Correction on Projections of lines on planes

2004-05-21
2004-09-02
  • Nobody/Anonymous

    Here:
    http://www.euclideanspace.com/maths/geometry/elements/plane/lineOnPlane/

    It is stated that:
    "So the direction is:

    (A x B) x B"

    It should be:
    B x (A x B)
    or:
    (B x A) x B

    (B x A) is indeed out of the page as the text says but (A x B) x B has opposite direction to A || B.

    I've also tried to implement the "Alternative using Matrix representation" without success. Since I'm pressed for time, I didn't try to find out why.

     
    • Martin Baker

      Martin Baker - 2004-05-24

      Thanks very much for this, Im away from my main computer at the moment but as soon as I get back I will work through this and update the webpage.

      Martin

       
    • Martin Baker

      Martin Baker - 2004-06-07

      Thanks very much, I have updated the page now. Sorry it took so long but I underestimated all the work waiting for me when I got back to base.

      Martin

       
    • Nobody/Anonymous

      Hello,

      Some typos :

      paragraph : Calculation of the projection on the plane
      But from this page we know that:  ...
                          _   _    _
      A || B = |A| xB x A x B  <- unit vectors A,B should be separated ?

      paragraph : Calculation of the perpendicular component
      Therefore combining these equations gives:

      A | B  <- instead of A || B
        ---

      grouping terms,

      Alternative using Matrix representation

      (A B)x = (Az * Bx* Bz - Bz * Ax* Bz - @ Ax * By* By + Bx * Ay* By) / (Bx2 + By2 + Bz2)
      @ missing a minus sign here

      Thanks for popularizing so complex stuffs !

      Nop

       
    • Martin Baker

      Martin Baker - 2004-09-02

      Thanks very much, I have fixed this page as you suggested.

      Martin

       

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