# DirectXMath vector operations precision

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Hello.

I'm having strange results of XMVector3AngleBetweenVectors function. Consider this code:

float angle = XMConvertToDegrees(XMVectorGetX(
XMVector3AngleBetweenVectors(GMathFV(XMFLOAT3(0.0f, 100.0f, 0.0f)),
GMathFV(XMFLOAT3(0.0f, 200.0f, 0.0f)))));


It's looking for angle between two 3D vectors, described by XMFLOAT3 structures. GMathFV is user-defined function which converts XMFLOAT3 to XMVECTOR as follows:

inline XMVECTOR GMathFV(XMFLOAT3& val)
{
}


Everything else is directxmath.h library. Here everything is fine and result angle is 0.00000 just as expected.

But for other vectors with negative y-axis value, for example:

float angle = XMConvertToDegrees(XMVectorGetX(
XMVector3AngleBetweenVectors(GMathFV(XMFLOAT3(0.0f, -100.0f, 0.0f)),
GMathFV(XMFLOAT3(0.0f, -99.0f, 0.0f)))));


Result is 0.0197823402, which I can hardly call a zero angle.

Please someone help me figure out the problem. Is it negative number precision, too close vector coordinates or maybe something else?

UPD: It's very strange, because it gives 0.0197823402 for a(0.0f, 100.0f, 0.0f) x b(0.0f, 99.0f, 0.0f), but 0.000000 for a(0.0f, 101.0f, 0.0f) x b(0.0f, 100.0f, 0.0f)

Edited by GuardianX

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When you want to find the angle, make sure that your vector are normalize first. Otherwise you will need to divide each vector by it's length first, which is the same as normalizing them.

Edited by BornToCode

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When you want to find the angle, make sure that your vector are normalize first. Otherwise you will need to divide each vector by it's length first, which is the same as normalizing them.

Wow, thank you! It looks like working now. But it doesnt make any sense to me actually - why do they provide XMVector3AngleBetweenNormals then as separate function, if it's similar to XMVector3AngleBetweenVectors?

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All of code for DirectXMath is provided inline in the header files, so if you want to see what's going on then you only need to look. Here's what XMVector3AngleBetweenVectors looks like (partially cleaned up for readibility):

inline XMVECTOR XMVector3AngleBetweenVectors(FXMVECTOR V1, FXMVECTOR V2)
{
XMVECTOR L1 = XMVector3ReciprocalLength(V1);
XMVECTOR L2 = XMVector3ReciprocalLength(V2);

XMVECTOR Dot = XMVector3Dot(V1, V2);

L1 = XMVectorMultiply(L1, L2);

XMVECTOR CosAngle = XMVectorMultiply(Dot, L1);
CosAngle = XMVectorClamp(CosAngle, g_XMNegativeOne.v, g_XMOne.v);

return XMVectorACos(CosAngle);
}


So what they've done here is they compute 1/||V1|| * 1 / ||V2||, and then they multiply that with the result of the dot product. So basically you end up with 1/||V1|| * 1/||V2||  * ||V1|| * ||V2|| * cos(Angle), which simplifies out to just cos(Angle). Then they compute acos(cos(Angle)) to get the actual angle itself. I'm not entirely sure why they implemented it this way, since it would seem that you could start to run into precision problems as ||V1|| and ||V2|| get larger.

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The problem might be a floating point issue ...

for example there is no way of computing the value of (0.1) squared with binary numbers, you would expect the result (0.01) but that is not what happens, instead you get a value close to (0.01). The information is all on here:

http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems

Edited by ray_intellect

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The problem might also be Gimbal Lock

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