The second transform maps from one local space to the next with a translation in x and y and a rotation about an axis in the z-direction。 Referring again to Fig。 6, the following matrix product

 cos α1         sin α1      0    0 1 −x0 

Fig。 7。    Dyad formed by gusset corner in tray carton。

commands for the constraint modelling environment created by the pre-processor。

dec mod3 mspc_guss1_posn, mspc_guss1_turn;

dec geom edge_guss1_00, edge_guss1_01,  edge_guss1_02;

dec mod3 mspc_guss2_posn, mspc_guss2_turn;

dec geom edge_guss2_00, edge_guss2_01,  edge_guss2_02;

mspc_guss1_posn = mod3( 0。0, 0。0, 0。0, 0。0, 0。0, 0。0, mspc_dsid1_turn );

mspc_guss1_turn = mod3( 0。0, 0。0, 0。0, 0。0, 0。0, 0。0, mspc_guss1_posn );

− sin α1 cos α1 0    0    1 −y0

where α1 is the angle between the joining edge for face f and the global x-axis, maps the space of face f so that its joining edge maps to the global x-axis with the end (x0, y0) mapping to the origin。

Let X¯0  and Y¯0  be the x and y coordinates of point (X0, Y0) under

this map。 Then the matrix

mspc_guss2_posn = mod3( 0。0, 0。0, 0。0, 0。0, 0。0, 0。0, mspc_dsid2_turn );

mspc_guss2_turn   =   mod3(   0。0,   0。0,   0。0,   。00,   0。0,    0。0,

cos α2 − sin α2 0

sin α2 cos α2 0

mspc_guss2_posn );

  0 0 1 0 

0 0 0 1

edge_guss2_00 = lin( 5。0, 0。0, 0。0, 0。0, 5。0, 0。0, mspc_guss2_turn );

where α2 is the angle between the two joining edges, creates the transform mapping the space of F  to that of f 。 The pre-processor edge_guss2_01 mspc_guss2_turn =

); lin( 0。0, 5。0, 0。0, 0。0, 0。0, 0。0,

uses the values in this matrix to create commands to set up the second transform。 edge_guss2_02

mspc_guss2_turn =

); lin( 0。0, 0。0, 0。0, 5。0, 0。0, 0。0,

The pre-processor always creates the commands which specify the constraints which need to be solved for the dyads。 The data file for the net declares these in terms of pairs of faces (between which a ‘‘cut’’ has been formed) and an indication of which points need to be brought together。 As noted earlier, each gusset corner can move inwards or outwards。 So it is also possible to specify bounds of the values for the angles of the folds so as to ensure motion in the appropriate direction。