1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Transformation Matrix Problem

  1. May 7, 2007 #1
    1. The problem statement, all variables and given/known data

    Consider the quadrilateral (namely Q) in R^3 formed by the points
    (1, 0, 0), (2, 0, 0), (1, 1, 3), and (2, 1, 3).

    a) What should the coordinates be for the figure R we get by rotating Q counterclockwise in the x-y plane by 45 degrees, then dilating it by a factor of 3/2, then translating it along the vector (-2, 1, -1)?

    b) Find the matrix that transforms Q into R.

    3. The attempt at a solution

    Okay, so what I did for (a) was I used the matrix

    cosθ -sinθ 0
    sinθ cosθ 0
    0 0 1

    Then substituted 45 for θ.

    After this, multiplied the identity matrix for R^3 by 3/2 and then multiplied it by the matrix with 45 substituted for θ.

    Then T(x,y,z) = (-2+3sqrt(2)x/4-3sqrt(2)y/4,1+3sqrt(2)x/4+3sqrt(2)y/4,-1+3z/2).

    I substituted each of the quadrilateral points in for T(x, y, z) to come up with the four points and got:


    (3/(2√2) - 2, 3/(2√2) + 1, -1),
    (3/√2 - 2, 3/√2 + 1, -1),
    (-2, 3/√2 + 1, 3.5),
    (3/(2√2) - 2, 9/(2√2) + 1, 3.5)

    I was wondering if someone could show me how to find the matrix that transforms Q into R. It would be greatly appreciated!
     
  2. jcsd
  3. May 8, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Translation in 3 dimensions cannot be written as a 3 by 3 matrix- it is a vector addition. However, using "projective coordinates", you can write any such transformation as a 4 by 4 matrix. Have you done anything with that?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Transformation Matrix Problem
Loading...