| Tl;dr: What is the universal name for [FONT=MathJax_Math-italic]C[/FONT] when comparing two transformations in [FONT=MathJax_Math-italic]C[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]B[/FONT][FONT=MathJax_Main]∗[/FONT][FONT=MathJax_Math-italic]A[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1[/FONT], assuming C is a transformation itself? I'm looking into comparing two transformations and extract a transformation that allows me to go from one to the other. But I don't know what to call this. In 3D graphics I see the word "delta" used a lot to mean a difference of position of vectors. So the delta from position [FONT=MathJax_Math-italic]A[/FONT] to position [FONT=MathJax_Math-italic]B[/FONT] is the vector [FONT=MathJax_Math-italic]A[/FONT][FONT=MathJax_Math-italic]B[/FONT]obtained through [FONT=MathJax_Math-italic]B[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]A[/FONT]. But this is a comparison of an additive property to used for Translation. What if, instead I compare two positions to extract a Scaling transformation between them? The "difference" (?) is not additive but multiplicative. Assuming two co-linear vectors, the Scaling to be applied to position [FONT=MathJax_Math-italic]A[/FONT] to become position [FONT=MathJax_Math-italic]B[/FONT] is like asking the question: "If position [FONT=MathJax_Math-italic]A[/FONT] were to be the multiplicative identity instead of [FONT=MathJax_Main]1[/FONT], how much would [FONT=MathJax_Math-italic]B[/FONT] be?". Which is obtained with [FONT=MathJax_Math-italic]B[/FONT][FONT=MathJax_Main]/[/FONT][FONT=MathJax_Math-italic]A[/FONT]. And the same can be applied to a "pack" of transformations like a Matrix. So I like to think about these as looking to one matrix from the "spacial context" (?) of another matrix, instead of the default identity, correct? If I put matrix [FONT=MathJax_Math-italic]B[/FONT] in the context of matrix [FONT=MathJax_Math-italic]A[/FONT] I do something like [FONT=MathJax_Math-italic]C[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]A^[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1 . [/FONT][FONT=MathJax_Math-italic]B[/FONT]. What do I call [FONT=MathJax_Math-italic]C[/FONT] then? The matrix delta? Or is there another better suited universal name for these type of transformations comparison and extraction of the difference (which is a transformation itself)?[FONT=MathJax_Main] [/FONT]Thanks a lot! |
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