static PyObject*
is_on(PygtsFace *self, PyObject *args)
{
PyObject *s_=NULL;
PygtsSurface *s=NULL;
SELF_CHECK
/* Parse the args */
if(! PyArg_ParseTuple(args, "O", &s_) )
return NULL;
/* Convert to PygtsObjects */
if( pygts_surface_check(s_) ) {
s = PYGTS_SURFACE(s_);
}
else {
PyErr_SetString(PyExc_TypeError, "expected a Surface");
return NULL;
}
if( gts_face_has_parent_surface(PYGTS_FACE_AS_GTS_FACE(self),
PYGTS_SURFACE_AS_GTS_SURFACE(s)) ) {
Py_INCREF(Py_True);
return Py_True;
}
else {
Py_INCREF(Py_False);
return Py_False;
}
}
static void mark_as_hole (GtsFace * f, GtsSurface * s)
{
GtsEdge * e1, * e2, * e3;
if (GTS_OBJECT (f)->reserved == f)
return;
GTS_OBJECT (f)->reserved = f;
e1 = GTS_TRIANGLE (f)->e1;
e2 = GTS_TRIANGLE (f)->e2;
e3 = GTS_TRIANGLE (f)->e3;
if (!GTS_IS_CONSTRAINT (e1)) {
GSList * i = e1->triangles;
while (i) {
GtsFace * f1 = i->data;
if (f1 != f && GTS_IS_FACE (f1) && gts_face_has_parent_surface (f1, s))
mark_as_hole (f1, s);
i = i->next;
}
}
if (!GTS_IS_CONSTRAINT (e2)) {
GSList * i = e2->triangles;
while (i) {
GtsFace * f1 = i->data;
if (f1 != f && GTS_IS_FACE (f1) && gts_face_has_parent_surface (f1, s))
mark_as_hole (f1, s);
i = i->next;
}
}
if (!GTS_IS_CONSTRAINT (e3)) {
GSList * i = e3->triangles;
while (i) {
GtsFace * f1 = i->data;
if (f1 != f && GTS_IS_FACE (f1) && gts_face_has_parent_surface (f1, s))
mark_as_hole (f1, s);
i = i->next;
}
}
}
/**
* gts_edge_swap:
* @e: a #GtsEdge.
* @s: a #GtsSurface.
*
* Performs an "edge swap" on the two triangles sharing @e and
* belonging to @s.
*/
void gts_edge_swap (GtsEdge * e, GtsSurface * s)
{
GtsTriangle * t1 = NULL, * t2 = NULL, * t;
GtsFace * f;
GSList * i;
GtsVertex * v1, * v2, * v3, * v4, * v5, * v6;
GtsEdge * e1, * e2, * e3, * e4;
GtsSegment * v3v6;
g_return_if_fail (e != NULL);
g_return_if_fail (s != NULL);
i = e->triangles;
while (i) {
if (GTS_IS_FACE (i->data) && gts_face_has_parent_surface (i->data, s)) {
if (!t1)
t1 = i->data;
else if (!t2)
t2 = i->data;
else
g_return_if_fail (gts_edge_face_number (e, s) == 2);
}
i = i->next;
}
g_assert (t1 && t2);
gts_triangle_vertices_edges (t1, e, &v1, &v2, &v3, &e, &e1, &e2);
gts_triangle_vertices_edges (t2, e, &v4, &v5, &v6, &e, &e3, &e4);
g_assert (v2 == v4 && v1 == v5);
v3v6 = gts_vertices_are_connected (v3, v6);
if (!GTS_IS_EDGE (v3v6))
v3v6 = GTS_SEGMENT (gts_edge_new (s->edge_class, v3, v6));
f = gts_face_new (s->face_class, e1, GTS_EDGE (v3v6), e4);
if ((t = gts_triangle_is_duplicate (GTS_TRIANGLE (f))) &&
GTS_IS_FACE (t)) {
gts_object_destroy (GTS_OBJECT (f));
f = GTS_FACE (t);
}
gts_surface_add_face (s, f);
f = gts_face_new (s->face_class, GTS_EDGE (v3v6), e2, e3);
if ((t = gts_triangle_is_duplicate (GTS_TRIANGLE (f))) &&
GTS_IS_FACE (t)) {
gts_object_destroy (GTS_OBJECT (f));
f = GTS_FACE (t);
}
gts_surface_add_face (s, f);
gts_surface_remove_face (s, GTS_FACE (t1));
gts_surface_remove_face (s, GTS_FACE (t2));
}
static void edge_mark_as_hole (GtsEdge * e, GtsSurface * s)
{
GSList * i = e->triangles;
while (i) {
GtsFace * f = i->data;
if (GTS_IS_FACE (f) &&
gts_face_has_parent_surface (f, s) &&
triangle_is_hole (GTS_TRIANGLE (f)))
mark_as_hole (f, s);
i = i->next;
}
}
/**
* gts_edge_has_parent_surface:
* @e: a #GtsEdge.
* @surface: a #GtsSurface.
*
* Returns: a #GtsFace of @surface having @e as an edge, %NULL otherwise.
*/
GtsFace * gts_edge_has_parent_surface (GtsEdge * e, GtsSurface * surface)
{
GSList * i;
g_return_val_if_fail (e != NULL, NULL);
i = e->triangles;
while (i) {
if (GTS_IS_FACE (i->data) &&
gts_face_has_parent_surface (i->data, surface))
return i->data;
i = i->next;
}
return NULL;
}
/**
* gts_edge_face_number:
* @e: a #GtsEdge.
* @s: a #GtsSurface.
*
* Returns: the number of faces using @e and belonging to @s.
*/
guint gts_edge_face_number (GtsEdge * e, GtsSurface * s)
{
GSList * i;
guint nt = 0;
g_return_val_if_fail (e != NULL, 0);
g_return_val_if_fail (s != NULL, 0);
i = e->triangles;
while (i) {
if (GTS_IS_FACE (i->data) &&
gts_face_has_parent_surface (GTS_FACE (i->data), s))
nt++;
i = i->next;
}
return nt;
}
/**
* gts_edge_is_boundary:
* @e: a #GtsEdge.
* @surface: a #GtsSurface or %NULL.
*
* Returns: the unique #GtsFace (which belongs to @surface) and which
* has @e as an edge (i.e. @e is a boundary edge (of @surface)) or %NULL
* if there is more than one or no faces (belonging to @surface) and
* with @e as an edge.
*/
GtsFace * gts_edge_is_boundary (GtsEdge * e, GtsSurface * surface)
{
GSList * i;
GtsFace * f = NULL;
g_return_val_if_fail (e != NULL, NULL);
i = e->triangles;
while (i) {
if (GTS_IS_FACE (i->data)) {
if (!surface || gts_face_has_parent_surface (i->data, surface)) {
if (f != NULL)
return NULL;
f = i->data;
}
}
i = i->next;
}
return f;
}
/**
* gts_edge_manifold_faces:
* @e: a #GtsEdge.
* @s: a #GtsSurface.
* @f1: pointer for first face.
* @f2: pointer for second face.
*
* If @e is a manifold edge of surface @s, fills @f1 and @f2 with the
* faces belonging to @s and sharing @e.
*
* Returns: %TRUE if @e is a manifold edge, %FALSE otherwise.
*/
gboolean gts_edge_manifold_faces (GtsEdge * e, GtsSurface * s,
GtsFace ** f1, GtsFace ** f2)
{
GSList * i;
g_return_val_if_fail (e != NULL, FALSE);
g_return_val_if_fail (s != NULL, FALSE);
g_return_val_if_fail (f1 != NULL, FALSE);
g_return_val_if_fail (f2 != NULL, FALSE);
*f1 = *f2 = NULL;
i = e->triangles;
while (i) {
if (GTS_IS_FACE (i->data) && gts_face_has_parent_surface (i->data, s)) {
if (!(*f1)) *f1 = i->data;
else if (!(*f2)) *f2 = i->data;
else return FALSE;
}
i = i->next;
}
return (*f1 && *f2);
}
static void gts_constraint_split (GtsConstraint * c,
GtsSurface * s,
GtsFifo * fifo)
{
GSList * i;
GtsVertex * v1, * v2;
GtsEdge * e;
g_return_if_fail (c != NULL);
g_return_if_fail (s != NULL);
v1 = GTS_SEGMENT (c)->v1;
v2 = GTS_SEGMENT (c)->v2;
e = GTS_EDGE (c);
i = e->triangles;
while (i) {
GtsFace * f = i->data;
if (GTS_IS_FACE (f) && gts_face_has_parent_surface (f, s)) {
GtsVertex * v = gts_triangle_vertex_opposite (GTS_TRIANGLE (f), e);
if (gts_point_orientation (GTS_POINT (v1),
GTS_POINT (v2),
GTS_POINT (v)) == 0.) {
GSList * j = e->triangles;
GtsFace * f1 = NULL;
GtsEdge * e1, * e2;
/* replaces edges with constraints */
gts_triangle_vertices_edges (GTS_TRIANGLE (f), e,
&v1, &v2, &v, &e, &e1, &e2);
if (!GTS_IS_CONSTRAINT (e1)) {
GtsEdge * ne1 =
gts_edge_new (GTS_EDGE_CLASS (GTS_OBJECT (c)->klass), v2, v);
gts_edge_replace (e1, ne1);
gts_object_destroy (GTS_OBJECT (e1));
e1 = ne1;
if (fifo) gts_fifo_push (fifo, e1);
}
if (!GTS_IS_CONSTRAINT (e2)) {
GtsEdge * ne2 =
gts_edge_new (GTS_EDGE_CLASS (GTS_OBJECT (c)->klass), v, v1);
gts_edge_replace (e2, ne2);
gts_object_destroy (GTS_OBJECT (e2));
e2 = ne2;
if (fifo) gts_fifo_push (fifo, e2);
}
/* look for face opposite */
while (j && !f1) {
if (GTS_IS_FACE (j->data) &&
gts_face_has_parent_surface (j->data, s))
f1 = j->data;
j = j->next;
}
if (f1) { /* c is not a boundary of s */
GtsEdge * e3, * e4, * e5;
GtsVertex * v3;
gts_triangle_vertices_edges (GTS_TRIANGLE (f1), e,
&v1, &v2, &v3, &e, &e3, &e4);
e5 = gts_edge_new (s->edge_class, v, v3);
gts_surface_add_face (s, gts_face_new (s->face_class, e5, e2, e3));
gts_surface_add_face (s, gts_face_new (s->face_class, e5, e4, e1));
gts_object_destroy (GTS_OBJECT (f1));
}
gts_object_destroy (GTS_OBJECT (f));
return;
}
}
i = i->next;
}
}
GSList *gts_vertex_faces( GtsVertex *v, GtsSurface *surface, GSList *list )
{
int eax;
GSList *i;
{
/* phantom */ int _g_boolean_var_;
if ( v == 0 )
{
g_return_if_fail_warning( 0, __PRETTY_FUNCTION__, "v != NULL" );
list = 0;
}
i = &v->segments;
if ( v->segments[4].next )
{
{
do
{
if ( gts_edge_class( ) == 0 )
{
g_return_if_fail_warning( 0, __PRETTY_FUNCTION__, "klass != NULL" );
i = &i->next;
if ( i->next == 0 )
break;
}
else
{
if ( i->data[0] )
{
if ( *(int*)(i->data[0]) == 0 )
{
g_return_if_fail_warning( 0, __PRETTY_FUNCTION__, "c != NULL" );
i = &i->next;
if ( i->next == 0 )
break;
}
else
do
{
if ( *(int*)(*(int*)(i->data[0]) + 64) == gts_edge_class( ) )
{
GSList *j = j[2].next;
if ( j[2].next )
{
{
do
{
if ( gts_face_class( ) == 0 )
g_return_if_fail_warning( 0, __PRETTY_FUNCTION__, "klass != NULL" );
else
if ( j )
{
if ( j->data[0] == 0 )
g_return_if_fail_warning( 0, __PRETTY_FUNCTION__, "c != NULL" );
else
do
{
if ( j->_GSList == gts_face_class( ) )
{
if ( ( !surface || gts_face_has_parent_surface( &j->data[0], surface ) ) && g_slist_find( list, &j ) == 0 )
{
list = g_slist_prepend( list, &j );
break;
}
else
break;
}
else
}
while ( j->_GSList );
}
j = j->next;
}
while ( j->next );
break;
}
}
else
break;
}
else
{
}
}
while ( *(int*)(*(int*)(*(int*)(i->data[0]) + 64) + 64) );
}
i = &i->next;
}
}
/**
* 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);
}
