GITBOOK-32: Adding text to Boundary Conditions

Author: juney-lee

gitbook/manual/boundary-conditions.md

@@ -24,7 +24,9 @@ In RhinoVAULT, a _support_ is defined as a vertex of the structure that is fixed
 | ----------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | - |
 | <img src="../.gitbook/assets/RV_relax.svg" alt="" data-size="original"> | <p><strong>Rhino command name</strong></p><p><code>RV_pattern_supports</code></p><p></p><p><strong>source file</strong></p><p><a href="../../plugin/RV_pattern_supports.py"><code>RV_pattern_supports.py</code></a></p> |   |
 
+An opening is a chain of edges at the boundary of a `Pattern`, in between two support vertices. In general, openings in TNA cannot be straight, unless there are no internal forces in the non-boundary edges at the openings (e.g. barrel vault or cross vault). In some applications where openings may already have some curvature, the relaxation will make the `Pattern` more "equilibrated" and optimal for the horizontal equilibrium solver later on.&#x20;
 
+This feature relaxes the entire `Pattern` using the _force density method_ ([Schek, 1974](https://www.sciencedirect.com/science/article/pii/0045782574900450)), resulting in curved openings. Force density of 1 is assigned to every edge. Note that supports should be properly defined in step 2a to achieve good results.
 
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@@ -34,3 +36,4 @@ In RhinoVAULT, a _support_ is defined as a vertex of the structure that is fixed
 | -------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | - |
 | <img src="../.gitbook/assets/RV_boundaries (1).svg" alt="" data-size="original"> | <p><strong>Rhino command name</strong></p><p><code>RV_pattern_bnoundaries</code></p><p></p><p><strong>source file</strong></p><p><a href="../../plugin/RV_pattern_boundaries.py"><code>RV_pattern_boundaries.py</code></a></p> |   |
 
+The treatment of the openings are very much dependent on the type of vault that is being investigated.  This feature enables users to control the curvature of each opening individually by defining the _sag_ value, which is calculated based on the percentage of the length of the opening. The $$q$$s for the boundary edges are automatically calculated based on the target _sag_ values, which are then used for the relaxation using the force density method.&#x20;