Get the new coordinate after rotation

[Time_Walker]

hello master:

  i had thought about this question and try to calculate it for two days. but i still can't get the right coordinate.

picture 1.bmp, the coordinate of point "P" and point "Q" is known.

after we rotated with 337.96289 degree, i took a picture 2.bmp, the coordinate of point "Q" in 2.bmp is known. now how can i calculate the coordinate of point "P" in 2.bmp? this problem was suffering me. it will be very appreciated for any help or suggestion. thanks.

[Hatef.fouladi]

knowing one point coordinate will not help you to find other points based on that point
for 2D area you need at least two known point or one point +rotation angle (theta) to find other points positions and for 3D you need at least 3 point or one point +two vertical rotation angle

[BruceAmmons · Accepted solution]

Something like this:

Create vector from first points which is distance from Q to P:  V(x,y) = P(x,y) - Q(x,y)

Create rotation matrix M using T=rotation angle:  First row = cos(T) sin(T)  Second row = -sin(T) cos(T).

Multiply matrix times vector:  Vnew(x,y) = M[2*2] * V(x,y)

Add Vnew to Qnew to get Pnew: Pnew(x,y) = Qnew(x,y) + Vnew(x,y)

I may have negative sine in wrong position, because I didn't look it up.  If the rotation is in the wrong direction, move the negative to the other sine.

Bruce

[Hatef.fouladi · Accepted solution]

hi Bruce

I always use bellow vi for this reason 

but as I told in my first post you can do this just when you have 

position of two points in one  2d plate ot you have position of one point + rotation angle of 2d plate 
with just one point it is impossible to find other point position based on that point 

[Time_Walker]

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BruceAmmons 已写：

Something like this:

Create vector from first points which is distance from Q to P:  V(x,y) = P(x,y) - Q(x,y)

Create rotation matrix M using T=rotation angle:  First row = cos(T) sin(T)  Second row = -sin(T) cos(T).

Multiply matrix times vector:  Vnew(x,y) = M[2*2] * V(x,y)

Add Vnew to Qnew to get Pnew: Pnew(x,y) = Qnew(x,y) + Vnew(x,y)

I may have negative sine in wrong position, because I didn't look it up.  If the rotation is in the wrong direction, move the negative to the other sine.

Bruce

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hello Bruce:

  i had used the way you described to solve the problem before i read your reply. anyway, thank you very much for your reply. your good advise will be the light at night for new comer. thanks~

[Time_Walker]

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Hatef.fouladi 已写：

hi Bruce

I always use bellow vi for this reason 

but as I told in my first post you can do this just when you have 

position of two points in one  2d plate ot you have position of one point + rotation angle of 2d plate 
with just one point it is impossible to find other point position based on that point 

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hello master:

  yes. i used the way which Bruse talked about. and then i used 2D Cartesian rotation.vi to finish the code. you are in the same way~ thanks for your reply.~

[Hatef.fouladi]

your welcome ,also you can use above vis for geometric calculation in image