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Evaluate a length on a quadric surface

  1. Jul 19, 2006 #1

    I define a sheet (Monge's) surface as [tex]z=z(x,y)[/tex] where z(x,y) is a quadric defined by :

    [tex]z=-\, \frac{1}{2} \mathbf{x}^T \mathbb{Q} \mathbf{x} [/tex]

    where [tex]\mathbf{x}^T=[x, y] [/tex] and [tex]\mathbb{Q}[/tex] a (symetric but not diagonal) curvature matrix.

    I've attached to this post a figure to describe the geometry.

    My question is : how can I manage to evaluate s(x,y) (the length of the red curve), knowing x and y (the red curve is starting from the origin) ? I think s(x,y) can be evaluate by a curvilinear integral, but I don't know how to write it...

    Thanks in advance for your answers.

    Attached Files:

    Last edited: Jul 19, 2006
  2. jcsd
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