Tips 2: Making a Plan View Model

Flat origami models come in two distinct types, which correspond to two different views of the subject. The most common is a "side view" model, which resembles the silhouette of the subject viewed from the side. (You can often make a side view model three-dimensional by opening out the body from the underside, but the base is still fundamentally side view.) UsingTreeMaker, it is very easy to make side view models; side view is the natural orientation of a uniaxial base.

However, many models --- especially insects --- look better in "plan view," that is, viewed as if you were looking down on them from above. Some of the time, you can make a plan view model out of a side view base by spreading the layers of the model to the left and right and flattening the result. But oftentimes, the base has an odd number of layers, or the layers don't spread sufficiently far apart, or it is necessary to spread-sink one or more corners in a way that ends up reducing the length of the attached points. For example, let's take the regular human tree (equal-length head, arms, legs, and body) oriented along the book direction.


Figure Ti-2-1. A tree for a human figure. Note the symmetry conditions on all leaf nodes.

If you set up the tree and symmetry line and run an optimization, you will arrive at the arrangement of nodes shown in Figure Ti-2-2, with crease pattern as shown in Figure Ti-2-3 and folded form shown in Figure Ti-2-4.


Figure Ti-2-2. The optimized pattern of nodes.


Figure Ti-2-3. The crease pattern.


Figure Ti-2-4. The folded form.

Now the problem with this crease pattern is that if you fold it up into a side view base, there is only one layer on the top, and if you try to squash-fold the layer to spread the arms and legs to either side and make a plan view base, you'll find that the base of the squash fold reduces the effective length of the legs considerably.

That's because we have overlooked an important requirement for making a plan view base. The way you make a side view base into a plan view base is to open the model along the line of symmetry, which means that all of the paper along the line of symmetry must run along the fold line by which you open flat the base. That is, all of the paper along the symmetry line must run along the axis of the base. In the interior of a base, axial paths are active paths. So, to make a plan view base, the line of symmetry must be entirely covered with active paths.

So we need to get active paths running along the line of symmetry. But since active paths only run between leaf nodes of the tree and there is currently only one leaf node on the line of symmetry (the head), we need to add more nodes to the tree --- solely for the purpose of creating active paths. These nodes don't correspond to features of the model; they're only there to make the base a plan view base. In particular, we need to add a node to the bottom of the square so that there is a terminus on the bottom edge of the square for the active paths that are to run along the line of symmetry.

So, we need to add a node along the bottom edge of the paper, i.e., between nodes 6 and 7. But the path between nodes 6 and 7 is already active; there's no room along it to add any other nodes. We will have to add a new node and re-optimize in order to make room for the new node. This is a very important point: there is no way to modify the original configuration of nodes to make a plan view base without rearranging the entire pattern of nodes!

We'll add a new node attached to node 5. We'll want the node to be located on the centerline between nodes 6 and 7. We'll make this forcing using conditions. There are a couple of ways we could do this. We could simultaneously fix the node to the symmetry line and to the edge of the paper, but since we know exactly where the node should lie, we can just use a Node fixed to position condition.

Create a new node attached to node 5 as shown in Figure Ti-2-5, and add a "Node(s) Fixed to Position..." condition.


Figure Ti-2-5. The folded form.

In the Inspector for this condition, turn on both of the "X position fixed" and "Y position fixed" checkboxes and enter "0.5" for the x position and "0.0" for the y position as in Figure Ti-2-6.


Figure Ti-2-6.

Then hit Enter.

There is still the question of how long to make the associated edge. For now, give it a length of 0.4 --- we'll discuss how length matters in a moment. After you re-run the optimization (Action->Scale Everything), you should get a modified arrangement of nodes as shown in Figure Ti-2-7.


Figure Ti-2-7.

Now we have nodes at the top and bottom of the paper along the symmetry line, but the path between them is not active --- yet. We must add one more node along the symmetry line, which will "sop up" the excess paper. As we did in the previous tip, there are several places to add a new node and edge. We could add the new edge to node 2; we could add it to node 5; or we could break edge 4 somewhere and add the new node in the middle.

Let's first try adding the new edge to node 2. Select node 2, click elsewhere to create the new node, select the new node and edge, and choose Action->Scale Selection to maximize the length of the edge. The result is shown in Figure Ti-2-8.


Figure Ti-2-8.

This new node has created active paths with nodes 1, 6, and 7. The path above lies on the symmetry line, but there is no active path with node 8.

So, let's add another node. Add a new node and edge to node 5 and optimize via Action->Scale Selection... again. The result is shown in Figure Ti-2-9.


Figure Ti-2-9.

This didn't work, because the optimization forced the new node off to one side. We can fix that by putting another symmetry constraint on the node, re-selecting and re-optimizing. The node is currently pinned, so TreeMaker won't recognize it as moveable. Option-click on the node and drag it out of position (Alt-click on Windows, Control- or Alt-click on Linux). Fix the node to the symmetry line (Condition->Node(s) Fixed to Symmetry Line). Then select the node and its edge and re-optimize the edge length (Action->Scale Selection...).


Figure Ti-2-10.

This node pattern now has active paths running all along the symmetry line, which means that its base can be opened out into plan view, so now we can build the creases.


Figure Ti-2-11. The crease pattern for a plan view base.


Figure Ti-2-12. Folded form for the plan view base.

The base shown in the Folded Form window will of course still be shown in side view. But because this base has axial creases running all along the line of symmetry, it will be openable into plan view, with right and left sides of the flap base mirror-symmetric with respect to one another.

Previous: Tips 1: Adding Nodes     Next: Tips 3: Forcing Edge Flaps