So apparently what the book Real-Time Rendering means by “row-major” or “column-major” is not the same thing other sources mean when they use these words (sources like FGED, Game Engine Architecture, or Wikipedia). TLDR, row-major is not the same concept as row-vector convention.
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Yes, this still misses the distinction. You can still use column vectors but have row-major matrix storage, and the translation components are *not* in the last 4 elements of the matrix data structure. (Same for row vectors and column-major matrix storage.)
I haven’t read the latest RTR, but, storage considerations aside, is there a name for the convention that selects pre- or post-multiplication? I always see it explained longhand, as in “by convention we treat vectors as columns and multiply with the matrix on the left”
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I’m wondering that as well. The closest I’ve found is “column vector convention” (which also yields results on Wikipedia, for whatever that’s worth). I tried to dig into the reasoning for using column vectors a while back, and I think it comes from systems of equations.
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I don’t see these terms in Arthur Cayley’s 1858 “A Memoir on the Theory of Matrices”, and vectors aren’t vertical that far back, but they are on the right side of the matrix, and the matrices do hold the typical appearance, being shorthand for systems of linear equations.
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I’ve seen “row vector convention” or “column vector convention” in a few books, and Strang’s Linear Algebra mentions “column vector”, but does not name a “convention”. Historically it seems the ordering came before naming the one part “vector” or considering it to be a matrix.
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(Judging by some of the earliest works, that is.) It seems Cayley considered what we think of as a vector to be part of an equation, and doesn’t give it a name (that I can see) or consider it to be a matrix. (He speaks of “the matrix”.) But the ordering is all there.
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So then it may be that an actual term came about when the thing became considered both a vector and a matrix and became by convention a column. Maybe the early 1900s? I think a lot of standardization/generalization work took place in the early 1900s.
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