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method3.c
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/*************************************************************
* This file is part of the Surface Evolver source code. *
* Programmer: Ken Brakke, [email protected] *
*************************************************************/
/*********************************************************************
*
* file: method3.c
*
* contents: quantities for facets, continuation of method2.c
*/
#include "include.h"
/*********************************************************************
facet_2form_integral method
Integral of 2-form over facet. Works in n dim.
2-form components in method instance expr list in lexicographic order,
i.e. 01,02,03,12,13,23.
*********************************************************************/
/*********************************************************************
*
* function: facet_2form_integral_init()
*
* purpose: Check illegalities
*
*/
void facet_2form_integral_init(
int mode,
struct method_instance *mi
)
{
if ( web.dimension != 2 )
kb_error(1778,"facet_2form_integral method only for 2D facets.\n",RECOVERABLE);
if ( web.modeltype == QUADRATIC )
kb_error(1779,"facet_2form_integral method only for LINEAR and LAGRANGE models.\n",RECOVERABLE);
} // end facet_2form_integral_init()
/*********************************************************************
*
* function: facet_2form_integral()
*
* purpose: method value
*
*/
REAL facet_2form_integral(struct qinfo *f_info)
{ int m,i,j,k;
REAL value=0.0;
REAL sign = (get_fattr(f_info->id) & NEGBOUNDARY) ? -1.0 : 1.0;
struct method_instance *mi = METH_INSTANCE(f_info->method);
if ( web.modeltype == LAGRANGE ) return facet_2form_integral_lagrange(f_info);
for ( m = 0 ; m < gauss2D_num ; m++ )
{
f_info->gauss_pt[m][2*SDIM] = m; /* kludge for attr interpolation. */
for ( i = 0, k = 0 ; i < SDIM ; i++ )
for ( j = i+1 ; j < SDIM ; j++,k++ )
{ REAL form = gauss2Dwt[m]*
eval(mi->expr[k],f_info->gauss_pt[m],f_info->id,NULL);
value += (f_info->sides[0][0][i]*f_info->sides[0][1][j]
- f_info->sides[0][0][j]*f_info->sides[0][1][i])*form;
}
}
return sign*value/2; /* 2 is triangle factor for normal */
} // end facet_2form_integral()
/*********************************************************************
*
* function: facet_2form_integral_grad()
*
* purpose: method gradient
*
*/
REAL facet_2form_integral_grad(struct qinfo *f_info)
{ int m,n,i,j,k;
REAL value = 0.0;
REAL form[MAXCOORD][MAXCOORD]; /* as antisymmetric matrix */
REAL derivs[MAXCOORD][MAXCOORD][MAXCOORD]; /* coord is last index */
REAL sum;
REAL sign = (get_fattr(f_info->id) & NEGBOUNDARY) ? -1.0 : 1.0;
struct method_instance *mi = METH_INSTANCE(f_info->method);
if ( web.modeltype == LAGRANGE )
return facet_2form_integral_lagrange_grad(f_info);
for ( i = 0 ; i < SDIM ; i++ ) form[i][i] = 0.0;
for ( m = 0 ; m < gauss2D_num ; m++ )
{ REAL weight = sign*gauss2Dwt[m];
f_info->gauss_pt[m][2*SDIM] = m; /* kludge for attr interpolation. */
for ( i = 0, k = 0 ; i < SDIM ; i++ )
{ for ( n = 0 ; n < SDIM ;n++ ) derivs[i][i][n] = 0.0;
for ( j = i+1 ; j < SDIM ; j++,k++ )
{ eval_all(mi->expr[k],f_info->gauss_pt[m],SDIM,
form[i]+j, derivs[i][j],f_info->id);
form[j][i] = - form[i][j];
for ( n = 0 ; n < SDIM ;n++ )
derivs[j][i][n] = -derivs[i][j][n];
}
}
for ( i = 0, sum = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
sum += f_info->sides[0][0][i]*form[i][j]*f_info->sides[0][1][j];
value += weight*sum;
for ( k = 0 ; k < SDIM ; k++ )
{ for ( i = 0, sum = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
sum += f_info->sides[0][0][i]*derivs[i][j][k]*f_info->sides[0][1][j];
f_info->grad[0][k] += weight*(gauss2Dpt[m][0]*sum
- SDIM_dot(form[k],f_info->sides[0][1])
+ SDIM_dot(form[k],f_info->sides[0][0]))/2;
f_info->grad[1][k] += weight*(gauss2Dpt[m][1]*sum
+ SDIM_dot(form[k],f_info->sides[0][1]))/2;
f_info->grad[2][k] += weight*(gauss2Dpt[m][2]*sum
- SDIM_dot(form[k],f_info->sides[0][0]))/2;
}
}
return value/2;
} // end facet_2form_integral_grad()
/*********************************************************************
*
* function: facet_2form_integral_hess()
*
* purpose: method gradient and hessian
*
*/
/* derivatives of facet sides with respect to vertices of facet */
int sign1[FACET_VERTS] = { -1, 1, 0 };
int sign2[FACET_VERTS] = { -1, 0, 1 };
REAL facet_2form_integral_hess(struct qinfo *f_info)
{ int m,n,i,j,k,p,q;
REAL value = 0.0;
REAL form[MAXCOORD][MAXCOORD]; /* as antisymmetric matrix */
REAL derivs[MAXCOORD][MAXCOORD][MAXCOORD]; /* coord is last index */
MAT4D(second,MAXCOORD,MAXCOORD,MAXCOORD,MAXCOORD);
REAL sum;
REAL *s1 = f_info->sides[0][0];
REAL *s2 = f_info->sides[0][1];
REAL s1Fu,s2Fu,Fvs1,Fvs2,s1Fuvs2;
REAL sign = (get_fattr(f_info->id) & NEGBOUNDARY) ? -1.0 : 1.0;
struct method_instance *mi = METH_INSTANCE(f_info->method);
if ( web.modeltype == LAGRANGE )
return facet_2form_integral_lagrange_hess(f_info);
for ( i = 0, k = 0 ; i < SDIM ; i++ )
{ form[i][i] = 0.0;
for ( n = 0 ; n < SDIM ;n++ )
{ derivs[i][i][n] = 0.0;
for ( j = 0 ; j < SDIM ;j++ )
second[i][i][n][j] = 0.0;
}
}
for ( m = 0 ; m < gauss2D_num ; m++ )
{ REAL weight = sign*gauss2Dwt[m];
f_info->gauss_pt[m][2*SDIM] = m; /* kludge for attr interpolation. */
for ( i = 0, k = 0 ; i < SDIM ; i++ )
{ for ( j = i+1 ; j < SDIM ; j++,k++ )
{ eval_second(mi->expr[k],f_info->gauss_pt[m],SDIM,
form[i]+j, derivs[i][j],second[i][j],f_info->id);
form[j][i] = - form[i][j];
for ( n = 0 ; n < SDIM ;n++ )
derivs[j][i][n] = -derivs[i][j][n];
for ( n = 0 ; n < SDIM ;n++ )
for ( p = 0 ; p < SDIM ;p++ )
second[j][i][n][p] = -second[i][j][n][p];
}
}
for ( i = 0, sum = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
sum += s1[i]*form[i][j]*s2[j];
value += weight*sum;
/* gradient */
for ( k = 0 ; k < SDIM ; k++ )
{ for ( i = 0, sum = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
sum += s1[i]*derivs[i][j][k]*s2[j];
f_info->grad[0][k] += weight*(gauss2Dpt[m][0]*sum
- SDIM_dot(form[k],s2)
+ SDIM_dot(form[k],s1))/2;
f_info->grad[1][k] += weight*(gauss2Dpt[m][1]*sum
+ SDIM_dot(form[k],s2))/2;
f_info->grad[2][k] += weight*(gauss2Dpt[m][2]*sum
- SDIM_dot(form[k],s1))/2;
}
/* hessian */
for ( p = 0 ; p < SDIM ; p++ )
for ( q = 0 ; q < SDIM ; q++ )
{ for ( i = 0, s1Fu = 0.0 ; i < SDIM ; i++ )
s1Fu += s1[i]*derivs[i][q][p];
for ( i = 0, s2Fu = 0.0 ; i < SDIM ; i++ )
s2Fu += s2[i]*derivs[i][q][p];
for ( i = 0, Fvs1 = 0.0 ; i < SDIM ; i++ )
Fvs1 += derivs[p][i][q]*s1[i];
for ( i = 0, Fvs2 = 0.0 ; i < SDIM ; i++ )
Fvs2 += derivs[p][i][q]*s2[i];
for ( i = 0, s1Fuvs2 = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
s1Fuvs2 += s1[i]*second[i][j][p][q]*s2[j];
for ( i = 0 ; i < FACET_VERTS ; i++ )
for ( j = 0 ; j < FACET_VERTS ; j++ )
f_info->hess[i][j][p][q] += weight*(
sign1[i]*form[p][q]*sign2[j] - sign2[i]*form[p][q]*sign1[j]
+ gauss2Dpt[m][i]*(s1Fu*sign2[j] - s2Fu*sign1[j])
+ gauss2Dpt[m][j]*(sign1[i]*Fvs2 - sign2[i]*Fvs1)
+ gauss2Dpt[m][i]*gauss2Dpt[m][j]*s1Fuvs2 )/2;
}
}
return value/2;
} // end facet_2form_integral_hess()
/******************************************************************************
facet_2form_integral Lagrangian model
******************************************************************************/
/*********************************************************************
*
* function: facet_2form_integral_lagrange()
*
* purpose: method value
*
*/
REAL facet_2form_integral_lagrange(struct qinfo *f_info)
{ int m,i,j,k;
REAL value=0.0,form;
REAL sign = (get_fattr(f_info->id) & NEGBOUNDARY) ? -1.0 : 1.0;
int dim = web.dimension;
struct gauss_lag *gl = &gauss_lagrange[dim][web.gauss2D_order];
struct method_instance *mi = METH_INSTANCE(f_info->method);
for ( i = 0, k = 0 ; i < SDIM ; i++ )
for ( j = i+1 ; j < SDIM ; j++,k++ )
{ for ( m = 0 ; m < gl->gnumpts ; m++ )
{
f_info->gauss_pt[m][2*SDIM] = m; /* kludge for attr interpolation. */
form = gl->gausswt[m]*
eval(mi->expr[k],f_info->gauss_pt[m],f_info->id,NULL);
value += (f_info->sides[m][0][i]*f_info->sides[m][1][j]
- f_info->sides[m][0][j]*f_info->sides[m][1][i])*form;
}
}
return sign*value/2; /* 2 is triangle factor */
} // end facet_2form_integral_lagrange()
/*********************************************************************
*
* function: facet_2form_integral_lagrange_grad()
*
* purpose: method gradient
*
*/
REAL facet_2form_integral_lagrange_grad(struct qinfo *f_info)
{ int m,n,i,j,k;
REAL value = 0.0;
REAL form[MAXCOORD][MAXCOORD]; /* as antisymmetric matrix */
REAL derivs[MAXCOORD][MAXCOORD][MAXCOORD]; /* coord is last index */
REAL sum;
int dim = web.dimension;
REAL sign = (get_fattr(f_info->id) & NEGBOUNDARY) ? -1.0 : 1.0;
struct gauss_lag *gl = &gauss_lagrange[dim][web.gauss2D_order];
int ctrl = web.skel[FACET].ctrlpts;
struct method_instance *mi = METH_INSTANCE(f_info->method);
for ( i = 0 ; i < SDIM ; i++ )
{ form[i][i] = 0.0;
for ( n = 0 ; n < SDIM ;n++ ) derivs[i][i][n] = 0.0;
}
for ( m = 0 ; m < gl->gnumpts ; m++ )
{ REAL weight = sign*gl->gausswt[m]/2;
f_info->gauss_pt[m][2*SDIM] = m; /* kludge for attr interpolation. */
for ( i = 0, k = 0 ; i < SDIM ; i++ )
{ for ( j = i+1 ; j < SDIM ; j++,k++ )
{ eval_all(mi->expr[k],f_info->gauss_pt[m],SDIM,
form[i]+j, derivs[i][j],f_info->id);
form[j][i] = - form[i][j];
for ( n = 0 ; n < SDIM ;n++ )
derivs[j][i][n] = -derivs[i][j][n];
}
}
for ( i = 0, sum = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
{
sum += f_info->sides[m][0][i]*form[i][j]*f_info->sides[m][1][j];
for ( n = 0 ; n < ctrl ; n++ )
{
f_info->grad[n][i] += weight*gl->gpolypart[m][0][n]*form[i][j]
*f_info->sides[m][1][j];
for ( k= 0 ; k < SDIM ; k++ )
f_info->grad[n][k] += weight*f_info->sides[m][0][i]
*gl->gpoly[m][n]*derivs[i][j][k]*f_info->sides[m][1][j];
f_info->grad[n][j] += weight*f_info->sides[m][0][i]*form[i][j]
*gl->gpolypart[m][1][n];
}
}
value += weight*sum;
}
return value;
} // end facet_2form_integral_lagrange_grad()
/*********************************************************************
*
* function: facet_2form_integral_lagrange_hess()
*
* purpose: method gradient and hessian
*
*/
REAL facet_2form_integral_lagrange_hess(struct qinfo *f_info)
{ int m,n,i,j,k,p;
REAL value = 0.0;
REAL form[MAXCOORD][MAXCOORD]; /* as antisymmetric matrix */
REAL derivs[MAXCOORD][MAXCOORD][MAXCOORD]; /* coord is last index */
MAT4D(second,MAXCOORD,MAXCOORD,MAXCOORD,MAXCOORD);
REAL sum;
REAL sign = (get_fattr(f_info->id) & NEGBOUNDARY) ? -1.0 : 1.0;
int dim = web.dimension;
struct gauss_lag *gl = &gauss_lagrange[dim][web.gauss2D_order];
int ctrl = web.skel[FACET].ctrlpts;
struct method_instance *mi = METH_INSTANCE(f_info->method);
for ( i = 0; i < SDIM ; i++ )
{ form[i][i] = 0.0;
for ( n = 0 ; n < SDIM ;n++ )
{ derivs[i][i][n] = 0.0;
for ( j = 0 ; j < SDIM ;j++ )
second[i][i][n][j] = 0.0;
}
}
for ( m = 0 ; m < gl->gnumpts ; m++ )
{ REAL weight = sign*gl->gausswt[m]/2;
f_info->gauss_pt[m][2*SDIM] = m; /* kludge for attr interpolation. */
for ( i = 0, k = 0 ; i < SDIM ; i++ )
{ for ( j = i+1 ; j < SDIM ; j++,k++ )
{ eval_second(mi->expr[k],f_info->gauss_pt[m],
SDIM, form[i]+j, derivs[i][j],second[i][j],f_info->id);
form[j][i] = - form[i][j];
for ( n = 0 ; n < SDIM ;n++ )
derivs[j][i][n] = -derivs[i][j][n];
for ( n = 0 ; n < SDIM ;n++ )
for ( p = 0 ; p < SDIM ;p++ )
second[j][i][n][p] = -second[i][j][n][p];
}
}
for ( i = 0, sum = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
{
sum += f_info->sides[m][0][i]*form[i][j]*f_info->sides[m][1][j];
for ( n = 0 ; n < ctrl ; n++ )
{ int nn,kk;
/* gradient terms */
f_info->grad[n][i] += weight*gl->gpolypart[m][0][n]*form[i][j]
*f_info->sides[m][1][j];
for ( k= 0 ; k < SDIM ; k++ )
f_info->grad[n][k] += weight*f_info->sides[m][0][i]
*gl->gpoly[m][n]*derivs[i][j][k]*f_info->sides[m][1][j];
f_info->grad[n][j] += weight*f_info->sides[m][0][i]*form[i][j]
*gl->gpolypart[m][1][n];
/* hessian terms */
for ( nn = 0; nn < ctrl ; nn++ )
{
for ( kk = 0 ; kk < SDIM ; kk++ )
f_info->hess[n][nn][i][kk] += weight*gl->gpolypart[m][0][n]
*gl->gpoly[m][nn]*derivs[i][j][kk]*f_info->sides[m][1][j];
f_info->hess[n][nn][i][j] += weight*gl->gpolypart[m][0][n]
*form[i][j]*gl->gpolypart[m][1][nn];
for ( k= 0 ; k < SDIM ; k++ )
{ f_info->hess[n][nn][k][i] += weight*gl->gpolypart[m][0][nn]
*gl->gpoly[m][n]*derivs[i][j][k]*f_info->sides[m][1][j];
for ( kk = 0 ; kk < SDIM ; kk++ )
f_info->hess[n][nn][k][kk] += weight*f_info->sides[m][0][i]
*gl->gpoly[m][n]*second[i][j][k][kk]*gl->gpoly[m][nn]
*f_info->sides[m][1][j];
f_info->hess[n][nn][k][j] += weight*f_info->sides[m][0][i]
*gl->gpoly[m][n]*derivs[i][j][k]*gl->gpolypart[m][1][nn];
}
f_info->hess[n][nn][j][i] += weight*gl->gpolypart[m][0][nn]
*form[i][j]*gl->gpolypart[m][1][n];
for ( kk = 0 ; kk < SDIM ; kk++ )
f_info->hess[n][nn][j][kk] += weight*f_info->sides[m][0][i]
*derivs[i][j][kk]*gl->gpoly[m][nn]*gl->gpolypart[m][1][n];
}
}
}
value += weight*sum;
}
return value;
} // end facet_2form_integral_lagrange_hess()
/*********************************************************************
facet_2form_sq_integral method
Integral of facetwise square of 2-form over facet. Works in n dim.
2-form components in method instance expr list in lexicographic order,
i.e. 01,02,03,12,13,23. For Andy Hanson's symplectic area minimization.
*********************************************************************/
/*********************************************************************
*
* function: facet_2form_sq_integral_init()
*
* purpose: Check illegalities
*
*/
void facet_2form_sq_integral_init(
int mode,
struct method_instance *mi
)
{
if ( web.dimension != 2 )
kb_error(2412,"facet_2form_sq_integral method only for 2D facets.\n",RECOVERABLE);
if ( web.modeltype != LINEAR )
kb_error(2413,"facet_2form_sq_integral method only for LINEAR model.\n",RECOVERABLE);
} // end facet_2form_sq_integral_init()
/*********************************************************************
*
* function: facet_2form_sq_integral()
*
* purpose: method value
*
*/
REAL facet_2form_sq_integral(struct qinfo *f_info)
{ int m,i,j,k;
REAL value=0.0;
struct method_instance *mi = METH_INSTANCE(f_info->method);
for ( m = 0 ; m < gauss2D_num ; m++ )
{
f_info->gauss_pt[m][2*SDIM] = m; /* kludge for attr interpolation. */
for ( i = 0, k = 0 ; i < SDIM ; i++ )
for ( j = i+1 ; j < SDIM ; j++,k++ )
{ REAL form = gauss2Dwt[m]*
eval(mi->expr[k],f_info->gauss_pt[m],f_info->id,NULL);
value += (f_info->sides[0][0][i]*f_info->sides[0][1][j]
- f_info->sides[0][0][j]*f_info->sides[0][1][i])*form;
}
}
return value*value/4; /* 2 is triangle factor for normal */
} // end facet_2form_sq_integral()
/*********************************************************************
*
* function: facet_2form_sq_integral_grad()
*
* purpose: method gradient
*
*/
REAL facet_2form_sq_integral_grad(struct qinfo *f_info)
{ int m,n,i,j,k;
REAL value = 0.0;
REAL form[MAXCOORD][MAXCOORD]; /* as antisymmetric matrix */
REAL derivs[MAXCOORD][MAXCOORD][MAXCOORD]; /* coord is last index */
REAL sum;
struct method_instance *mi = METH_INSTANCE(f_info->method);
for ( i = 0 ; i < SDIM ; i++ ) form[i][i] = 0.0;
for ( m = 0 ; m < gauss2D_num ; m++ )
{ REAL weight = gauss2Dwt[m];
f_info->gauss_pt[m][2*SDIM] = m; /* kludge for attr interpolation. */
for ( i = 0, k = 0 ; i < SDIM ; i++ )
{ for ( n = 0 ; n < SDIM ;n++ ) derivs[i][i][n] = 0.0;
for ( j = i+1 ; j < SDIM ; j++,k++ )
{ eval_all(mi->expr[k],f_info->gauss_pt[m],SDIM,
form[i]+j, derivs[i][j],f_info->id);
form[j][i] = - form[i][j];
for ( n = 0 ; n < SDIM ;n++ )
derivs[j][i][n] = -derivs[i][j][n];
}
}
for ( i = 0, sum = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
sum += f_info->sides[0][0][i]*form[i][j]*f_info->sides[0][1][j];
value += weight*sum;
for ( k = 0 ; k < SDIM ; k++ )
{ for ( i = 0, sum = 0.0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
sum += f_info->sides[0][0][i]*derivs[i][j][k]*f_info->sides[0][1][j];
f_info->grad[0][k] += weight*(gauss2Dpt[m][0]*sum
- SDIM_dot(form[k],f_info->sides[0][1])
+ SDIM_dot(form[k],f_info->sides[0][0]))/2;
f_info->grad[1][k] += weight*(gauss2Dpt[m][1]*sum
+ SDIM_dot(form[k],f_info->sides[0][1]))/2;
f_info->grad[2][k] += weight*(gauss2Dpt[m][2]*sum
- SDIM_dot(form[k],f_info->sides[0][0]))/2;
}
}
/* adjust grad for being the square */
for ( i = 0 ; i < FACET_VERTS ; i++ )
for ( k = 0 ; k < SDIM ; k++ )
f_info->grad[i][k] *= value;
return value*value/4;
} // end facet_2form_sq_integral_grad()
/******************************************************************************
Soapfilm Gravity quantity stuff
******************************************************************************/
/***************************************************************
*
* function: gravity_init()
*
* purpose: initialization for gravity method
*/
void gravity_init(
int mode, /* energy or gradient */
struct method_instance *mi
)
{
/* method modulus is gravitation constant */
if ( gravity_quantity_num >= 0 )
GEN_QUANT(gravity_quantity_num)->modulus =
web.gravflag ? web.grav_const : 0.0;
} // end gravity_init()
/**********************************************************************************
*
* function: full_gravity_init()
*
* purpose: initialization for gravity method using built-in G and body densities
*/
void full_gravity_init(
int mode, /* energy or gradient */
struct method_instance *mi
)
{
/* method modulus is gravitation constant */
mi->flags &= FAKE_IMPLICIT;
GEN_QUANT(gravity_quantity_num)->modulus =
web.gravflag ? web.grav_const : 0.0;
} // end full_gravity_init()
/**************************************************************
*
* function: gravity_all()
*
* purpose: calculates value, gradient, and hessian of one
* facet due to gravitational potential.
*
* input: info about vertex is in qinfo structure.
*
*/
REAL gravity_all_q(struct qinfo *,int);
REAL gravity_all_lagrange(struct qinfo *,int);
REAL gravity_all(
struct qinfo *f_info,
int mode /* METHOD_VALUE, METHOD_GRADIENT, or METHOD_HESSIAN */
)
{
int i,j;
REAL jac; /* jacobian */
REAL sum = 0.0; /* quadratic z sum of facet */
REAL djdx[MAXCOORD],djdy[MAXCOORD],dsdz[MAXCOORD];
REAL c = 1/24.; /* coefficient */
body_id b_id;
REAL gdensity;
struct method_instance *mi = METH_INSTANCE(f_info->method);
if ( web.modeltype == QUADRATIC ) return gravity_all_q(f_info,mode);
if ( web.modeltype == LAGRANGE )
return gravity_all_lagrange(f_info,mode);
b_id = get_facet_body(f_info->id);
if ( mi->flags & (IMPLICIT_INSTANCE|FAKE_IMPLICIT) )
{ /* include density difference */
gdensity = 0.0;
if ( valid_id(b_id) )
gdensity += get_body_density(b_id);
b_id = get_facet_body(facet_inverse(f_info->id));
if ( valid_id(b_id) )
gdensity -= get_body_density(b_id);
if ( gdensity == 0.0 )
return 0.0;
c *= gdensity;
}
jac = f_info->sides[0][0][0]*f_info->sides[0][1][1]
- f_info->sides[0][1][0]*f_info->sides[0][0][1];
for ( i = 0 ; i < f_info->vcount ; i++ )
for ( j = 0 ; j <= i ; j++ )
sum += f_info->x[i][2]*f_info->x[j][2];
if ( mode == METHOD_VALUE ) return jac*sum*c;
djdx[0] = (-f_info->sides[0][1][1] + f_info->sides[0][0][1]);
djdx[1] = f_info->sides[0][1][1];
djdx[2] = -f_info->sides[0][0][1];
djdy[0] = (-f_info->sides[0][0][0] + f_info->sides[0][1][0]);
djdy[1] = -f_info->sides[0][1][0];
djdy[2] = f_info->sides[0][0][0];
dsdz[0] = 2*f_info->x[0][2]+f_info->x[1][2]+f_info->x[2][2];
dsdz[1] = f_info->x[0][2]+2*f_info->x[1][2]+f_info->x[2][2];
dsdz[2] = f_info->x[0][2]+f_info->x[1][2]+2*f_info->x[2][2];
for ( i = 0 ; i < 3; i++ )
{ f_info->grad[i][0] = djdx[i]*sum*c;
f_info->grad[i][1] = djdy[i]*sum*c;
f_info->grad[i][2] = dsdz[i]*jac*c;
}
if ( mode == METHOD_GRADIENT ) return jac*sum*c;
/* second partials, self */
for ( i = 0 ; i < 3; i++ )
{ f_info->hess[i][i][0][2] = f_info->hess[i][i][2][0] = djdx[i]*dsdz[i]*c;
f_info->hess[i][i][1][2] = f_info->hess[i][i][2][1] = djdy[i]*dsdz[i]*c;
f_info->hess[i][i][2][2] = 2*jac*c;
f_info->hess[i][i][0][0] = f_info->hess[i][i][0][1]
= f_info->hess[i][i][1][0] = f_info->hess[i][i][1][1] = 0.0;
}
/* second partials, mixed */
for ( i = 0 ; i < 3 ; i++ )
for ( j = 0 ; j < 3 ; j++ )
{ if ( j == i ) continue;
f_info->hess[i][j][0][0] = f_info->hess[i][j][1][1] = 0.0;
f_info->hess[i][j][0][1] = (j==((i+1)%3)) ? sum*c : -sum*c;
f_info->hess[i][j][1][0] = (j==((i+1)%3)) ? -sum*c : sum*c;
f_info->hess[i][j][0][2] = djdx[i]*dsdz[j]*c;
f_info->hess[i][j][2][0] = djdx[j]*dsdz[i]*c;
f_info->hess[i][j][1][2] = djdy[i]*dsdz[j]*c;
f_info->hess[i][j][2][1] = djdy[j]*dsdz[i]*c;
f_info->hess[i][j][2][2] = jac*c;
}
return jac*sum*c;
} // end gravity_all()
/**************************************************************
*
* function: gravity_all_q()
*
* purpose: calculates value, gradient, and hessian of one
* facet due to gravitational potential. Quadratic model.
*
* input: info about vertex is in qinfo structure.
*
*/
REAL gravity_all_q(
struct qinfo *f_info,
int mode /* METHOD_VALUE, METHOD_GRADIENT, or METHOD_HESSIAN */
)
{
int k,kk,m;
REAL jac; /* jacobian */
REAL **x,**tang;
REAL **g=NULL,****h=NULL;
REAL value = 0.0;
body_id b_id;
REAL gdensity = 1.0;
struct method_instance *mi = METH_INSTANCE(f_info->method);
x = f_info->x;
if ( mode == METHOD_GRADIENT )
{ g = f_info->grad;
}
else if ( mode == METHOD_HESSIAN )
{ g = f_info->grad;
h = f_info->hess;
}
if ( mi->flags & (IMPLICIT_INSTANCE|FAKE_IMPLICIT) )
{ /* include density difference */
b_id = get_facet_body(f_info->id);
gdensity = 0.0;
if ( valid_id(b_id) )
gdensity += get_body_density(b_id);
b_id = get_facet_body(facet_inverse(f_info->id));
if ( valid_id(b_id) )
gdensity -= get_body_density(b_id);
if ( gdensity == 0.0 ) return 0.0;
}
for ( m = 0 ; m < gauss2D_num ; m++ )
{ REAL weight = gdensity*gauss2Dwt[m]/2;
REAL z;
for ( k = 0, z = 0.0 ; k < ctrl_num ; k++ )
z += gpoly[m][k]*x[k][2];
tang = f_info->sides[m];
jac = tang[0][0]*tang[1][1] - tang[0][1]*tang[1][0];
value += weight*z*z*jac/2;
if ( mode == METHOD_VALUE ) continue;
for ( k = 0 ; k < ctrl_num ; k++ )
{ g[k][0] += weight*z*z/2*(gpolypartial[m][0][k]*tang[1][1]
- tang[0][1]*gpolypartial[m][1][k]);
g[k][1] += weight*z*z/2*(tang[0][0]*gpolypartial[m][1][k]
- gpolypartial[m][0][k]*tang[1][0]);
g[k][2] += weight*z*gpoly[m][k]*jac;
}
if ( mode == METHOD_GRADIENT ) continue;
/* hessian */
for ( k = 0 ; k < ctrl_num ; k++ )
for ( kk = 0 ; kk < ctrl_num ; kk++ )
{
h[k][kk][0][1] += weight*z*z/2*(gpolypartial[m][0][k]*gpolypartial[m][1][kk]
- gpolypartial[m][0][kk]*gpolypartial[m][1][k]);
h[k][kk][0][2] += weight*z*gpoly[m][kk]*(gpolypartial[m][0][k]*tang[1][1]
- tang[0][1]*gpolypartial[m][1][k]);
h[k][kk][1][0] += weight*z*z/2*(gpolypartial[m][0][kk]*gpolypartial[m][1][k]
- gpolypartial[m][0][k]*gpolypartial[m][1][kk]);
h[k][kk][1][2] += weight*z*gpoly[m][kk]*(tang[0][0]*gpolypartial[m][1][k]
- gpolypartial[m][0][k]*tang[1][0]);
h[k][kk][2][0] += weight*z*gpoly[m][k]*(gpolypartial[m][0][kk]*tang[1][1]
- tang[0][1]*gpolypartial[m][1][kk]);
h[k][kk][2][1] += weight*z*gpoly[m][k]*(tang[0][0]*gpolypartial[m][1][kk]
- gpolypartial[m][0][kk]*tang[1][0]);
h[k][kk][2][2] += weight*gpoly[m][kk]*gpoly[m][k]*jac;
}
}
return value;
} // end gravity_all_q()
/**************************************************************
*
* function: gravity_all_lagrange()
*
* purpose: calculates value, gradient, and hessian of one
* facet due to gravitational potential. Lagrange model.
*
* input: info about vertex is in qinfo structure.
*
*/
REAL gravity_all_lagrange(
struct qinfo *f_info,
int mode /* METHOD_VALUE, METHOD_GRADIENT, or METHOD_HESSIAN */
)
{
REAL value = 0.0;
body_id b_id;
REAL gdensity = 1.0;
int i,m,j,k,jj,ii,kk;
REAL z;
REAL val;
MAT2D(mat,MAXCOORD,MAXCOORD);
REAL sign = (get_fattr(f_info->id) & NEGBOUNDARY) ? -1.0 : 1.0;
int dim = web.dimension;
struct gauss_lag *gl = &gauss_lagrange[dim][web.gauss2D_order];
MAT4D(dethess,MAXCOORD,MAXCOORD,MAXCOORD,MAXCOORD);
struct method_instance *mi = METH_INSTANCE(f_info->method);
if ( mi->flags & (IMPLICIT_INSTANCE|FAKE_IMPLICIT) )
{ /* include density difference */
b_id = get_facet_body(f_info->id);
gdensity = 0.0;
if ( valid_id(b_id) )
gdensity += get_body_density(b_id);
b_id = get_facet_body(facet_inverse(f_info->id));
if ( valid_id(b_id) )
gdensity -= get_body_density(b_id);
if ( gdensity == 0.0 ) return 0.0;
}
for ( j = 0 ; j < SDIM ; j++ )
mat[web.dimension][j] = 0.0;
for ( m = 0 ; m < gl->gnumpts ; m++ )
{ REAL det;
REAL weight = sign*gdensity*gl->gausswt[m]/factorial[dim];
for ( i = 0 ; i < web.dimension ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
mat[i][j] = f_info->sides[m][i][j]; /* mat destroyed by det */
z = f_info->gauss_pt[m][SDIM-1];
val = z*z/2;
mat[web.dimension][SDIM-1] = val;
if ( mode == METHOD_HESSIAN ) det_hess(mat,dethess,SDIM);
det = det_adjoint(mat,SDIM);
value += weight*det;
if ( mode == METHOD_VALUE ) continue;
/* gradient */
for ( k = 0 ; k < gl->lagpts; k++ )
for ( j = 0 ; j < SDIM ; j++ )
for ( i = 0 ; i < dim ; i++ )
{ f_info->grad[k][j] += weight*gl->gpolypart[m][i][k]*mat[j][i];
}
for ( k = 0 ; k < gl->lagpts ; k++ )
f_info->grad[k][SDIM-1] += weight*gl->gpoly[m][k]*z*mat[SDIM-1][dim];
if ( mode == METHOD_GRADIENT ) continue;
/* hessian */
for ( k = 0 ; k < gl->lagpts ; k++ )
for ( kk = 0 ; kk < gl->lagpts ; kk++ )
{ REAL h;
for ( j = 0 ; j < SDIM ; j++ )
for ( jj = 0 ; jj < SDIM ; jj++ )
{ h = 0.0;
for ( i = 0 ; i < dim ; i++ )
for ( ii = 0 ; ii < dim ; ii++ )
{ h += dethess[i][j][ii][jj]
*gl->gpolypart[m][i][k]*gl->gpolypart[m][ii][kk];
}
f_info->hess[k][kk][j][jj] += weight*h;
}
for ( j = 0 ; j < SDIM ; j++ )
{ h = 0.0;
for ( i = 0 ; i < dim ; i++ )
h += dethess[i][j][dim][SDIM-1]*gl->gpolypart[m][i][k]
*gl->gpoly[m][kk]*z;
f_info->hess[k][kk][j][SDIM-1] += weight*h;
}
for ( jj = 0 ; jj < SDIM ; jj++ )
{ h = 0.0;
for ( ii = 0 ; ii < dim ; ii++ )
h += dethess[dim][SDIM-1][ii][jj]*gl->gpolypart[m][ii][kk]
*gl->gpoly[m][k]*z;
f_info->hess[k][kk][SDIM-1][jj] += weight*h;
}
h = gl->gpoly[m][k]*gl->gpoly[m][kk]*mat[SDIM-1][web.dimension];
f_info->hess[k][kk][SDIM-1][SDIM-1] += weight*h;
}
}
return value;
} // end gravity_all_lagrange()
/**************************************************************
*
* function: gravity_energy()
*
* purpose: calculates energy of one facet due to potential
*
* input: info about vertex is in qinfo structure.
*
*/
REAL gravity_energy(struct qinfo *f_info)
{
return gravity_all(f_info,METHOD_VALUE);
}
/**************************************************************
*
* function: gravity_grads()
*
* purpose: calculates gradient of one facet due to potential
*
* input: info about vertex is in qinfo structure.
*
*/
REAL gravity_grads(struct qinfo *f_info)
{
return gravity_all(f_info,METHOD_GRADIENT);
}
/**************************************************************
*
* function: gravity_hessian()
*
* purpose: calculates hessian of one facet due to potential
*
* input: info about vertex is in qinfo structure.
*
*/
REAL gravity_hessian(struct qinfo *f_info)
{
return gravity_all(f_info,METHOD_HESSIAN);
}
/******************************************************************
*
* function: pos_area_hess()
*
* purpose: facet area hessian adjustable to force it to be
* positive definite.
*
*/
REAL gga_coeff; /* term coefficient for part of hessian */
REAL fgagfa_coeff; /* term coefficient for part of hessian */
REAL gfa_2_coeff; /* term coefficient for part of hessian */
REAL gfagfa_coeff; /* term coefficient for neg part of hessian */
REAL gfaafg_coeff; /* term coefficient for correction */
void pos_area_hess_init(
int mode,
struct method_instance *mi
)
{ int k;
k = lookup_global("gga_coeff");
if ( k >= 0 )
gga_coeff = globals(k)->value.real;
else gga_coeff = 1.0;
k = lookup_global("fgagfa_coeff");
if ( k >= 0 )
fgagfa_coeff = globals(k)->value.real;
else fgagfa_coeff = -1.0;
k = lookup_global("gfa_2_coeff");
if ( k >= 0 )
gfa_2_coeff = globals(k)->value.real;
else gfa_2_coeff = 1.0;
k = lookup_global("gfagfa_coeff");
if ( k >= 0 )
gfagfa_coeff = globals(k)->value.real;
else gfagfa_coeff = -1.0;
k = lookup_global("gfaafg_coeff");
if ( k >= 0 )
gfaafg_coeff = globals(k)->value.real;
else gfaafg_coeff = 0.0;
} // end pos_area_hess_init()
REAL pos_area_hess(struct qinfo *f_info)
{
MAT2D(Ainv,MAXCOORD,MAXCOORD);
MAT2D(FtAinv,MAXCOORD,MAXCOORD);
MAT2D(FtAF,MAXCOORD,MAXCOORD);
MAT2D(FtAAF,MAXCOORD,MAXCOORD);
int i,j,m,n;
int dim = web.dimension;
REAL area;
mat_mul_tr(f_info->sides[0],f_info->sides[0],Ainv,dim,SDIM,dim);
area = det_adjoint(Ainv,dim);
if ( area == 0.0 ) return area;
for ( i = 0 ; i < dim ; i++ ) /* get true inverse */
for ( j = 0 ; j < dim ; j++ )
Ainv[i][j] /= area;
area = sqrt(area)/web.simplex_factorial; /* simplex area */
tr_mat_mul(f_info->sides[0],Ainv,FtAinv,dim,SDIM,dim);
mat_mult(FtAinv,f_info->sides[0],FtAF,SDIM,dim,SDIM);
mat_mul_tr(FtAinv,FtAinv,FtAAF,SDIM,dim,SDIM);
/* gradient */
for ( i = 0 ; i < dim ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
{ f_info->grad[i+1][j] = FtAinv[j][i]*area;
f_info->grad[0][j] -= FtAinv[j][i]*area;
}
/* approximate hessian */
for ( m = 0 ; m < dim ; m++ )
for ( n = 0 ; n < dim ; n++ )
for ( i = 0 ; i < SDIM ; i++ )
for ( j = 0 ; j < SDIM ; j++ )
{ REAL val;
val = (i==j) ? gga_coeff*Ainv[m][n] : 0.0;
val += gfagfa_coeff*FtAinv[i][n]*FtAinv[j][m];