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Define boundary conditions of a polygon in a unit square cell 
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#1
Aug2414, 04:30 AM

P: 20

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. 


#2
Aug2414, 04:58 AM

P: 998

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 halfplanes defined by the corresponding inequalities.



#3
Aug2414, 05:50 AM

Sci Advisor
P: 1,810

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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