This section contains several shorter tutorials that illustrate additional features of TreeMaker. The tips tutorials are:
Once you have defined a tree and found an optimum configuration of nodes, you have several options for filling in the remaining creases. In this section, I'll demonstrate several different treatments of the same tree. Construct a "generic mammal" tree with equal-length head, tail, four legs, and a body --- that is, with all edges of unit length --- as shown in Figure Ti-1-1.
Figure Ti-1-1.
Select command Action->Scale Everything; you should arrive at a distribution of leaf nodes as shown in Figure Ti-1-2.
Figure Ti-1-2.
This crease pattern gives a single active polygon, which is a hexagon. Now, as I said, there are several ways to add creases to this pattern to complete the base. The simplest is the one we have already learned; simply select Action->Build Crease Pattern, then View->Creases View. This selection fills in the active polygon with the "universal molecule" crease pattern. This is the simplest pattern and produces the least total crease length of all possible molecules for a given polygon.
Figure Ti-1-3.
Although the universal molecule is the simplest molecule, it produces a base with wide flaps; that is, the hinges at each flap are relatively long. In some cases, the flaps in a universal molecule are actually wider than they are long! To obtain long, skinny flaps (as in insect legs), the universal molecule must be repeatedly sunk in and out to narrow its flaps. The folded form of this molecule can be seen by making the Folded Form window visible (View->Folded Form).
Figure Ti-1-4.
It is possible to narrow flaps by adding new nodes to the tree and inflating them to break up the active polygon into smaller pieces. For example, in the tree shown above, kill the crease pattern (Action->Kill Crease Pattern), then add a node and edge to node 2, as shown in Figure Ti-1-5.
Figure Ti-1-5.
Observe that this new node has created some infeasible paths (indicated by their red coloration). That's OK; we'll let TreeMaker find the right length and position. Select both the new node and its incident edge and choose Action->Scale Selection. This will expand the new edge to its maximum possible size, creating new active paths that effectively break up the hexagon into smaller active polygons --- in this case, two triangles and two quadrilaterals, as shown in Figure Ti-1-6.
Figure Ti-1-6.
Building creases gives the crease pattern shown in Figure Ti-1-7, which has the folded form shown in Figure Ti-1-8.
Figure Ti-1-7.
Figure Ti-1-8.
This new folded base has all the flaps of the original base, plus one extra one. The paper for the new flap had to come from somewhere; and since it couldn't come from the length of the existing flaps, it had to come from their width. And, as you see, the upper flaps are now not as wide as the lower flaps.
Alternatively, you could have added the new edge to node 5, which would give you the same crease pattern flopped end-for-end.
With either of these two patterns, you get a crease pattern in which the "head" and "tail" are folded differently. For reasons of symmetry, you might want the head and tail to be symmetric, in which case, if you add a new edge, you need to put it in the middle of edge 4. Let's try that now. Go back to Design View, and delete node 9 (which will also remove edge 8).
Select edge 4, and choose Edit->Split->Selected Edge.... This brings up a small dialog:
Figure Ti-1-9.
This command will break the edge into two edges, adding a new node at the break, from where you can add a new edge. To make the base symmetric, you should split the edge exactly in half. Since its current length is 1.0, the split location should be halfway from node 2 to node 5, i.e., 0.5. Enter that value and click OK. The resulting tree is shown in Figure Ti-1-10.
Figure Ti-1-10.
Now you can add the new edge. Click on node 9, then click elsewhere to create a new node and edge, as shown in Figure Ti-1-11.
Figure Ti-1-11.
Select the new node and edge and choose Action->Scale Selection. After optimization, the new node will be pinned with four active paths, but will now be located in the middle of the paper, as shown in Figure Ti-1-12.
Figure Ti-1-12.
Build creases and convert to Creases View to see the new crease pattern.
Figure Ti-1-13.
And the folded form is shown here. This time, all four flaps have had their width reduced to some degree to accommodate the new flap.
Figure Ti-1-14.
Suppose after seeing the result, we didn't want to do this after all. You can remove the node by deleting node 10. But you will still be left with an extra node in the middle of the model. A node with only two edges connected is called a "redundant node." You can remove a single redundant node by selecting it and choosing the command Edit->Absorb->Selected Nodes. This command is only enabled if you only have redundant nodes in the selection. If you don't want to track down all redundant nodes, you can choose Edit->Absorb->Redundant Nodes to remove all redundant nodes from the tree.
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