Optimize orthonormal basis generation using Pixar 2017 method

[RohithPariki]

Resolves upstream issue #73.

Implemented XMVector3OrthogonalBasis utilizing the Pixar 2017 method ("Building an Orthonormal Basis, Revisited" by Duff et al.) to compute a tangent and bitangent from a unit normal. This ensures numeric stability across all edge cases (particularly along the Z-axis, which causes singularities in naive cross-product derivations) while remaining branchless.

changes:

• Added XMVector3OrthogonalBasis to DirectXMath.h
• Implemented XMVector3OrthogonalBasis in DirectXMathVector.inl
• Maintained scalar compatibility with #if defined(_XM_NO_INTRINSICS_)
• Optimized SIMD intrinsic execution pathway (reusing vectors and leveraging XMVectorAndInt/XMVectorOrInt for fast copysign replacement).

how i verified.

I verified the implementation by writing a test script against the critical edge cases (vectors perfectly aligned with the axes, which often cause singularities in branchless ONB generation).

#include <iostream>
#include <DirectXMath.h>
using namespace DirectX;

void VerifyONB(float x, float y, float z) {
    XMVECTOR N = XMVectorSet(x, y, z, 0);
    XMVECTOR T, B;
    
    // Generate Orthogonal Basis
    XMVector3OrthogonalBasis(&T, &B, N);
    
    // Verify Orthogonality
    float dot_NT = XMVectorGetX(XMVector3Dot(N, T));
    float dot_NB = XMVectorGetX(XMVector3Dot(N, B));
    float dot_TB = XMVectorGetX(XMVector3Dot(T, B));
    
    XMFLOAT4 nf, tf, bf;
    XMStoreFloat4(&nf, N); XMStoreFloat4(&tf, T); XMStoreFloat4(&bf, B);
    
    std::cout << "Normal: (" << nf.x << ", " << nf.y << ", " << nf.z << ")\n";
    std::cout << "Tangent: (" << tf.x << ", " << tf.y << ", " << tf.z << ")\n";
    std::cout << "Bitangent: (" << bf.x << ", " << bf.y << ", " << bf.z << ")\n";
    std::cout << "Verification [N.T, N.B, T.B]: " << dot_NT << ", " << dot_NB << ", " << dot_TB << "\n\n";
}

int main() {
    VerifyONB(0, 0, 1);
    VerifyONB(0, 0, -1);
    VerifyONB(1, 0, 0);
    VerifyONB(0.57735f, 0.57735f, 0.57735f); // Arbitrary unit vector
    return 0;
}

the output :

Normal: (0, 0, 1)
Tangent: (1, -0, -0)
Bitangent: (-0, 1, -0)
Verification [N.T, N.B, T.B]: 0, 0, 0

Normal: (0, 0, -1)
Tangent: (1, -0, 0)
Bitangent: (0, -1, -0)
Verification [N.T, N.B, T.B]: 0, 0, 0

Normal: (1, 0, 0)
Tangent: (0, -0, -1)
Bitangent: (-0, 1, -0)
Verification [N.T, N.B, T.B]: 0, 0, 0

Normal: (0.57735, 0.57735, 0.57735)
Tangent: (0.788675, -0.211325, -0.57735)
Bitangent: (-0.211325, 0.788675, -0.57735)
Verification [N.T, N.B, T.B]: 3.35524e-07, 3.35524e-07, -1.10278e-07

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[walbourn]

Should this be if (pTangent) { *pTangen t==...} so the parameter can be _Out_opt_?

[walbourn]

Might have to investigate how far back copysignf can be found in MSVC. There are some compilation scenarios for DirectXMath that may require a different solution.