Creating Isolate Face Sets
- Select a Primal or Dual Isolate tab on the Toolbar.
- Set the Isolate Mode by clicking the Face button.
- Click on a face in the manifold.
- Unique faces are printed in the Log along with their respective properties.
- The Isolate Face pop-up menu activates with a list of isolate sets. When you select an item from the Isolate menu, only the selected set appears in the view with its respective labels, whilst other sets are hidden.
Using this method you can see at a glance all the panels required to cover a dome – both their relation to each other, and their quantities. These geodesic subdivision patterns are also artistic and aesthetically pleasing:
Isolate Faces requires that the Isolate sets for Edges are generated first, otherwise the Edge labels for each face will be missing in the log. Typical output of the default options are given below:
UNIQUE CELLS [Weak method] Scale Factor = 10.000000000 Units = Feet and Inches TsQEIcosahedron 4V, Class I, Method 1 Primal Lattice Total cells = 320 Unique cells = 5 Cell Quantity Area F1  3.036490888 Sq Feet or 437.254687901 Sq Inches. Edges: E3 E1 E1 F2  3.762349227 Sq Feet or 541.778288702 Sq Inches. Edges: E2 E2 E3 F3  3.940941268 Sq Feet or 567.495542549 Sq Inches. Edges: E2 E5 E4 F4  4.343903088 Sq Feet or 625.522044614 Sq Inches. Edges: E6 E5 E5 F5  4.571436727 Sq Feet or 658.286888702 Sq Inches. Edges: E6 E6 E6
The default method uses equivalence by area alone. Hold down the Control key when clicking on a face to perform a more robust equivalance test. When the Control is down the following criteria are met for each unique set:
- Areas are equivalent.
- Vertex counts are equivalent.
- Apex/centroid angles are equivalent.
- If the vertex order of face B is different to A, the code also checks if face B can be superimposed on face A by successive rotations of B. In this case, the faces are considered equivalent.
The robust test uses a ‘Flip Symmetric’ option as default; this ‘flips’ facets over and tests the apex/centroid angles again. Thus any ‘reversed’ facets are also considered equivalent.
When the Control and Shift keys are down, the ‘Flip Symmetric’ option is turned OFF. Thus reversed facets are not considered equivalent. Consider the following:
When Flip Symmetric is OFF, the reversed F2 set in the top image becomes a new F3 set in the bottom image. The point being, that F2 and F3 are identical – but for their orientation in the subdivision… So you might ask, “Why turn ‘Flip Symmetric’ OFF?” Well, it all depends on how important the orientation is with regard to the fabribcation process. For example, you can’t flip a stellated face, because the stellation would point inward. When in doubt, it is best to visualise both options, first with the Control key, and then with the additional Shift key. Of course, if you are just covering a dome with fabric or panels, then turning ‘Flip Symmetric’ OFF is not recommended. (Unless your weatherproof membrane is already applied to one side). The following diagram should make things clear:
In figures 1 & 2, face A can be superimposed on face B either by rotating A by 180° or by using ‘Flip Symmetric’. But in figures 3 & 4, face A cannot be superimposed on face B by rotation – it can only be superimposed by using ‘Flip Symmetric’.
Here is the isolate system on an 8V Class I Method 1 Dual cells: