Math Is Fun Forum

model

Member

Registered: 2011-08-10

Posts: 142

Rotation in Homogeneous coordinate

Hy All,

I am not understanding this eq in link : http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/geometry/geo-tran.html

, rotating a line Ax + By + C = 0 about the origin a degree brings it to a new equation:

(Acosa - Bsina)x' + (Asina + Bcosa)y' + C = 0

How did he get the equation ? ? ?

Also how did he use this equation  in the above link .
as shown in figure this : http://imageshack.us/photo/my-images/853/2drottran.jpg/

How did he combine it to make it translation and rotation ?

Please help me to understand  it thanks

Could any one tell me ?
thanks

Last edited by model (2012-04-07 05:27:53)

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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Rotation in Homogeneous coordinate

Hi hammana

I suggest you learn to use LaTeX for greater readability of you posts.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

hammana

Member

Registered: 2012-03-02

Posts: 48

Re: Rotation in Homogeneous coordinate

I assume you know these basic formula of trigonometry

Consider point M1 of polar coordonates r ,b its cartesian coordinates are

If we rotate it by an angle a we obtain point  M2 polar coordinates

, its cartesian coordinates would be

Develop cos(a+b) and sin(a+b) as indicated above, replace  r*cos(b)  by

, r*sin(b) by   

you get

equivalent to:

(Note that you go from M2 to M1 by changing a to -a)
In equation

,  replace 

by their values as functions of

you get:

Last edited by hammana (2012-04-12 00:03:37)

hammana

Member

Registered: 2012-03-02

Posts: 48

Re: Rotation in Homogeneous coordinate

Hi anonimnystefy

Thanks for the advice. I still have some progress to make

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Rotation in Homogeneous coordinate

Hi hammana

You are welcome. Just delete that stuff from the last anding math tag. The last line ddn't convert to LaTeX.

I would also suggest using \sin and\cos instead of just sin and cos.

Last edited by anonimnystefy (2012-04-10 06:05:14)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.