half.slope.ratio=function (sx, sy, px, py)
{
tx = (sx^px - 1)/px
ty = (sy^py - 1)/py
b.left = diff(ty[1:2])/diff(tx[1:2])
b.right = diff(ty[2:3])/diff(tx[2:3])
return(b.right/b.left)
}
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