This section contains tutorial introductions to the capabilities of TreeMaker. I will walk you through the basic process of setting of a TreeMaker design and constructing a crease pattern. The tutorials are:
In this tutorial, you will work through the design of a 4-legged animal with a head and tail and will learn the fundamentals of designing a model with TreeMaker. Before starting it, you should understand the fundamentals of origami design, such as the difference between corner, edge, and middle flaps and be familiar with the basic origami procedures and terms such as valley fold, mountain fold, reverse fold, rabbit ear, et cetera.
TreeMaker designs an origami base that can be represented by a stick figure. You specify the desired proportions of your base by drawing a stick figure in the square and specifying its dimensions. If you have ever used a vector drawing program like Macromedia Freehand, Adobe Illustrator, Deneba Canvas, Corel Draw, etc., you should have no trouble in figuring out how to draw a figure, but if you haven't, we'll walk you through it.
Begin by double-clicking on the TreeMaker icon to launch it. This will create a new, untitled window that displays a square --- the default shape of paper. Later, you will see how to change the size and shape of the paper (you can even design for a rectangle if you like) but for now we'll use a square.
If TreeMaker is already running, you can create a new, untitled document by selecting the File->New menu command.
Figure Tu-1-1. A new, untitled TreeMaker document shows a
blank square.
Initially, the square is blank. We will define the tree by drawing on the square, but the tree is really an abstract concept. Several points on the tree correspond to distinct, identifiable points on the square, so as a matter of convenience we will draw the tree on the square.
Even before we've drawn anything, there is one important attribute of the design: the scale, which is always displayed in the bottom of the design window. The scale is the ratio between the characteristic size of the base and the size of the square, so larger is better: a larger scale gives a larger base in the end. The scale always starts out with a value of 0.1, but over the course of the design, we will find a better value for this quantity.
Click once in the middle of the square. You will see a dot appear with a number above it and a circle around it as in Figure Tu-1-2. This dot is a node; the number is the index of the node, which is used to identify the node later on. Each node is assigned a unique index. You can ignore the index for now. If you clicked just once, the node is a big dot, which means that it is selected. If the node is a small dot, it is deselected. A node represents either the tip of a flap or a point where multiple flaps come together. The circle represents the amount of paper required to form the flap whose tip is represented by a node.
Figure Tu-1-2. A single node in the new tree.
If exactly one node is selected and you click somewhere else, a new node will be placed at the click location with a line connecting the nodes. The line between the two nodes is called an edge. We'll do this now. Make sure the node is selected (click once on it so that it is highlighted) and then click once above the node; you have now created an edge connecting the two nodes. Note that the new node is now selected (highlighted), as is the edge, as shown in Figure Tu-1-3.
Figure Tu-1-3. Two nodes and an edge in the tree.
The edge displays two numbers near its midpoint: the index, which serves to identify the edge, and another number below it, which is the desired length of the edge. The length of the edge is proportional to the length of the corresponding flap on the base. The proportionality constant is the aforementioned scale.
All edges start out with a length of 1.000 by default; later you'll learn how to change the length of an edge. Note too that the displayed length of the edge doesn't change when you drag nodes and edges around. This is an important point: the displayed length is not the actual length of the drawn line; it's the desired length of the corresponding flap.
There are two types of nodes in a tree. Leaf nodes are nodes that have only one edge incident upon them. Branch nodes have two or more edges incident upon them. Leaf nodes correspond to the tips of flaps; branch nodes correspond to points where multiple flaps come together. Leaf nodes (and only leaf nodes) are drawn with circles around them; the radius of the circle is the scaled length (edge length times tree scale) of the incident edge. The size of the circle indicates the minimum area of the paper needed fr the flap that corresponds to the incident edge; longer edges mean larger circles. Larger circles consume more paper, leaving less paper for other parts of the tree. The process of designing a uniaxial origami base amounts to laying out the nodes in a way that insures that every flap gets the right amount of paper; the node circles provide some visual feedback of how much paper is needed by the leaf nodes --- or rather, by the edges that are incident to the leaf nodes.
As mentioned earlier, if you click on an existing node, it becomes selected. If you hold down the mouse button after clicking you can drag the node around on the square. If exactly one node is already selected and you click elsewhere in the square, you create a new node at the click location and create a new edge connected to the selected node. (If zero or two or more nodes are selected and you click elsewhere, everything gets deselected.) You can also click on edges and drag them; dragging an edge drags the nodes at each end. You can select more than one node or edge at a time by holding down the Shift key when you click on nodes or edges. The collection of selected nodes and edges is called the selection.
The following are all the things you do with clicks:
By clicking and dragging, you can change the position of a node or edge. As you build up constraints on the position of a node, a node can become "pinned" and you won't be able to drag it around any more. However, if you hold down the appropriate modifier key (Option on Mac, Alt on Windows, Alt or Control on Linux) while clicking, you can override this behavior and drag a pinned node.
To delete a node or edge, you can either hit the Backspace or Delete key or select Edit->Clear. Although you can't drag a pinned node without holding down a modifier key, you can delete any node at any time.
Keyboard commands for editing are:
Deleting a leaf node also removes the attached edge. Similarly, deleting an edge also deletes any nodes that would otherwise be orphaned.
Now we will build a tree. Choose Edit->Select->All and then choose Edit->Clear (or hit Delete) to get rid of what's currently on the square. Now, starting near the bottom of the square, click once to place a node; then click once about 1/3 of the way up; click once again about 2/3 of the way up; and click once near the top of the square. You will have created a line of four nodes and three edges as shown in Figure Tu-1-4.
Figure Tu-1-4.
This line of nodes represents the head (top), body (middle) and tail (bottom) of the animal. Note that only the two leaf nodes have node circles drawn around them.
Now we will add side branches to the tree. Click once on node 2 to select it, then click once to the left of node 2; this adds a leg. Click again on node 2 to select it and click once to the right of node 2; this adds another leg, as shown in Figure Tu-1-5.
Figure Tu-1-5.
Got the hang of it? Now try to add two more legs to node 3, so that you wind up with something that looks like Figure Tu-1-6.
Figure Tu-1-6.
This stick figure represents an animal with a head, two front legs, a body, two rear legs, and a tail. It will be used to define a base with flaps for the head, legs, body, and tail. Since all of the edges of the stick figure have the same relative length, each of the flaps of the base (and the body) will be the same length in this example.
Note that the nodes are outlined by amber lines. These lines are called border paths; they'll define the usable region of the square when we're done.
At this stage of the game, you can click on nodes and edges and move them about rather easily because none of them are pinned. Click on nodes 7 and 8 and drag them upward so that they lie above node 4, as shown in Figure Tu-1-7.
Figure Tu-1-7.
When you have defined the stick figure, it's time to start computing the crease pattern. Go to the Action menu and select the command Action->Scale Everything. This starts the computation of the crease pattern. You can tell that the calculation is running from two things: first, a small window will pop up as the calculation proceeds; second, the positions of the nodes will change and move around. Depending on the power of your machine, the calculation can take anywhere from a few seconds to a few minutes.
Let this calculation run until the progress window disappears and things stop moving around. You should see a pattern something like Figure Tu-1-8. (Your example might look like the figure turned upside-down; if it does, don't worry about it.)
Figure Tu-1-8.
There is a lot of information in this figure, so let me spend a few minutes describing what we're seeing. Several green lines have appeared that connect leaf nodes and they have dots and numbers along them. The stick figure has been distorted because the leaf nodes have moved. The node circles have expanded until some of them touch each other. And last, the scale displayed at the bottom of the window has changed from 0.10000 to 0.2669.
Here's what this all means. The green lines between them indicate fold lines in the base. (They will be mountain folds most of the time). They are called active paths (for reasons that will come later).
The tree as drawn has been distorted because the leaf nodes have been moved. Note, however, that the numbers along each edge that specify the desired flap length have not changed. Each leaf node corresponds to a unique identifiable vertex in the crease pattern (which is the vertex at the tip of the corresponding flap); we draw the leaf nodes at the positions of their corresponding vertices. That is, when you fold the base, the tip of the head flap will come from the point on the paper where the leaf node that corresponds to the head is located.
The scale, too, has changed; it is now larger, with a value of 0.2669. That means that a flap that is 1.0 units long on the tree will actually be 0.2669 units long on the paper. The scale thus specifies the overall size of the base. Since the scale has gotten larger, the circle sizes (which, recall, are the product of the tree scale and the length of the edge incident to the node at the circle center) are also correspondingly larger. The circles have expanded until they touch, but they don't overlap. Recall that each circle encloses the minimum paper needed for its corresponding flap. If two circles overlapped, the paper in the overlap would belong to two different flaps.
What Action->Scale Everything actually does is to move around the leaf nodes to try to find an arrangement that gives the largest possible base, subject to the proviso that all of the edges maintain the same lengths relative to each other and all of the paper in the tree ends up in at most one flap. In Figure Tu-1-8, there is a large region of paper that doesn't seem to belong to any circle, but it still belongs to a flap: in this case, the flap corresponding to edge 2. Since edge 2 isn't incident to any leaf nodes, it doesn't have a circle --- but it still requires a certain amount of paper.
Although all of the edges are enlarged by the same amount, at the optimum configuration, at least some of the edges cannot be enlarged any more by any node movement whatsoever. Such edges are called "pinned" edges. In this optimization, all of the edges are pinned. In general, for small trees, after you have run the Scale Everything command, all or nearly all of the edges will be in this state. Pinned edges are shown in a lighter shade of blue than unpinned edges.
Most of these dots, lines, circles, and numbers are here for illustrative purposes and you will learn later how to turn on and off their display. The green lines, however, correspond to actual creases in the base; the folds are (usually) mountain folds. The folds along these lines will run along the axis of the folded base, and they are called axial folds.
The green lines are not themselves creases; rather, they are visual representations of relationships between nodes, called paths. For any two leaf nodes on the tree, there is a path, which relates two distances: the distance between the two nodes on the paper (or rather, between the vertices that correspond to the two nodes); and the distance between the two nodes as measured along the tree and scaled to the paper. If the distance between the nodes on the paper is greater than or equal to the scaled distance between the two nodes on the tree, the path is said to be feasible. If not, it is infeasible. if the two distances are exactly equal, the path is said to be active. Paths are color-coded in the Design window. Infeasible paths are shown in red, active paths in green, merely feasible paths in amber. Active paths give rise to creases in the base. They divide the paper up into a network of polygons, each of which can be filled in with a pattern of creases known as a molecule. The network of polygons and molecules gives rise to the full crease pattern.
Bases are built in two stages. First, you optimize, which places the nodes within the square and identifies the active paths of the crease pattern that form a network of polygons. This explicitly defines the overall structure of the base and actually implicitly defines the entire crease pattern. Once you have found a configuration of nodes for which (a) all paths are feasible, (b) every node in the interior of the paper is pinned, the crease pattern can be constructed in a second stage.
We'll do this second stage now. Go to the Action menu and select Action->Build Crease Pattern. You will see a bunch of new lines and polygons appear, as shown in Figure Tu-1-9.
Figure Tu-1-9.
That's it: we have now computed the full crease pattern, although it's not completely obvious from the Design window. In fact, you are seeing several different sets of information overlaid on one another. The tree (shades of blue) displays the abstract structure of the tree. The yellow polygons display the underlying structure of the crease pattern. The crease lines display the creases themselves. In this view, the creases are colored according to their structural role in the base, rather than by their fold direction. This color scheme is called AGRH coloring.
Because the creases are overlaid on top of everything else, the display gets rather busy when all of the creases are present. You can choose to display just the creases by choosing the View->Creases View command, getting the result shown in Figure Tu-1-10. This turns off the display of everything but creases, and also uses a different color scheme for the creases, called MVF coloring.
Figure Tu-1-10.
MVF coloring is closer to the color scheme you might be familiar with from published origami patterns. In this scheme, creases are colored not according to their structural role, but according to their fold direction:
You might wonder why I don't use dashed and chain lines for valley and mountain folds, since they are standard origami usage for step-by-step folding sequences. The reason is that in large complex crease patterns, the traditional line patterns are difficult to distinguish, and it is more illuminating to use both color and pattern to distinguish mountain and valley folds.
Finally, we have the crease pattern for the base --- the thing we were looking for all along. There are two ways to get the crease pattern from the screen onto a piece of paper. First, you can simply print it using the File->Print command and fold up the printout. You can also choose View->Plan View, which displays the crease pattern along with the coordinates of key vertices. You can print this out and use the coordinates to plot vertices on another sheet of paper to fold it by hand, or use a program like ReferenceFinder to find folding sequences for the key reference points.
That's all for this example. You have learned the basics of TreeMaker: how to define a stick figure using the point-and-click interface and how to construct a basic crease pattern. In the next example, you'll learn how to modify the stick figure to alter proportions, how to incorporate symmetry, and how to customize the screen and printed image.
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