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1 | 1 | # 5. Horizontal equilibrium |
2 | 2 |
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3 | | -| | | | |
4 | | -| ----------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | - | |
5 | | -| <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></p><p><strong>source file</strong></p><p><a href="../../plugin/RV_pattern.py"><code>RV_tna_horizontal.py</code></a></p> | | |
| 3 | +| | | | |
| 4 | +| ----------------------------------------------------------------------------------- | ------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------- | |
| 5 | +| <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> | |
| 6 | + |
| 7 | +## Alpha |
| 8 | + |
| 9 | +In RV2, 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 RV2 is `alpha`, which is the weighting factor for the calculation of the target vectors. |
| 10 | + |
| 11 | +If `alpha = 100`, the target vectors are completely defined by the vectors of the edges of the Form Diagram. This means that only the geometry of the Force Diagram will be updated to achieve horizontal equilibrium. This is the default. |
| 12 | + |
| 13 | +If `alpha = 0`, the target vectors are completely defined by the edges of the force diagram. Therefore only the Form Diagram will be updated. |
| 14 | + |
| 15 | +For all other values, the target vectors are calculated using the following formula: |
| 16 | + |
| 17 | +$$ |
| 18 | +t_i = \alpha \cdot \hat{e}_{i, form} + (1 - \alpha) \cdot \hat{e}_{i, force} |
| 19 | +$$ |
| 20 | + |
| 21 | +Note that using `alpha` efficiently requires a bit of practice and experience. Since the Form Diagram defines the intended layout of horizontal forces and RV2 has many tools for designing force layouts that provide a good starting point for form finding explorations, it is usually a good idea to start with `alpha = 100`. However, once you have the horizontal equilibrium under control, playing around with lower `alpha` values can have a significant influence on finding nicely balanced force distributions. |
| 22 | + |
| 23 | +## Iterations |
| 24 | + |
| 25 | +Computing horizontal equilibrium is an iterative process. The default number of iterations is `100`. For sensible force layouts, this value should go a long way. However, there are many cases in which more iterations are required. For example, if the Form Diagram has multiple open/unsupported edges, and especially if those edges have a low "sag" value, more iterations will typically be required to reduce all angle deviations between corresponding edges to less than 5 degrees. |
| 26 | + |
| 27 | +Computing horizontal equilibrium is quite fast. Therefore, don't hesitate to set the number of iterations to `1000` or more if the need arises. However, don't go completely overboard either (`10000` iterations is quite excessive in most cases), because the calculation has no stoppage criterion, since it tends to be more computationally expensive to check for convergence than to just run all the requested iterations. |
| 28 | + |
| 29 | +Furthermore, resolving all angle deviations is not an absolute requirement, and is in many cases unnecessary. For example, the angle deviations between very short edges tend to be quite persistent as they are dominated by edges with (much) longer lengths during the calculation process. Since short edges in the Force Diagram also represent (relatively) small horizontal forces, these deviations can often be ignored. |
| 30 | + |
| 31 | +## Refreshrate |
| 32 | + |
| 33 | +The iterations of the horizontal equilibrium calculation process is dynamically visualised. The rate at which the diagrams are updated is controlled by the refreshrate. The default value is `10`, which means that the diagrams are updated every 10 iterations. |
| 34 | + |
| 35 | +For large diagrams the dynamic visualisation slows down the calculations a little bit. In these cases, and/or for high numbers of iterations (`> 1000`), it is therefore advisable to set the refreshrate to a higher value. For example, if the number of iterations is `1000`, then a refresh rate of `100` seems more appropriate. |
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