Matrix Multiplication Explained
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I've written another appendix for the tutorial. It explains matrix multiplication. Hopefully, this explanation is a lot clearer than most of what you find if you search the web for this topic. It answers that burning question:
Why isn't matrix multiplication commutative?
I've also made some improvements to the "how does the transformation matrix work" appendix.
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Matrix Multiplication - change .txt to .html
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Nice explanation, bit programming orientated in my opinion but shouldnt cause any problems given the target audience. If i was being pedantic, id also say it doesnt really explain why matrix multiplication is non-commutative, rather it demonstrates that it is non-commutative (probably a good thing though, as id guess the answer is largely irrelevant to the typical sketchup scripter and would add a great deal of complexity.)
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Saved your post for a later day:-) Thanks.
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@remus said:
as id guess the answer [why not commutative?] is largely irrelevant to the typical sketchup scripter and would add a great deal of complexity.)
I'd guess that the non-commutative part bites everyone who codes with transformations. Let's see, is that rotation * scale or ... It's got me more than once.
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@martinrinehart said:
@remus said:
as id guess the answer [why not commutative?] is largely irrelevant to the typical sketchup scripter and would add a great deal of complexity.)
I'd guess that the non-commutative part bites everyone who codes with transformations. Let's see, is that rotation * scale or ... It's got me more than once.
"non-commutative"
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Sorry, poor wording on my part. I meant why matrix multiplication is non-commutative probably isnt important to most scripters, whereas the fact that it is non-commutative is clearly very important.
Thom, commutativity is the property that "order doesnt matter", for example 23 = 32 and 4+5 = 5+4, but if youve got 2 matrices A and B, AB != BA. Multiplication and addition are said to be commutative and matrix multiplication is said to be non-commutative.
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Ah yea - I've been puzzled by that. Why a
scale * rotateisn't the same asrotate * scale. -
But that is the same as doing it manually ?
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That 'that' is manually rotating about a point and then scaling in a certain axis often gives quite different results from scaling in a certain axis then rotating about the same point
That is that !
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