Results 1 to 1 of 1

Math Help - help: LinearTransformation into an interval [a,b]

  1. #1
    Newbie
    Joined
    Dec 2007
    Posts
    14

    help: LinearTransformation into an interval [a,b]

    Hi,

    I need a Linear Transformation for following usecase:

    I have an 2D space and a certain boundary (minX, minY, maxX, maxY). With boundary I mean, that I consider only vectors which are inside a certian parallelogram, where its left down corner is the vector (minX, minY) and its right upper corner is the vector (maxX, maxY) : see blue area of first attachment.

    How can I transform a vector inside this parallelogram so that it is projected inside [a,b] x [a,b] (see red area of first attachment)

    an example: [0,1] x [0,1]

    But, the following must apply:
    the vector of the left down corner of the parallelogram must become (a,a) and the vector of the right upper corner must become (b,x) with x <= b
    (see second attachment)

    it is important that the parallelogram does not loose its form, so it must not become a square (see second attachment). This is the reason why the right upper corner must not become (b,b) . Only if the original boundaries form a square.

    update: I have uploaded some pictures, which illustrate the problem.


    hope you can help,
    Andreas
    Attached Thumbnails Attached Thumbnails help: LinearTransformation into an interval [a,b]-parallelogramtransformation.jpg   help: LinearTransformation into an interval [a,b]-parallelogramtransformation2.png  
    Last edited by sirandreus; December 9th 2007 at 07:00 AM. Reason: upload pucture
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 3rd 2011, 04:05 PM
  2. What is NOT an interval?
    Posted in the Discrete Math Forum
    Replies: 16
    Last Post: October 31st 2009, 09:26 AM
  3. Interval
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 17th 2009, 04:47 AM
  4. Interval
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 14th 2007, 11:05 PM
  5. Increasing interval and decreasing interval
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 24th 2006, 09:49 AM

Search Tags


/mathhelpforum @mathhelpforum