GITBOOK-81: vertical equilibrium

Author: juney-lee

gitbook/manual/fitting.md

@@ -14,8 +14,8 @@ A `ThrustDiagram` is represented by the mesh datastructure. 
 
 ### Target Height
 
-Once the Form and Force Diagrams have been created and horizontal equilibrium has been established through parallelisation, the distribution of horizontal forces in the system is fixed. The actual magnitude of the horizontal forces depends on a _scale factor_ and will determine the _target height_ of the final thrust diagram. A higher scale factor results in higher horizontal forces and therefore a shallower three-dimensional shape. Vice versa, a lower scale factor results in lower horizontal thrust and thus a deeper solution.
+Once the `FormDiagram` and `ForceDiagram` have been created and horizontal equilibrium has been found, the distribution of horizontal forces in the system is fixed. The actual magnitude of the horizontal forces depends on a _scale factor_ and will determine the _target height_ of the final `ThrustDiagram`. A higher scale factor results in higher horizontal forces and therefore a shallower shell. Vice versa, a lower scale factor results in lower horizontal thrust and thus a deeper solution.
 
-The meaning of the scale factor and the magnitude of horizontal forces is related to the magnitude of the loads, which in turn are related to the self-weight of the resulting three-dimensional geometry. Rather than asking you to "guess" the scale factor to get the three-dimensional shape you want, RhinoVAULT will determine the scale for you based on the desired height of the final solution. The default value for the target height is 25% of the length of the diagonal of the bounding box of the Form Diagram (essentially of the bounding box of the footprint of your shell). This value tends to produce well-proportioned geometries.
+The meaning of the scale factor and the magnitude of horizontal forces is related to the magnitude of the loads, which in turn are related to the self-weight of the resulting three-dimensional geometry. Rather than asking you to "guess" the scale factor to get the three-dimensional shape you want, RhinoVAULT will determine the scale for you based on the desired height of the final solution. The default value for the target height is 25% of the length of the diagonal of the bounding box of the `FormDiagram` (essentially of the bounding box of the footprint of your shell). This value tends to produce well-proportioned geometries.
 
-<figure><img src="../.gitbook/assets/RV_vertical-equilibrium_cropped.gif" alt=""><figcaption></figcaption></figure>
+<figure><img src="../.gitbook/assets/RV_vertical-equilibrium_cropped.gif" alt=""><figcaption><p>Animation showing the varying geometry of the <code>ThrustDiagram</code> with different target heights.</p></figcaption></figure>

gitbook/manual/horizontal-equilibrium.md

@@ -4,7 +4,7 @@
 | ----------------------------------------------------------------------------------- | ------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------- |
 | <img src="../.gitbook/assets/RV_horizontal-eq (1).svg" alt="" data-size="original"> | <p><strong>Rhino command name</strong></p><p><code>RV_tna_horizontal</code></p> | <p><strong>source file</strong></p><p><a href="../../plugin/RV_tna_horizontal.py"><code>RV_tna_horizontal.py</code></a></p> |
 
-`RV_tna_horizontal` geometrically reconfigures the the edges of the `ForceDiagram`, such that the corresponding edges of the `FormDiagram` and `ForceDiagram` become parallel to each another (in the conventional graphic statics sense), or perpendicular (the 90° rotated, RhinoVAULT convention). The resulting `ForceDiagram` and `FormDiagram` are _reciprocal_ when the two diagrams are topological duals of the other and all pairs of corresponding edges are parallel (within tolerance).
+`RV_tna_horizontal` geometrically reconfigures the the edges of the `ForceDiagram`, such that the corresponding edges of the `FormDiagram` and `ForceDiagram` become parallel to each another (in the conventional graphic statics sense), or perpendicular (the 90° rotated, RhinoVAULT convention). The resulting `ForceDiagram` and `FormDiagram` are _reciprocal_ when the two diagrams are topological duals of the other and all pairs of corresponding edges are perpendicular (within tolerance).
 
 
 
@@ -26,7 +26,7 @@ Once the `FormDiagram` and `ForceDiagram` are reciprocal, they describe the hori
 
 ### Alpha
 
-In RhinoVAULT, horizontal equilibrium is computed by parallelising the edges of the Form and Force Diagram to corresponding target vectors. These target vectors are defined as the weighted average of the vectors of corresponding edge pairs. Therefore, the most important parameter for the calculation of horizontal equilibrium in RhinoVAULT is `alpha`, which is the weighting factor for the calculation of the target vectors.
+In RhinoVAULT, horizontal equilibrium is computed by paralleli-izing or perpendicular-izing the edges of the Form and Force Diagram to corresponding target vectors. These target vectors are defined as the weighted average of the vectors of corresponding edge pairs. Therefore, the most important parameter for the calculation of horizontal equilibrium in RhinoVAULT is `alpha`, which is the weighting factor for the calculation of the target vectors.
 
 If `alpha = 100`, the target vectors are completely defined by the vectors of the edges of the `FormDiagram`. This means that only the geometry of the `ForceDiagram` will be updated to achieve horizontal equilibrium. This is the default. If `alpha = 0`, the target vectors are completely defined by the edges of the `ForceDiagram`. Therefore only the `FormDiagram` will be updated. For all other values, the target vectors are calculated using the following formula: