Hi there, Please I have a Computer Graphics question and i don't have any idea how to solve it. I've searched dreamincode and i've googled it as well but i don't seem to find any document that answers it. Please, before you start telling me the rules, i know them already. But in my case i don't have any idea how to go about it.
Here is the question:
Prove that two successive 2D Rotations are additive.
Thanks in advance for your help.
3 Replies  7919 Views  Last Post: 08 May 2010  06:38 AM
#1
Rotation in Transformation A Computer Graphics Question
Posted 05 May 2010  03:32 PM
Replies To: Rotation in Transformation A Computer Graphics Question
#2
Re: Rotation in Transformation A Computer Graphics Question
Posted 06 May 2010  07:54 AM
nkasei28, on 05 May 2010  04:32 PM, said:
Hi there, Please I have a Computer Graphics question and i don't have any idea how to solve it. I've searched dreamincode and i've googled it as well but i don't seem to find any document that answers it. Please, before you start telling me the rules, i know them already. But in my case i don't have any idea how to go about it.
Here is the question:
Prove that two successive 2D Rotations are additive.
Thanks in advance for your help.
Here is the question:
Prove that two successive 2D Rotations are additive.
Thanks in advance for your help.
Wouldn't your math book have a this laid out for you? I would figure it's like vector math... vector a's head is the start of vector b's tail. Vector b's head is the end point. The total transformation is the hypotenuse of B's head to A's tail.
#3
Re: Rotation in Transformation A Computer Graphics Question
Posted 06 May 2010  08:05 AM
Are you using homogeneous coordinates?
Do you by 2D rotation mean that you rotate using an affine transformation?
Anyway, let's say we have a function rotate(coord, rad) which takes some 2D homogeneous coordinates and the amount of radians to rotate. It returns the coordinates after applying the rotation.
My guess is that you'll have to prove that rotate(coord, r1+r2) = rotate(rotate(coord, r2),r1)
Is this what you are trying to do?
Do you by 2D rotation mean that you rotate using an affine transformation?
Anyway, let's say we have a function rotate(coord, rad) which takes some 2D homogeneous coordinates and the amount of radians to rotate. It returns the coordinates after applying the rotation.
My guess is that you'll have to prove that rotate(coord, r1+r2) = rotate(rotate(coord, r2),r1)
Is this what you are trying to do?
#4
Re: Rotation in Transformation A Computer Graphics Question
Posted 08 May 2010  06:38 AM
It's possible that if you translate your vectors into polar cooardinates, this will become quite clear.
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