Returns $\alpha_j$( $\alpha_i$(*dh)).

Overloads of this member function are defined that take from one to nine integer as arguments. For each function, alphas are applied in the same order as their indices are given as parameters.

For example alpha(dh,1)= $\alpha_1$(*dh), and alpha(dh,1,2,3,0)= $\alpha_0$( $\alpha_3$( $\alpha_2$( $\alpha_1$(*dh)))).

Precondition

0 $\leq$ i $\leq$ dimension, 0 $\leq$ j $\leq$ dimension and *dh $\in$ darts().

Returns $\alpha_j$( $\alpha_i$(*dh)).

Overloads of this member function are defined that take from one to nine integer as arguments.

Precondition

0 $\leq$ i $\leq$ dimension, 0 $\leq$ j $\leq$ dimension and *dh $\in$ darts().

Returns $\alpha_j$( $\alpha_i$(*dh)).

Overloads of this member function are defined that take from one to nine integer as template arguments. For each function, alphas are applied in the same order as their indices are given as template arguments.

For example alpha<1>(dh)= $\alpha_1$(*dh), and alpha<1,2,3,0>(dh)= $\alpha_0$( $\alpha_3$( $\alpha_2$( $\alpha_1$(*dh)))).

Precondition

0 $\leq$ i $\leq$ dimension, 0 $\leq$ j $\leq$ dimension and *dh $\in$ darts().

Returns $\alpha_j$( $\alpha_i$(*dh)).

Overloads of this member function are defined that take from one to nine integer as template arguments.

Precondition

0 $\leq$ i $\leq$ dimension, 0 $\leq$ j $\leq$ dimension and *dh $\in$ darts().

Returns true iff *dh1 can be i-sewn with *dh2 by keeping the generic map valid.

This is true if there is a bijection f between all the darts of the orbit D1= $\langle{}$ $\alpha_0$, $\ldots$, $\alpha_{i-2}$, $\alpha_{i+2}$, $\ldots$, $\alpha_d$ $\rangle{}$(*dh1) and D2= $\langle{}$ $\alpha_0$, $\ldots$, $\alpha_{i-2}$, $\alpha_{i+2}$, $\ldots$, $\alpha_d$ $\rangle{}$(*dh2) satisfying:

• f(*dh1)=*dh2,
• $\forall$ e $\in$ D1, $\forall$ j $\in$ {1, $\ldots$,i-2,i+2, $\ldots$,d}, f( $\alpha_j$(e))= $\alpha_j$(f(e)).

Precondition

0 $\leq$ i $\leq$ dimension, *dh1 $\in$ darts(), and *dh2 $\in$ darts().

Returns true iff the generalized map is valid.

A generalized map is valid (see Sections Mathematical Definitions and Generalized Map Properties) if for all its darts d $\in$ darts():

• $\forall$ i, 0 $\leq$ i $\leq$ dimension: $\alpha_i(\alpha_i(d))=d$;
• $\forall$ i, $\forall$ j such that 0 $\leq$ i $\leq$ dimension-2 and i+2 $\leq$ j $\leq$ dimension: $\alpha_j(\alpha_i(\alpha_j(\alpha_i(d))))=d$;
• $\forall$ i, 0 $\leq$ i $\leq$ dimension such that i-attributes are non void:
  • $\forall$ d2 in the same i-cell than d: d and d2 have the same i-attribute;
  • $\forall$ d2 in a different i-cell than d: d and d2 have different i-attributes.

Links *dh1 and *dh2 by $\alpha_i$.

The generalized map can be no longer valid after this operation. If are_attributes_automatically_managed()==true, non void attributes of *dh1 and *dh2 are updated: if one dart has an attribute and the second dart not, the non null attribute is associated to the dart having a null attribute. If both darts have an attribute, the attribute of *dh1 is associated to *dh2.

Precondition

0 $\leq$ i $\leq$ dimension, *dh1 $\in$ darts(), *dh2 $\in$ darts() and (i $<$ 2 or dh1 $\neq$dh2).

i-sew darts *dh1 and *dh2, by keeping the generic map valid.

Links by $\alpha_i$ two by two all the darts of the orbit D1= $\langle{}$ $\alpha_0$, $\ldots$, $\alpha_{i-2}$, $\alpha_{i+2}$, $\ldots$, $\alpha_d$ $\rangle{}$(*dh1) and D2= $\langle{}$ $\alpha_0$, $\alpha_2$, $\ldots$, $\alpha_{i-2}$, $\alpha_{i+2}$, $\ldots$, $\alpha_d$ $\rangle{}$(*dh2) such that d2=f(d1), where f is the bijection between D1 and D2 satisfying: f(*dh1)=*dh2, and for all e $\in$ D1, for all j $\in$ {1, $\ldots$,i-2,i+2, $\ldots$,d}, f( $\alpha_j$(e))= $\alpha_j$(f(e)).

If are_attributes_automatically_managed()==true, when necessary, non void attributes are updated to ensure the validity of the generic map: for each j-cells c1 and c2 which are merged into one j-cell during the sew, the two associated attributes attr1 and attr2 are considered. If one attribute is NULL and the other not, the non NULL attribute is associated to all the darts of the resulting cell. When the two attributes are non NULL, functor Attribute_type<i>::type::On_merge is called on the two attributes attr1 and attr2. If set, the dynamic onmerge function of i-attributes is also called on attr1 and attr2. Then, the attribute attr1 is associated to all darts of the resulting j-cell. Finally, attribute attr2 is removed from the generic map.

Precondition

is_sewable<i>(dh1,dh2).

Unlinks *dh and $\alpha_i$(*dh) by $\alpha_i$.

The generalized map can be no longer valid after this operation. Attributes of *dh and $\alpha_i$(*dh) are not modified.

Precondition

0 $\leq$ i $\leq$ dimension, *dh $\in$ darts(), and *dh is not i-free.

i-unsew darts *dh and *opposite<i>(*dh), by keeping the generic map valid.

Unlinks by $\alpha_i$ all the darts in the orbit $\langle{}$ $\alpha_0$, $\ldots$, $\alpha_{i-2}$, $\alpha_{i+2}$, $\ldots$, $\alpha_d$ $\rangle{}$(*dh).

If are_attributes_automatically_managed()==true, when necessary, non void attributes are updated to ensure the validity of the generic map: for each j-cell c split in two j-cells c1 and c2 by the operation, if c is associated to a j-attribute attr1, then this attribute is duplicated into attr2, and all the darts belonging to c2 are associated with this new attribute. Finally, the functor Attribute_type<i>::type::On_split is called on the two attributes attr1 and attr2. If set, the dynamic onsplit function of i-attributes is also called on attr1 and attr2.

Precondition

0 $\leq$ i $\leq$ dimension, *dh $\in$ darts() and *dh is not i-free.