JOAS Special issue. Folded by Mariano Zavala. Grasshopper - perched Insects. Grasshopper - walking Insects. Guy Fawkes mask People. Personal Collection. Iron Man - Armor mask Media and Culture. Tanteidan 15th convention read full review. Folded from a square of duo origami foil by Gilad Aharoni. Kraken attacking ship Imaginary beings. BOS Convention Autumn.
Folded by Travis Nolan. Leaf Katydid Insects. Origami USA Convention read full review. Folded by Fujikura Atsuo. Tanteidan 12th convention read full review. A flap is a hinged portion of paper folded into a thin limb, often in the shape of a cone or long rectangle. Unfolded, an origami flap takes up an approximately circular portion of paper, where the tip of the flap is the center of the circle, and the length of the flap is the same as the radius.
If the tip of the flap is on the edge or a corner of the paper, then the paper making up the flap only corresponds to the part of the circle that lands on the paper.
A corner flap is mad out of a quarter circle of paper while a center flap is made of a full circle. To design an origami base that can be folded into a particular figurine, the flaps of the model must be arranged on the the paper to be folded in a way that matches with the geometry. The adjacent limbs and features on the final model that correspond to different flaps need to have their circles be adjacent. So a head and two legs may be three different circles, two longer and one shorter that are all touching on the paper.
Parts of the model that would not be limbs on a stick figure, such as the torso, must separate the circles on the paper. So there must be a distance of at least the length of the torso between, say, the rear and front pairs of legs.
These portions of the model are called rivers and are the second piece in circle-river packing. Here is the circle-river packing diagram as seen on the crease pattern for a very complicated figurine lucanus cervus by brian chan. One of our goals is to build origami models that have the most efficient paper usage, or the largest flap-size to paper size ratio.
Since center flaps use four times the amount of paper that corner flaps use edge flaps use twice the amount that corner flaps use , an important result is that most of the flaps should be centered on the edges or corners of the paper where possible. This problem is called the scale optimization problem, and is one of several nonlinear constrained optimizations involved in origami design.
It is the only one that this problem solves. It is a set of i nodes , and edges E. A node of the graph can be a leaf node or a branch node , where leaf nodes are only connected to one edge and branch nodes are connected to multiple.
The graph has a mapping to the paper and the coordinate system associated with it. After the mapping the nodes have a one to one relationship to a set of vertices U , where each vector vertex u i has coordinate variables u i,x and u i,y. U t is the set of leaf vertices which correspond to leaf nodes. A path p ij is a sequence of edges which connect two nodes i and j. Define P to be the set of all paths, and P t to be the set of all leaf paths , or paths that connect two leaf nodes.
Each path has a length l ij , given by the sum of the strained lengths of the edges in the path. The scale optimization problem is the optimzation of the positition of all leaf vertices and the overall scale. It is a nonlinear constrained optimization problem, with these constraints:. The separation between any two vertices on the square must be at least as large as the scaled length of the path between their corresponding two nodes as measured along the tree.
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