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Matrix question

Started by Godden Nov 18, 2004 at 9:57 AM 1 replies 900+ views

Original Post

Nov 18, 2004 at 9:57 AM

Hey, Over the next couple of days ill proberly ask a few newb questions, atm i am tring to figure this out Suppose T represents a translation while R represents a rotation. Under what circumstances is the effect of RT the same as TR on a point P in the 2D plane? [ a b 0] T =[ c d 0] [ 0 0 1] [ 1 0 0] R =[ 0 1 0] [ e f 1] were a,b,c,d,e,f can be any value. Please explain it as much and you can, any links to help me out are also welcome thanks

Paradigm Shifter

Nov 18, 2004 at 11:18 AM

Sounds like homework to me.
Also, T in your example looks like it should be the rotation matrix and R the translation (in 3x3 homogenous coordinates).

Can't you just apply TR and RT to a 3x1 homogeneous point vector and solve the simultaneous equations to get the answer?
TRv = RTv and solve for v?

LilBudyWizer

Nov 18, 2004 at 2:14 PM

You can leave v out of it assuming it is for any point P. So it is just when RT=TR. You additionally have that det(R)=1 and that the 2 norm of a vector forming a column or row of R is 1. Generally with R a=d and b=-c so you can eliminate c and d right from the start.

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