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rhinoVAULT

Quick Reference for

rhinoVAULT Beta Version 0.2

2012-05-10

by

Matthias Rippmann

Lorenz Lachauer

Philippe Block

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1 Introduction ..................................................................................................................................................................................... 3

2 Technical Requirements and Installation ....................................................................................................................................... 4

2.1 Requirements ................................................................................................................................................................................. 4

2.2 Installation....................................................................................................................................................................................... 4

2.3 Tool Package .................................................................................................................................................................................. 4

3 The Tool ......................................................................................................................................................................................... 4

3.1 Layer Structure – Data Handling in RhinoVAULT ........................................................................................................................... 6

3.2 RhinoVault Settings - rvSettings ..................................................................................................................................................... 6

3.2.1 Vault Height Scale – Changing the Overall Height of the Vault ............................................................................................. 7

3.2.2 AngleTolerance – Maximum Deviation Tolerance Angel between Form and Force Edges .................................................. 7

3.2.3 EdgeMin / EdgeMax – Control the Lengths of the Form and Force Edges .......................................................................... 7

3.2.4 Iterations and Step Size – Control the Max Iterations and Step Size of Iterative Procedures ............................................... 7

3.2.5 High Precision/Runge Kutta 4th Order – Changing the Type of Solver .................................................................................. 7

3.2.6 Show Color Analysis/ Show Mesh /Show Pipes – Visualize the Three-Dimensional Result .................................................. 7

3.3 Generate Form Diagram - rvForm .................................................................................................................................................. 7

3.4 Generate Dual Graph - rvDual ........................................................................................................................................................ 8

3.5 Relax and smoothen the Form Diagram - rvRelax ......................................................................................................................... 8

3.6 Modify Diagram - rvModify ............................................................................................................................................................. 8

3.6.1 Move/Scale2D/Scale1D/Bend - Manipulate the Form and Force Diagram to Change the Thrust Network ......................... 8

3.6.2 Supports – Manipulate the Supports ..................................................................................................................................... 9

3.6.3 Openings – Define one or more Oculus ................................................................................................................................ 9

3.6.4 NodeWeight – Change the Inertia of Nodes ........................................................................................................................ 10

3.7 Horizontal Equilibrium - rvHorizontal ............................................................................................................................................ 10

3.8 Vertical Equilibrium - rvVertical ..................................................................................................................................................... 11

3.9 Info ................................................................................................................................................................................................ 11

4 Additional Information .................................................................................................................................................................. 11

5 Copyright ...................................................................................................................................................................................... 12

6 Contact ....................................................................................................................................................................................... 12

7 Acknowledgements ...................................................................................................................................................................... 12

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1 Introduction

This is the quick reference for the plug-in RhinoVAULT Beta Version 0.2 for Rhinoceros® 4.0 with SR 9.0 or higher for Windows. It is a

form finding tool to intuitively design compression-only, vaulted structures. It can be seen as a hanging chain model but then a more

controllable, flexible and comprehensible digital version. The tool is based on the Thrust Network Approach – TNA, which is described

by P. Block in his Ph.D. dissertation Thrust Network Analysis: Exploring Three-dimensional Equilibrium at MIT, Cambridge, MA, USA in

2009. The method uses the two fundamental elements of graphic statics:

- Form Diagram

- Force Diagram

Fig.1-1. Form (left) and Force (right) diagram in the x,y-plane

The form and force diagram are in horizontal equilibrium, which means that corresponding edges in both diagrams are parallel and

properly orientated. Based on the configuration of both two-dimensional diagrams, the calculation of the vertical equilibrium results in a

three-dimensional thrust network, which represents the shape of the compression-only structure.

Fig.1-2. Three-dimensional thrust network representing the compression-only structure

In simple terms, the form diagram defines the perimeter and force pattern, representing the predefined “flow of forces”, of the vault

design in plan. The force diagram defines the horizontal force components in the structure, and how they are proportionally

distributed/related. RhinoVAULT was developed to generate, shape and adapt the user’s design by manipulating both diagrams in a

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bidirectional and interactive manner. The Rhino plug-in is based on current research done by the BLOCK Research Group at ETH

Zurich, Switzerland on structural form finding using the Thrust-Network-Approach (TNA) to intuitively create and explore compression-

only structures. Our goal is to share key aspects of our research in a comprehensible and transparent setup, to let you not only create

beautiful shapes but also to give you an understanding of the underlying structural principles.

The plug-in is still in its beta testing phase and under continuous development. Errors and crashes might occur! Nevertheless, enjoy

designing awesome structures! Happy form finding!

2 Technical Requirements and Installation

2.1 Requirements

RhinoVAULT Beta is a plug-in for the CAD NURBS modeling software Rhino. It is freely available for download from

http://block.arch.ethz.ch/tools/rhinovault. An installed version of Rhino 4.0 with SR 9.0 or higher for Windows needs to run on your

system. The evaluation version of Rhino 4.0 can be downloaded for free from

http://download.rhino3d.com/rhino/4.0/evaluation/download/.

2.2 Installation

Unzip the package, save the RhinoVAULT_Beta.rhp to your hard disk and drag and drop RhinoVAULT_Beta.rhp to a new session of

Rhino.

Drag and drop the toolbar RhinoVAULT_Beta.rui (Rhino 5) or RhinoVAULT_Beta.tb (Rhino 4) to an open Rhino session. Toolbars will

not show at this point. To view them, you need to go to ->Tools/Toolbar Layout, select RhinoVAULT_Beta and check its menu. Next

time you open Rhino, the toolbar will show in your workspace. If there are problems with the installation try to first unblock the file

RhinoVAULT.rhp as described here: http://wiki.mcneel.com/rhino/unblockplugin.

2.3 Tool Package

The plug-in features 8 RhinoVAULT-specific commands starting with “_rv”. They can be executed by typing the command name into

the command line, by using the RhinoVAULT menu in the top main control bar or by clicking on the specific buttons in the RhinoVAULT

toolbar.

Fig.2-1. Toolbar from left to right: RhinoVault Settings (command: _rvSettings), Generate Form Diagram (_rvForm), Generate Dual Graph (_rvDuality), Relax Form Diagram (_rvRelax), Modify Diagram (_rvModify), Horizontal Equilibrium (_rvHorizontal), Vertical Equilibrium (_rvVertical), Info (_rvInfo)

3 The Tool

This section describes the RhinoVAULT commands in the order as they appear in the RhinoVAULT toolbar from left to right. The order

of buttons is based on the procedural TNA form finding process, in which first the form diagram needs to be defined, followed by the

calculation of the horizontal equilibrium, before calculating the vertical equilibrium to determine the final shape of the vault. If any

modification is done to either the form diagram or the force diagram, one needs to ensure to always re-calculate the horizontal

equilibrium before calculating the vertical equilibrium. The software will automatically warn the user if the defined, sequential process is

violated. The following flow diagram shows the main steps of the design workflow using RhinoVAULT.

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Fig.3-1. Overview of the main steps of the design workflow.

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3.1 Layer Structure – Data Handling in RhinoVAULT

Every single object used to visualize and store the most recent RhinoVAULT result is assigned to a specific layer. This process is

automatically controlled by the plug-in and ensures the continuation of a RhinoVAULT project saved as a Rhino files (*.3dm). It is

important to keep this layer structure at all time and to keep the layers free of other elements not linked to the RhinoVAULT procedure.

Fig.3-2. The default layer structure of Rhino VAULT for the geometry objects used in Rhino

3.2 RhinoVault Settings - rvSettings

The various settings of RhinoVAULT need to be specifically adjusted depending on the complexity, size and density of the form

and force diagram. Most parameters have a significant influence on the smooth generation of a possible form and force diagram in

equilibrium and the three-dimensional thrust network. Most often, the default values can be used, but in some cases the adjustment of

interdependent parameters needs experience and ideally a basic understanding of graphic statics and structural design. The following

default parameters can be changed by the user:

Fig.3-3. The default settings to control the different commands of RhinoVAULT.

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3.2.1 Vault Height Scale – Changing the Overall Height of the Vault

The vault height scale factor defines the overall height of the thrust network, i.e. the compression equilibrium solution. A higher number

will increase the overall height of the vault. Changing the scale factor is equivalent to uniformly scaling the force diagram in the x-y-

plane.

3.2.2 AngleTolerance – Maximum Deviation Tolerance Angel between Form and Force Edges

This value defines the maximal deviation between corresponding edges of the form and the force diagram. The iterative process to find

a parallel and properly orientated configuration of both diagrams will only stop if this deviation falls under the defined angle tolerance

(or if the maximum number of iterations is reached). For this horizontal equilibrium a deviation of 5°-10° is usually acceptable for the

design stage. A smaller value will increase computation time but will result in a more accurate solution. This value represents the

degree of inequilibrium allowed.

3.2.3 EdgeMin / EdgeMax – Control the Lengths of the Form and Force Edges

The minimum and maximum length of all edges in both diagrams can be limited. These values can be used to avoid extreme local

forces and numerical conflicts due to very small edge lengths during the calculation of the horizontal equilibrium. The values describe

the allowed proportion between the minimum and maximum edge length of each diagram individually.

3.2.4 Iterations and Step Size – Control the Max Iterations and Step Size of Iterative Procedures

The iterative process to find a relaxed form diagram, to find a parallel and properly orientated configuration of both diagrams in

horizontal equilibrium, and to find the three-dimensional thrust network in vertical equilibrium will only stop if the maximum number of

iterations is reached (or a certain threshold value e.g. angle tolerance is reached). Heavy computing is used to find a horizontal and

vertical equilibrium, which can slow down the overall design process significantly. The maximum number of iterations depends on the

density and complexity of the diagram and should usually not be much higher than 600. If more iterations are needed for solving, it is

usually better to repeat the process by using the command again.

The step size visual value defines the number of iterations passed until the viewport gets updated. To increase the computational

speed this value can be set to a number higher than the maximum number of iterations. However, often it is useful for the design

process to see the diagrams and thrust network converging towards the optimized configuration.

3.2.5 High Precision/Runge Kutta 4th Order – Changing the Type of Solver

Enabling this option affects the solver used to calculate the vertical equilibrium respectively to generate the thrust network. Using the 4th

order Runge Kutta solver can speed up the iterative process but it is more likely to cause instabilities during the calculation.

3.2.6 Show Color Analysis/ Show Mesh /Show Pipes – Visualize the Three-Dimensional Result

The result of the three-dimensional structure is represented by a spatial network of lines or optional mesh geometry. Enabling the show

color analysis function displays a color scheme showing the magnitude of forces in proportion. Moreover, this force distribution can be

visualized by a colored mesh and a network of pipes with force-dependent proportions. The minimum and maximum diameter of the

pipes can be adjusted according to the scale and size of the form diagram.

3.3 Generate Form Diagram - rvForm

The first initial form diagram defines the layout of forces in plan and the perimeter of the vault. The topology of the network can

be chosen freely. Open-end edges define end nodes which will remain their position and thus represent supports of the structure. The

form diagram can be drawn manually, generated with the help of internal Rhino commands and external programs, or defined with the

build-in RhinoVAULT function _rvForm. It is important to ensure that generated or manually drawn diagrams don’t content overlapping

or duplicate edges and that all edges are assigned to the 01_FormEdges layer.

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3.4 Generate Dual Graph - rvDual

To generate a possible force diagram based on the defined form diagram, one should first generate the dual graph of the form

diagram. This graph is rotated by 90° and represents the force diagram in a non-equilibrium state, meaning that corresponding edges

are not yet parallel and have not yet the same direction. Numbers (annotation dots) at edges which are not in equilibrium will show the

specific angle deviation.

3.5 Relax and smoothen the Form Diagram - rvRelax

This option redistributes the form diagram in a way that all edges tend to minimize their length. This globally relaxes the

diagram usually resulting in a smoother solution. The NodeWeight option in the rvModify dialog can be used to specifically control the

inertia of individual nodes during the relaxation process.

Fig.3-4. A distorted, poorly distributed form and force diagram (left). A relaxed and smooth form and force diagram (right).

3.6 Modify Diagram - rvModify

This command helps the user to perform different modifications on both diagrams and the thrust network. Selectable

modification options are: Move, Scale2D, Scale1D, Bend, Supports, Openings, NodeWeight.

3.6.1 Move/Scale2D/Scale1D/Bend - Manipulate the Form and Force Diagram to Change the Thrust Network

Modifications of either the form or the force diagram in the x-y-plane will affect the three-dimensional thrust network. By moving or

scaling parts of the force diagram the forces in the structure are redistributed, causing geometrical changes in the resulting shape.

Modifying the form diagram will most likely change the perimeter, thus the global shape of the structure. Both diagrams are

interdependent such that corresponding edges need to stay parallel and orientated properly during the entire process; only the length

can vary. This important requirement for a structurally correct solution will mostly be ensured by the software using the rvHorizontal

command. Moving or scaling parts of the diagrams should be done in a way that most edges are only getting stretched without

causing a major direction deviation in comparison to the starting configuration.

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Fig.3-5. Modifications of the force diagram which mostly affect the length of the edges in comparison to the starting configuration (grey). Colored numbers (annotation dots) indicate the resulting direction changes of individual edges in degrees.

3.6.2 Supports – Manipulate the Supports

By using the Supports feature, the user can manipulate the height of the individual supports. Using the perspective or a side view

works best to control the height properly. Use MoveVertical, if you want to move individual supports in z-direction or the Project

command to project selected support nodes onto an existing surface or mesh. To add supports which take vertical thrust only, the

ToggleSupport command can be used.

Fig.3-6. The defined support nodes can be moved vertically, changing the height of supports in space (left). Inner nodes can be re-defined as support nodes to create a column-like alteration of the thrust network (right).

3.6.3 Openings – Define one or more Oculus

Side openings respectively open edge arches of the structure are automatically detected and taken into consideration for the

calculation of the vertical equilibrium. The Openings command is used for the definition of openings (oculus) in the structure. It

basically changes the applied loads of the nodes surrounding the opening. Enabling the Show Mesh feature in the settings dialog

helps to identify openings in the structure.

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Fig.3-7. A typical oculus opening in a vaulted structure before (left) and after the correct assignment (right).

3.6.4 NodeWeight – Change the Inertia of Nodes

The NodeWeight option can be used to control the inertia of individual nodes. This affects the rvRelax and the rvHorizontal RhinoVAULT

command. To each node of the form and force diagram a value between 0 (fixed) and 1 (free) can be assigned. The default is 1 except

for all initial support nodes of the form diagram.

3.7 Horizontal Equilibrium - rvHorizontal

The horizontal equilibrium ensures that that corresponding edges of the form and force diagram are parallel and properly

orientated. Thus, the horizontal force components within the structure are perfectly balanced. Since both diagrams are interdependent,

changes will always influence both diagrams.

Fig.3-8. Colored numbers (annotation dots) indicate corresponding edges which are not parallel and do not have the same direction. The form and force diagram are not in horizontal equilibrium.

In order to weight the influence one diagram has on its counterpart, the user is asked to weight the influence of the force diagram on

the form diagram and vice versa. For example, by setting the value to Neutral, both diagrams will adjust their configuration to find a

mean solution. If one wants the force diagram to completely adapt based on the direction of edges in the form diagram one should

choose Force100.

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Fig.3-9. In the left image, based on the initial configuration in Fig.3-8, the force diagram is adjusted according to the form diagram with the setting Force100. The process is reversed in the right image using the setting Form100.

The angle deviation value in the settings dialog defines the maximal deviation between corresponding edges of the form and the force

diagram. A deviation of 5°-10° is usually acceptable for the design stage. A smaller value will increase computation time. The specific

deviations of corresponding edges will be shown in degrees if the horizontal equilibrium cannot be computed within the defined angle

deviation and number of iterations. Some topologies and specific configurations are very constraint, making it impossible to find a

satisfactory horizontal equilibrium. One might try this to find a solution:

- Use the rvHorizontal command repeatedly (decrease the number of maximum iterations)

- Relax your Form Diagram again with the rvRelax command

- Allow the diagrams to move freely. Check for fixed nodes -> rvModify -> NodeWeight

- Increase the Min/Max Form and Force Edge value in the settings dialog

- Adjust problematic areas of the diagrams manually using -> rvModify -> Move

- Start again with a less constrained topology ;)

3.8 Vertical Equilibrium - rvVertical

The result is generated, respectively updated, by an iterative approach based on the horizontal equilibrium of the form and force

diagram. The vertical equilibrium of the forces ensures a compression-only solution under dominant self-weight. The Vault Height Scale

value in the settings dialog controls the height of the structure. The solution can be visualized by a network of lines, pipes and a

continuous mesh. If the vertical equilibrium fails to fully compute the thrust network will be shown in red. In this case use the rvVertical

command again (you might want to increase the maximum number of iterations -> Interations Max Vertical). If you run into instability

problems, make sure the Runge Kutta 4th Order solver is deactivated in the settings dialog.

3.9 Info

Guides you to the RhinoVAULT website, where you can learn more about the plug-in and the used methods.

4 Additional Information

The tool was developed to support the user in the form finding process of vaulted compression structures in the early design phase. It

is obvious that prior to any realization of structures based on designs obtained with RhinoVAULT, a detailed structural analysis is

necessary.

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5 Copyright

The development of RhinoVAULT is currently supported by the BLOCK Research Group at ETH Zurich, Switzerland. It is shared freely in

the hope that students and professionals will enjoy it and use it for original and creative work. It can be freely shared and used for

academic and commercial purposes, but with proper attribution.

This work is licensed under: Creative Commons - Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)

http://creativecommons.org/licenses/by-sa/3.0/

- Matthias Rippmann (project leader)

- Lorenz Lachauer

- Philippe Block

BLOCK Research Group, ETH Zurich, Switzerland

http://block.arch.ethz.ch

6 Contact

Dipl.-Ing. Matthias Rippmann | Research Assistant Assistant Chair of Building Structure | Prof. Dr. Philippe Block ITA - Institute of Technology in Architecture

ETH Zurich Wolfgang-Pauli-Str. 15, HIL E 45.2 8093 Zurich, SWITZERLAND

T +41 (0)44 633 28 03 F +41 (0)44 633 10 41 E rippmann@arch.ethz.ch W www.block.arch.ethz.ch

7 Acknowledgements

The authors would like to thank Diederik Veenendaal for his assistance in implementing the 4th order Runge Kutta solver, Ramon Weber for his contribution to the tutorial material and beta testing and Tom Van Mele for creating the rhinoVAULT tools page under the http://block.arch.ethz.ch domain. In addition we would like to thank our workshop participants for their patience and feedback during the first phase of development.