root / bin / compute_energy_and_forces.cpp @ 1
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| 1 | 1 | akiss | #include "compute_energy_and_forces.h" |
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| 2 | 1 | akiss | #include "constants.h" |
| 3 | 1 | akiss | #include "compute_areas.h" |
| 4 | 1 | akiss | #include "compute_cell_areas.h" |
| 5 | 1 | akiss | #include "compute_shapes.h" |
| 6 | 1 | akiss | #include "compute_barycenters.h" |
| 7 | 1 | akiss | #include "compute_lengths.h" |
| 8 | 1 | akiss | #include <math.h> |
| 9 | 1 | akiss | #include <stdio.h> |
| 10 | 1 | akiss | #include <nlopt.h> |
| 11 | 1 | akiss | #include <omp.h> |
| 12 | 1 | akiss | |
| 13 | 1 | akiss | /* this function computes the mechanical energy and its derivatives (basically only math equations) */
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| 14 | 1 | akiss | |
| 15 | 1 | akiss | double compute_energy_and_forces(unsigned n, const double *vertices, double *forces, void *parameters){ |
| 16 | 1 | akiss | |
| 17 | 1 | akiss | struct parameters_list {int vertices_number; int cell_number; int *cells_vertices; int *vertices_number_in_each_cell; double *barycenters; double *shapes; double *targets; double *areas; double *cell_areas; |
| 18 | 1 | akiss | int *wall_vertices; int wall_number; double *lengths; double *target_lengths; int *boundary; double *tissue_target; int anisotropy; double *relative_pressure;}; |
| 19 | 1 | akiss | |
| 20 | 1 | akiss | int j,previous; double N,energy=0; |
| 21 | 1 | akiss | |
| 22 | 1 | akiss | compute_lengths((double*)vertices, ((parameters_list*)parameters)->wall_vertices, ((parameters_list*)parameters)->wall_number, ((parameters_list*)parameters)->lengths);
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| 23 | 1 | akiss | compute_barycenters((double*)vertices, ((parameters_list*)parameters)->vertices_number, ((parameters_list*)parameters)->cells_vertices,
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| 24 | 1 | akiss | ((parameters_list*)parameters)->vertices_number_in_each_cell, ((parameters_list*)parameters)->cell_number, ((parameters_list*)parameters)->barycenters); |
| 25 | 1 | akiss | compute_areas((double*)vertices, ((parameters_list*)parameters)->cells_vertices, ((parameters_list*)parameters)->vertices_number_in_each_cell,
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| 26 | 1 | akiss | ((parameters_list*)parameters)->cell_number, ((parameters_list*)parameters)->areas); |
| 27 | 1 | akiss | compute_cell_areas((double*)vertices, ((parameters_list*)parameters)->cells_vertices, ((parameters_list*)parameters)->vertices_number_in_each_cell,
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| 28 | 1 | akiss | ((parameters_list*)parameters)->cell_number, ((parameters_list*)parameters)->areas, ((parameters_list*)parameters)->cell_areas); |
| 29 | 1 | akiss | compute_shapes((double*)vertices, ((parameters_list*)parameters)->cells_vertices, ((parameters_list*)parameters)->vertices_number_in_each_cell,
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| 30 | 1 | akiss | ((parameters_list*)parameters)->cell_number, ((parameters_list*)parameters)->barycenters, ((parameters_list*)parameters)->shapes); |
| 31 | 1 | akiss | |
| 32 | 1 | akiss | |
| 33 | 1 | akiss | if (forces){ for (int i=0;i<2*((parameters_list*)parameters)->vertices_number;i++){forces[i]=0.;}} |
| 34 | 1 | akiss | |
| 35 | 1 | akiss | //for (int i=0;i<((parameters_list*)parameters)->vertices_number;i++){
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| 36 | 1 | akiss | // if (vertices[2*i+1]>7.){ forces[2*i+1]+=0.01*sinh(vertices[2*i+1]-7.);}
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| 37 | 1 | akiss | // if (vertices[2*i+1]<-7.){ forces[2*i+1]+=0.01*sinh(vertices[2*i+1]+7.);}
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| 38 | 1 | akiss | // if (vertices[2*i+1]>7.){ energy+=0.01*(cosh(vertices[2*i+1]-7.)-1.);}
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| 39 | 1 | akiss | // if (vertices[2*i+1]<-7.){ energy+=0.01*(cosh(vertices[2*i+1]+7.)-1.);}
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| 40 | 1 | akiss | //}
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| 41 | 1 | akiss | |
| 42 | 1 | akiss | double ablation;
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| 43 | 1 | akiss | for (int i=0;i<((parameters_list*)parameters)->cell_number;i++){ |
| 44 | 1 | akiss | ablation=(double)(i!=ablated_cell);
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| 45 | 1 | akiss | if (forces){
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| 46 | 1 | akiss | for (j=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i];j<(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1];j++){ |
| 47 | 1 | akiss | previous=j-1; if (j==(((parameters_list*)parameters)->vertices_number_in_each_cell)[i]){ previous=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1]-1;} |
| 48 | 1 | akiss | /* derivatives of the area in the pressure energy */
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| 49 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]]-=0.5*ablation*pressure*(((parameters_list*)parameters)->relative_pressure)[i]*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1]); |
| 50 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]-=0.5*ablation*pressure*(((parameters_list*)parameters)->relative_pressure)[i]*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]]); |
| 51 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[previous]]-=0.5*ablation*pressure*(((parameters_list*)parameters)->relative_pressure)[i]*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]); |
| 52 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1]-=0.5*ablation*pressure*(((parameters_list*)parameters)->relative_pressure)[i]*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]]); |
| 53 | 1 | akiss | } |
| 54 | 1 | akiss | } |
| 55 | 1 | akiss | /* pressure energy */
|
| 56 | 1 | akiss | energy+=-pressure*(((parameters_list*)parameters)->relative_pressure)[i]*ablation*(((parameters_list*)parameters)->cell_areas)[i]; |
| 57 | 1 | akiss | } |
| 58 | 1 | akiss | |
| 59 | 1 | akiss | double boundary;
|
| 60 | 1 | akiss | for (int i=0;i<((parameters_list*)parameters)->cell_number;i++){ |
| 61 | 1 | akiss | // for (j=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i];j<(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1];j++){
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| 62 | 1 | akiss | // previous=j-1; if (j==(((parameters_list*)parameters)->vertices_number_in_each_cell)[i]){ previous=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1]-1;}
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| 63 | 1 | akiss | // boundary=(double)((((parameters_list*)parameters)->boundary)[j]);
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| 64 | 1 | akiss | // if (forces){
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| 65 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[j]]-=boundary*0.5*pressure*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1]);
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| 66 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]-=boundary*0.5*pressure*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]]);
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| 67 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[previous]]-=boundary*0.5*pressure*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]);
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| 68 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1]-=boundary*0.5*pressure*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]]);
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| 69 | 1 | akiss | // }
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| 70 | 1 | akiss | //
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| 71 | 1 | akiss | // energy-=boundary*0.5*pressure*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]]*vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]-
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| 72 | 1 | akiss | // vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]]*vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1]);
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| 73 | 1 | akiss | // }
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| 74 | 1 | akiss | } |
| 75 | 1 | akiss | |
| 76 | 1 | akiss | double trace;
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| 77 | 1 | akiss | for (int i=0;i<((parameters_list*)parameters)->cell_number;i++){ |
| 78 | 1 | akiss | trace=(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->targets)[3*i+1]; |
| 79 | 1 | akiss | N=(double)((((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1])-(double)((((parameters_list*)parameters)->vertices_number_in_each_cell)[i]); |
| 80 | 1 | akiss | ablation=(double)(i!=ablated_cell);
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| 81 | 1 | akiss | if (forces){
|
| 82 | 1 | akiss | for (j=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i];j<(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1];j++){ |
| 83 | 1 | akiss | previous=j-1; if (j==(((parameters_list*)parameters)->vertices_number_in_each_cell)[i]){ previous=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1]-1;} |
| 84 | 1 | akiss | /* derivatives of the shape matrix */
|
| 85 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]]+=ablation*shear_modulus*4.0*((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i]) |
| 86 | 1 | akiss | *(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]]-(((parameters_list*)parameters)->barycenters)[2*i])* |
| 87 | 1 | akiss | (((parameters_list*)parameters)->cell_areas)[i]/(trace*trace*N); |
| 88 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]]+=ablation*shear_modulus*4.0*((((parameters_list*)parameters)->shapes)[3*i+2]-(((parameters_list*)parameters)->targets)[3*i+2]) |
| 89 | 1 | akiss | *(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]-(((parameters_list*)parameters)->barycenters)[2*i+1])* |
| 90 | 1 | akiss | (((parameters_list*)parameters)->cell_areas)[i]/(trace*trace*N); |
| 91 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]+=ablation*shear_modulus*4.0*((((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1]) |
| 92 | 1 | akiss | *(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]-(((parameters_list*)parameters)->barycenters)[2*i+1])* |
| 93 | 1 | akiss | (((parameters_list*)parameters)->cell_areas)[i]/(trace*trace*N); |
| 94 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]+=ablation*shear_modulus*4.0*((((parameters_list*)parameters)->shapes)[3*i+2]-(((parameters_list*)parameters)->targets)[3*i+2]) |
| 95 | 1 | akiss | *(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]]-(((parameters_list*)parameters)->barycenters)[2*i])* |
| 96 | 1 | akiss | (((parameters_list*)parameters)->cell_areas)[i]/(trace*trace*N); |
| 97 | 1 | akiss | /* derivatives of the area */
|
| 98 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]]+=ablation*shear_modulus*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1])* |
| 99 | 1 | akiss | (pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i],2.)+ |
| 100 | 1 | akiss | pow((((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.) |
| 101 | 1 | akiss | +2.*pow((((parameters_list*)parameters)->shapes)[3*i+2]-(((parameters_list*)parameters)->targets)[3*i+2],2.))/(2.*trace*trace); |
| 102 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]+=ablation*shear_modulus*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]])* |
| 103 | 1 | akiss | (pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i],2.)+ |
| 104 | 1 | akiss | pow((((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.) |
| 105 | 1 | akiss | +2.*pow((((parameters_list*)parameters)->shapes)[3*i+2]-(((parameters_list*)parameters)->targets)[3*i+2],2.))/(2.*trace*trace); |
| 106 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[previous]]+=ablation*shear_modulus*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1])* |
| 107 | 1 | akiss | (pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i],2.)+ |
| 108 | 1 | akiss | pow((((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.) |
| 109 | 1 | akiss | +2.*pow((((parameters_list*)parameters)->shapes)[3*i+2]-(((parameters_list*)parameters)->targets)[3*i+2],2.))/(2.*trace*trace); |
| 110 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1]+=ablation*shear_modulus*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]])* |
| 111 | 1 | akiss | (pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i],2.)+ |
| 112 | 1 | akiss | pow((((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.) |
| 113 | 1 | akiss | +2.*pow((((parameters_list*)parameters)->shapes)[3*i+2]-(((parameters_list*)parameters)->targets)[3*i+2],2.))/(2.*trace*trace); |
| 114 | 1 | akiss | } |
| 115 | 1 | akiss | } |
| 116 | 1 | akiss | /* shape energy, contribution from the shear modulus */
|
| 117 | 1 | akiss | energy+=ablation*shear_modulus*(((parameters_list*)parameters)->cell_areas)[i]*(pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i],2.) |
| 118 | 1 | akiss | +pow((((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.) |
| 119 | 1 | akiss | +2.*pow((((parameters_list*)parameters)->shapes)[3*i+2]-(((parameters_list*)parameters)->targets)[3*i+2],2.))/(trace*trace);//(((parameters_list*)parameters)->cell_areas)[i]; |
| 120 | 1 | akiss | } |
| 121 | 1 | akiss | |
| 122 | 1 | akiss | /* contribution of the first lame parameter, this term was neglected in the final version of the paper as it has no impact */
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| 123 | 1 | akiss | for (int i=0;i<((parameters_list*)parameters)->cell_number;i++){ |
| 124 | 1 | akiss | // min=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i]; max=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1];
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| 125 | 1 | akiss | // trace=(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->targets)[3*i+1];
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| 126 | 1 | akiss | // N=(double)(max)-(double)(min);
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| 127 | 1 | akiss | // if (forces){
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| 128 | 1 | akiss | // for (j=0;j<max-min;j++){ previous=j-1; if (j==0){ previous=max-min-1;}
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| 129 | 1 | akiss | // /* derivatives of the shape matrix */
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| 130 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[min+j]]+=lame_first_periclinal*4.0*(((parameters_list*)parameters)->cell_areas)[i]*
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| 131 | 1 | akiss | // ((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1])
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| 132 | 1 | akiss | // *(vertices[2*(((parameters_list*)parameters)->cells_vertices)[min+j]]-(((parameters_list*)parameters)->barycenters)[2*i])
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| 133 | 1 | akiss | // /(trace*trace*N);
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| 134 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[min+j]+1]+=lame_first_periclinal*4.0*(((parameters_list*)parameters)->cell_areas)[i]*
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| 135 | 1 | akiss | // ((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1])
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| 136 | 1 | akiss | // *(vertices[2*(((parameters_list*)parameters)->cells_vertices)[min+j]+1]-(((parameters_list*)parameters)->barycenters)[2*i+1])
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| 137 | 1 | akiss | // /(trace*trace*N);
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| 138 | 1 | akiss | // /* derivatives of the area */
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| 139 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[min+j]]+=lame_first_periclinal*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[min+previous]+1])*
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| 140 | 1 | akiss | // pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.)
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| 141 | 1 | akiss | // /(2.*trace*trace);
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| 142 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[min+j]+1]+=lame_first_periclinal*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[min+previous]])*
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| 143 | 1 | akiss | // pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.)
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| 144 | 1 | akiss | // /(2.*trace*trace);
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| 145 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[min+previous]]+=lame_first_periclinal*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[min+j]+1])*
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| 146 | 1 | akiss | // pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.)
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| 147 | 1 | akiss | // /(2.*trace*trace);
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| 148 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->cells_vertices)[min+previous]+1]+=lame_first_periclinal*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[min+j]])*
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| 149 | 1 | akiss | // pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.)
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| 150 | 1 | akiss | // /(2.*trace*trace);
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| 151 | 1 | akiss | // }
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| 152 | 1 | akiss | // }
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| 153 | 1 | akiss | // /* area energy */
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| 154 | 1 | akiss | // energy+=lame_first_periclinal*(((parameters_list*)parameters)->cell_areas)[i]*
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| 155 | 1 | akiss | // pow((((parameters_list*)parameters)->shapes)[3*i]-(((parameters_list*)parameters)->targets)[3*i]+(((parameters_list*)parameters)->shapes)[3*i+1]-(((parameters_list*)parameters)->targets)[3*i+1],2.)
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| 156 | 1 | akiss | // /(trace*trace);
|
| 157 | 1 | akiss | } |
| 158 | 1 | akiss | |
| 159 | 1 | akiss | /* energy of the anticlinal walls */
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| 160 | 1 | akiss | for (int i=0;i<((parameters_list*)parameters)->wall_number;i++){ |
| 161 | 1 | akiss | // /* derivatives of the lengths of the walls */
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| 162 | 1 | akiss | // if (forces){
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| 163 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->wall_vertices)[2*i]]+=lame_first_anticlinal/*(((parameters_list*)parameters)->wall_out)[i]*/*2.*((((parameters_list*)parameters)->lengths)[i]-(((parameters_list*)parameters)->target_lengths)[i])*
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| 164 | 1 | akiss | // (vertices[2*(((parameters_list*)parameters)->wall_vertices)[2*i]]-vertices[2*(((parameters_list*)parameters)->wall_vertices)[2*i+1]])/
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| 165 | 1 | akiss | // ((((parameters_list*)parameters)->lengths)[i]*(((parameters_list*)parameters)->target_lengths)[i]);
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| 166 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->wall_vertices)[2*i+1]]+=lame_first_anticlinal/*(((parameters_list*)parameters)->wall_out)[i]*/*2.*((((parameters_list*)parameters)->lengths)[i]-(((parameters_list*)parameters)->target_lengths)[i])*
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| 167 | 1 | akiss | // (vertices[2*(((parameters_list*)parameters)->wall_vertices)[2*i+1]]-vertices[2*(((parameters_list*)parameters)->wall_vertices)[2*i]])/
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| 168 | 1 | akiss | // ((((parameters_list*)parameters)->lengths)[i]*(((parameters_list*)parameters)->target_lengths)[i]);
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| 169 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->wall_vertices)[2*i]+1]+=lame_first_anticlinal/*(((parameters_list*)parameters)->wall_out)[i]*/*2.*((((parameters_list*)parameters)->lengths)[i]-(((parameters_list*)parameters)->target_lengths)[i])*
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| 170 | 1 | akiss | // (vertices[2*(((parameters_list*)parameters)->wall_vertices)[2*i]+1]-vertices[2*(((parameters_list*)parameters)->wall_vertices)[2*i+1]+1])/
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| 171 | 1 | akiss | // ((((parameters_list*)parameters)->lengths)[i]*(((parameters_list*)parameters)->target_lengths)[i]);
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| 172 | 1 | akiss | // forces[2*(((parameters_list*)parameters)->wall_vertices)[2*i+1]+1]+=lame_first_anticlinal/*(((parameters_list*)parameters)->wall_out)[i]*/*2.*((((parameters_list*)parameters)->lengths)[i]-(((parameters_list*)parameters)->target_lengths)[i])*
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| 173 | 1 | akiss | // (vertices[2*(((parameters_list*)parameters)->wall_vertices)[2*i+1]+1]-vertices[2*(((parameters_list*)parameters)->wall_vertices)[2*i]+1])/
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| 174 | 1 | akiss | // ((((parameters_list*)parameters)->lengths)[i]*(((parameters_list*)parameters)->target_lengths)[i]);
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| 175 | 1 | akiss | // }
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| 176 | 1 | akiss | // /* walls energy */
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| 177 | 1 | akiss | // /* the 2. factor comes from the fact that each wall is counted twice in the sum over the cells */
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| 178 | 1 | akiss | // energy+=lame_first_anticlinal*pow((((parameters_list*)parameters)->lengths)[i]-(((parameters_list*)parameters)->target_lengths)[i],2.)/(((parameters_list*)parameters)->target_lengths)[i];
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| 179 | 1 | akiss | } |
| 180 | 1 | akiss | |
| 181 | 1 | akiss | /* contribution from the anisotropic stress that mimics curvature */
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| 182 | 1 | akiss | if (((parameters_list*)parameters)->anisotropy==1){ |
| 183 | 1 | akiss | double tissue_area=0.; int boundary_vertices_number=0; |
| 184 | 1 | akiss | double tissue_shape[2]={0.,0.}; double tissue_barycenter[2]={0.,0.}; |
| 185 | 1 | akiss | for (int i=0;i<((parameters_list*)parameters)->cell_number;i++){ |
| 186 | 1 | akiss | for (j=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i];j<(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1];j++){ |
| 187 | 1 | akiss | previous=j-1; if (j==(((parameters_list*)parameters)->vertices_number_in_each_cell)[i]){ previous=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1]-1;} |
| 188 | 1 | akiss | boundary_vertices_number+=(((parameters_list*)parameters)->boundary)[j]; |
| 189 | 1 | akiss | boundary=(double)((((parameters_list*)parameters)->boundary)[j]);
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| 190 | 1 | akiss | tissue_area+=boundary*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]]*vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]- |
| 191 | 1 | akiss | vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]]*vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1])/2.; |
| 192 | 1 | akiss | tissue_barycenter[0]+=boundary*vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]]; |
| 193 | 1 | akiss | tissue_barycenter[1]+=boundary*vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]; |
| 194 | 1 | akiss | } |
| 195 | 1 | akiss | } |
| 196 | 1 | akiss | tissue_barycenter[0]/=boundary_vertices_number;
|
| 197 | 1 | akiss | tissue_barycenter[1]/=boundary_vertices_number;
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| 198 | 1 | akiss | for (int i=0;i<(((parameters_list*)parameters)->vertices_number_in_each_cell)[((parameters_list*)parameters)->cell_number];i++){ |
| 199 | 1 | akiss | boundary=(double)((((parameters_list*)parameters)->boundary)[i]);
|
| 200 | 1 | akiss | tissue_shape[0]+=boundary*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[i]]-tissue_barycenter[0])*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[i]]-tissue_barycenter[0]); |
| 201 | 1 | akiss | tissue_shape[1]+=boundary*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[i]+1]-tissue_barycenter[1])*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[i]+1]-tissue_barycenter[1]); |
| 202 | 1 | akiss | } |
| 203 | 1 | akiss | tissue_shape[0]/=boundary_vertices_number;
|
| 204 | 1 | akiss | tissue_shape[1]/=boundary_vertices_number;
|
| 205 | 1 | akiss | trace=(((parameters_list*)parameters)->tissue_target)[0]+(((parameters_list*)parameters)->tissue_target)[1]; |
| 206 | 1 | akiss | if (forces){
|
| 207 | 1 | akiss | for (int i=0;i<((parameters_list*)parameters)->cell_number;i++){ |
| 208 | 1 | akiss | for (j=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i];j<(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1];j++){ |
| 209 | 1 | akiss | previous=j-1; if (j==(((parameters_list*)parameters)->vertices_number_in_each_cell)[i]){ previous=(((parameters_list*)parameters)->vertices_number_in_each_cell)[i+1]-1;} |
| 210 | 1 | akiss | boundary=(double)((((parameters_list*)parameters)->boundary)[j]);
|
| 211 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]]-=boundary*tissue_area*first_shape_derived_stress*2.*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]]-tissue_barycenter[0])/ |
| 212 | 1 | akiss | (trace*boundary_vertices_number); |
| 213 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]-=boundary*tissue_area*second_shape_derived_stress*2.*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]-tissue_barycenter[1])/ |
| 214 | 1 | akiss | (trace*boundary_vertices_number); |
| 215 | 1 | akiss | |
| 216 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]]-=boundary*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1])* |
| 217 | 1 | akiss | (first_shape_derived_stress*(tissue_shape[0]-(((parameters_list*)parameters)->tissue_target)[0])+ |
| 218 | 1 | akiss | second_shape_derived_stress*(tissue_shape[1]-(((parameters_list*)parameters)->tissue_target)[1]))/(2.*trace); |
| 219 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[previous]]-=boundary*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]+1])* |
| 220 | 1 | akiss | (first_shape_derived_stress*(tissue_shape[0]-(((parameters_list*)parameters)->tissue_target)[0])+ |
| 221 | 1 | akiss | second_shape_derived_stress*(tissue_shape[1]-(((parameters_list*)parameters)->tissue_target)[1]))/(2.*trace); |
| 222 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[j]+1]-=boundary*(vertices[2*(((parameters_list*)parameters)->cells_vertices)[previous]])* |
| 223 | 1 | akiss | (first_shape_derived_stress*(tissue_shape[0]-(((parameters_list*)parameters)->tissue_target)[0])+ |
| 224 | 1 | akiss | second_shape_derived_stress*(tissue_shape[1]-(((parameters_list*)parameters)->tissue_target)[1]))/(2.*trace); |
| 225 | 1 | akiss | forces[2*(((parameters_list*)parameters)->cells_vertices)[previous]+1]-=boundary*(-vertices[2*(((parameters_list*)parameters)->cells_vertices)[j]])* |
| 226 | 1 | akiss | (first_shape_derived_stress*(tissue_shape[0]-(((parameters_list*)parameters)->tissue_target)[0])+ |
| 227 | 1 | akiss | second_shape_derived_stress*(tissue_shape[1]-(((parameters_list*)parameters)->tissue_target)[1]))/(2.*trace); |
| 228 | 1 | akiss | } |
| 229 | 1 | akiss | } |
| 230 | 1 | akiss | } |
| 231 | 1 | akiss | energy-=tissue_area*(first_shape_derived_stress*(tissue_shape[0]-(((parameters_list*)parameters)->tissue_target)[0])+ |
| 232 | 1 | akiss | second_shape_derived_stress*(tissue_shape[1]-(((parameters_list*)parameters)->tissue_target)[1]))/trace; |
| 233 | 1 | akiss | } |
| 234 | 1 | akiss | |
| 235 | 1 | akiss | return(energy);
|
| 236 | 1 | akiss | |
| 237 | 1 | akiss | } |