A generative design method of building layout generated by path

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Model parameters and mathematical expressions of doors and windows

Model category	Iutput	Output	Mathematical expression
Swing door	P(x, y), xl, xr, yl, yr, Hi	Holtal Sdi(Pd1 Pd2 Pd3 Pd4)Form of Ds (Direct-section + arc)	(33)–(40)(33), (42)–(45)
Sliding window	P(x, y), xl, xr, yl, yr, Hi, Ho	Holtal Swi(Pw1 Pw2 Pw3 Pw4)Window Form Ws(Swi+ Rectangle)	(33)–(40)(33), (35), (46), (47)
Wall openings	Sdi, Swi, W	Hole Wo	(41)

Wall model parameters and mathematical expressions

Input	Output	Mathematical expression
Path shape (Ai)	Out ring (outer wall axis B)	B = A1 ∪ A2 ∪ A3 ∪ … (29)
Offset distance (Ho, Hi)	Outer wall outline (outer ring O), building space inner outline (inner ring li), wall shape W	W = O − I1 − I2 − I3 − … (30)
Offset distance (Ho, Hi)	Wall thickness (H)	H = Ho + Hi (31)
Path shape (C), offset distance (H1, H2)	Outer ring C1, C2 and balcony, verandah outer contour shape L	L = O −C1 −C2 (32)

Four space types and their parameter variable symbols

Spatial orientation	Orientation point (entrance)	Space length	Space width
Upward spaces	{Pun}	{Lun}	{Wun}
Downward spaces	{Pdn}	{Ldn}	{Wdn}
Leftward spaces	{Pln}	{Lln}	{Wln}
Rightward spaces	{Prn}	{Lrn}	{Wrn}

Analysis of algorithm usage for generating paths

Algorithm application	Input	Output analysis
Up-branch algorithm, used alone	Randomly input 6 branch points, a total of 5 times, the following input remains unchanged:Lu1=1, Lu2=1.5, Lu3=1, Lu4=1.5, Lu5=1.5, Lu6=1.7, Wu ln=0.6, Wur1=2, Wur2=3, Wur3=3.5, Wur4=2, Wur5=2.5, Wur6=3.5	Figure a: Randomly changing the position of the branch point can generate a new layout
Combination of positioning algorithm and upper branch algorithm	Change the item value and number of {xun} and [15], the following parameters remain unchanged: Lu1= 3, Lu2= 3, Lu3=2, Lu4= 2, Wuln=0.6, Wurn=2	Figure b: Using positioning algorithms, you can freely adjust the new layout according to the design goals
Up-branch algorithm, used alone	Change the item values of {Lun}, {Wuln}, {Wurn}, and randomly input points P1, P2, P3, P4 and keep them unchanged	Figure c: Changing the value of a series item can generate a new layout

Beam parts of the bureau method process

Stage	Function bubble chart	Axis plan	Building layout
Constraints	Spatial connectivity	Spatial connectivitySpatial geometry relationship	Spatial connectivitySpatial relationshipGraphic geometric relationships

Path model parameters and mathematical expressions

Parametric model category	Input	Output	Mathematical expression
Positioning model	P(a, b), ({xun}, [15]), ({xdn}, {ydn}), ({xln}, {yln}), ({xrn}, {yrn})	Branch point (Pun, Pdn, Pln, Prn)	(1)–(8)
Upper branch	Pun, {Lun}, {Wuln}, {Wurn}	Branch shape Run (Pu1 Pu2 Pu3)Window positioning point (Puu, Pul, Pur)	(2), (9)–(11), (21), (22)
Downward branch	Pdn, {Ldn}, {Wdln}, {Wdrn}	Branch shape Rdn (Pd1 Pd2 Pd3)Window positioning point (Pdd, Pdl, Pdr)	(4), (12)–(14), (23), (24)
Left branch	Pln, {Lln}, {Wlln}, {Wlrn}	Branch shape Rln (Pl1 Pl2 Pl3)Window positioning point (Plu, Pll, Pld)	(5), (15)–(17), (25), (26)
Right branch	Prn, {Lrn}, {Wrln}, {Wrrn}	Branch shape Rrn (Pr1 Pr2 Pr3)Window positioning point (Pru, Prd, Prr)	(7), (18)–(20), (27), (28)