The geometric algorithm of the concept design applies to the rest of the design, following the tower enlargement and relocation, retaining however the plant minor diagonals anchored at the concept design outer corners EE, page 116.
The remaining task is to complete the courtyard wall. The indoor face of the courtyard wall can be drawn as an octagon inside the façade wall separated by the room width, which remains unchanged from the concept design.
However, it seems prudent to retrace the geometric algorithm in this respect; this means finding the cross vault center next.
The issue with critical corners has focused the geometric discussion on the plant minor diagonals as the face line of the lateral thrust masonry struts. However, the more significant reference is the center line of the cross vault. This center line is defined as a line parallel to the plant minor diagonals and offset by the footing width f away from the critical corners, folio 117:01.
This is part of the geometric algorithm in the concept design (page 140-120, folio 121:04).
The intersection of the plant minor diagonals going through the critical corners M is at the distance j" from the indoor face of the façade wall, following the tower enlargement and relocation, folio 117:02.
The cross vault centerlines are separated from the plant minor diagonals by the measure f; their intersection is located at the distance f√2 from the plant minor diagonal intersection, folio 117:02.
Half of the room width is therefore the measure:
w/2 = j” + f∙√2
Where w is the room width variable.
Per the geometric design algorithm, the indoor face of the courtyard has to be at the same measure w/2 from the center of the cross vault for the latter to be a perfect square. This means that the indoor face of the courtyard wall is drawn as a parallel octagon side inward at a the distance w/2 from the cross vault center, folio 117:03.
The reference for the indoor side of both the façade and courtyard walls is the finishing face, knowing that the stone face is separated by the measure (m-n).
The indoor face of the façade wall is expected to move by the measure 2n outward along the plant side direction because the room width remains unchanged and the cross vault has moved outward by the measure 2n.
The final item to define is the outdoor face of the courtyard wall. The definition of this element is retained unchanged from the concept design. It is the inside octagon delimited by the plant minor diagonals anchored at the center of the concept design tower octagons, folio 117:04.
The procedure for the design of the courtyard wall is in essence the definition of a leftover space.
The detailed geometric methodology is covered on page 122 of file 140-120, the concept design section.
The separation between the indoor and outdoor faces is the measure of the courtyard wall thickness, a variable labeled b.
The thickness of the courtyard wall increases by the measure m+n in the modified design. The increment corresponds to the relocation amount of the cross vault square along the plant side direction resulting from the tower relocation, folio 117:05.
The resulting design puts the masonry struts for the lateral thrusts well within the courtyard wall space, folio 117:05.
The outdoor face of the courtyard wall marks the perimeter of the courtyard and completes the geometric algorithm for the plant design.