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smoother.h
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smoother.h
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#ifndef SMOOTHER_H
#define SMOOTHER_H
#include "global.h"
#include <math.h>
#define MALLOC(var, type, size, subr_name) \
if (((var) = (type *) malloc ((size) * sizeof(type))) == (type *) NULL)
#define ABS(a) ((MACRO_ABS_arg=(a)) >= 0. ? MACRO_ABS_arg : -MACRO_ABS_arg)
#define SQUARE(a) ((a) * (a))
#define SIGN(a,b) (MACRO_SIGN_arg = ABS(a), \
(b) >= 0. ? MACRO_SIGN_arg : -MACRO_SIGN_arg)
#define RMAX(a,b) (MACRO_RMAX_arg1=(a), MACRO_RMAX_arg2=(b), \
(MACRO_RMAX_arg1 > MACRO_RMAX_arg2) ? MACRO_RMAX_arg1 : MACRO_RMAX_arg2)
#define IMIN(a,b) (MACRO_IMIN_arg1=(a), MACRO_IMIN_arg2=(b), \
(MACRO_IMIN_arg1 < MACRO_IMIN_arg2) ? MACRO_IMIN_arg1 : MACRO_IMIN_arg2)
#define TOL_EQ(a,b,tol) (ABS((b) - (a)) <= (tol))
#define ZERO (0.0L)
#define ALMOST_ZERO (1.0e-30L)
#define SQRT_ALMOST_ZERO (1.0e-15L)
template<class Mesh>
class SmootherT
{
public:
typedef typename Mesh::Scalar Scalar;
typedef typename Mesh::Point Point;
typedef typename Mesh::Normal Normal;
typedef typename Mesh::VertexHandle VertexHandle;
typedef typename Mesh::HalfedgeHandle HalfedgeHandle;
typedef typename Mesh::EdgeHandle EdgeHandle;
typedef typename Mesh::FaceHandle FaceHandle;
// enum/struct definition
SmootherT(Mesh& _mesh);
~SmootherT();
public:
void smooth();
//void edge_swap();
//bool is_swap_legal(EdgeHandle _eh) const;
void set_smmethod(int _smmethod) { smmethod_ = _smmethod; }
void set_nsmoothsurf(int _nsmoothsurf) { nsmoothsurf_ = _nsmoothsurf; }
void set_relaxsurf(float _relaxsurf) { relaxsurf_ = _relaxsurf; }
private:
/** Calculate the closest point at a line segment from the point coord. Also
* return as the function value the square of the distance between the points.
* NOTE: projCoord, distFrom1 and lineLeng can be NULL.
*/
Scalar closest_to_line_segment3d(const Point& _pnt, const Point& _ln_pnt1,
const Point& _ln_pnt2, Point& _projected_pnt) const;
/** Compute the area of a 2d triangle, the parameter is in 3d
* The sign of the area is used to indicate the location of a point to a line
*/
Scalar calc_triangle2d_area(const Point _tri_pnt[]) const;
/** Determine in 2D whether a point is inside a triangle or not
* Although the parameter is in 3D, only the first two coordinates are used
*/
bool is_inside_triangle2d(const Point& _pnt, const Point _tri_pnt[]) const;
/** Calculates the closest point to the triangle of coord and returns that
* value. Also returns the square of the distance between coord and the
* triangle.
*/
Scalar closest_to_triangle3d(const Point& _pnt, const Point _tri_pnt[], Point& _projected_pnt) const;
// solvers
/**
* This is the singular value decomposition routine as found in the book
* Numerical Recipes by Press, Flannery, Teukolsky and Vetterling.
*
* Given a matrix a, with logical dimensions m by n and physical
* dimensions mp by np, this routine computes its singular value
* decomposition, a=u w tran(v). The matrix u replaces a on output.
* The diagonal matrix of singular values, w, is output as a vector.
* The matrix v (not its transpose) is output. m must be greater or
* equal to n; if it is smaller, the a should be filled up to square
* with zero rows. rv1 is a work area which should be of size np.
*
* ierr returns the follow values:
* 0 => everything is ok
* 1 => dimensions are incorrect (No longer checks this)
* 2 => procedure did not converge
*/
void svdcmp(double *a, int m, int n, int mp, int np, double *w, double *v, int *ierr);
double LENGTH2D(double a, double b);
/**
* This is the singular value decomposition back substitution routine as
* found in the book Numerical Recipes by Press, Flannery, Teukolsky and
* Vetterling.
*
* Given the matrices u, w and v from a previous singular value
* decomposition with logical dimensions m by n and physical dimensions
* mp by np, this routine does the back substitution for a x = b. The
* diagonal matrix of singular values, w, is a vector. The matrix v
* (not its transpose) is input. m must be greater or equal to n.
* tmp is a work area which must be of size np.
*/
void svbksb (double *u, double *w, double *v, int m, int n, int mp, int np, double *b, double *x);
private:
Mesh& mesh_;
int smmethod_;
int nsmoothsurf_;
float relaxsurf_;
};
template<class Mesh>
SmootherT<Mesh>::SmootherT(Mesh &_mesh) : mesh_(_mesh)
{
}
template<class Mesh>
SmootherT<Mesh>::~SmootherT()
{
}
template<class Mesh>
typename Mesh::Scalar
SmootherT<Mesh>::closest_to_line_segment3d(const Point& _pnt, const Point& _ln_pnt1,
const Point& _ln_pnt2, Point& _projected_pnt) const
{
Scalar dist_from_pnt1;
Point ln_vec = _ln_pnt2 - _ln_pnt1;
Scalar ln_length = ln_vec.norm();
Point delta_vec = _pnt - _ln_pnt1;
if (ln_length <= 1.0e-6) // the tolerance should actually be determined by BBox
{
// 将节点还原为原始位置
_projected_pnt = _ln_pnt1;
return delta_vec.sqrnorm();
}
dist_from_pnt1 = ln_vec | delta_vec / ln_length;
if (dist_from_pnt1 < 0.0)
{
// 投影在反向延长线上，取_ln_pnt1
_projected_pnt = _ln_pnt1;
return delta_vec.sqrnorm();
}
if (dist_from_pnt1 > ln_length)
{
// 投影在正向延长线上，取_ln_pnt2
_projected_pnt = _ln_pnt2;
return (_pnt - _ln_pnt2).sqrnorm();
}
// 投影到线段内部
_projected_pnt = _ln_pnt1 + ln_vec * (dist_from_pnt1 / ln_length);
Point norm = ln_vec % delta_vec;
return norm.sqrnorm() / ln_vec.sqrnorm();
}
template<class Mesh>
typename Mesh::Scalar
SmootherT<Mesh>::calc_triangle2d_area(const Point _tri_pnt[]) const
{
Scalar area2 = (_tri_pnt[1][0] - _tri_pnt[0][0]) * (_tri_pnt[2][1] - _tri_pnt[0][1])
- (_tri_pnt[2][0] - _tri_pnt[0][0]) * (_tri_pnt[1][1] - _tri_pnt[0][1]);
return area2 / 2.0;
}
template<class Mesh>
bool SmootherT<Mesh>::is_inside_triangle2d(const Point& _pnt, const Point _tri_pnt[]) const
{
Scalar tri_area = calc_triangle2d_area(_tri_pnt); // must be wrong
Point pnt[3] = {_tri_pnt[0], _tri_pnt[1], _tri_pnt[2]};
Scalar area;
int i;
for (i = 0; i < 3; ++i)
{
pnt[i] = _pnt;
area = calc_triangle2d_area(pnt);
if (tri_area * area < 0.0)
return false;
pnt[i] = _tri_pnt[i];
}
return true;
}
template<class Mesh>
typename Mesh::Scalar
SmootherT<Mesh>::closest_to_triangle3d(const Point& _pnt, const Point _tri_pnt[], Point& _projected_pnt) const
{
Scalar dist, dist_square, tmp_dist_square;
Point origin, xaxis, yaxis, zaxis, vec[3], pnt2d;
Point tmp_vec;
int i, j, use_as_x;
// First, calculate a new coordinate system based on the three points and put
// all the points into that coordinate system.
dist_square = -1.0e20;
for (i = 0, j = 1; i < 3; ++i, ++j)
{
if (j >= 3)
j = 0;
vec[i] = _tri_pnt[j] - _tri_pnt[i];
tmp_dist_square = vec[i].sqrnorm();
if (tmp_dist_square < 1.0e-12) // should be determined by BBox
goto UseEdges;
if (tmp_dist_square > dist_square)
{
dist_square = tmp_dist_square;
use_as_x = i;
origin = _tri_pnt[i];
}
}
xaxis = vec[use_as_x] / vec[use_as_x].norm();
j = use_as_x + 1;
if (3 == j)
j = 0;
zaxis = xaxis % vec[j];
if (zaxis.norm() < 1.0e-6)
goto UseEdges;
zaxis.normalize_cond();
yaxis = zaxis % xaxis;
yaxis.normalize_cond();
// Project all the points into this new coordinate system.
vec[0] = _pnt - origin;
pnt2d[0] = vec[0] | xaxis;
pnt2d[1] = vec[0] | yaxis;
pnt2d[2] = vec[0] | zaxis;
for (i = 0; i < 3; ++i)
{
tmp_vec = _tri_pnt[i] - origin;
vec[i][0] = tmp_vec | xaxis;
vec[i][1] = tmp_vec | yaxis;
vec[i][2] = 0.0;
}
/** See if the point is inside the triangle. If it is inside, the projection
* point becomes the closest point and the distance is the distance between
* the point and the project point. If the point is outside, the distance
* is the closest distance to any of the triangle sides.
*/
if (!is_inside_triangle2d(pnt2d, vec))
goto UseEdges;
_projected_pnt[0] = origin[0] + pnt2d[0]*xaxis[0] + pnt2d[1]*yaxis[0];
_projected_pnt[1] = origin[1] + pnt2d[0]*xaxis[1] + pnt2d[1]*yaxis[1];
_projected_pnt[2] = origin[2] + pnt2d[0]*xaxis[2] + pnt2d[1]*yaxis[2];
return pnt2d[2] * pnt2d[2];
/**
* The triangle is degenerate or the projection point is outside the
* triangle. Calculate the distance to the triangle edges and return the
* smallest value is the distance to this triangle.
*/
UseEdges:
dist_square = 1.0e20;
for (i = 0, j = 1; i < 3; ++i, ++j)
{
if (j >= 3)
j = 0;
tmp_dist_square = closest_to_line_segment3d(_pnt, _tri_pnt[i], _tri_pnt[j], tmp_vec);
if (tmp_dist_square < dist_square)
{
dist_square = tmp_dist_square;
_projected_pnt = tmp_vec;
}
}
return dist_square;
}
template<class Mesh>
double SmootherT<Mesh>::LENGTH2D(double a, double b)
{
// Local variables needed for macro definitions.
double MACRO_SQUARE_arg;
if (a < ZERO) a = -a;
if (b < ZERO) b = -b;
if (a > b) return a * sqrt((1.0) + SQUARE(b/a));
if (b > ZERO) return b * sqrt(SQUARE(a/b) + (1.0));
return ZERO;
}
template<class Mesh>
void SmootherT<Mesh>::svdcmp (double *a, int m, int n, int mp, int np, double *w, double *v, int *ierr)
{
// Local variables needed for macro definitions.
double MACRO_ABS_arg;
int MACRO_IMIN_arg1, MACRO_IMIN_arg2;
double MACRO_RMAX_arg1, MACRO_RMAX_arg2;
double MACRO_SQUARE_arg;
double MACRO_SIGN_arg;
/*
* DIMENSION A(MP,NP), W(NP), V(NP,NP), RV1(NP)
*/
#define A(i,j) (a[(i)*np + (j)])
#define V(i,j) (v[(i)*np + (j)])
#define MAXITERS 30
int svdcmp_fix = 0; // extern
int i, j, jj, k, l, its, nm, flag;
double g, scale, anorm, s, f, h, tmp, c, y, z, x, *rv1=NULL, localTol;
static char *name = "svdcmp";
/*
* Householder reduction to bidiagonal form.
*
* There is a bug in the SGI compiler supplied with IRIX 5.3 that causes this
* alloca to generate code that generates a SIGTRAP signal. SGI was not able
* to provide a fix for the problem at this level of the operating system so
* the alloca is replaced with malloc.
*/
/*ALLOCA (rv1, REAL, n, name);*/
MALLOC (rv1, double, n, name); //rv1[n]用来存放Householder reduction后的bidiagonal matrix的上次对角线元素吧
g = 0.0;
scale = 0.0;
anorm = 0.0;
for (i=0; i<n; i++)
{
l = i + 1;
rv1[i] = scale * g;
g = 0.0;
s = 0.0;
scale = 0.0;
if (i < m)
{
for (k=i; k<m; k++)
scale += ABS(A(k,i));
if (scale != 0.0)
{
for (k=i; k<m; k++)
{
A(k,i) /= scale;
s += SQUARE(A(k,i));
}
f = A(i,i);
g = -SIGN(sqrt(s), f);
h = f*g - s;
A(i,i) = f - g;
for (j=l; j<n; j++)
{
s = 0.0;
for (k=i; k<m; k++)
s += A(k,i) * A(k,j);
f = s / h;
for (k=i; k<m; k++)
A(k,j) += f * A(k,i);
}
for (k=i; k<m; k++)
A(k,i) *= scale;
}
}
w[i] = scale * g;
g = 0.0;
s = 0.0;
scale = 0.0;
if (i < m && i+1 != n)
{
for (k=l; k<n; k++)
scale += ABS(A(i,k));
if (scale != 0.0)
{
for (k=l; k<n; k++)
{
A(i,k) /= scale;
s += SQUARE(A(i,k));
}
f = A(i,l);
g = -SIGN(sqrt(s), f);
h = f*g - s;
A(i,l) = f - g;
for (k=l; k<n; k++)
rv1[k] = A(i,k) / h;
for (j=l; j<m; j++)
{
s = 0.0;
for (k=l; k<n; k++)
s += A(j,k) * A(i,k);
for (k=l; k<n; k++)
A(j,k) += s * rv1[k];
}
for (k=l; k<n; k++)
A(i,k) *= scale;
}
}
anorm = RMAX (anorm, (ABS(w[i]) + ABS(rv1[i])));
}
/* Needed if svdcmp_fix is TRUE. */
localTol = anorm * 1.0e-6;
if (localTol < ALMOST_ZERO) localTol = ALMOST_ZERO;
/*
* Accumulation of right-hand transformations.
*/
for (i=n-1; i>=0; i--)
{
if (i+1 < n)
{
if (g != 0.0)
{
for (j=l; j<n; j++)
{
/*
* Order is important in following statement to avoid possible
* underflow.
*/
tmp = A(i,j) / A(i,l);
V(j,i) = tmp / g;
}
for (j=l; j<n; j++)
{
s = 0.0;
for (k=l; k<n; k++)
s += A(i,k) * V(k,j);
for (k=l; k<n; k++)
V(k,j) += s * V(k,i);
}
}
for (j=l; j<n; j++)
{
V(i,j) = 0.0;
V(j,i) = 0.0;
}
}
V(i,i) = 1.0;
g = rv1[i];
l = i;
}
/*
* Accumulation of left-hand transformations.
*/
for (i=IMIN(m,n)-1; i>=0; i--)
{
l = i + 1;
g = w[i];
for (j=l; j<n; j++)
A(i,j) = 0.0;
if (g != 0.0)
{
g = 1.0 / g;
for (j=l; j<n; j++)
{
s = 0.0;
for (k=l; k<m; k++)
s += A(k,i) * A(k,j);
tmp = s / A(i,i);
f = tmp * g;
for (k=i; k<m; k++)
A(k,j) += f * A(k,i);
}
for (j=i; j<m; j++)
A(j,i) *= g;
}
else
{
for (j=i; j<m; j++)
A(j,i) = 0.0;
}
A(i,i)++;
}
/*
* Diagonalization of the bidiagonal form.
* Loop over singular values.
*/
for (k=n-1; k>=0; k--)
{
/*
* Loop over allowed iterations.
*/
for (its=1; its<=MAXITERS; its++)
{
flag = 1;
for (l=k; l>=0; l--)
{
nm = l - 1;
if (!svdcmp_fix)
{
if ((ABS(rv1[l]) + anorm) == anorm) { flag = 0; break; }
if ((ABS(w[nm]) + anorm) == anorm) break;
}
else
{
if (TOL_EQ (rv1[l], 0.0, localTol)) { flag = 0; break; }
if (TOL_EQ (w[nm], 0.0, localTol)) break;
}
}
if (flag)
{
c = 0.0;
s = 1.0;
for (i=l; i<=k; i++)
{
f = s * rv1[i];
rv1[i] *= c;
if (!svdcmp_fix)
{
if ((ABS(f) + anorm) == anorm) break;
}
else
{
if (TOL_EQ (f, 0.0, localTol)) break;
}
g = w[i];
h = LENGTH2D (f, g);
w[i] = h;
h = (1.0) / h;
c = (g * h);
s = -(f * h);
for (j=0; j<m; j++)
{
y = A(j,nm);
z = A(j,i);
A(j,nm) = (y * c) + (z * s);
A(j,i) = -(y * s) + (z * c);
}
}
}
z = w[k];
if (l == k)
{
if (z < ZERO)
{
w[k] = -z;
for (j=0; j<n; j++)
V(j,k) = -V(j,k);
}
break;
}
if (its == MAXITERS)
{
*ierr = 2;
goto FreeAndReturn;
}
x = w[l];
nm = k - 1;
y = w[nm];
g = rv1[nm];
h = rv1[k];
f = ((y - z) * (y + z) + (g - h) * (g + h)) / ((2.0) * h * y);
g = LENGTH2D (f, (1.0));
f = ((x - z) * (x + z) + h * ((y / (f + SIGN (g, f))) - h)) / x;
/*
* Next qr transformation.
*/
c = (1.0);
s = (1.0);
for (j=l; j<=nm; j++)
{
i = j + 1;
g = rv1[i];
y = w[i];
h = s * g;
g = c * g;
z = LENGTH2D (f, h);
rv1[j] = z;
c = f / z;
s = h / z;
f = (x * c) + (g * s);
g = -(x * s) + (g * c);
h = y * s;
y *= c;
for (jj=0; jj<n; jj++)
{
x = V(jj,j);
z = V(jj,i);
V(jj,j) = (x * c) + (z * s);
V(jj,i) = -(x * s) + (z * c);
}
z = LENGTH2D (f, h);
w[j] = z;
/*
* Rotation can be arbitrary if z = 0.
*/
if (z != 0.0)
{
c = f / z;
s = h / z;
}
f = (c * g) + (s * y);
x = -(s * g) + (c * y);
for (jj=0; jj<m; jj++)
{
y = A(jj,j);
z = A(jj,i);
A(jj,j) = (y * c) + (z * s);
A(jj,i) = -(y * s) + (z * c);
}
}
rv1[l] = 0.0;
rv1[k] = f;
w[k] = x;
}
}
*ierr = 0;
FreeAndReturn:
if (rv1)
free(rv1);
return;
#undef A
#undef V
#undef MAXITERS
}
template<class Mesh>
void SmootherT<Mesh>::svbksb (double *u, double *w, double *v, int m, int n, int mp, int np, double *b, double *x)
{
// DIMENSION U(MP,NP), W(NP), V(NP,NP), B(MP), X(NP), TMP(NP)
#define U(i,j) (u[(i)*np + (j)])
#define V(i,j) (v[(i)*np + (j)])
int i, j, jj;
double s, *tmp;
static char *name = "svbksb";
MALLOC (tmp, double, n, name);
// Calculate tran(u) b.
for (j=0; j<n; j++)
{
s = ZERO;
if (w[j] != ZERO)
{
for (i=0; i<m; i++)
s += U(i,j) * b[i];
s /= w[j];
}
tmp[j] = s;
}
// Matrix multiply by v to get answer.
for (j=0; j<n; j++)
{
s = ZERO;
for (jj=0; jj<n; jj++)
s += V(j,jj) * tmp[jj];
x[j] = s;
}
#undef U
#undef V
}
/**
// copied and modified from RemesherT<class Mesh>
template<class Mesh>
bool SmootherT<Mesh>::is_swap_legal(EdgeHandle _eh) const
{
}
template<class Mesh>
void SmootherT<Mesh>::edge_swap()
{
}
*/
template<class Mesh>
void SmootherT<Mesh>::smooth()
{
MyMesh ref_mesh;
ref_mesh = mesh_; // seems ok
// setup and initialization
const int max_global_iter_num = 10;
const int max_smooth_iter_num = 50;
const int max_min_func_iter_num = 50;
float relax1 = 0.1;
float relax2 = 0.1; // ?
float mu = 0.01;
float wl = 0.1;
float wa = 0.9;
float wmax, epsw;
float epsres = 5.0e-1;
float rden, rnum, residual, residual0; // for residual
float dist, dist_square, weight, weight_sum, fac;
int step, iter;
Point dc_vec, cg_vec, cur_pnt, vec1, vd1, delta_vec, normal;
Point *initial_vertex_displacement = new Point[mesh_.n_vertices()];
Point *vertex_displacement = new Point[mesh_.n_vertices()];
Point *smooth_vertex_displacement = new Point[mesh_.n_vertices()];
int i, num;
bool ended;
typename Mesh::VertexIter v_it;
typename Mesh::VertexVertexIter vv_it;
typename Mesh::VertexOHalfedgeIter voh_it;
EdgeHandle eh;
VertexHandle vh;
HalfedgeHandle heh;
// evaluate initial cell normal and area
// check for possible overlaps
// evaluate vertex normal using singular value decomposition
// finding discontinuity points
// finding corners
// stepping toward the final surface
for (step = 0; step < max_global_iter_num; step++)
{
// evaluate new cell normal and area
mesh_.update_face_normals();
// check for possible overlaps
// evaluate guess vertex displacement
rden = 0.0; // //如6748.6946, 所有节点的偏移向量长度平方的累加，下面作为指示器有用
// 对所有节点循环,计算其偏移向量
for (v_it = mesh_.vertices_begin(); v_it != mesh_.vertices_end(); ++v_it)
{
cg_vec = (Point)(0.0, 0.0, 0.0);
dc_vec = (Point)(0.0, 0.0, 0.0);
if (mesh_.property(node_type, v_it).is_boundary() || mesh_.property(node_type, v_it).is_corner())
goto skip;
else if (mesh_.property(node_type, v_it).is_ridge()) // && mesh_.property(node_type, v_it).is_corner()
{
num = 0;
for (voh_it = mesh_.voh_iter(v_it); voh_it; ++voh_it)
{
if (ET_Ridge == mesh_.property(edge_type, mesh_.edge_handle(voh_it)))
{
num++;
cg_vec += mesh_.point(mesh_.to_vertex_handle(voh_it));
}
}
if (2 != num)
{
cerr << "Error in function smooth: the number of adjacent ridge edges of a ridge node is not 2!";
// todo: use UI to inform users
}
// cg_vec /= num;
}
else if (mesh_.property(node_type, v_it).is_flat()) // only "else" should be ok
{
for (voh_it = mesh_.voh_iter(v_it), num = 0; voh_it; ++voh_it, ++num)
cg_vec += mesh_.point(mesh_.to_vertex_handle(voh_it));
}
cg_vec /= (float)num;
dc_vec = cg_vec - mesh_.point(v_it);
skip:
vertex_displacement[v_it.handle().idx()] = dc_vec; // is here idx() in squential order ?!
rden += dc_vec.sqrnorm();
if (0 == step)
initial_vertex_displacement[v_it.handle().idx()] = vertex_displacement[v_it.handle().idx()];
}
// evaluate vertex normal using single value decomposition, is it ok not to use it ?
mesh_.update_vertex_normals();
// deal with points on edges first (ridge nodes)
ended = false;
for (iter = 0; iter < max_smooth_iter_num && !ended; iter++) // // 等于50，50次循环, 每一个step中都这样循环一遍
{
rnum = 0.0;
// 对每个point on edges节点，计算其新的偏移向量，即其新的位置
for (v_it = mesh_.vertices_begin(); v_it != mesh_.vertices_end(); ++v_it)
{
dist_square = vertex_displacement[v_it.handle().idx()].sqrnorm();
if (mesh_.property(node_type, v_it).is_ridge() && dist_square > 0.0)
{
weight_sum = 0.0;
cur_pnt = mesh_.point(v_it);
vd1 = (Point)(0.0, 0.0, 0.0);
num = 0;
for (voh_it = mesh_.voh_iter(v_it); voh_it; ++voh_it)
{
eh = mesh_.edge_handle(voh_it);
if (ET_Ridge == mesh_.property(edge_type, eh))
{
++num;
vh = mesh_.to_vertex_handle(voh_it);
if (mesh_.property(node_type, vh).is_ridge() || mesh_.property(node_type, vh).is_corner())
{
delta_vec = mesh_.point(vh) - cur_pnt;
weight = 1.0 / (delta_vec.norm() + 1.0e-20);
weight_sum += weight;
delta_vec = vertex_displacement[vh.idx()];
vd1 += weight*delta_vec;
}
}
}
if (2 != num)
{
cerr << "Error in function smooth: the number of adjacent ridge edges is not 2!";
// todo: to inform users this situation
}
fac = 1.0 / (weight_sum + 1.0e-20);
vec1 = vd1 * fac;
delta_vec = vec1 - vertex_displacement[v_it.handle().idx()];
rnum += delta_vec.sqrnorm();
delta_vec = vec1 * relax1 + vertex_displacement[v_it.handle().idx()] * (1.0 - relax1);
vertex_displacement[v_it.handle().idx()] = delta_vec;
}
} // end of "for (v_it = mesh_.vertices_begin(); v_it != mesh_.vertices_end(); ++v_it)"
residual = sqrt(rnum / rden);
if (residual < epsres)
ended = true;
} // end of computing displacements for ridge nodes, "for (iter = 0; iter < max_smooth_iter_num && !ended; iter++)"
// deal with continuous points
ended = false;
for (iter = 0; iter < max_smooth_iter_num && !ended; iter++) // // 等于50，50次循环, 每一个step中都这样循环一遍
{
rnum = 0.0;
// 对每个point on edges节点，计算其新的偏移向量，即其新的位置
for (v_it = mesh_.vertices_begin(); v_it != mesh_.vertices_end(); ++v_it)
{
if (mesh_.property(node_type, v_it).is_flat())
{
weight_sum = 0.0;
cur_pnt = mesh_.point(v_it);
vd1 = (Point)(0.0, 0.0, 0.0);
for (voh_it = mesh_.voh_iter(v_it); voh_it; ++voh_it)
{
eh = mesh_.edge_handle(voh_it);
vh = mesh_.to_vertex_handle(voh_it);
delta_vec = mesh_.point(vh) - cur_pnt;
weight = 1.0 / (delta_vec.norm() + 1.0e-20);
weight_sum += weight;
delta_vec = vertex_displacement[vh.idx()];
vd1 += weight*delta_vec;
}
fac = 1.0 / (weight_sum + 1.0e-20);
vec1 = vd1 * fac;
delta_vec = vec1 - vertex_displacement[v_it.handle().idx()];
rnum += delta_vec.sqrnorm();
delta_vec = vec1 * relax1 + vertex_displacement[v_it.handle().idx()] * (1.0 - relax1);
vertex_displacement[v_it.handle().idx()] = delta_vec;
}
} // end of "for (v_it = mesh_.vertices_begin(); v_it != mesh_.vertices_end(); ++v_it)"
//residual check
residual = sqrt(rnum / rden);
if (residual < epsres)
ended = true;
} // end of computing displacements for ridge nodes, "for (iter = 0; iter < max_smooth_iter_num && !ended; iter++)"
// copy and save, 当上面两种类型节点都处理以后(经过了50次循环后的结果)，得到所有节点新的偏移向量
for (i = 0; i < mesh_.n_vertices(); ++i)
smooth_vertex_displacement[i] = vertex_displacement[i];
// MINIMIZING FUNCTIONALS
// todo: to be continued
if (2 != smmethod_)
goto skip3;
float reducfac = 0.50;
// relax = relax_functional; relax2
float areafac, fac;
float rho, length2;
int nreduc = 0;
int nincre = 0;
int maxreduc = 5;
int maxincre = 1;
int k, valence, ierr;
double daa[9], dbb[3], c[3][3];
double w[3], v[3][3];
double bb[3], xx[3];
Point p0_old, p2_old, p1_new, p2_new, p_res;
minimize:
ended = false;
float resold = 1.0;
residual = 0.0;
for (iter = 0; iter < max_min_func_iter_num && !ended; ++iter) // 外层50次循环，中间可根据情况中断
{
rnum = 0.0;
for (v_it = mesh_.vertices_begin(); v_it != mesh_.vertices_end(); ++v_it) // 对所有节点循环
{
if (!mesh_.property(node_type, v_it).is_flat()) // 只处理flat node
continue;
for (i = 0; i < 9; i++)
daa[i] = 0.0;
for (i = 0; i < 3; i++)
dbb[i] = 0.0;
valence = mesh_.valence(v_it);
for (voh_it = mesh_.voh_iter(v_it); voh_it; ++voh_it)
{
heh = mesh_.next_halfedge_handle(voh_it);
vh = mesh_.to_vertex_handle(heh);
p0_old = mesh_.point(v_it);
p2_old = mesh_.point(mesh_.to_vertex_handle(voh_it));
p1_new = mesh_.point(vh) + vertex_displacement[vh.idx()];
p2_new = p2_old + vertex_displacement[mesh_.to_vertex_handle(voh_it).idx()];
delta_vec = p1_new - p2_new;
// matrix for area functional
areafac = wa / (float)mesh_.calc_sector_area(voh_it);
c[0][0] = delta_vec[1]*delta_vec[1] + delta_vec[2]*delta_vec[2];
c[0][1] = -delta_vec[0]*delta_vec[1];
c[0][2] = -delta_vec[0]*delta_vec[2];
c[1][0] = -delta_vec[1]*delta_vec[0];
c[1][1] = delta_vec[2]*delta_vec[2] + delta_vec[0]*delta_vec[0];
c[1][2] = -delta_vec[1]*delta_vec[2];
c[2][0] = -delta_vec[2]*delta_vec[0];
c[2][1] = -delta_vec[2]*delta_vec[1];
c[2][2] = delta_vec[0]*delta_vec[0] + delta_vec[1]*delta_vec[1];
daa[0] += areafac * c[0][0];
daa[1] += areafac * c[0][1];
daa[2] += areafac * c[0][2];
daa[3] += areafac * c[1][0];
daa[4] += areafac * c[1][1];
daa[5] += areafac * c[1][2];
daa[6] += areafac * c[2][0];
daa[7] += areafac * c[2][1];
daa[8] += areafac * c[2][2];
dbb[0] += areafac*(c[0][0]*p2_new[0] + c[0][1]*p2_new[1] + c[0][2]*p2_new[2]);
dbb[1] += areafac*(c[1][0]*p2_new[0] + c[1][1]*p2_new[1] + c[1][2]*p2_new[2]);
dbb[2] += areafac*(c[2][0]*p2_new[0] + c[2][1]*p2_new[1] + c[2][2]*p2_new[2]);
// matrix for length functional
fac = wl / valence;
daa[0] += 1.0*fac;
daa[4] += 1.0*fac;
daa[8] += 1.0*fac;
dbb[0] += 1.0*p2_new[0];
dbb[1] += 1.0*p2_new[1];