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Apply TranslationTransform on a matrix

Hongyi Zhao
Posted 3 years ago
POSTED BY: Hongyi Zhao
7 Replies
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Hongyi Zhao
Hongyi Zhao
Posted 3 years ago

Thank you Hans,

This is perhaps the most flexible and versatile solution to such problems.
POSTED BY: Hongyi Zhao
Hans Milton
Hans Milton
Posted 3 years ago

You could make your own Operator style function:

In[1]:= transTransform = OperatorApplied[#2 . (TranslationTransform[#1] // TransformationMatrix) &, {1, 2}];

In[2]:= vec = {1/8, 1/8, 1/8};
matrix = {{3/4, 5/8, 5/8, 0}, {5/8, 3/4, 5/8, 0}, {5/8, 5/8, 3/4, 0}, {0, 0, 0, 1}};

In[4]:= transTransform[vec][matrix]
Out[4]= {{3/4, 5/8, 5/8, 1/4}, {5/8, 3/4, 5/8, 1/4}, {5/8, 5/8, 3/4, 1/4}, {0, 0, 0, 1}}
POSTED BY: Hans Milton
Eric Rimbey
Eric Rimbey
Posted 3 years ago

I don't know. I don't know what the "obvious geometric meaning" is.
POSTED BY: Eric Rimbey
Hongyi Zhao
Hongyi Zhao
Posted 3 years ago

I mean something similar to the following:

TranslationTransform[vec][matrix]

If TranslationTransform can not do this due to its working mechanism in design, are there other similar commands that can do this?
POSTED BY: Hongyi Zhao
Eric Rimbey
Eric Rimbey
Posted 3 years ago

apply the translation transformation as an operator function on the matrix

If what you mean by this is that you want to specifically use the symbol TranslationTransform, then I don't think this is possible, at least not in any straightforward way. Maybe I'm missing something, and maybe someone with more expertise can correct me, but from what I think I understand right now, that's just not how TranslationTransform works, and that's by design.
POSTED BY: Eric Rimbey
Hongyi Zhao
Hongyi Zhao
Posted 3 years ago

My goal is to find a way to apply the translation transformation as an operator function on the matrix, so that the calculation process has obvious geometric meaning and can be understood intuitively.
POSTED BY: Hongyi Zhao
Eric Rimbey
Eric Rimbey
Posted 3 years ago

I don't think TranslationTransform operates on matrices per se. It operates on nested lists by operating on the low-level elements of the list that have the right "structure" for the dimensions of the given translation parameter. So, in your case, it's just being applied to each 4-element list in the bigger list.
POSTED BY: Eric Rimbey
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