addendum_4_algorithm.md

Algorithm

For each closed-polygonal-chain $B_z$, the following cycle is repeated several times (iterations), up to the first iteration at which none new module (b) is created (cf. Figure 4):

• for each open-polygonal-chain $P^*=P_1^H,P_2^H,\ldots,P_M^H,P_1^V,P_2^V,\ldots,P_N^V$ (either horizontal or vertical):

  find modules (a) – more than one module can be found within a single polygonal-chain $P^*$ –, each one:

  • with the maximum-possible length $T^{+}\ge T$

  • where all elements are quadrilateral and associated to $B_z$

  • and where, on the yet to come module (b), each element:

    • height is lower than $h_{MAX}$ aforementioned

    • shape-factors H/V and V/H are lower than those defined into inner-block maximum_element_shape_factor multiplied by relevant values within inner-block element_shape_factor_multiplier

  then: any module (a) which is found and for which all the above constraints are fulfilled, is reshaped as a module (b):

  • both extremities $F_0,F_{T^+}$, which are initially composed by two quadrilateral-elements each (cf. Figure 4a), are reshaped as (cf. Figure 4b):

    • three triangular-elements each (if triangular_extremities_tf is set to true, i.e.: cyan bounds in Figure 4b are included)

    • one quadirateral and one triangular elements (if triangular_extremities_tf is set to false, i.e.: cyan bounds are omitted)

    with an exception when, among these extremities, one or both touch any conditioned-boundary (cf. inner-block boundary_conditions); in this latter case, extremities touching conditioned-boundaries are reshaped using just quadrilateral-elements, in the same way as it is done for central elements $F_1,F_2,\ldots,F_{T^+-1}$, where each couple of quadrilateral-elements is reshaped to a single quadrilateral-element (cf. Figure 4)