/* vim: set ts=4 sts=4 sw=4 noet : */
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#include<stdlib.h>
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#include "general.h"
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#include "energy.h"
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#include "vertex.h"
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#include<math.h>
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#include<stdio.h>
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/** @brief Wrapper that calculates energy of every vertex in vesicle
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*
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* Function calculated energy of every vertex in vesicle. It can be used in
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* initialization procedure or in recalculation of the energy after non-MCsweep * operations. However, when random move of vertex or flip of random bond occur * call to this function is not necessary nor recommended.
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* @param *vesicle is a pointer to vesicle.
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* @returns TS_SUCCESS on success.
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*/
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ts_bool mean_curvature_and_energy(ts_vesicle *vesicle){
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ts_uint i;
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ts_vertex_list *vlist=vesicle->vlist;
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ts_vertex **vtx=vlist->vtx;
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for(i=0;i<vlist->n;i++){
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energy_vertex(vtx[i]);
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}
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return TS_SUCCESS;
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}
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/** @brief Calculate energy of a bond (in models where energy is bond related)
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*
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* This function is experimental and currently only used in polymeres calculation (PEGs or polymeres inside the vesicle).
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*
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* @param *bond is a pointer to a bond between two vertices in polymere
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* @param *poly is a pointer to polymere in which we calculate te energy of the bond
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* @returns TS_SUCCESS on successful calculation
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*/
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inline ts_bool bond_energy(ts_bond *bond,ts_poly *poly){
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//TODO: This value to be changed and implemented in data structure:
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ts_double d_relaxed=1.0;
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bond->energy=poly->k*pow(bond->bond_length-d_relaxed,2);
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return TS_SUCCESS;
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};
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/** @brief Calculation of the bending energy of the vertex.
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*
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* 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,
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* \f$c/2\f$ is spontaneous curvature and \f$s\f$ is area per vertex \f$i\f$.
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*
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* Nearest neighbors (NN) must be ordered in counterclockwise direction for this function to work.
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* 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$c_{tn}\f$.
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*
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\begin{tikzpicture}{
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\coordinate[label=below:$i$] (i) at (2,0);
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\coordinate[label=left:$j_m$] (jm) at (0,3.7);
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\coordinate[label=above:$j$] (j) at (2.5,6.4);
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\coordinate[label=right:$j_p$] (jp) at (4,2.7);
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\draw (i) -- (jm) -- (j) -- (jp) -- (i) -- (j);
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\begin{scope}
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\path[clip] (jm)--(i)--(j);
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\draw (jm) circle (0.8);
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\node[right] at (jm) {$\varphi_m$};
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\end{scope}
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\begin{scope}
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\path[clip] (jp)--(i)--(j);
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\draw (jp) circle (0.8);
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\node[left] at (jp) {$\varphi_p$};
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\end{scope}
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%%vertices
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\draw [fill=gray] (i) circle (0.1);
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\draw [fill=white] (j) circle (0.1);
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\draw [fill=white] (jp) circle (0.1);
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\draw [fill=white] (jm) circle (0.1);
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%\node[draw,circle,fill=white] at (i) {};
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\end{tikzpicture}
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* The curvature is then calculated as \f$\mathbf{h}=\frac{1}{2}\Sigma_{k=0}^{\mathrm{neigh\_no}} c_{tp}^{(k)}+c_{tm}^{(k)} (\mathbf{j_k}-\mathbf{i})\f$, where \f$c_{tp}^{(k)}+c_{tm}^k=2\sigma^{(k)}\f$ (length in dual lattice?) and the previous equation can be written as \f$\mathbf{h}=\Sigma_{k=0}^{\mathrm{neigh\_no}}\sigma^{(k)}\cdot(\mathbf{j}-\mathbf{i})\f$ (See Kroll, p. 384, eq 70).
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*
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* From the curvature the enery is calculated by equation \f$E=\frac{1}{2}\mathbf{h}\cdot\mathbf{h}\f$.
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* @param *vtx is a pointer to vertex at which we want to calculate the energy
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* @returns TS_SUCCESS on successful calculation.
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*/
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inline ts_bool energy_vertex(ts_vertex *vtx){
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ts_uint jj;
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ts_uint jjp,jjm;
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ts_vertex *j,*jp, *jm;
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ts_triangle *jt;
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ts_double s=0.0,xh=0.0,yh=0.0,zh=0.0,txn=0.0,tyn=0.0,tzn=0.0;
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ts_double x1,x2,x3,ctp,ctm,tot,xlen;
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ts_double h,ht;
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for(jj=1; jj<=vtx->neigh_no;jj++){
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jjp=jj+1;
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if(jjp>vtx->neigh_no) jjp=1;
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jjm=jj-1;
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if(jjm<1) jjm=vtx->neigh_no;
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j=vtx->neigh[jj-1];
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jp=vtx->neigh[jjp-1];
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jm=vtx->neigh[jjm-1];
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jt=vtx->tristar[jj-1];
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x1=vtx_distance_sq(vtx,jp); //shouldn't be zero!
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x2=vtx_distance_sq(j,jp); // shouldn't be zero!
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x3=(j->x-jp->x)*(vtx->x-jp->x)+
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(j->y-jp->y)*(vtx->y-jp->y)+
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(j->z-jp->z)*(vtx->z-jp->z);
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#ifdef TS_DOUBLE_DOUBLE
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ctp=x3/sqrt(x1*x2-x3*x3);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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ctp=x3/sqrtf(x1*x2-x3*x3);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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ctp=x3/sqrtl(x1*x2-x3*x3);
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#endif
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x1=vtx_distance_sq(vtx,jm);
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x2=vtx_distance_sq(j,jm);
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x3=(j->x-jm->x)*(vtx->x-jm->x)+
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(j->y-jm->y)*(vtx->y-jm->y)+
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(j->z-jm->z)*(vtx->z-jm->z);
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#ifdef TS_DOUBLE_DOUBLE
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ctm=x3/sqrt(x1*x2-x3*x3);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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ctm=x3/sqrtf(x1*x2-x3*x3);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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ctm=x3/sqrtl(x1*x2-x3*x3);
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#endif
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tot=ctp+ctm;
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tot=0.5*tot;
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xlen=vtx_distance_sq(j,vtx);
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/*
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#ifdef TS_DOUBLE_DOUBLE
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vtx->bond[jj-1]->bond_length=sqrt(xlen);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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vtx->bond[jj-1]->bond_length=sqrtf(xlen);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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vtx->bond[jj-1]->bond_length=sqrtl(xlen);
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#endif
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vtx->bond[jj-1]->bond_length_dual=tot*vtx->bond[jj-1]->bond_length;
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*/
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s+=tot*xlen;
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xh+=tot*(j->x - vtx->x);
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yh+=tot*(j->y - vtx->y);
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zh+=tot*(j->z - vtx->z);
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txn+=jt->xnorm;
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tyn+=jt->ynorm;
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tzn+=jt->znorm;
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}
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h=xh*xh+yh*yh+zh*zh;
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ht=txn*xh+tyn*yh + tzn*zh;
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s=s/4.0;
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#ifdef TS_DOUBLE_DOUBLE
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if(ht>=0.0) {
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vtx->curvature=sqrt(h);
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} else {
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vtx->curvature=-sqrt(h);
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}
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#endif
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#ifdef TS_DOUBLE_FLOAT
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if(ht>=0.0) {
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vtx->curvature=sqrtf(h);
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} else {
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vtx->curvature=-sqrtf(h);
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}
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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if(ht>=0.0) {
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vtx->curvature=sqrtl(h);
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} else {
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vtx->curvature=-sqrtl(h);
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}
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#endif
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// c is forced curvature energy for each vertex. Should be set to zero for
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// normal circumstances.
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/* 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) */
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vtx->energy=0.5*s*(vtx->curvature/s-vtx->c)*(vtx->curvature/s-vtx->c);
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return TS_SUCCESS;
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}
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ts_bool sweep_attraction_bond_energy(ts_vesicle *vesicle){
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int i;
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for(i=0;i<vesicle->blist->n;i++){
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attraction_bond_energy(vesicle->blist->bond[i], vesicle->tape->w);
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}
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return TS_SUCCESS;
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}
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inline ts_bool attraction_bond_energy(ts_bond *bond, ts_double w){
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if(fabs(bond->vtx1->c)>1e-16 && fabs(bond->vtx2->c)>1e-16){
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bond->energy=-w;
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}
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else {
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bond->energy=0.0;
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}
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return TS_SUCCESS;
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}
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ts_double direct_force_energy(ts_vesicle *vesicle, ts_vertex *vtx, ts_vertex *vtx_old){
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if(fabs(vtx->c)<1e-15) return 0.0;
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// printf("was here");
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if(fabs(vesicle->tape->F)<1e-15) return 0.0;
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ts_double norml,ddp=0.0;
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ts_uint i;
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ts_double xnorm=0.0,ynorm=0.0,znorm=0.0;
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/*find normal of the vertex as sum of all the normals of the triangles surrounding it. */
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for(i=0;i<vtx->tristar_no;i++){
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xnorm+=vtx->tristar[i]->xnorm;
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ynorm+=vtx->tristar[i]->ynorm;
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znorm+=vtx->tristar[i]->znorm;
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}
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/*normalize*/
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norml=sqrt(xnorm*xnorm+ynorm*ynorm+znorm*znorm);
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xnorm/=norml;
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ynorm/=norml;
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znorm/=norml;
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/*calculate ddp, perpendicular displacement*/
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ddp=xnorm*(vtx->x-vtx_old->x)+ynorm*(vtx->y-vtx_old->y)+znorm*(vtx->z-vtx_old->z);
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/*calculate dE*/
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// printf("ddp=%e",ddp);
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return vesicle->tape->F*ddp;
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}
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void stretchenergy(ts_vesicle *vesicle, ts_triangle *triangle){
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triangle->energy=vesicle->tape->xkA0/2.0*pow((triangle->area/vesicle->tlist->a0-1.0),2);
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}
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