Museo Soumaya: Facade Design to Fabrication by Gehry Technologies

MUSEO SOUMAYA

facade design TO fabrication

MUSEO SOUMAYA

facade design TO fabrication

table of contents Project Data ............................................................................................................... 4-5 Global Delivery ......................................................................................................... 6-7 process ........................................................................................................................ 8-9 defining the shape of soumaya .............................................................................. 10-11 building diagrams ..................................................................................................... 12-13 Surface Analysis ....................................................................................................... 14-15 pattern analysis with one size panel ................................................................. 16-17 nested sphere packing surface rationalization .............................................. 18-19 sphere radius optimization and Wireframe pattern generation ................. 20-21 Pattern Distortion and Stretching Process ..................................................... 22-23 Pattern with Unique Hexagons ............................................................................. 24-25 Naming Convention and Panel Organization ..................................................... 26-27 Panel Node Data Extraction ................................................................................... 28-29 Generation of node vectors ................................................................................... 30-31 engineering/design of Secondary structure .................................................... 32-33 node Mapping .............................................................................................................. 34-35 Facade assembly of components ........................................................................... 36-37 Survey of Primary Structure ................................................................................. 38-39 Simulation of local node adjustments ............................................................... 40-41 Node adjustment Analysis zone 26-B .................................................................. 42-43 Survey of Node Points .............................................................................................. 44-45 Secondary Structure Installation ....................................................................... 46-53 Panel connection Design constraints ................................................................. 54-55 Panel Connection Studies ........................................................................................ 56-57 Panel Data extraction of geometric properties ................................................ 58-61 clustering Panel Data into families ..................................................................... 62-63 Family Dendrogram .................................................................................................... 64-65 Family Options Analysis ............................................................................................ 66-67 80/20 Family Distribution ........................................................................................ 68-69 Gap verification and family tuning process ....................................................... 70-71 The 52 Families for 80% of the facade .................................................................. 72-73 Final Facade Pattern with Families ...................................................................... 74-79 Panel finish study ..................................................................................................... 80-81 Entrance panels ........................................................................................................ 82 panel submission packages ..................................................................................... 83-89 Panel installation .................................................................................................... 90-97 Time-lapse facade installation ............................................................................ 98-99 Mockups ....................................................................................................................... 100-105 Mechanical Systems Coordination........................................................................ 106-107 construction progress ........................................................................................... 108-141 Completed facade ...................................................................................................... 142-147 Project Credits .......................................................................................................... 148

MUSEO SOUMAYA

facade design TO fabrication

project data name Museo Soumaya Location Mexico city, Mexico Type facade & interior construction Size 8080m2 of facade surface / 6000m2 of exhibition space duration june 2009 â&#x20AC;&#x201C; march 2011 client grupo carso project manager PC Constructores main contractor Carso Infrastructura y ConstrucciĂłn design architect Fernando romero enterprise (free)

Global Delivery

LOS ANGELES GEHRY TECHNOLOGIES PROJECT COORDINATION

MONTERREY GEOMETRICA FABRICATION

MEXICO CITY SOUMAYA/FR-EE/GEHRY TECHNOLOGIES/IASA/CARSO OWNER/DESIGN/COORDINATION/FABRICATION/CONSTRUCTION

PITTSBURGH SMART ARCHITECTURE DESIGN CONSULTING

Process

design intent

24 21

22 23 33

38 31 32 37

9 14 10 13 11 12

34 25 26 35

Surface analysis

pattern wireframe

29 30

27 28

extract panels

unique pattern

data clustering

connection design

Pattern Stretching extract nodes

node vectors

G F E D C B A

organization 10

engineering/design

family options gap tuning

fabrication installation

node mapping fabrication

installation

as-built survey

node adjustment

completion 11

defining The Shape of soumaya The iconic shape the Museo Soumaya was originally quite different. Architect Fernando Romero explored several formal configurations before arriving at the final shape. After construction of the museum began and primary steel had already been ordered the architect sought the help of Gehry Technologies to help design and deliver the unique hexagon facade of the musem.

building diagrams

Surface Analysis The architectâ&#x20AC;&#x2122;s design intent called for a seamless pattern on a closed surface. Generating seamless geometric patterns on closed rational surfaces like a shpere [7] is easier than closed irrational surfaces [6]. GT began the first phase of the pattern design process with a detailed surface analysis [2-5] to identify zones of high curvature. Controlling pattern distortion in these zones would be challenging because of the double curvature of the surface [1].

2 - Gaussian curvature analysis 3 - 5deg tangent highlight line surface analysis

5 - Surface draft analysis

4 - 5deg normal highlight line surface analysis

pattern analysis with One Size panel The original vision of the architect was to have a hexagon pattern with only one size panel. GT implemented a series of studies to try and achieve the original design intent. However, due to the topology of the irrational master design surface it was agreed that the pattern could not be completed with just one size panel. The double curvature zones distorted the pattern and because the surface was a deformed closed shape achieving a seamless pattern would be impossible with just one panel. The image to the right is the result of a test attempting to generate the pattern with one hexagon. Blue panels were geometrically identical and red panels were not. After completing the studies and having a discussion with the architect it was decided that the pattern would be stretched in zones of high curvature.

nested sphere packing surface rationalization Since the master design surface could not be modified GT used a surface rationalization technique that adjusted to the curvature of the surface. Nested sphere packing is a simple technique that can be applied in many conditions with different results depending on the curvature of the surface. 1 The packing algorithm needs a path along the surface to follow, a start point on the path, a sphere radius, and a direction to travel [1]. One sphere is constructed at the start point and then intersects the surface creating a circle. The 2 second sphere center point along the path is created at the intersection of the circle and the path in the predetermined direction of travel [2]. When the second sphere is generated and intersected with the surface and path the third point is created along with the first point for the second row [3]. This process is repeated until the surface is populated with 3 spheres and intersection points [4]. Finally the intersection points are connected into triangles [5]. On a flat surface with zero curvature the resulting triangles will be equal. However, when the surface is convex or concave the resulting triangles are deformed. This type of rationalization process follows the natural topology of the surface creating a non-uniform pattern ideal for irrational geometry.

Zero Curvature

Co e

at ur

nv ex

sphere radius optimization AND wireframe pattern generation After working with the architect to decide on the desired size of the smallest panel GT could begin generating the final pattern. The initial path for the nested sphere packing algorithm was located about half way up the building where the perimeter of a horizontal intersection was smallest [1]. Then the start point was placed at a point on the path optimized to where the surface had the least amount of curvature. The total number of spheres needed was calculated by dividing the length of the path by the radius of the ideal panel size. However, after propagating the resulting number of spheres along the path there was a remainder. Finally, an optimization process was used to slightly change the radius of every sphere along the path until the remainder was nearly zero [2,3]. The wireframe components of the pattern were created by the nested sphere packing algorithm. Since the initial path was in the middle of the building the pattern was created in upper and lower parts [4]. After the sphere intersections and points were generated the hexagons were created [5].

radius

0mm

pattern Distortion and stretching process The new design intent for the pattern was composed of stretched corners in the zones with high curvature. After the nested sphere packing process the resulting pattern was compressed instead of stretched in the corners of the facade [1]. GT developed a method to parametrically stretch the pattern so that the architect could choose how far he wanted to stretch the panels [2,3]. Stretching the pattern according to the architectâ&#x20AC;&#x2122;s design intent was achieved by creating a parametric rig. This enabled the architect to easily see many iterations of the pattern with different ratios of stretching. The overall construction of the rig was simple. First, a series of splines were constructed by vertically connecting wireframe intersection points and extended along the master design surface [4]. Then the intersection points could be redistributed along the spline at different ratios until the desired effect was attained [5-7].

Before Pattern Stretching Process

After Pattern Stretching Process

7 25

Pattern with all unique hexagons The pattern at this point conformed with the design intent of a seamless stretched pattern with uniform gaps, but there were over 15,000 uniquely shaped hexagon panels. From here the design of the secondary structure and the development of panels into families were done in parallel helping to save time in the accelerated construction schedule.

G F E D C B A

naming convention and panel organization

02 03

04 05

06 07

22 21

08 20

19 18

10 17

F E D C B 2

Horizontal Vertical Panel/Node Zone Zone Unique ID

Family Type

Finish Type

01_A_12352_01_3 4

#12352

panel node data extraction GT worked with the engineers and fabricators to create a naming convention to manage the large number of panels that needed to be fabricated, tracked, and installed. Using the natural grid created by the primary steel as a guide, an alphanumeric name was generated from the location of each panel node in relation to the primary steel elements. There were 28 columns around the perimeter of the building and 7 horizontal rings and depending on the X,Y,Z coordinate of the node the zone prefix would be a number between 1-28 and a letter from A-G [see page 26 fig. 1-3] followed by the unique ID of the node. The suffix of the final panel name is represented by the family type and panel finish [see page 27 fig. 4]. Geometrica required the name of each node and its X,Y,Z coordinate to start designing and engineering the secondary facade. The necessary data was extracted from the design model [1-3]. Extra nodes were included above and below the limits of the facade to allow the structure to be trimmed [4&5].

Y G F E D C B A X

01_X_12352

Generation of node vectors The Geometrica secondary structure was designed as a 2-layer system that would enclose the primary steel. Since the panel nodes were generated at the panel finish surface Geometrica needed a way to ensure that the nodes could be accurately offset in to achieve the correct system depth. GT generated a vector at each node normal to the panel providing a path to constrain the movement in the nodes of the secondary structure. The 3d model enabled a high degree of coordination between the facade pattern, primary, and secondary structure.

Panel Node

14_A_13934 Vector Node

14_A_13934_V

engineering/design of secondary structure from nodes and vectors GT submitted a spreadsheet containing point coordinates of panel nodes and key coordinate points of slab edges, wall edges, and column locations. Then Geometrica engineered the entire 2 -layer (TC layer and BC layer) secondary structure and returned to GT a spreadsheet of node locations and a key to map the node connections. To further coordinate the secondary structure design with the design model GT built a 3d model from Geometricaâ&#x20AC;&#x2122;s data [see page 34 fig. 1-3]. Since the panels were designed to be a rain screen the waterproofing for the building was built into Geometricaâ&#x20AC;&#x2122;s system [see page 37].

TC Layer

BC Layer

node mapping

BC Layer

TC Layer

facade assembly of components

BC Layer Nodes and Bars

BC/TC Connection Bars

Geometrica TC Layer Nodes and Bars

IASA Panel Edge Connection

Exterior Panel Waterproofing Substrate

Structural Spacer

Panel Connection

Hexagon Panel

survey of primary structure This project utilized as-built survey data to coordinate the design, engineering, and installation of the secondary structure in relation to the primary steel elements. Primary columns were rebuilt in the 3d model according to the surveyed data and compared with the design model [1]. The data showed that the columns and slab edges were shifted to one side of the building which could cause clashing with other building elements. Geometrica imported the data into their model and locally adjusted large areas of nodes around possible conflicts with primary structure elements. After the adjustments were completed the nodes were sent to GT and rebuilt in the 3d model environment. GT analyzed how the nodes were different from the original and discovered that the nodes were not transitioned very smoothly in and out of the adjusted zones. This would affect the panels at the finish surface so Geometrica improved the transition around the adjusted nodes. The colors in the diagrams represent how far the adjusted node were from the original node [see page 40 fig. 1-3]. GT performed a detailed analysis of the adjusted nodes in Zone 26-B to demonstrate how the adjustments could be improved [see page 42 fig. 1-8]. By connecting the nodes in the zone with a series of splines the curvature could be analyzed. The original adjusted nodes degraded the curvature of the surface by adding inflection points. Removing the inflection point required a small adjustment and greatly improved surface curvature [see page 43 fig. 9-10]. Nodes of the secondary structure were surveyed during the installation process. Geometrica installation crews temporarily attached the network of nodes and connecting bars to the primary structure and used survey data to push and pull the system into place. A few node points from each zone were surveyed and verified in the 3d model to calculate the difference from the design model. The differences were averaged and shown in a spreadsheet similar to an unfolded view of the facade to find where nodes needed to be adjusted before the final attachment to the building [see page 44 fig. 1-3].

Simulation of local node point adjustments

Before 42

Panel Offset from Design Node [mm] + offset to the exterior of the facade - offset to the interior of the facade 19.277 + 15.163 to 19.277 11.048 to 15.163 6.9335 to 11.048 2.8189 to 6.9335 Ͳ1.296 to Ͳ2.8189 Ͳ5.4104 to Ͳ1.2958 Ͳ9.525 to Ͳ5.4104 Ͳ9.525

After 43

node adjustments analysis zone 26-b

Zone 26-B

Current adjusted Geometrica nodes 1

Current location of node 11283 degrades curvature 4

Curvature analysis reveals inflection point on curve 5

GT proposes to move node 1.52cm along node vector 6

Curvature after moving proposed node 7

Curvature of original design nodes in 3D model 8

Splines connecting nodes to analyze curvature

Original GT nodes before adjustment Curvature is generally consistent between neighboring curves.

Current adjusted nodes Sometimes curvature is not consistent between neighboring curves.

10 45

survey of node points

Average Deviation Per Zone

GT Survey Analysis

0-4 cm Low impact on overall pattern design

4-10 cm Medium impact on overall pattern design 10+ cm High impact on overall pattern design G F E D C

9.09

6.99

5.19

3.6

2.29

3.65

2.32

3.69

5.35

4.95

14.67

19.35 20.99

21.32

21.27

22.04

22.16

12.37

7.91

6.81

10.5

5.1

2.43

2.64

3.14

6.5

7.77

11.93

14.45

19.6

23.07

21.92

22.33

22.29

22.36

23.6

Average deviation per zone in cm

3.21

23.04

21.49

18.8

13.6

29.68

4.18

24.26

23.07

22.19

16.7

14.12

28 47

secondary structure installation

panel connection design constraints

V_Angle_1-6

6 5 4

1 3

1 P_Ang _6

A P_

E1_1

le_1

E1_2

Edge_1

E6_2

_1 Edge_2 le_2 P_Ang

E2 _2 Edge_3

5 P_Angle_

E3_1

E6_1

Edge_6

E3_2

Edge_5

E5 _1

E4_2

E4_1 Edge_4

P_An

le_

g An

gle_4

panel connection studies

24 21

22 23 33

38 31 32 37

9 14 10 13 11 12

34 25 26 35

36 29 30

27 28

panel data extraction of geometric properties

GTâ&#x20AC;&#x2122;s role in the design and fabrication of the panels involved managing large amounts of data and packaging data in ways to inform design decisions. Engineering the panel connection elements required the minimum and maximum distances between several elements of various design constraints. For example, the diagrams on pages 5455 show the range of motion the panel connections needed to accommodate in the first ring of the building. This information was used in a series of studies to design the panel connection elements [see page 56]. The family creation process began with extracting and organizing data from the panels. Geometric properties [1,2] of each hexagon were distilled and captured in massive arrays of data [3 & page 60]. K-means clustering algorithms were used to sort the panels into a predetermined number of families chosen by the architect and fabricators. The process stacked all panels (up to 16,000 panels) in the same spot. Then two panels were chosen from the stack and differences were measured between inherent geometric properties to see if they could be in the same family. This was repeated until all panels have been compared against each other. Finally, the panels were cataloged into families and the name of each centroid panel (the most representative of its family) was given along with all of its similar family members [see page 62].

3 8

1 2

7 19

18 6

The dendrogram on page 64 illustrates the resulting family tree of a hierarchical clustering algorithm. Panels were compared against each other, similar panels were grouped, and groups were progressively merged into larger clusters. Families were created by choosing a branch of the tree and listing the names of the panels within that branch. For example, to make only two families you would follow the tree to the end where there are only two branches. Then all the panels on the first branch would be the first family and the all the panels on the second would the second family. Based on this analysis GT learned that about 80% of the panels were very similar. GT worked closely with the architect and fabricators to determine how many families were needed to realistically achieve the design intent. The fabricators wanted fewer families to produce while the architect wanted the gaps between the panels to be as uniform as possible. Some early family option studies are shown on page 66.

24 21

22 23 33

38 31 32 37

14 10 13 11 12

34 25 26 35

36 29 30 2

27 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Variable Skew Factor 1 Skew Factor 2 EdgeLength1 EdgeLength2 EdgeLength3 EdgeLength4 EdgeLength5 EdgeLength6 InteriorAngle1 InteriorAngle2 InteriorAngle3 InteriorAngle4 InteriorAngle5 InteriorAngle6 ExteriorAngle1 ExteriorAngle2 ExteriorAngle3 ExteriorAngle4 ExteriorAngle5 ExteriorAngle6 StackedP1x StackedP1y StackedP2x StackedP2y StackedP3x StackedP3y StackedP4x StackedP4y StackedP5x StackedP5y StackedP6x StackedP6y Area1 Area2 Area3 Area4 Area5 Area6 AreaTotal

without missing data 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152 16152

Minimum 71.038 70.593 287.749 352.155 351.424 288.114 352.128 351.411 41.189 39.059 37.324 41.159 39.277 39.074 108.071 111.492 95.096 108.060 111.300 86.159 455.352 290 366 290.366 466.801 290.022 919.218 227.175 510.479 641.353 483.505 562.086 906.978 224.261 47425.652 48017.448 47887.464 46989.566 47875.845 48085.671 286420.340

Maximum 109.929 109.294 939.419 771.329 701.634 973.160 783.134 703.264 88.453 73.283 70.124 89.691 73.487 69.533 140.979 140.738 137.036 139.392 142.381 136.967 466.801 638 480 638.480 455.352 553.962 933.597 230.335 456.886 291.700 457.157 291.918 972.539 231.591 237688.342 239731.670 253161.984 252366.361 247754.147 233911.301 1464600.799

Mean 89.797 89.342 430.809 425.743 424.426 436.952 428.895 422.070 60.512 59.826 59.445 60.913 60.049 59.254 120.451 120.960 119.321 119.727 120.323 119.218 5.035 366 724 366.724 5.035 362.089 9.960 2.964 5.241 368.495 5.218 363.865 9.982 6.511 79719.027 79993.307 80864.621 81400.605 81018.532 80066.957 483063.050

Std. 5.073 5.103 105.396 69.428 61.923 110.341 72.338 60.934 7.745 5.106 5.383 7.899 4.985 5.438 4.883 5.203 7.127 4.459 4.878 7.321 220.109 57 303 57.303 220.109 47.876 442.591 53.937 224.054 58.241 223.382 48.790 443.256 54.321 28684.797 28447.161 29336.209 30294.093 29796.233 28713.263 175134.557 61

UniqueID 7322.1 7323.1 7324.1 7325.1 7326.1 7327.1 7328.1 7329.1 7330.1 7331.1 7332.1 7333.1 7334.1 7335.1 7336.1 7337.1 7338.1 7339.1 7340.1 7341.1 7342.1 7343.1 7344.1 7345.1 7346.1 7347.1 7348.1 7349.1 7350.1 7351.1 7352.1 7353.1 7354.1 7355.1 7356.1 7357.1 7358.1 7359.1 7360.1 7361.1 7362.1 7363.1 7364.1 7365.1 7366.1 7367.1 7368.1 7369.1 7370.1 7371.1 7372.1 7373.1 7374.1 7375.1 7376.1 7377.1 7378.1 7379.1 7380.1 7381.1 7382.1 7383.1 7384.1 62 7385.1 7386.1

Edge_1 702.61 742.12 797.67 827.96 841.97 832.67 819.50 821.15 808.61 795.95 757.61 707.24 653.45 595.99 540.76 493.63 453.94 418.49 391.00 374.73 366.25 366.44 369.87 376.87 395.07 406.82 415.17 423.20 431.49 440.51 448.71 457.10 465.65 469.52 468.70 468.80 469.66 468.62 474.85 486.85 499.90 515.85 536.74 560.63 585.73 625.16 643.92 665.77 691.24 711.96 732.29 750.84 758.51 756.61 763.63 773.78 788.31 794.79 803.45 802.27 804.96 796.13 775.41 755.45 734.10

Edge_2 639.10 655.71 668.59 671.09 655.03 627.77 601.30 569.35 549.52 541.62 531.37 523.34 512.66 504.44 503.62 506.36 508.64 508.51 507.36 506.03 504.68 506.64 507.69 506.48 509.31 511.82 514.57 517.82 521.57 524.41 526.37 528.96 531.00 531.65 529.42 526.46 523.22 520.19 519.84 523.00 529.40 537.79 548.60 561.84 575.10 592.78 609.34 625.86 640.40 653.06 661.03 662.39 650.20 630.76 608.22 585.72 568.05 562.98 564.43 571.55 584.39 592.12 591.93 592.00 589.75

Edge_3 477.92 483.26 496.55 522.66 562.22 600.74 647.98 693.20 715.47 720.07 699.86 674.46 645.30 613.96 579.32 551.17 528.58 509.67 496.70 490.06 486.15 484.38 481.96 485.20 491.54 493.82 494.49 494.39 494.51 494.53 496.15 497.73 499.73 501.50 504.26 507.48 510.66 513.47 515.36 515.38 514.09 511.96 509.62 506.81 504.23 500.62 495.67 491.08 486.82 485.43 485.09 497.94 520.12 545.44 574.89 600.77 633.18 647.87 653.85 655.99 654.31 647.03 631.18 621.63 616.51

Edge_4 727.66 765.24 824.80 855.53 871.34 860.63 842.97 843.01 827.62 817.91 780.79 730.72 676.81 618.08 561.18 512.07 471.15 432.83 400.65 381.22 370.09 368.76 371.23 374.04 395.91 410.30 419.80 428.57 437.28 447.30 455.38 464.06 473.46 476.65 474.56 474.70 475.98 474.56 483.26 498.53 512.91 530.25 552.76 577.48 603.25 645.87 659.97 680.30 706.11 726.49 746.93 766.77 775.54 772.79 780.45 791.00 806.15 813.28 824.62 824.91 831.05 824.29 802.98 782.28 760.53

Edge_5 666.00 685.01 706.69 712.61 694.64 654.35 604.86 556.81 514.46 499.60 493.36 495.56 491.29 486.99 487.03 489.37 492.42 495.55 497.48 497.83 498.28 500.57 503.63 504.84 505.36 507.25 509.54 512.70 516.17 519.71 522.11 523.99 526.17 526.21 522.76 518.45 514.81 510.32 510.13 514.56 522.68 531.97 544.74 561.50 576.27 601.98 618.08 630.52 642.90 651.26 657.03 657.62 644.53 619.77 595.14 572.53 558.39 545.20 550.82 555.89 561.88 560.79 564.89 565.08 558.37

Edge_6 530.40 535.61 555.89 572.78 592.46 612.13 626.77 656.66 670.56 668.90 653.79 628.03 608.45 589.74 569.31 548.91 529.56 512.49 500.91 495.40 492.81 491.74 490.48 493.61 498.95 501.51 502.59 503.15 503.72 504.17 505.94 507.57 509.19 510.80 511.66 515.05 518.93 522.45 526.31 529.56 530.96 530.86 531.35 530.54 526.74 531.13 526.15 521.56 523.65 529.10 538.34 552.38 571.04 587.49 612.43 639.72 664.39 672.78 671.16 663.66 654.39 636.93 622.97 610.72 599.45

IAng1 73.89 76.91 81.16 83.53 84.85 84.40 83.55 83.39 82.10 81.15 78.34 74.68 70.34 65.43 60.52 56.23 52.49 49.01 46.17 44.43 43.52 43.51 43.87 44.64 46.57 47.79 48.64 49.45 50.27 51.17 52.00 52.82 53.67 54.05 53.99 54.01 54.11 54.00 54.60 55.76 56.99 58.47 60.36 62.47 64.63 67.94 69.32 70.90 72.77 74.21 75.65 77.12 77.91 77.97 78.65 79.28 80.26 80.62 81.42 81.49 81.78 81.26 79.86 78.47 76.91

IAng2 62.17 60.75 57.58 54.86 51.49 48.73 46.00 42.45 40.97 40.73 41.99 44.11 46.39 49.24 53.12 57.27 61.23 64.89 67.74 69.34 70.16 70.64 70.89 69.97 68.43 67.74 67.49 67.40 67.32 67.12 66.69 66.32 65.85 65.53 65.13 64.45 63.69 63.10 62.45 62.03 62.05 62.19 62.26 62.42 62.51 61.87 62.58 62.97 62.73 62.38 61.62 59.83 57.34 54.87 51.54 48.43 45.39 44.31 43.90 44.33 45.12 46.30 47.73 48.97 49.99

IAng3 41.37 39.97 38.73 39.42 42.00 45.78 50.51 54.87 58.18 59.59 60.96 62.45 64.13 65.73 66.24 66.17 65.88 65.68 65.74 65.93 66.01 65.57 64.87 65.15 64.71 64.06 63.41 62.64 61.86 61.08 60.68 60.24 59.84 59.84 60.47 61.15 61.76 62.49 62.33 61.28 59.83 58.08 55.95 53.57 51.38 48.31 46.46 44.64 42.88 41.66 40.74 41.02 42.79 45.48 48.21 50.59 52.83 53.79 53.56 53.37 52.50 52.16 52.06 52.32 53.12

IAng4 75.75 78.49 82.77 84.82 85.84 85.31 84.04 83.70 82.48 81.65 79.07 75.35 71.32 66.76 62.23 58.07 54.36 50.65 47.36 45.30 44.11 43.96 44.20 44.51 46.84 48.34 49.32 50.20 51.07 52.06 52.86 53.73 54.64 54.96 54.78 54.84 54.99 54.89 55.75 57.23 58.59 60.18 62.18 64.27 66.38 69.80 70.81 72.37 74.42 76.09 77.80 79.41 80.24 80.23 80.93 81.65 82.39 82.79 83.40 83.30 83.71 83.24 81.83 80.37 78.79

IAng5 61.98 60.73 57.88 55.68 52.85 49.91 46.68 42.45 39.62 38.95 40.17 42.79 45.12 47.87 51.46 55.37 59.26 63.18 66.38 68.18 69.23 69.78 70.24 69.71 67.86 67.04 66.71 66.58 66.46 66.30 65.91 65.48 65.02 64.67 64.23 63.43 62.62 61.89 61.18 60.74 60.83 60.98 61.11 61.46 61.67 61.32 62.05 62.16 61.58 60.76 59.58 57.73 55.33 52.84 49.57 46.49 43.92 42.49 42.53 43.05 43.57 44.41 46.01 47.28 48.10

IAng6 44.84 43.14 41.88 41.70 42.96 45.87 49.21 53.14 56.65 57.93 59.48 60.60 62.68 64.97 66.41 66.88 66.78 66.59 66.61 66.82 66.96 66.55 65.93 66.03 65.58 65.02 64.43 63.73 63.01 62.27 61.86 61.42 60.98 60.95 61.40 62.12 62.82 63.64 63.70 62.96 61.71 60.10 58.14 55.81 53.43 50.75 48.79 46.97 45.63 44.90 44.60 44.89 46.40 48.62 51.11 53.57 55.20 56.01 55.19 54.46 53.33 52.62 52.51 52.58 53.10

EAng1 121.01 122.19 125.30 127.73 130.47 132.57 134.06 137.04 137.92 137.95 136.57 134.61 132.57 130.05 126.71 122.92 119.25 115.84 113.24 111.79 111.07 110.75 110.51 111.41 112.77 113.43 113.68 113.80 113.94 114.10 114.55 114.88 115.31 115.59 115.77 116.34 117.07 117.62 118.32 118.95 119.19 119.17 119.26 119.31 118.99 120.16 119.50 118.91 119.19 119.61 120.42 122.07 124.32 126.22 129.28 131.98 135.06 135.75 136.09 135.83 135.00 133.26 131.97 130.75 129.55

EAng2 134.11 135.79 136.87 137.47 136.51 133.97 131.84 128.52 125.80 124.97 123.39 122.12 119.70 117.17 115.45 115.10 115.21 115.14 114.75 114.35 113.94 114.31 114.54 114.32 115.05 115.63 116.19 116.84 117.55 118.17 118.55 119.01 119.45 119.52 119.10 118.48 117.84 117.15 117.06 117.67 118.80 120.21 122.02 124.19 126.30 128.67 130.63 132.33 133.46 134.23 134.41 134.38 133.05 131.02 128.60 126.17 124.81 124.39 125.29 126.30 127.79 128.74 128.72 128.82 128.57

EAng3 111.41 108.28 104.85 101.54 99.09 97.83 95.65 94.35 94.01 94.26 97.36 101.05 105.89 111.27 116.66 120.87 124.51 128.28 131.52 133.55 134.95 134.94 135.35 134.77 132.39 131.24 130.45 129.76 128.93 128.33 127.55 126.67 125.83 125.32 125.17 125.05 124.99 124.97 124.68 124.03 123.11 122.01 120.57 118.84 117.14 114.95 113.21 111.44 109.91 108.28 107.18 105.37 104.21 103.52 102.60 102.36 100.83 99.80 98.97 97.99 96.84 96.77 98.37 99.33 100.10

EAng4 114.98 116.39 118.77 121.41 124.69 128.30 132.42 136.86 139.85 140.33 138.78 136.38 133.95 131.13 127.56 123.81 120.15 116.54 113.74 112.13 111.13 110.76 110.11 110.89 112.56 113.15 113.38 113.43 113.55 113.54 113.94 114.36 114.77 115.20 115.76 116.49 117.18 117.88 118.25 118.29 118.10 117.81 117.50 117.10 116.74 116.65 116.41 116.49 116.90 117.76 118.67 120.50 122.94 125.56 128.82 131.40 134.20 135.61 135.51 135.47 135.14 134.29 132.76 131.74 131.21

EAng5 137.51 139.05 140.19 139.90 137.28 133.41 128.48 123.51 119.49 117.52 116.16 114.76 113.30 112.18 112.09 112.58 113.03 113.48 113.77 113.87 114.04 114.65 115.36 115.66 115.72 116.10 116.59 117.27 117.99 118.65 119.08 119.47 119.80 119.86 119.19 118.50 117.90 117.23 117.28 118.21 119.69 121.26 123.32 125.71 127.56 130.62 132.72 134.25 135.77 137.00 137.93 137.90 136.30 133.65 130.94 128.84 126.90 125.73 125.77 125.67 126.07 125.67 125.84 125.62 124.57

EAng6 100.99 98.30 94.02 91.95 91.95 93.92 97.54 99.71 102.94 104.97 107.74 111.09 114.59 118.19 121.53 124.72 127.85 130.71 132.98 134.33 134.87 134.59 134.13 132.95 131.51 130.46 129.71 128.90 128.05 127.20 126.32 125.61 124.85 124.51 125.02 125.15 125.02 125.16 124.41 122.85 121.11 119.53 117.34 114.85 113.27 108.95 107.54 106.58 104.77 103.12 101.39 99.78 99.18 100.02 99.77 99.25 98.20 98.73 98.37 98.73 99.16 101.27 102.35 103.75 105.99

StP1x -341.88 359.85 387.97 405.23 417.05 415.92 409.28 404.97 -393.00 -384.99 -367.20 -344.78 -319.54 -292.57 -267.19 -245.46 226.59 209.21 195.49 187.31 183.04 183.08 184.74 188.31 197.46 203.34 207.49 211.46 215.54 219.99 224.08 228.26 232.53 234.49 234.18 234.33 234.82 234.31 237.41 243.41 249.95 257.86 -268.08 -279.50 -291.17 -309.65 -317.16 -326.00 -337.15 -346.50 -356.56 -367.37 -374.78 -376.85 -381.81 385.86 390.10 391.64 396.17 396.50 399.37 396.33 386.77 377.23 366.71

StP1y 544.51 554.58 556.18 547.18 517.62 477.62 438.98 392.54 367.57 361.58 369.06 381.89 392.07 403.80 419.35 434.68 446.78 455.53 460.84 463.22 464.20 465.90 467.46 465.72 464.32 464.38 465.36 467.02 468.85 470.46 470.73 471.38 471.66 471.18 468.92 465.51 461.87 458.50 456.88 457.62 461.23 466.54 473.62 482.97 493.34 504.94 518.62 531.71 541.69 548.78 551.76 545.99 526.03 500.26 467.87 438.64 410.34 399.94 399.35 404.09 414.35 426.47 436.05 443.10 446.33

1 8 8 8 2 2 8 4 7 8 6 9 7 0 5 8 8 3 4 2 0 0 6 2 2 8 6 2 5 6 3 8 6 8 2 1 7 0 8 2 3 4 2 7 4 4 2 1 9 8 6 9 3 6 7 4 4 4 5 9 5 7 5 0 3

StP2x 341.88 -359.85 -387.97 -405.23 -417.05 -415.92 -409.28 -404.97 393.00 384.99 367.20 344.78 319.54 292.57 267.20 245.46 -226.59 -209.22 -195.49 -187.31 -183.04 -183.08 -184.73 -188.30 -197.46 -203.34 -207.49 -211.46 -215.54 -219.99 -224.09 -228.26 -232.53 -234.49 -234.18 -234.33 -234.82 -234.30 -237.41 -243.41 -249.95 -257.86 268.09 279.50 291.17 309.66 317.16 326.00 337.15 346.50 356.56 367.38 374.78 376.85 381.81 -385.86 -390.10 -391.64 -396.18 -396.50 -399.36 -396.32 -386.77 -377.23 -366.71

StP2y 382.87 373.57 371.29 377.85 402.81 440.59 478.22 527.77 557.47 563.22 555.16 539.02 528.38 517.03 502.11 486.37 472.92 462.45 456.54 454.15 453.13 451.79 450.24 451.75 453.43 453.57 452.91 451.64 450.25 448.78 448.65 448.35 448.10 448.78 450.85 454.24 457.75 461.27 463.16 462.58 459.57 455.04 448.87 440.25 430.40 419.61 407.86 397.05 389.61 385.59 385.30 391.39 409.88 433.88 464.26 494.95 523.13 534.75 532.47 525.65 514.27 500.84 489.91 481.72 477.85

StP3x 669.20 -704.18 -756.66 -796.57 -826.35 -831.25 -831.36 -828.07 810.11 797.75 759.64 714.53 660.86 604.01 550.65 507.08 -469.41 -432.86 -402.86 -384.69 -373.82 -373.72 -373.89 -379.63 -400.30 -412.36 -420.62 -428.27 -436.63 -444.53 -452.59 -461.14 -469.84 -474.08 -473.66 -474.20 -475.09 -474.39 -480.01 -490.97 -503.48 -518.06 537.20 558.91 579.88 613.37 628.47 645.15 664.54 682.65 699.70 723.28 740.65 747.50 758.99 -765.03 -777.77 -783.80 -794.06 -800.79 -812.01 -808.37 -788.20 -771.41 -753.90

StP3y -166.05 -184.46 -186.46 -167.33 -108.59 -30.15 49.96 146.79 199.71 212.53 196.91 168.65 145.85 120.21 85.84 52.84 25.98 5.76 -6.50 -11.79 -14.11 -17.62 -20.90 -17.20 -13.75 -13.62 -15.44 -18.60 -22.14 -25.12 -25.53 -26.59 -26.92 -25.82 -21.32 -14.40 -7.04 -0.20 3.41 1.88 -5.17 -15.61 -29.18 -47.19 -66.99 -89.45 -115.96 -141.32 -160.77 -174.32 -179.70 -167.26 -127.61 -76.49 -12.89 48.51 107.92 130.82 132.14 121.64 100.46 75.61 54.89 40.03 33.00

StP4x 376.38 -393.28 -426.44 -441.56 -448.46 -439.12 -416.91 -404.67 383.40 373.52 357.91 337.36 315.38 291.49 269.04 248.13 -229.65 -212.44 -197.98 -189.34 -185.08 -184.81 -187.36 -189.79 -199.30 -206.34 -211.03 -215.57 -219.92 -225.26 -229.49 -233.54 -238.12 -239.46 -237.38 -237.13 -237.94 -236.95 -242.05 -251.27 -259.94 -269.46 281.94 295.35 307.27 331.77 336.65 343.48 355.93 365.83 377.97 389.25 395.67 393.34 396.61 -400.98 -404.39 -402.55 -407.82 -406.06 -407.02 -400.06 -391.59 -380.83 -367.09

StP4y -543.76 -554.43 -557.30 -550.92 -524.87 -485.26 -448.15 -402.08 -374.58 -369.30 -376.16 -390.49 -399.17 -408.26 -420.43 -433.71 -445.09 -453.77 -458.99 -461.23 -462.12 -463.65 -465.30 -463.71 -462.31 -462.41 -463.32 -464.89 -466.63 -468.38 -468.69 -469.23 -469.68 -469.06 -466.80 -463.10 -459.29 -455.47 -453.72 -454.36 -457.91 -463.16 -470.27 -480.08 -491.17 -503.37 -516.63 -528.83 -537.27 -542.11 -542.74 -536.53 -516.87 -491.31 -459.19 -429.40 -403.46 -392.99 -395.44 -402.31 -413.46 -426.31 -436.12 -443.58 -447.06

StP5x -333.20 350.34 377.51 397.17 415.34 420.72 425.16 427.47 -422.24 -419.29 -400.52 -376.38 -347.64 -316.16 -286.02 -261.33 240.78 220.33 202.64 191.77 184.83 183.67 183.47 183.99 196.46 203.82 208.59 212.72 216.97 221.51 225.36 229.95 234.75 236.66 236.83 237.44 238.03 237.60 241.17 247.24 252.97 260.67 -270.27 -280.55 -292.69 -308.45 -313.97 -323.36 -333.61 -342.08 -350.16 -361.77 -371.13 -376.59 -383.83 388.00 393.78 399.44 405.95 409.83 418.00 420.89 409.59 400.50 392.79

StP5y -382.54 -373.82 -373.00 -382.16 -410.54 -448.48 -487.26 -537.03 -564.06 -570.37 -561.71 -547.08 -535.08 -521.26 -503.12 -485.38 -471.19 -460.65 -454.66 -452.14 -451.03 -449.52 -448.07 -449.74 -451.42 -451.59 -450.86 -449.50 -448.02 -446.68 -446.60 -446.18 -446.10 -446.63 -448.70 -451.82 -455.16 -458.24 -460.01 -459.35 -456.29 -451.70 -445.57 -437.42 -428.26 -418.17 -405.94 -394.19 -385.20 -378.88 -376.24 -381.91 -400.73 -424.94 -455.68 -485.92 -516.52 -528.04 -528.76 -523.96 -513.35 -500.47 -489.78 -481.97 -478.27

StP6x -712.38 747.12 805.59 840.96 859.47 849.66 823.11 805.27 -771.27 -751.98 -717.03 -675.52 -628.59 -579.35 -533.67 -493.89 458.27 424.97 398.20 382.27 374.07 374.86 377.78 385.43 403.15 414.88 423.06 431.12 439.57 448.28 456.72 464.73 473.20 476.87 474.21 473.89 474.99 473.74 480.90 495.00 510.44 526.85 -548.88 -573.70 -594.46 -636.69 -651.15 -665.27 -686.87 -706.40 -727.52 -750.76 -765.19 -764.26 -771.77 778.02 788.38 786.91 795.94 797.02 801.03 787.54 770.19 751.74 728.20

StP6y 164.97 184.58 189.28 175.39 123.57 45.67 -31.75 -128.00 -186.10 -197.66 -183.26 -151.99 -132.05 -111.52 -83.75 -54.80 -29.40 -9.33 2.78 7.79 9.92 13.10 16.57 13.17 9.74 9.66 11.34 14.35 17.69 20.94 21.45 22.26 22.94 21.55 17.05 9.57 1.87 -5.85 -9.72 -8.37 -1.43 8.88 22.52 41.48 62.68 86.44 112.06 135.58 151.94 160.94 161.62 148.32 109.30 58.61 -4.36 -66.79 -121.43 -144.49 -139.76 -125.10 -102.27 -76.15 -54.95 -39.31 -31.86

A1 158528.57 166997.20 179917.04 187424.07 191933.02 190953.65 187695.18 186349.00 181769.71 178019.25 169687.84 158756.44 147059.10 134702.79 123104.23 113039.71 104199.30 96027.87 89666.61 85915.55 83955.50 84005.82 84765.25 86381.75 90609.57 93327.39 95267.71 97129.19 99053.20 101110.27 103009.05 104968.53 106934.50 107861.25 107693.60 107765.13 107973.41 107753.45 109211.62 111992.89 115075.90 118820.19 123653.59 129018.71 134482.32 143145.56 146919.06 151389.52 156995.94 161879.52 167056.69 172184.24 175380.99 176013.41 177946.38 180118.89 182072.76 183030.84 184581.94 184321.83 185429.87 183759.32 179065.85 174435.26 169454.69

A2 156493.67 164718.90 176641.39 184394.84 189075.97 189390.72 188561.57 188792.26 186561.68 183742.93 174708.88 163497.98 151286.95 138560.74 126775.25 116829.67 108053.71 99485.58 92595.52 88459.11 85984.27 86033.84 86100.42 87368.49 92111.87 94901.82 96853.87 98679.42 100682.14 102511.40 104387.56 106410.12 108396.04 109405.53 109269.14 109388.01 109562.23 109434.26 110757.12 113327.40 116337.91 119882.34 124478.66 129623.56 134541.24 142537.10 146550.43 151114.07 156560.43 161811.83 166832.56 172265.28 175702.08 176574.32 178642.32 179965.19 182386.56 183952.04 185232.15 186349.78 188736.69 187449.49 182455.85 178250.63 174075.59

A3 150693.36 158936.83 171084.64 182479.17 192514.11 195065.63 196699.30 196174.31 190010.11 186997.58 178110.05 167955.02 154897.50 140817.28 127300.21 116519.63 107447.68 98822.45 91809.58 87600.17 85068.65 85008.29 85028.82 86387.24 91163.51 93933.94 95810.53 97545.90 99438.42 101274.90 103133.41 105085.68 107131.98 108092.51 108020.52 108093.15 108264.57 108012.40 109307.75 111775.29 114601.01 117868.59 122200.96 127192.20 132117.73 139536.21 142823.34 146314.80 149908.82 153150.12 155919.68 161478.68 166160.61 168585.50 171704.30 173977.44 178719.76 180343.39 183946.66 185777.07 188308.75 187432.56 182620.00 178712.01 174576.84

A4 162580.70 170628.97 184722.90 193775.83 201055.34 200547.95 196837.07 194597.25 187210.92 183945.10 175848.39 165766.96 153761.31 140510.57 127804.33 116889.63 107689.23 98919.91 91512.92 87030.10 84446.92 84118.58 84659.13 85336.89 90397.71 93713.00 95892.63 97895.81 99886.01 102184.71 104056.97 106050.79 108241.74 108979.25 108533.06 108548.57 108811.07 108400.27 110384.19 113877.10 117222.76 121221.64 126361.48 131938.69 137677.22 147001.51 149434.08 153199.28 158172.74 162026.29 166128.18 171377.80 175190.43 176086.81 178488.96 180724.70 183875.29 184767.96 188083.68 188818.82 190885.55 189822.44 185211.06 180602.11 175585.02

A5 163742.10 171977.40 185968.81 195519.09 202084.33 200136.32 193782.85 188869.33 178228.91 173016.21 164681.25 156178.79 145220.81 133366.96 122271.76 112700.44 104427.16 96852.62 90803.77 87167.50 85274.31 85456.27 86155.62 87882.08 91950.81 94662.07 96554.18 98420.96 100386.24 102439.24 104402.60 106236.71 108239.30 109043.68 108409.55 108191.63 108321.50 107849.12 109436.51 112654.64 116275.10 120146.30 125326.14 131292.20 136464.11 146454.96 149757.48 153041.35 157637.16 161347.88 165156.82 170188.93 173600.18 173420.46 175003.21 176069.39 179697.43 178902.46 182060.11 183169.20 184231.60 181043.97 177356.85 173284.58 167879.88

A6 165750.57 173956.49 187307.32 194538.55 196671.52 193409.60 187161.71 183969.38 178318.37 173997.35 165961.21 155190.04 144322.38 133283.44 123084.38 114065.31 105705.58 97768.32 91480.75 87808.22 85914.16 86123.82 86769.12 88509.09 92632.16 95347.78 97261.15 99152.42 101139.67 103146.49 105092.43 106992.33 108927.12 109819.81 109185.61 109179.14 109473.48 109290.30 111009.15 114278.24 117894.59 121753.50 126962.18 132743.41 137510.79 147361.51 151078.26 154765.94 160423.46 165947.62 171891.43 177706.70 180774.63 180121.87 181375.79 183521.04 185437.07 185651.04 186614.29 185833.10 186374.84 183021.07 178547.77 63 173963.00 168349.75

Atotal 9577 10072 10856 11381 11733 11695 11507 11387 11020 10797 10289 9673 8965 8212 7503 6900 6375 5878 5478 5239 5106 5107 5134 5218 5488 5658 5776 5888 6005 6126 6240 6357 6478 6532 6511 6511 6524 6507 6601 6779 6974 7196 7489 7818 8127 8660 8865 9098 9396 9661 9929 10252 10468 10508 10631 10743 10921 10966 11105 11142 11239 11125 10852 10592 10299

clustering panel data into families

7.8

5 21.3

32.6

.04

104.74

7 11

6.3

36.1

.25 137

36.2

0.3

33.1 8.1

Distances between the central objects:

_CSphereN83_257 _CSphereN40_184_CSphereN59_197_ _CSphereN44_143_CSphereN66_166 _CSphereN68_79_CSphereN51_19_CSphereN60_322 6_CSphereN78_256 1 (N75_163_CSphereN75_164_CSphereN76_165_CSphereN77_164 75_164_CSphereN76_165_CSphereN77_164_CSphereN77_16 0 210289.418 471692.847 341504.052 183044.098 130936.012 72233.375 408903.000 375386.497 93190.447 81_257_CSphereN82_258_CSphereN83_257_CSphereN83_25 210289.418 0 681964.277 551775.955 393283.385 341213.337 282456.433 619175.248 585657.523 117197.796 38_184_CSphereN39_184_CSphereN40_184_CSphereN40_18 471692.847 681964.277 0 130192.420 288690.545 340759.600 399516.706 62791.125 96310.354 564804.003 57_197_CSphereN58_198_CSphereN59_197_CSphereN59_19 341504.052 551775.955 130192.420 0 158514.817 210572.099 269332.583 67402.801 33898.657 434617.444 42_143_CSphereN43_143_CSphereN44_143_CSphereN44_14 183044.098 393283.385 288690.545 158514.817 0 52167.917 110855.852 225905.911 192391.287 276133.194 64_166_CSphereN65_166_CSphereN66_166_CSphereN66_16 130936.012 341213.337 340759.600 210572.099 52167.917 0 58801.380 277970.260 244453.698 224069.147 eN66_79_CSphereN67_79_CSphereN68_79_CSphereN68_78_ 72233.375 282456.433 399516.706 269332.583 110855.852 58801.380 0 336729.409 303212.843 165303.889 49_194_CSphereN50_195_CSphereN51_194_CSphereN51_19 408903.000 619175.248 62791.125 67402.801 225905.911 277970.260 336729.409 0 33526.932 502017.102 58 322 CSphereN59 322 CSphereN60 322 CSphereN60 32 375386.497 58_322_CSphereN59_322_CSphereN60_322_CSphereN60_32 585657.523 96310.354 33898.657 192391.287 244453.698 303212.843 33526.932 0 468498.990 76_256_CSphereN77_256_CSphereN78_256_CSphereN78_2 93190.447 117197.796 564804.003 434617.444 276133.194 224069.147 165303.889 502017.102 468498.990 0 52_325_CSphereN53_325_CSphereN54_325_CSphereN54_3 440506.501 650777.838 31199.965 99011.001 257506.726 309573.841 368332.826 31612.309 65124.326 533621.535 89_254_CSphereN90_255_CSphereN91_254_CSphereN91_2 363991.921 153775.793 835645.183 705459.691 546979.092 494912.766 436156.864 772858.715 739342.426 270863.742 51_179_CSphereN52_180_CSphereN53_179_CSphereN53_1 307016.836 517289.484 164679.283 34501.122 124029.948 176083.819 234848.257 101889.853 68381.388 400136.758 47_209_CSphereN48_210_CSphereN49_209_CSphereN49_2 501578.399 711844.600 29937.372 160084.640 318571.199 370647.146 429396.032 92688.493 126202.550 594685.366 56_175_CSphereN57_175_CSphereN58_175_CSphereN58_1 229512.066 439784.671 242185.560 111995.938 46580.506 98580.215 157347.151 179396.323 145882.874 322629.669 55_182_CSphereN56_183_CSphereN57_182_CSphereN57_1 270611.616 480883.818 201085.621 70897.002 87637.251 139679.484 198445.149 138295.913 104784.826 363730.401 51_131_CSphereN52_132_CSphereN53_131_CSphereN53_1 529460.402 739726.904 57800.137 187966.500 346455.079 398529.468 457278.764 120569.473 154082.474 622567.227 41_218_CSphereN42_219_CSphereN43_218_CSphereN43_2 556100.178 766367.446 84426.334 214605.186 373094.102 425168.694 483917.896 147206.087 180721.899 649207.356 37_230_CSphereN38_231_CSphereN39_230_CSphereN39_2 581949.178 792216.776 110271.748 240454.435 398943.234 451017.537 509766.892 173054.518 206570.304 675056.668 eN35_26_CSphereN36_27_CSphereN37_26_CSphereN37_25 605873.424 816146.041 134189.065 264376.665 422874.251 474941.340 533696.564 196975.343 230492.312 698985.929 eN27_56_CSphereN28_57_CSphereN29_56_CSphereN29_55 628497.488 838769.892 156810.920 287000.188 445496.737 497565.136 556320.104 219598.563 253115.867 721609.470 15 239 CSphereN16 240 CSphereN17 239 CSphereN17 2 15_239_CSphereN16_240_CSphereN17_239_CSphereN17_2 648926 055 648926.055 859194 080 859194.080 177242 364 177242.364 307430 424 307430.424 465918 721 465918.721 517993 833 517993.833 576743 421 576743.421 240029 311 240029.311 273546 091 273546.091 742033 605 742033.605 eN3_194_CSphereN4_195_CSphereN5_194_CSphereN5_193 667340.304 877608.495 195655.216 325843.812 484333.025 536408.039 595157.334 258442.939 291960.049 760446.771 11_345_CSphereN12_346_CSphereN13_345_CSphereN13_3 695213.697 905485.813 223526.190 353716.013 512212.034 564281.451 623035.228 286314.788 319831.974 788323.567

8.1

3.6

.04

7 11

6 8.2

9.4

9.1

6.3

2.7

7.2

_CSphereN54_32 5_CSphereN91_254_CSphereN53_17_CSphereN49_20_CSphereN58_17_CSphereN57_18_CSphereN53_13 _CSphereN43_21 _CSphereN39_23 _CSphereN37_26 _CSphereN29_56 _CSphereN17_23 _CSphereN5_194_CSphereN13_345_ 440506.501 363991.921 307016.836 501578.399 229512.066 270611.616 529460.402 556100.178 581949.178 605873.424 628497.488 648926.055 667340.304 695213.697 650777.838 153775.793 517289.484 711844.600 439784.671 480883.818 739726.904 766367.446 792216.776 816146.041 838769.892 859194.080 877608.495 905485.813 31199.965 835645.183 164679.283 29937.372 242185.560 201085.621 57800.137 84426.334 110271.748 134189.065 156810.920 177242.364 195655.216 223526.190 99011.001 705459.691 34501.122 160084.640 111995.938 70897.002 187966.500 214605.186 240454.435 264376.665 287000.188 307430.424 325843.812 353716.013 257506.726 546979.092 124029.948 318571.199 46580.506 87637.251 346455.079 373094.102 398943.234 422874.251 445496.737 465918.721 484333.025 512212.034 309573.841 494912.766 176083.819 370647.146 98580.215 139679.484 398529.468 425168.694 451017.537 474941.340 497565.136 517993.833 536408.039 564281.451 368332.826 436156.864 234848.257 429396.032 157347.151 198445.149 457278.764 483917.896 509766.892 533696.564 556320.104 576743.421 595157.334 623035.228 31612.309 772858.715 101889.853 92688.493 179396.323 138295.913 120569.473 147206.087 173054.518 196975.343 219598.563 240029.311 258442.939 286314.788 65124.326 739342.426 68381.388 126202.550 145882.874 104784.826 154082.474 180721.899 206570.304 230492.312 253115.867 273546.091 291960.049 319831.974 533621.535 270863.742 400136.758 594685.366 322629.669 363730.401 622567.227 649207.356 675056.668 698985.929 721609.470 742033.605 760446.771 788323.567 0 804463.569 133494.307 61092.350 211002.635 169901.796 88968.746 115605.301 141452.420 165372.489 187995.675 208426.490 226840.998 254712.522 804463.569 0 670979.738 865526.611 593474.180 634573.593 893408.125 920048.046 945897.343 969825.913 992449.289 1012873.969 1031286.586 1059162.207 133494.307 670979.738 0 194571.185 77511.268 36409.643 222454.307 249092.232 274941.069 298863.682 321486.900 341916.309 360330.470 388203.508 61092.350 865526.611 194571.185 0 272076.330 230976.819 27886.891 54523.591 80373.534 104309.814 126931.820 147351.431 165765.807 193645.388 211002.635 593474.180 77511.268 272076.330 0 41103.204 299959.238 326597.891 352447.114 376370.357 398993.810 419423.070 437836.695 465709.791 169901.796 634573.593 36409.643 230976.819 41103.204 0 258859.882 285498.386 311347.588 335270.590 357893.950 378323.339 396737.197 424610.260 88968.746 893408.125 222454.307 27886.891 299959.238 258859.882 0 26645.599 52493.488 76431.087 99052.779 119471.819 137886.117 165764.592 115605.301 920048.046 249092.232 54523.591 326597.891 285498.386 26645.599 0 25850.308 49794.947 72413.198 92828.648 111242.860 139123.363 141452.420 945897.343 274941.069 80373.534 352447.114 311347.588 52493.488 25850.308 0 23963.237 46569.568 66978.891 85393.518 113275.039 165372.489 969825.913 298863.682 104309.814 376370.357 335270.590 76431.087 49794.947 23963.237 0 22625.380 43072.542 61480.689 89341.608 187995.675 992449.289 321486.900 126931.820 398993.810 357893.950 99052.779 72413.198 46569.568 22625.380 0 20468.093 38863.008 66717.457 208426 490 208426.490 1012873 969 1012873.969 341916 309 341916.309 147351 431 147351.431 419423 070 419423.070 378323 339 378323.339 119471 819 119471.819 92828 648 92828.648 66978 891 66978.891 43072 542 43072.542 20468 093 20468.093 0 18417 546 18417.546 46309 070 46309.070 226840.998 1031286.586 360330.470 165765.807 437836.695 396737.197 137886.117 111242.860 85393.518 61480.689 38863.008 18417.546 0 27903.528 254712.522 1059162.207 388203.508 193645.388 465709.791 424610.260 165764.592 139123.363 113275.039 89341.608 66717.457 46309.070 27903.528 0

6 65

Family dendrogram 5_D_20 24_D_223 19_D_200 2_E_250 26_E_359 12_E_301 5_D_390 17_D_193 4_D_384 11_D_48 6_E_276 22_E_338 28_D_120 25_E_351 6_D_150 12_D_52 26_D_112 20_D_326 2_D_377 5_D_16 8_D_164 9_E_291 18_E_319 8_D_161 27_E_363 4_D_15 6_D_151 21_E_332 5_D_144 22_D_88 11_E_298 12_D_179 10_D_172 5_E_270 5_D_19 20_D_203 4_D_11 13_D_57 3_D_134 10_E_294 19_D_75 6_D_25 24_D_97 4_D_387 24_D_226 26_D_233 5_D_141 23_D_217 4_D_12 13_D_181 4_D_136 2_D_129 5_D_17 11_D_49 11_D_50 11_D_175 11_D_174 3_E_256 24_E_348 4_D_14 6_D_152 25_D_230 8_E_287 12_E_303 4_D_13 21_D_84 7_E_281 26_D_236 14_D_184 10_D_47 18_D_70 22_D_212 27_D_242 4_E_261 5_E_265 7_D_157 3_D_382 10_D_169 20_D_329 1_D_125 25_E_356 25_D_105 6_D_28 7_D_154 9_D_166 18_D_196 16_E_313 23_D_92 8_D_36 14_E_307 12_D_178 2_E_253 21_D_86 16_D_66 28_D_246 20_D_81 5_D_21 24_D_102 27_D_116 8_D_39 7_D_33 15_D_189 20_D_206 5_E_268 15_D_64 21_E_334 3_D_10

family options analysis

24 Families

Clustering data includes geometric attributes and panel area. Panel edges intersect Average gap: 6.7-7.5 cm

49 Families

Clustering data includes only geometric attributes. Panel edges intersect Average gap: 4.7-6.6 cm

Clustering data includes geometric attributes and panel area. Panel edges intersect Average gap: 7.0-8.0 cm

106 Families

24 Families

106 Families

Clustering data includes geometric attributes and panel area. Uniform edges Average gap: 4.1-7.3 cm

Clustering data includes only geometric attributes. Uniform edges Average gap: 4.5-6.0 cm

150 Families

Clustering data includes only geometric attributes. Uniform edges, higher density of families formed in corners. Average gap: 4.6-5.8 cm

80/20 family distribution In depth analysis of the clustering data showed that about 80% of the panels in the facade were quite similar. GT proposed that instead of clustering all the panels into a specific number of families it would be better to remove the similar panels and perform a separate clustering algorithm for each zone. This provided a more flexible solution to how the total number of families were used. Now a smaller number of families could be used in the zone with the highest number of panels and a larger number of families in zones where there was more diversity. Eventually, a scheme was developed where 52 families [see page 72] were used for 80% of the panels and 250 families in the remaining 20%. The majority of the facade surface curvature was fairly flat indicated by the green zone in the image to the right. Zones of high curvature were identified in the upper and lower corners of the facade shown in orange. The final number of panels was about 15,000 composed of 300 families [see page 74-79]. See below for detailed information about the different zones and number of panels per clustering zone.

zone

# of panels per zone

413

534

459

497

542

345

11,523

52 Total Families

253

242

495 Total Panels 0 Total Families

2,790 Total Panels 250 Total Families

20% Zone - Areas of the surface with high curvature. 80% Zone - Areas of the surface with low curvature. Border - Unique edge conditions.

3 1

5 9

gap verification and family tuning process

the 52 families for 80% of the facade

final families

panel finish study

entrance panels The panels near the entrance received special design consideration since it was the only location where guests would be able to reach out and touch the facade. Panels directly adjacent to the walkway that cut in to the building were joined together in one seamless continuous form. The number of families was increased in the panels surrounding the highly visible entrance to improve the resolution of the pattern [1].

1 9 6

Z o n e s

Ring A 1_A 2_A 3_A 4_A 5_A 6_A 7_A 8_A 9_A 10_A 11_A 12_A 13_A 14_A 15_A 16_A 17_A 18_A 19_A 20_A 21_A 22_A 23_A 24_A 25_A 26_A 27_A 28_A

Total

Qty. Panels 68 72 74 82 73 65 79 100 93 75 58 50 41 49 63 59 73 79 85 88 88 74 59 60 70 62 58 63

Ring B 1_B 2_B 3_B 4_B 5_B 6_B 7_B 8_B 9_B 10_B 11_B 12_B 13_B 14_B 15_B 16_B 17_B 18_B 19_B 20_B 21_B 22_B 23_B 24_B 25_B 26_B 27_B 28_B

Qty. Panels 70 63 62 65 73 65 75 85 68 54 48 44 42 46 51 45 47 45 49 60 71 73 79 74 71 75 76 73

1960

Ring C 1_C 2_C 3_C 4_C 5_C 6_C 7_C 8_C 9_C 10_C 11_C 12_C 13_C 14_C 15_C 16_C 17_C 18_C 19_C 20_C 21_C 22_C 23_C 24_C 25_C 26_C 27_C 28_C

1749 203

Qty. Panels 75 74 72 80 102 96 101 93 70 64 61 53 54 56 51 48 41 48 55 72 90 90 90 88 88 95 88 80

Ring D 1_D 2_D 3_D 4_D 5_D 6_D 7_D 8_D 9_D 10_D 11_D 12_D 13_D 14_D 15_D 16_D 17_D 18_D 19_D 20_D 21_D 22_D 23_D 24_D 25_D 26_D 27_D 28_D

2075 183

Qty. Panels 66 64 72 81 107 98 103 83 69 59 64 56 55 49 48 40 40 49 59 80 92 80 85 88 94 91 78 70

Ring E 1_E 2_E 3_E 4_E 5_E 6_E 7_E 8_E 9_E 10_E 11_E 12_E 13_E 14_E 15_E 16_E 17_E 18_E 19_E 20_E 21_E 22_E 23_E 24_E 25_E 26_E 27_E 28_E

2020

Qty. Panels 52 60 68 90 96 87 95 76 61 61 55 57 52 47 44 40 49 56 70 81 67 72 75 83 94 78 67 61

Ring F 1_F 2_F 3_F 4_F 5_F 6_F 7_F 8_F 9_F 10_F 11_F 12_F 13_F 14_F 15_F 16_F 17_F 18_F 19_F 20_F 21_F 22_F 23_F 24_F 25_F 26_F 27_F 28_F

1894

110

Qty. Panels 57 68 85 119 98 90 92 86 80 72 69 66 61 58 57 66 73 90 98 79 66 70 80 88 104 80 72 64

Ring G 1_G 2_G 3_G 4_G 5_G 6_G 7_G 8_G 9_G 10_G 11_G 12_G 13_G 14_G 15_G 16_G 17_G 18_G 19_G 20_G 21_G 22_G 23_G 24_G 25_G 26_G 27_G 28_G

2188 183

Qty. Panels 72 84 111 129 99 91 92 98 96 91 95 86 76 75 78 91 112 126 119 79 71 77 96 95 106 101 81 73 2600

775

= NOT ISSUED

TOTAL PANELS =

14486

= TOTAL PANELS STILL IN PROGRESS Í˛ NOT ISSUED

TOTAL NOT ISSUED =

4054

2600

1 9 6

Z o n e s

Ring A

Total

1_A 2_A 3_A 4_A 5_A 6_A 7_A 8_A 9_A 10_A 11_A 12_A 13_A 14_A 15_A 16_A 17_A 18_A 19_A 20_A 21_A 22_A 23_A 24_A 25_A 26_A 27_A 28_A

Qty. Panels 67 69 73 81 70 64 79 101 94 75 58 52 51 57 64 69 75 82 88 92 89 73 56 57 68 62 57 61 1984

Ring B 1_B 2_B 3_B 4_B 5_B 6_B 7_B 8_B 9_B 10_B 11_B 12_B 13_B 14_B 15_B 16_B 17_B 18_B 19_B 20_B 21_B 22_B 23_B 24_B 25_B 26_B 27_B 28_B

Qty. Panels 70 63 62 65 73 65 75 85 68 54 48 44 44 46 51 45 47 45 49 60 71 73 79 74 71 75 76 73 1751

Ring C 1_C 2_C 3_C 4_C 5_C 6_C 7_C 8_C 9_C 10_C 11_C 12_C 13_C 14_C 15_C 16_C 17_C 18_C 19_C 20_C 21_C 22_C 23_C 24_C 25_C 26_C 27_C 28_C

Qty. Panels 75 74 72 80 102 96 101 93 70 64 61 53 54 56 51 48 41 48 55 72 90 90 90 88 88 95 88 80 2075

Ring D 1_D 2_D 3_D 4_D 5_D 6_D 7_D 8_D 9_D 10_D 11_D 12_D 13_D 14_D 15_D 16_D 17_D 18_D 19_D 20_D 21_D 22_D 23_D 24_D 25_D 26_D 27_D 28_D

Qty. Panels 66 65 72 81 107 98 103 83 69 59 64 56 55 49 48 40 40 49 59 80 92 80 85 88 94 91 78 70 2021

Ring E 1_E 2_E 3_E 4_E 5_E 6_E 7_E 8_E 9_E 10_E 11_E 12_E 13_E 14_E 15_E 16_E 17_E 18_E 19_E 20_E 21_E 22_E 23_E 24_E 25_E 26_E 27_E 28_E

Qty. Panels 52 60 68 90 100 88 95 76 61 61 55 57 52 47 44 40 49 56 70 81 67 72 75 83 94 78 67 61 1899

Ring F 1_F 2_F 3_F 4_F 5_F 6_F 7_F 8_F 9_F 10_F 11_F 12_F 13_F 14_F 15_F 16_F 17_F 18_F 19_F 20_F 21_F 22_F 23_F 24_F 25_F 26_F 27_F 28_F

Qty. Panels 57 68 85 119 98 90 92 86 80 72 69 66 61 58 57 66 73 90 98 79 66 70 80 88 104 80 72 64 2188

Ring G 1_G 2_G 3_G 4_G 5_G 6_G 7_G 8_G 9_G 10_G 11_G 12_G 13_G 14_G 15_G 16_G 17_G 18_G 19_G 20_G 21_G 22_G 23_G 24_G 25_G 26_G 27_G 28_G

Qty. Panels 73 85 111 129 99 91 92 100 96 91 95 86 76 75 79 92 112 126 119 79 71 77 96 95 106 101 81 73 2606 85

panel submission packages During the course of the project GT generated hundreds of drawings and documents used to track, fabricate, and install the panels for the 196 zones of the facade. Documents containing panel data such as the total panels per zone [see page 83 fig. 3] were used by IASA to schedule the fabrication and installation of panels. Typical submission packages for fabrication included a total list of panels issued and not issued [see page 83 fig. 2], detailed revision descriptions for panels per zone [1-2], shop drawings for panels in each zone [3-4], and individual zone maps to assist the installation of the panels [see page 86-89]. The shop drawings were created by an automated process that extracted data from the model and generated dimensioned drawings.

1 Soumaya FaĂ§ade Í˛ Drawing Matrix

GT_ENV_Drawing Submittal_R16_101110

Zone Sheets Drawing Ref.

Zone

Drawing Name

Status

Release Date

Building Elevations A2.12

A2.12

Complete

Ring A ELE_N_R02_092710 ELE_N_R01_091410 ELE_N_R01_081010 ELE_N_R00_080910 ELE_S_R02_092710 ELE_S_R01_091410 ELE_S_R01_081010 ELE_S_R00_080910 ELE_E_R02_092710 ELE_E_R01_091410 ELE_E_R01_081010 ELE_E_R00_080910 ELE_O_R02_092710 ELE_O_R01_091410 ELE_O_R01_081010 ELE_O_R00_080910

Current Superseded Superseded Superseded Current Superseded Superseded Superseded Current Superseded Superseded Superseded Current Superseded Superseded Superseded

September 27, 2010 September 14, 2010 August 10, 2010 August 9, 2010 September 27, 2010 September 14, 2010 August 10, 2010 August 9, 2010 September 27, 2010 September 14, 2010 August 10, 2010 August 9, 2010 September 27, 2010 September 14, 2010 August 10, 2010 August 9, 2010

NCO_01_R01_081010 NCO_01_R00_080910

Current Superseded

August 10, 2010 August 9, 2010

A2.12

01_A

A2.12

02_A

A2.12

03_A

A2.12

04_A

A2.12

05_A

A2.12

06_A

A2.12

07_A

A2.12

08_A

A2.12

09_A

A2.12

10_A

A2.12

11_A

A2.12

12_A

A2.12 A2.12

13_A 14_A

Information Sheets A2.12

na na na

ZON_01_A_R01_081010 ZON_01_A_R00_080910 ZON_02_A_R01_081010 ZON_02_A_R00_080910 ZON_03_A_R02_090810 ZON_03_A_R01_090610 ZON_03_A_R00_081410 ZON_04_A_R01_081910 ZON_04_A_R00_081410 ZON_05_A_R03_090210 ZON_05_A_R02_082010 ZON_05_A_R01_081910 ZON_06_A_R02_100110 ZON_06_A_R01_090610 ZON_06_A_R00_081810 ZON_07_A_R03_100110 ZON_07_A_R02_091310 ZON_07_A_R01_082010

Current Superseded Current Superseded Current Superseded Superseded Current Superseded Current Superseded Superseded Current Superseded Superseded Current Superseded Superseded

August 10, 2010 August 9, 2010 August 10, 2010 August 9, 2010 September 8, 2010 September 6, 2010 August 16,2010 August 19,2010 August 16,2010 September 2, 2010 August 20,2010 August 19,2010 October 1, 2010 September 6, 2010 August 18,2010 October 1, 2010 September 13, 2010 August 20,2010

ZON_07_A_R00_081810 ZON_08_A_R02_100110 ZON_08_A_R01_082010 ZON_08_A_R00_081810 ZON_09_A_R03_092010 ZON_09_A_R02_082010 ZON_09_A_R01_081810

Superseded Current Superseded Superseded Current Superseded Superseded

August 18,2010 October 1, 2010 August 20,2010 August 18,2010 September 20, 2010 August 20,2010 August 18,2010

ZON_10_A_R03_092010 ZON_10_A_R02_082010 ZON_05_A_R01_081910 ZON_11_A_R02_092010 ZON_11_A_R01_081910 ZON_11_A_R00_081410 ZON_12_A_R02_081810 ZON_12_A_R01_081810 ZON_12_A_R00_081410 ZON_13_A_R00_081410 ZON_14_A_R00_081410

Current Superseded Superseded Current Superseded Superseded Current Superseded Superseded Current Current

September 20, 2010 August 20,2010 August 19,2010 September 20, 2010 August 19,2010 August 16,2010 August 18,2010 August 18,2010 August 16,2010 August 16,2010 August 16,2010

Y Y Y

Y Y

Panel Installation

7/29/2010 14:44

8/5/2010 15:06

8/12/2010 14

10/7/2010 14:06

10/18/2010 13:45

10/20/2010 12

11/9/2010 16:25

11/15/2010 14:31

11/17/2010 16

12/3/2010 15:26

12/7/2010 14:52

12/8/2010 16

1/27/2011 13:16

2/5/2011 19:40

2/12/2011 17

100