1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rotating a row of points

  1. Aug 8, 2010 #1
    1. The problem statement, all variables and given/known data
    I need to find the x,y coordinates of the points that neighbor a center point that has been rotated around yet another point. An illustration is best:
    Given: point of origin, angle, p1, p2
    Needed: p1 a, b, c etc, p2 a, b, c, etc

    2. Relevant equations
    for p1/p2 I just do:
    ax = cosine(angle)
    ay = sine(angle)
    new x = ax * distance from origin + origin x
    new y = ay * distance from origin + origin y

    3. The attempt at a solution
    I thought I just add/subtract an amount somehow, somewhere? Tried, couldn't find the right stuff.
  2. jcsd
  3. Aug 8, 2010 #2


    User Avatar
    Homework Helper

    Think in vectors. See attachment. The position vector of a point is

    [tex]\vec r=\vec u+\vec v[/tex]


    Attached Files:

  4. Aug 9, 2010 #3
    Sorry, but I'm not a student so I don't remember what those lines above the letters mean :( You're talking to a philosophy degree turned web/game developer.

    It looks like you're referring to the Pythagorean theorem, which doesn't work very well for this situation. I need to get to the new coordinates as cheaply (fast for the computer to crunch) as possible (I'm working on a game). Using angles and distances like that means a lot of unnecessary arctangent and square root operations, which are expensive.

    Can't I just add/subtract some values and use the cos/sin I already have to determine the new coordinates?

    I could add/subtract 90 degrees from the angle I have and do another sin/cos + distance but that seems like a waste. There has to be a cheaper way to do it...
  5. Aug 9, 2010 #4


    User Avatar
    Homework Helper

    Those letters mean vectors, which are given by their vertical and horizontal components. When you add two vectors, these components add up.
    If the length of the vector u is u, (this is the distance of the midpoint of the stick on which your points sit) its horizontal component is u*cosθ, the vertical component is u*sinθ. If v is the position of a dot on the stick, the components of the v vector are
    -vsinθ and vcosθ. You can assign a v value to each of your points. The position of a selected point is the vector r,sum of u and v, you get its components by adding up those of u and v:

    The horizontal component is ucosθ-vsinθ, the vertical one is usinθ+vcosθ.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook