DirectXMath vector operations precision

Graphics and GPU Programming Programming

Started by iskatsu February 11, 2013 01:21 PM

4 comments, last by ray_intellect 11 years, 2 months ago

iskatsu

1,587

Author

February 11, 2013 01:21 PM

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)
{
    return XMLoadFloat3(&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)

BornToCode

1,185

February 11, 2013 05:42 PM

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.

iskatsu

1,587

Author

February 11, 2013 06:20 PM

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?

MJP

20,295

February 11, 2013 09:37 PM

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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ray_intellect

254

February 13, 2013 04:33 AM

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

ray_intellect

254

February 13, 2013 10:42 PM

The problem might also be Gimbal Lock

DirectXMath vector operations precision

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