Results 1 to 5 of 5

Math Help - Rotating points around a known center

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    9

    Rotating points around a known center

    I don't know if this is the right forum, but here we go.

    I have the situation where I have several known points in the plane that I want to rotate 45 degrees counterclockwise around a known center which is not (0,0). How do I do this, i.e. how do I find the new coordinates for each point?

    I am using Matlab, if that matters.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Nov 2006
    Posts
    9
    Actually, I figured it out on my own. But now I have a different problem. I am plotting an ellipse in Matlab, and I want to rotate it 45 degrees, now clockwise, around it's center. Any ideas?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Say the point is (1,1).
    And we want to find how it rotates ("a rotation matrix", but if that terms confuses you, ignore it).

    Draw a new coordinate system having (1,1) in its center pararrel and perpindicular to the original system.

    Then point (x,y) relative to the new coordinate system gets mapped to,
    x'=sqrt{2}/2*x-sqrt{2}/2*y
    y'=sqrt{2}/2*x+sqrt{2}/2*y

    Thus, (x',y') is the new coordinate relative to the new coordinate system.
    But relative to the old coordinate system it is,
    (x'+1,y'+1)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    767
    Hello, changing_seasons!

    I think I've worked this out correctly . . .


    I have several known points in the plane that I want to rotate 45° CCW
    around a known center which is not (0,0).
    How do I find the new coordinates for each point?
    Let P(x,y) be any point.
    Let C(h,k) be the given center.

    We will need two quantities:
    . . . . . . . . . . . . - - - . . .______________
    The distance CP: . r .= .√(x - h)² + (y - k)²
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y - k
    The angle θ that CP makes with the positive x-axis: . tan θ .= .------
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x - h

    Then: . x' .= .h + r·cos(θ + 45°)
    . . . . . .y' .= .k + r·sin(θ + 45°)

    . . I think . . .

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2006
    Posts
    9
    Thanks for the help guys, but I found a way to solve both my problems.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: September 15th 2011, 12:21 PM
  2. Find center of sphere from 3 points
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: March 10th 2010, 02:20 PM
  3. Rotating triangle on lattice points
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 5th 2009, 07:00 AM
  4. Replies: 0
    Last Post: April 9th 2009, 04:12 AM
  5. diagonal center points
    Posted in the Geometry Forum
    Replies: 3
    Last Post: February 1st 2008, 10:47 AM

Search Tags


/mathhelpforum @mathhelpforum