Orthonormal bases can be constructed using Gram-Schmidt, but how are examples of Fourier bases found such that in addition to the orthonormal constraint there is the property of having a notion of different frequencies/being able to capture various granularities of approximation as you take into account the higher and higher frequencies?
Koke_Cacao
Frequency encoding appears a lot in many papers. For example: https://bmild.github.io/fourfeat/index.html
Also, spherical harmonics are just Fourier encodings on spherical functions. It allows us to use less space when storing spherical functions that might be useful in, for example, representing irradiance from a point. Can you think of other usages in CG?
elouie2
In which assignments are we going to be using this method?
jesshuifeng
Are there any other places we can use Fourier decompositions in CG? And how?
Orthonormal bases can be constructed using Gram-Schmidt, but how are examples of Fourier bases found such that in addition to the orthonormal constraint there is the property of having a notion of different frequencies/being able to capture various granularities of approximation as you take into account the higher and higher frequencies?
Frequency encoding appears a lot in many papers. For example: https://bmild.github.io/fourfeat/index.html
Also, spherical harmonics are just Fourier encodings on spherical functions. It allows us to use less space when storing spherical functions that might be useful in, for example, representing irradiance from a point. Can you think of other usages in CG?
In which assignments are we going to be using this method?
Are there any other places we can use Fourier decompositions in CG? And how?
Very interesting