hmm :)
yuppp do i need to get in to harmonics functions calculation right now, maybe tomorrow but not today:)
just using its fourier like ortonormal basis situation to do convolution fastly is enough now:)
so this is all we have in maths i wonder.
about orthonormality. for to use in faster convolution or as a model tool that models a function very nicely with intended level of detail and also enables very fast convolution on it.
what i would say is: remembering number theory knowledge, i think that side might create a new form of fourier way. should reread number theory to remember that but what firstly came up to my mind is those type of things.
anyway lets continue maths study tomorrow night.
but lets code the seed of my game engine today:)
what also queries my mind: if we think a matrice's rows from 0 to nth row for a m columns holding matrice, if we store as if its a time series from 0th to nth row for m column vectors as SH (in m dimensional space) thats compressed could we compress matrices like that? or multiply two matrices usingsuch compressed forms?
if thats correct, i might figured out a newer SVD method to such domain right now :P but if that were true, others would invented before me. something maybe faster than MF methods? (that guhu has invented with brainstorming on it. ? or imght my brainstorming be incorrect. but felt as might be correct. then yayyy i would be a new SVD method inventor:P but must others had done it before me if such method is possible i think.. i think variance based compression and compressing along such ways seems better for sure. so PCA or SVD like methods would be better. but shouldnt have it limit my brainstorming on this. if we bind similar selection criterion to dimensional compressing with SH based on variance, then SH would work also similarly good i think. how to compress a m dimensional vector of n rows have various ways for sure :) not simply PCA like things )
the SH and Fourier is such a lovely LOD mechanism :)
i always loved LOD concept in games. but seeing this SH based things, i saw the SH and Fourier's LOD mechanism is also lovely :)
if we do SH we add more dimensions to a vector but i think it could be also utilized to compress still and reduce necessary effort in any matrice multiplication.lets clarify the supposed methodology in my mind first. should i use SH in 3d or d dimensions. i think 3d dimension could be also utilized. ok method is not any clear in my own head so might be any not possible way and just an intuition thats incorrect. lets see.
anyway a new hobby goal added. brain storm on how to use SH as a way to do LOD in matrice or tensor multiplication. dot product of a d dimensional vector, v1 dot v2, can v1 and v2 reduced to lesser lod forms but still creating similar dot product value is the query to be investigated. how to put standard d dimensional vector dot product in such perspective. normally if we use as if those each dimension is that orthonormal basis's dimension with 1 to 1 mapping in hand, we have the normal as expected dot product with no compression nor gain from SH. hmm anyway to think on. i think its legit to put this as a braintorming area since might find out someway. ok everyroad goes to PCA in some brainstorming. but as told, there would be a brainstorming on this to be done still. LOD'ing for dot product. some area to be investigated. i figured out LOD is fun in any area, not limited to game engines. added as a fun side task for to brainstorm on this. but all initial brainstormings goes to variance based ways or PCA based ways initially. but shouldnt limit brainstorming to early results like that. might stuck in early results in the end and might say its not possible to do it in a differnt way. but right now at the beginning of this new side study i am. so nothing i could say initially.
---
i
cant stop thinking of cloth dynamics with some unrelated stuff. would check how people render cloth dynamics. secondarily. its tiny little bit relatedness to ising. thirdly, many other ways of gravitation center computations. that would learn aobut. though just this cloth dynamics is also very interesting topic i think. if i had some Anthem like characters, in their rendering of outfits' cloth parts.
yuppp do i need to get in to harmonics functions calculation right now, maybe tomorrow but not today:)
just using its fourier like ortonormal basis situation to do convolution fastly is enough now:)
so this is all we have in maths i wonder.
about orthonormality. for to use in faster convolution or as a model tool that models a function very nicely with intended level of detail and also enables very fast convolution on it.
what i would say is: remembering number theory knowledge, i think that side might create a new form of fourier way. should reread number theory to remember that but what firstly came up to my mind is those type of things.
anyway lets continue maths study tomorrow night.
but lets code the seed of my game engine today:)
what also queries my mind: if we think a matrice's rows from 0 to nth row for a m columns holding matrice, if we store as if its a time series from 0th to nth row for m column vectors as SH (in m dimensional space) thats compressed could we compress matrices like that? or multiply two matrices usingsuch compressed forms?
if thats correct, i might figured out a newer SVD method to such domain right now :P but if that were true, others would invented before me. something maybe faster than MF methods? (that guhu has invented with brainstorming on it. ? or imght my brainstorming be incorrect. but felt as might be correct. then yayyy i would be a new SVD method inventor:P but must others had done it before me if such method is possible i think.. i think variance based compression and compressing along such ways seems better for sure. so PCA or SVD like methods would be better. but shouldnt have it limit my brainstorming on this. if we bind similar selection criterion to dimensional compressing with SH based on variance, then SH would work also similarly good i think. how to compress a m dimensional vector of n rows have various ways for sure :) not simply PCA like things )
the SH and Fourier is such a lovely LOD mechanism :)
i always loved LOD concept in games. but seeing this SH based things, i saw the SH and Fourier's LOD mechanism is also lovely :)
if we do SH we add more dimensions to a vector but i think it could be also utilized to compress still and reduce necessary effort in any matrice multiplication.lets clarify the supposed methodology in my mind first. should i use SH in 3d or d dimensions. i think 3d dimension could be also utilized. ok method is not any clear in my own head so might be any not possible way and just an intuition thats incorrect. lets see.
anyway a new hobby goal added. brain storm on how to use SH as a way to do LOD in matrice or tensor multiplication. dot product of a d dimensional vector, v1 dot v2, can v1 and v2 reduced to lesser lod forms but still creating similar dot product value is the query to be investigated. how to put standard d dimensional vector dot product in such perspective. normally if we use as if those each dimension is that orthonormal basis's dimension with 1 to 1 mapping in hand, we have the normal as expected dot product with no compression nor gain from SH. hmm anyway to think on. i think its legit to put this as a braintorming area since might find out someway. ok everyroad goes to PCA in some brainstorming. but as told, there would be a brainstorming on this to be done still. LOD'ing for dot product. some area to be investigated. i figured out LOD is fun in any area, not limited to game engines. added as a fun side task for to brainstorm on this. but all initial brainstormings goes to variance based ways or PCA based ways initially. but shouldnt limit brainstorming to early results like that. might stuck in early results in the end and might say its not possible to do it in a differnt way. but right now at the beginning of this new side study i am. so nothing i could say initially.
---
i
cant stop thinking of cloth dynamics with some unrelated stuff. would check how people render cloth dynamics. secondarily. its tiny little bit relatedness to ising. thirdly, many other ways of gravitation center computations. that would learn aobut. though just this cloth dynamics is also very interesting topic i think. if i had some Anthem like characters, in their rendering of outfits' cloth parts.
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