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A Monotone Test problem

  1. May 18, 2009 #1
    Hi all:
    Hi all:

    Assume in 3D space there is a point [tex]v=[v_x, v_y, v_z][/tex] , and a normal vector associate with it as [tex]n=[n_x, n_y, n_z][/tex] . A line function is defined as [tex]u=w+t\cdot[/tex] where [tex]w=[w_x, w_y, w_z][/tex] is a point, and [tex]l=[l_x, l_y, l_z][/tex] is the normalized direction of the line. l and n are normalized. Assume there is a function defined as:

    [tex]K =\frac{(u-v)\cdot n}{||u-v||^2}[/tex]

    My question is when point u varies on the line, is the function K varies monotonically???

    I've tried to compute [tex]\frac{dK}{dt}[/tex] , but I can't really see if it's monotone or not, can some one help me please?

  2. jcsd
  3. May 18, 2009 #2


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    Last edited by a moderator: Apr 24, 2017
  4. May 18, 2009 #3
    Last edited by a moderator: Apr 24, 2017
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