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A `Pattern` describes the topology of the `formdiagram`. A `pattern` is a collection of vertices interconnected by lines or "edges". RhinoVAULT provides several methods for generating a `Pattern` and various mechanisms to modify and refine its geometry.
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{% endstep %}
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### 2. Define Boundary Conditions
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{% step %}
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### Define Boundary Conditions
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In this step, additional information is added to the `Pattern`, such as identification of the support vertices and refinement of the geometry of the unsupported boundaries.
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{% endstep %}
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### 3. Create Form Diagram
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{% step %}
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### Create Form Diagram
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Once the support vertices have been defined and the boundaries have been properly modified, the `FormDiagram` can be created from the `pattern`.
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{% endstep %}
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### 4. Create Force Diagram
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{% step %}
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### Create Force Diagram
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Once the `FormDiagram` has been successfully created, the `ForceDiagram` can be created. In its initial state, the `ForceDiagram` is the topological dual of the `FormDiagram`; the two diagrams are not yet reciprocal.  
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{% endstep %}
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### 5. Horizontal Equilibrium
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{% step %}
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### Horizontal Equilibrium
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In order for the `FormDiagram` and the `ForceDiagram` to be reciprocal, the edges of one diagram needs to be perpendicular to the corresponding edge in the other diagram. Horizontal equilibrium solver iteratively repositions the vertices of the `FormDiagram` and/or `ForceDiagram` until the perpendicularity criteria (within desired angle tolerance) is met.
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{% endstep %}
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### 6. Vertical Equilibrium
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{% step %}
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### Vertical Equilibrium
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Once the `FormDiagram` and `ForceDiagram` are reciprocal (in other words, in horizontal equilibrium), the geometry of the `ThrustDiagram` can be computed. The `ThrustDiagram` is equivalent to the `FormDiagram` with the updated z coordinates of its vertices (therefore updated self-weight at each vertex). 
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Given a desired target height of the eventual `ThrustDiagram`, vertical equilibrium solver iteratively re-scales the `ThrustDiagram` in the z-axis, until the highest vertex of the `ThrustDigram` lies at the desired target height.
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{% endstep %}
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### 7. Modify Diagrams
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{% step %}
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### Modify Diagrams
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Once the vertical equilibrium has been computed, the three diagrams can be interactively modified by the user to continue form finding explorations.
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{% endstep %}
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### 8. Utilities
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{% step %}
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### Utilities
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There are several utility functions povided by RhinoVAULT: opening and saving RhinoVAULT session files; redo and undo; redraw scene; and clear scene.
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There are several utility functions provided by RhinoVAULT: opening and saving RhinoVAULT session files; redo and undo; redraw scene; and clear scene.
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{% endstep %}
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### 9. Settings
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{% step %}
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### Settings
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Settings allows you to modify various parameters for the solving algorithms and display options.
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@@ -14,4 +14,4 @@ Since its release in 2014, RhinoVAULT has been downloaded by more than 30.000 pe
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* Rippmann M., Lachauer L. and Block P. [RhinoVAULT - Interactive Vault Design](https://block.arch.ethz.ch/brg/publications/414), _International Journal of Space Structures_, 27(4): 219-230, 2012.
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* Rippmann, M., & Block, P. (2013). Funicular shell design exploration. In _Proceedings of the 33rd Annual Conference of the ACADIA_ (Waterloo/Buffalo/Nottingham, Canada).
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* Rippmann M. [Funicular Shell Design: Geometric Approaches to Form Finding and Fabrication of Discrete Funicular Structures](https://block.arch.ethz.ch/brg/publications/591), Doctoral dissertation, Department of Architecture, ETH Zurich, 2016.
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* Rippmann M. [Funicular Shell Design: Geometric Approaches to Form Finding and Fabrication of Discrete Funicular Structures](https://block.arch.ethz.ch/brg/publications/591), Doctoral dissertation, Department of Architecture, ETH Zurich, 2016.
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