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Probably really easy but I need some help

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Hi, I''m wondering if anyone can enlighten me as to the difference between right-multiplication and left-multiplication? On a completely different note, how does one calculate the gradient of a Bezier curve? Thanks.

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It has to do with the fact that matrix multiplication is not commutative. Given two matrices A and B, ( AB != BA ). The left and right refer to which side you are going to operate. So, if I have a matix A and I want to right multiply it by B, I have AB. And vice versa.

Are you starting with a curve formula, a set of control points or are you interpretting from data?


Edited by - The Bear on January 30, 2002 3:54:53 PM

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A curve formula. It would also be useful to be able to work it out from a set of control points. I must admit I assumed you''d have to work it out from the formula; any technique would help, at this point.

Thanks.

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If A and B are matrices and Tr() is a function taking a matrix and returning its transpose then A*B=Tr(Tr(B)*Tr(A)). The main reason for mentioning that is that you can do transforms as either a left or right multiplication, i.e. a row vector times a matrix or a matrix times a column vector. The vectors are obviously transposes of one another, but so is the matrix, i.e. they are not the same matrix, but they are transposes of one another. You also of course either get a row or column vector out depending upon which you fed in. B would be your vector and you add transforms (multiply matrices) on the far side of A.

If you know the form of your equation then you can use linear algebra to find the coefficents given the points. Basically you call your coefficents variables and your variables coefficents. So you could find the coefficents for a quadradic space curve as though you were finding the intersection of three planes. The point of intersection is the coefficents you are looking for.

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