Questions about caculate the highlight direction from spherical harmonics functions.

Recently I‘m working on a Precomputed GI Project



I'm trying to use a technique called AHD, Amibent Highlight Direction, rendering my project;

I use Unity and my target platform is Android.



First:

Unity SH is the result of Encoded and Scaled, I want to get the original SH

I'm trying try to decode it, but there are several problems with the sixth coefficient;

I found some documents that said unity moved the constant part of L6(band l = 2,order m = 0) to the L0(band l = 0, order m = 0), is that true?

If that's right, how can I get the right original SH?



There are some trying of myself, I have tried to calculate the constant part and recalculate the L0 and L6, but it seem not to be correct, in fact, I don't know how to verify it.

    #define k01 0.2820947918 // sqrt(  1/PI)/2



    #define k02 0.4886025119 // sqrt(  3/PI)/2



    #define k03 1.0925484306 // sqrt( 15/PI)/2



    #define k04 0.3153915652 // sqrt(  5/PI)/4



    #define k05 0.5462742153 // sqrt( 15/PI)/4



    float3 SampleRawSH9(float4 SHCoefficients[7], float3 N) {



        float3 n = N.zxy;



   



        float4 shAr = SHCoefficients[0];



        float4 shAg = SHCoefficients[1];



        float4 shAb = SHCoefficients[2];



        float4 shBr = SHCoefficients[3];



        float4 shBg = SHCoefficients[4];



        float4 shBb = SHCoefficients[5];



        float4 shCr = SHCoefficients[6];



   



        //band0



        //l0 + l6 constant part



        float3 L0 = float3(shAr.w, shAg.w, shAb.w);



        float3 L6c = -float3(shBr.z, shBg.z, shBb.z)* k04/4.;



        L6c = 0;



        L0 = (L0 - L6c) / k01;



   



        //band1



        //m=-1



        float3 L1 = float3(shAr.y * n.y, shAg.y * n.y, shAb.y * n.y);



        L1 = L1 * 1.5 / (-k02);



        //m=0



        float3 L2 = float3(shAr.z * n.z, shAg.z * n.z, shAb.z * n.z);



        L2 = L2 * 1.5 / (k02);



        //m=1



        float3 L3 = float3(shAr.x * n.x, shAg.x * n.x, shAb.x * n.x);



        L3 = L3 * 1.5 / (-k02);



   



        //band2



        //m=-2



        float3 L4 = float3(shBr.x * n.x * n.y, shBg.x * n.x * n.y, shBb.x * n.x * n.y);



        L4 = L4 * 4. / (k03);



        //m=-1



        float3 L5 = float3(shBr.y * n.y * n.z, shBg.y * n.y * n.z, shBb.y * n.y * n.z);



        L5 = L5 * 4. / (-k03);



        //m=0



        float3 L6cos = float3(shBr.z * n.z * n.z, shBg.z * n.z * n.z, shBb.z * n.z * n.z);



        float3 L6 = L6cos * 4. / (k04 * 3.0) + L6c * 4. / (k04);



        //m=1



        float3 L7 = float3(shBr.w * n.x * n.z, shBg.w * n.x * n.z, shBb.w * n.x * n.z);



        L7 = L7 * 4. / (-k03);



        //m=2



        float3 L8 = shCr.rgb * (n.x * n.x - n.y * n.y);



        L8 = L8 * 4. / (k05);



   



        return L0 + L1 + L2 + L3 + L4 + L5 + L6 + L7 + L8;



    }

Second:

I try to rebuild my AHD from SH.

I'm confused with amibentColor part. Does it contain the part of Directional Light Diffuse term?

The results look strange;

Same as the previous one, I still can't verify the correctness of my calculation

    void SampleRawSHAHD(float3 normalWS, out float highLightFactor, out float3 highLightDir, out float3 highLightColor, out float3 ambientColor) {



            real4 SHCoefficients[7];



            SHCoefficients[0] = unity_SHAr;



            SHCoefficients[1] = unity_SHAg;



            SHCoefficients[2] = unity_SHAb;



            SHCoefficients[3] = unity_SHBr;



            SHCoefficients[4] = unity_SHBg;



            SHCoefficients[5] = unity_SHBb;



            SHCoefficients[6] = unity_SHC;



   



            highLightDir = SampleRawSHDir(SHCoefficients, normalWS);



            highLightFactor = length(highLightDir) * PI * 16 / 17;



            highLightDir = normalize(highLightDir);



            highLightColor = highLightFactor * SampleRawSH(highLightDir) * 867. / (316. * PI);



            ambientColor = (SampleRawSH(0) - highLightColor * 8. * sqrt(PI) / 17.) * sqrt(PI) / 2.;



    }

I really appreciate someone who can give me some guidance!



My reference：



https://www.ppsloan.org/publications/StupidSH36.pdf

http://graphics.stanford.edu/papers/envmap/envmap.pdf