Esempio n. 1
0
/**
 * gts_triangle_area:
 * @t: a #GtsTriangle.
 *
 * Returns: the area of the triangle @t.
 */
gdouble gts_triangle_area (GtsTriangle * t)
{
    gdouble x, y, z;

    g_return_val_if_fail (t != NULL, 0.0);

    gts_triangle_normal (t, &x, &y, &z);

    return sqrt (x*x + y*y + z*z)/2.;
}
Esempio n. 2
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/**
 * gts_triangles_angle:
 * @t1: a #GtsTriangle.
 * @t2: a #GtsTriangle.
 *
 * Returns: the value (in radians) of the angle between @t1 and @t2.
 */
gdouble gts_triangles_angle (GtsTriangle * t1,
                             GtsTriangle * t2)
{
    gdouble nx1, ny1, nz1, nx2, ny2, nz2;
    gdouble pvx, pvy, pvz;
    gdouble theta;

    g_return_val_if_fail (t1 != NULL && t2 != NULL, 0.0);

    gts_triangle_normal (t1, &nx1, &ny1, &nz1);
    gts_triangle_normal (t2, &nx2, &ny2, &nz2);

    pvx = ny1*nz2 - nz1*ny2;
    pvy = nz1*nx2 - nx1*nz2;
    pvz = nx1*ny2 - ny1*nx2;

    theta = atan2 (sqrt (pvx*pvx + pvy*pvy + pvz*pvz),
                   nx1*nx2 + ny1*ny2 + nz1*nz2) - M_PI;
    return theta < - M_PI ? theta + 2.*M_PI : theta;
}
Esempio n. 3
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static void write_face (GtsTriangle * t)
{
  GtsVertex * v1, * v2, * v3;
  GtsVector n;

  gts_triangle_vertices (t, &v1, &v2, &v3);
  gts_triangle_normal (t, &n[0], &n[1], &n[2]);
  gts_vector_normalize (n);
  printf ("facet normal %g %g %g\nouter loop\n", n[0], n[1], n[2]);
  printf ("vertex %g %g %g\n", 
	  GTS_POINT (v1)->x, GTS_POINT (v1)->y, GTS_POINT (v1)->z);
  printf ("vertex %g %g %g\n", 
	  GTS_POINT (v2)->x, GTS_POINT (v2)->y, GTS_POINT (v2)->z);
  printf ("vertex %g %g %g\n", 
	  GTS_POINT (v3)->x, GTS_POINT (v3)->y, GTS_POINT (v3)->z);
  puts ("endloop\nendfacet");
}
Esempio n. 4
0
	void _gts_face_to_stl(GtsTriangle* t,_gts_face_to_stl_data* data){
		GtsVertex* v[3];
		Vector3r n;
		gts_triangle_vertices(t,&v[0],&v[1],&v[2]);
		if(data->clipCell && data->scene->isPeriodic){
			for(short ax:{0,1,2}){
				Vector3r p(GTS_POINT(v[ax])->x,GTS_POINT(v[ax])->y,GTS_POINT(v[ax])->z);
				if(!data->scene->cell->isCanonical(p)) return;
			}
		}
		gts_triangle_normal(t,&n[0],&n[1],&n[2]);
		n.normalize();
		std::ofstream& stl(data->stl);
		stl<<"  facet normal "<<n[0]<<" "<<n[1]<<" "<<n[2]<<"\n";
		stl<<"    outer loop\n";
		for(GtsVertex* _v: v){
			stl<<"      vertex "<<GTS_POINT(_v)->x<<" "<<GTS_POINT(_v)->y<<" "<<GTS_POINT(_v)->z<<"\n";
		}
		stl<<"    endloop\n";
		stl<<"  endfacet\n";
		data->numTri+=3;
	}
Esempio n. 5
0
/** 
 * gts_vertex_principal_directions:
 * @v: a #GtsVertex.  
 * @s: a #GtsSurface.
 * @Kh: mean curvature normal (a #GtsVector).
 * @Kg: Gaussian curvature (a gdouble).
 * @e1: first principal curvature direction (direction of largest curvature).
 * @e2: second principal curvature direction.
 *
 * Computes the principal curvature directions at a point given @Kh
 * and @Kg, the mean curvature normal and Gaussian curvatures at that
 * point, computed with gts_vertex_mean_curvature_normal() and
 * gts_vertex_gaussian_curvature(), respectively. 
 *
 * Note that this computation is very approximate and tends to be
 * unstable.  Smoothing of the surface or the principal directions may
 * be necessary to achieve reasonable results.  
 */
void gts_vertex_principal_directions (GtsVertex * v, GtsSurface * s,
                                      GtsVector Kh, gdouble Kg,
				      GtsVector e1, GtsVector e2)
{
  GtsVector N;
  gdouble normKh;
  GSList * i, * j;
  GtsVector basis1, basis2, d, eig;
  gdouble ve2, vdotN;
  gdouble aterm_da, bterm_da, cterm_da, const_da;
  gdouble aterm_db, bterm_db, cterm_db, const_db;
  gdouble a, b, c;
  gdouble K1, K2;
  gdouble *weights, *kappas, *d1s, *d2s;
  gint edge_count;
  gdouble err_e1, err_e2;
  int e;

  /* compute unit normal */
  normKh = sqrt (gts_vector_scalar (Kh, Kh));

  if (normKh > 0.0) {
    N[0] = Kh[0] / normKh;
    N[1] = Kh[1] / normKh;
    N[2] = Kh[2] / normKh;
  } else {
    /* This vertex is a point of zero mean curvature (flat or saddle
     * point).  Compute a normal by averaging the adjacent triangles
     */
    N[0] = N[1] = N[2] = 0.0;
    i = gts_vertex_faces (v, s, NULL);
    while (i) {
      gdouble x, y, z;
      gts_triangle_normal (GTS_TRIANGLE ((GtsFace *) i->data),
                           &x, &y, &z);
      N[0] += x;
      N[1] += y;
      N[2] += z;

      i = i->next;
    }
    g_return_if_fail (gts_vector_norm (N) > 0.0);
    gts_vector_normalize (N);
  }
    

  /* construct a basis from N: */
  /* set basis1 to any component not the largest of N */
  basis1[0] =  basis1[1] =  basis1[2] = 0.0;
  if (fabs (N[0]) > fabs (N[1]))
    basis1[1] = 1.0;
  else
    basis1[0] = 1.0;
    
  /* make basis2 orthogonal to N */
  gts_vector_cross (basis2, N, basis1);
  gts_vector_normalize (basis2);

  /* make basis1 orthogonal to N and basis2 */
  gts_vector_cross (basis1, N, basis2);
  gts_vector_normalize (basis1);
  
  aterm_da = bterm_da = cterm_da = const_da = 0.0;
  aterm_db = bterm_db = cterm_db = const_db = 0.0;

  weights = g_malloc (sizeof (gdouble)*g_slist_length (v->segments));
  kappas = g_malloc (sizeof (gdouble)*g_slist_length (v->segments));
  d1s = g_malloc (sizeof (gdouble)*g_slist_length (v->segments));
  d2s = g_malloc (sizeof (gdouble)*g_slist_length (v->segments));
  edge_count = 0;

  i = v->segments;
  while (i) {
    GtsEdge * e;
    GtsFace * f1, * f2;
    gdouble weight, kappa, d1, d2;
    GtsVector vec_edge;

    if (! GTS_IS_EDGE (i->data)) {
      i = i->next;
      continue;
    }

    e = i->data;

    /* since this vertex passed the tests in
     * gts_vertex_mean_curvature_normal(), this should be true. */
    g_assert (gts_edge_face_number (e, s) == 2);

    /* identify the two triangles bordering e in s */
    f1 = f2 = NULL;
    j = e->triangles;
    while (j) {
      if ((! GTS_IS_FACE (j->data)) || 
          (! gts_face_has_parent_surface (GTS_FACE (j->data), s))) {
        j = j->next;
        continue;
      }
      if (f1 == NULL)
        f1 = GTS_FACE (j->data);
      else {
        f2 = GTS_FACE (j->data);
        break;
      }
      j = j->next;
    }
    g_assert (f2 != NULL);

    /* We are solving for the values of the curvature tensor 
     *     B = [ a b ; b c ].  
     * The computations here are from section 5 of [Meyer et al 2002].  
     *
     * The first step is to calculate the linear equations governing
     * the values of (a,b,c).  These can be computed by setting the
     * derivatives of the error E to zero (section 5.3).
     * 
     * Since a + c = norm(Kh), we only compute the linear equations
     * for dE/da and dE/db.  (NB: [Meyer et al 2002] has the
     * equation a + b = norm(Kh), but I'm almost positive this is
     * incorrect.)
     *
     * Note that the w_ij (defined in section 5.2) are all scaled by
     * (1/8*A_mixed).  We drop this uniform scale factor because the
     * solution of the linear equations doesn't rely on it.
     *
     * The terms of the linear equations are xterm_dy with x in
     * {a,b,c} and y in {a,b}.  There are also const_dy terms that are
     * the constant factors in the equations.  
     */

    /* find the vector from v along edge e */
    gts_vector_init (vec_edge, GTS_POINT (v), 
                     GTS_POINT ((GTS_SEGMENT (e)->v1 == v) ? 
                                GTS_SEGMENT (e)->v2 : GTS_SEGMENT (e)->v1));
    ve2 = gts_vector_scalar (vec_edge, vec_edge);
    vdotN = gts_vector_scalar (vec_edge, N);

    /* section 5.2 - There is a typo in the computation of kappa.  The
     * edges should be x_j-x_i.
     */
    kappa = 2.0 * vdotN / ve2;

    /* section 5.2 */

    /* I don't like performing a minimization where some of the
     * weights can be negative (as can be the case if f1 or f2 are
     * obtuse).  To ensure all-positive weights, we check for
     * obtuseness and use values similar to those in region_area(). */
    weight = 0.0;
    if (! triangle_obtuse(v, f1)) {
      weight += ve2 * 
        cotan (gts_triangle_vertex_opposite (GTS_TRIANGLE (f1), e), 
               GTS_SEGMENT (e)->v1, GTS_SEGMENT (e)->v2) / 8.0;
    } else {
      if (angle_obtuse (v, f1)) {
        weight += ve2 * gts_triangle_area (GTS_TRIANGLE (f1)) / 4.0;
      } else {
        weight += ve2 * gts_triangle_area (GTS_TRIANGLE (f1)) / 8.0;
      }
    }

    if (! triangle_obtuse(v, f2)) {
      weight += ve2 * 
        cotan (gts_triangle_vertex_opposite (GTS_TRIANGLE (f2), e), 
               GTS_SEGMENT (e)->v1, GTS_SEGMENT (e)->v2) / 8.0;
    } else {
      if (angle_obtuse (v, f2)) {
        weight += ve2 * gts_triangle_area (GTS_TRIANGLE (f2)) / 4.0;
      } else {
        weight += ve2 * gts_triangle_area (GTS_TRIANGLE (f2)) / 8.0;
      }
    }

    /* projection of edge perpendicular to N (section 5.3) */
    d[0] = vec_edge[0] - vdotN * N[0];
    d[1] = vec_edge[1] - vdotN * N[1];
    d[2] = vec_edge[2] - vdotN * N[2];
    gts_vector_normalize (d);
    
    /* not explicit in the paper, but necessary.  Move d to 2D basis. */
    d1 = gts_vector_scalar (d, basis1);
    d2 = gts_vector_scalar (d, basis2);

    /* store off the curvature, direction of edge, and weights for later use */
    weights[edge_count] = weight;
    kappas[edge_count] = kappa;
    d1s[edge_count] = d1;
    d2s[edge_count] = d2;
    edge_count++;

    /* Finally, update the linear equations */
    aterm_da += weight * d1 * d1 * d1 * d1;
    bterm_da += weight * d1 * d1 * 2 * d1 * d2;
    cterm_da += weight * d1 * d1 * d2 * d2;
    const_da += weight * d1 * d1 * (- kappa);

    aterm_db += weight * d1 * d2 * d1 * d1;
    bterm_db += weight * d1 * d2 * 2 * d1 * d2;
    cterm_db += weight * d1 * d2 * d2 * d2;
    const_db += weight * d1 * d2 * (- kappa);

    i = i->next;
  }

  /* now use the identity (Section 5.3) a + c = |Kh| = 2 * kappa_h */
  aterm_da -= cterm_da;
  const_da += cterm_da * normKh;

  aterm_db -= cterm_db;
  const_db += cterm_db * normKh;
  
  /* check for solvability of the linear system */
  if (((aterm_da * bterm_db - aterm_db * bterm_da) != 0.0) &&
      ((const_da != 0.0) || (const_db != 0.0))) {
    linsolve (aterm_da, bterm_da, -const_da,
              aterm_db, bterm_db, -const_db,
              &a, &b);

    c = normKh - a;

    eigenvector (a, b, c, eig);
  } else {
    /* region of v is planar */
    eig[0] = 1.0;
    eig[1] = 0.0;
  }

  /* Although the eigenvectors of B are good estimates of the
   * principal directions, it seems that which one is attached to
   * which curvature direction is a bit arbitrary.  This may be a bug
   * in my implementation, or just a side-effect of the inaccuracy of
   * B due to the discrete nature of the sampling.
   *
   * To overcome this behavior, we'll evaluate which assignment best
   * matches the given eigenvectors by comparing the curvature
   * estimates computed above and the curvatures calculated from the
   * discrete differential operators.  */

  gts_vertex_principal_curvatures (0.5 * normKh, Kg, &K1, &K2);
  
  err_e1 = err_e2 = 0.0;
  /* loop through the values previously saved */
  for (e = 0; e < edge_count; e++) {
    gdouble weight, kappa, d1, d2;
    gdouble temp1, temp2;
    gdouble delta;

    weight = weights[e];
    kappa = kappas[e];
    d1 = d1s[e];
    d2 = d2s[e];

    temp1 = fabs (eig[0] * d1 + eig[1] * d2);
    temp1 = temp1 * temp1;
    temp2 = fabs (eig[1] * d1 - eig[0] * d2);
    temp2 = temp2 * temp2;

    /* err_e1 is for K1 associated with e1 */
    delta = K1 * temp1 + K2 * temp2 - kappa;
    err_e1 += weight * delta * delta;

    /* err_e2 is for K1 associated with e2 */
    delta = K2 * temp1 + K1 * temp2 - kappa;
    err_e2 += weight * delta * delta;
  }
  g_free (weights);
  g_free (kappas);
  g_free (d1s);
  g_free (d2s);

  /* rotate eig by a right angle if that would decrease the error */
  if (err_e2 < err_e1) {
    gdouble temp = eig[0];

    eig[0] = eig[1];
    eig[1] = -temp;
  }

  e1[0] = eig[0] * basis1[0] + eig[1] * basis2[0];
  e1[1] = eig[0] * basis1[1] + eig[1] * basis2[1];
  e1[2] = eig[0] * basis1[2] + eig[1] * basis2[2];
  gts_vector_normalize (e1);

  /* make N,e1,e2 a right handed coordinate sytem */
  gts_vector_cross (e2, N, e1);
  gts_vector_normalize (e2);
}