Define boundary conditions of a polygon in a unit square cell

  1. Hi,

    I am wondering as to how to define the boundary condition for a shape in a unit cell. Just imagine that the shape is the hole for the unit cell. Hence, for a constant thickness on the untextured boundary, thickness is, lets say C, then for the circle, it's C+depth.

    For example for a unit cell with width 2r1 by 2r1 with a circle inside the unit cell, the boundary condition is:

    h(x,y) = C+depth, if x^2+y^2<r^2, and
    h(x,y) = C, if x^2+y^2>r^2.

    I am wondering how to do this with complicated polygons, like hexagon and stuff or if there is a formula or principle that i dont know of.

    Thank you heaps.

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  2. jcsd
  3. jbriggs444

    jbriggs444 2,225
    Science Advisor

    Each of the sides of a polygon is definable by a simple linear equation in x and y. The interior of a convex polygon is the intersection of the half-planes defined by the corresponding inequalities.
    Last edited: Aug 24, 2014
  4. disregardthat

    disregardthat 1,817
    Science Advisor

    For convex polygons, the most economic way would probably be to restrict the boundary conditions to particular angles. For more complex polygons, a piecewise defined curve is probably the best way.
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