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ISSN 2309-0103 www.enhsa.net/archidoct Vol. 6 (2) / February 2019
with being an exponent which can be used to control different types of repulsion forces. (Figure 4) 1 −
(Figure 6).

= (−| −|)∙∙
4.2.5 Planarization by local normal force

| − |
The spring constant of Hooke’s law can vary between different types of cells (Fenster & Ugural 2011). 2011).The exponent m can be set to 1 for springs which are acting linearly proportional to their
= ( −)×( −)∗−1∗(−)∙(( −)×( −))
The spring constant k of Hooke’s law can vary between different types of cells (Fenster & Ugural
The exponent can be set to 1 for springs which are acting linearly proportional to their displacement as displacement as in Hooke’s law, or otherwise to define non-linearly acting springs.
in Hooke’s law, or otherwise to define non-linearly acting springs.
4.2.4 Planarization by attraction force
Surface-based cellular systems require a forceto generate local planarity,so that volumetric accu-
astaticcewllitnheighbeoinrghoaondexanpodnneontewdhgiechcocanndibtieonus,etdhitsocaontbroeladcifhfeierevnetdtytpherosuogfhreapucolsmiobninfoartcioesn.o(Ffigure4)
mulations of cells are avoided. In surface based manifold systems as described in 3.2, which have
4.2.3 Strata force

11 −
an attraction force between neighboring cells and a repulsion force between non-neighboring cells
= = ∙ ( −| −|)∙∙∙
with being anexponent which ca|nb−e us|ed to control different types of repulsion forces. (Fi
= ( − ) × ( − = ) ∙ − ∙

For surface-based non-manifold systems as described in13.2, a planarization by attraction force will 1 −
The spring constant of Hooke’s law can vary between different types of cells (Fenster & Ugural 2011).
= (−| −|)∙∙
In the case of layers parallel to the YZ-plane, = 0,the force is
causecellsThateedxgpeonceontditiocannsbtoesoentlytob1efpourlslepdriningwswarhdicshsoartehactttinhgelwinehaorlelygperopmoertiroynaclotnottihneuiorudsislyplacementas
1
0 | − |
contracts.iTnoHaovokide’sthlaisw, a, loter ronthateirvwelisyecetollsdecfainebneopnu-lilneedatrolywaacrtdinsgtshperipnlgasn.e through its three closest
The spring constant of Hooke’s law can vary between different types of cells (Fenster & Ug
neighbors (Figure 7). The exponent 1 can be set to 1 for springs which are acting linearly proportional to their displ
= ( −)×(−−)∗−1∗(−)∙(( −)×( −))
in Hooke’s⎛law, or otherwise t⎞o define non-linearly acting springs.

= ,
4.2.6 Strata force ⎜ 0 ⎟
0 ⎠ = ( −)×( −)∗−1∗(−)∙(( −)×( −))
4.2.3 Strata force ⎝
In order to generate parallel strata of cells, in an architectural context for example for the gen-
eration of parallel floor plates, a strata force can be applied to the cell.The direction of the strata
From this, select the coordinate axis that represents the maximum of the coordinate values: =max||,,|| 1 1
is defined by the given normal N.A plane is defined with the normal N and with its origin at the
center of the cell’s neig4h.b2o.3rs.TShterasttarafotarcfoerce then pulls the cell towards the closest point on this

plane (Figure 8). = ∙ − ∙
In the case of layers parallel to the YZ-plane, = 0, the force is
If, for example, = , then the YZ plane is regarded as the best fitting orthogonal plane and the
0
orthogonal force pushes in direction of the plane with normal through the centre point of all of its
neighbors.
1
In the case of layers parallel to the YZ-plane, = 10, the force is
= 10 ⎛ , − ⎞ 0 = ⎜ ⎟
0 ⎝ 0 1⎠ Thus the force according to 4.2.6 would be
= ⎛ , − ⎞
=(−)×(−) 1 ⎝ 0
⎜⎟
⎠
From this, select the coordinate axis that represents the maximum of the coordinate values:
h =⎛ ,−⎞
4.2.7 Orthogonal force ⎜ = max||,,||
0
⎟ ⎝0⎠
=( −)×( −)
If, for example, = , then the YZ plane is regarded as the best fitting orthogonal plane and the
done via identifying theFprolamnethoisf ,thseleccetllt’shelocoaol redninviartoenamxeisnt,tthaet prelapnrestehnatts pthaessmesatxhimrouumghofitshethcroeoerdinate values:
orthogonal force pushes in direction of the plane with normal through the centre point of all of its closest neighbors. Depending if this plane’s orientation is closest to the XY, XZ or YZ plane, a force
A force can be applied to the cells that directs them into orthogonal arrangements.This can be
neighbors.
= max||,,||
1 If, for example, = , then the YZ plane is regarded as the best fitting orthogonal plane and t N and with its origin at the centre of the cell’s neighbors.The orthogonal force then pulls the cell
is applied along the normal N=Z ̂, N=Y ̂ or N=X ̂ respectively. A plane is defined with the normal
= 0 orthogonal force pushes in direction of the plane with normal through the centre point of towards the closest point on this plane (Figure 9).
0 neighbors.
Thus the force acco1rding to 4.2.6 would be = 0
//
Cellular Design
Christoph Klemmt
1 Thustheforceaccordingto4.2−.6wouldbe
h = ⎛ , ⎞ ⎜⎟
g
u a
h a