From b026f1b1cd355bc3f8314d0c7f933a3acb81478d Mon Sep 17 00:00:00 2001 From: interl0per Date: Sun, 6 Sep 2015 11:23:00 -0400 Subject: [PATCH] nothing changed --- notes.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notes.tex b/notes.tex index c242e3e..1f1b0ee 100644 --- a/notes.tex +++ b/notes.tex @@ -14,7 +14,7 @@ From the springs an embedding can be found. If this embedding is a circle packin \paragraph{} You can probably get the primal radii more directly, by using the fact that $k_{uv} = \frac{r_w+r_z}{r_u+r_v}$, for an edge $(u,v)$ perpendicular to the dual edge $(w,z)$. From this we have a system of $f+v=2+e$ unknowns and $e$ equations (what are the stresses for edges on the outer face?). However since each dual radii can be expressed by the three primal radii defining the face (using heron's formula), it's really a nonlinear system of $v$ unknowns and $e$ equations. -\section{Necessary/sufficent circle packing conditions} +\section{Necessary/sufficient circle packing conditions} The following are necessary conditions for a circle packing:\\ 1). For all edges $(u,v)$ perpendicular to the dual edge $(w,z), k_{uv} = \frac{r_w+r_z}{r_u+r_v}$\\