Sign in to follow this  
terryeverlast

Change of coordinate matrix

Recommended Posts

terryeverlast    277

How do I do what is in the picture?

2unvsxd.jpg

 

I took the point * change of coordinate matrix * scale matrix but it didn't work.

 

[1,1,0,1] * [1 0 0 0, 0 1 0 0, 0 0 1 0, 2 2 0 1] * [2 0 0 0, 0 1 0 0, 0 0 1 0, 0 0 0 1]

 

this didn't work.

 

Share this post


Link to post
Share on other sites
alvaro    21266
You need to apply a translation to move the point (2,2) to the origin, then do the scaling, then undo the translation.

http://www.wolframalpha.com/input/?i={{1%2C0%2C2}%2C{0%2C1%2C2}%2C{0%2C0%2C1}}.{{2%2C0%2C0}%2C{0%2C1%2C0}%2C{0%2C0%2C1}}.{{1%2C0%2C-2}%2C{0%2C1%2C-2}%2C{0%2C0%2C1}}

EDIT: Sorry, I follow the convention that points and vectors are columns, not rows. Transpose everything if you wish. Edited by Álvaro

Share this post


Link to post
Share on other sites
terryeverlast    277

Ok. after I multiply all these matrix with the point, will one matrix do it all for all four points of the box. or do I have to change the coordinate of the points .that is one negative x value and the other positive .

 

like in order to make [1,1,0]  to [4,1,0]......I use point [1,1,0]

to make [1,1,0] to [0,1,0]..I use point [-1,1,0]

Share this post


Link to post
Share on other sites
alvaro    21266
Yes, one matrix is used to transform all the points.

The matrix I provided is used in the following way: If you multiply it by the column (1,1,1) on the right, you'll get the column (0,1,1) back. Similarly, if you multiply it by the column (3,3,1), you'll get (4,3,1) back.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this