll.y = asin(-2.0f * (x * z - y * w));
pitchYawRoll.z = atan2(2.0f * (x * y + z * w), (sqx - sqy - sqz + sqw));

pitchYawRoll.x = asin(2.0f * (w * x - y * z));
pitchYawRoll.y = atan2(2.0f * (x * z + y * w), (-sqx - sqy + sqz + sqw));
pitchYawRoll.z = atan2(2.0f * (x * y + z * w), (-sqx + sqy - sqz + sqw));


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Hi.

does xna math not have this function

D3DXQuaternionToAxisAngle(
CONST D3DXQUATERNION *pQ,
D3DXVECTOR3 *pAxis,
FLOAT *pAngle

and maybe your animation is wrong.???????

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Oh yes, maybe that function can solve this problem.

Thanks.

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