From e6efc61995516174081e923004477e3ff0853515 Mon Sep 17 00:00:00 2001
From: Samo Penic <samo.penic@gmail.com>
Date: Tue, 19 Sep 2017 12:35:28 +0000
Subject: [PATCH] Added comments for spontaneous curvature in energy.c and tape
---
src/energy.c | 8 ++++++--
1 files changed, 6 insertions(+), 2 deletions(-)
diff --git a/src/energy.c b/src/energy.c
index 996fb16..4d27995 100644
--- a/src/energy.c
+++ b/src/energy.c
@@ -44,9 +44,12 @@
return TS_SUCCESS;
};
-/** @brief Calculation of energy of the vertex
+/** @brief Calculation of the bending energy of the vertex.
*
- * Main function that calculates energy of the vertex \f$i\f$. Nearest neighbors (NN) must be ordered in counterclockwise direction for this function to work.
+ * Main function that calculates energy of the vertex \f$i\f$. Function returns \f$\frac{1}{2}(c_1+c_2-c)^2 s\f$, where \f$(c_1+c_2)/2\f$ is mean curvature,
+ * \f$c/2\f$ is spontaneous curvature and \f$s\f$ is area per vertex \f$i\f$.
+ *
+ * Nearest neighbors (NN) must be ordered in counterclockwise direction for this function to work.
* Firstly NNs that form two neighboring triangles are found (\f$j_m\f$, \f$j_p\f$ and common \f$j\f$). Later, the scalar product of vectors \f$x_1=(\mathbf{i}-\mathbf{j_p})\cdot (\mathbf{i}-\mathbf{j_p})(\mathbf{i}-\mathbf{j_p})\f$, \f$x_2=(\mathbf{j}-\mathbf{j_p})\cdot (\mathbf{j}-\mathbf{j_p})\f$ and \f$x_3=(\mathbf{j}-\mathbf{j_p})\cdot (\mathbf{i}-\mathbf{j_p})\f$ are calculated. From these three vectors the \f$c_{tp}=\frac{1}{\tan(\varphi_p)}\f$ is calculated, where \f$\varphi_p\f$ is the inner angle at vertex \f$j_p\f$. The procedure is repeated for \f$j_m\f$ instead of \f$j_p\f$ resulting in \f$c_{tn}\f$.
*
\begin{tikzpicture}{
@@ -181,6 +184,7 @@
#endif
// c is forced curvature energy for each vertex. Should be set to zero for
// normal circumstances.
+/* the following statement is an expression for $\frac{1}{2}\int(c_1+c_2-c_0^\prime)^2\mathrm{d}A$, where $c_0^\prime=2c_0$ (twice the spontaneous curvature) */
vtx->energy=0.5*s*(vtx->curvature/s-vtx->c)*(vtx->curvature/s-vtx->c);
return TS_SUCCESS;
--
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