A question about the normal definition

[Riga2]

Hi, thanks for your nice work!

Since the normal is the reverse of the ray direction in the local Gaussian space, does this mean that when viewing the same Gaussian from different ray directions, the normals of the Gaussian also change?

Thank you again.

[niujinshuchong]

Hi, Yes. The normal depends on the ray direction.

[shewangmu]

Hi, Yes. The normal depends on the ray direction.

Thank you for your work. I have another question about the normal.
In gaussian coordinate system, the normal is parallel to the ray. When converting to the world space, just with some rotation, translation and scaling. Why are parallel rays no longer parallel?
In other words, the normalize process multiply Sk-1, why the inverse normalization process also multiply Sk-1 but not Sk?

[niujinshuchong]

Hi, please refer to Figure 3 in the paper. The normal is always perpendicular to the intersection plane. The inverse normalization should multiply S_k for the plane but the normal should be multiplied by S_k^-1

[Murnomous24]

Hi, please refer to Figure 3 in the paper. The normal is always perpendicular to the intersection plane. The inverse normalization should multiply S_k for the plane but the normal should be multiplied by S_k^-1

Thank you for your great work! But i want to ask that in your explanation, the point on plane of local coordinate system multiply S_{k} and R^{-1} to world space, so the normal of plane n_{i} should be -S_{k}^{-1}Rr_{g} ? I am confused about why n_{i} should be -S_{k}^{-1}R^{T}*r_{g}