Origami, Kirigami, and the Modeling of Leaves: An Interactive Computer Application

Sahar Jazebi


This thesis describes an interactive computer program, called "KiriSim", which allows manipulation of a virtual paper for modeling purposes. KiriSim is primarily designed and developed for modeling leaf shapes by folding and cutting a simulated sheet of paper. In many plants, leaves grow folded inside the bud, where the final shape of the leaf is affected by the way it is folded within the bud. Inspired by this observation, the final shape of the leaf can be modeled by folding a sheet of paper properly, and cutting it along a curve delimiting the leaf's margin. Consequently, KiriSim is used to explore the strong points and shortcomings of modeling leaf shapes with kirigami (the art of making models with folding and cutting paper). Aside from its application for modeling leaf shapes, KiriSim can be used to simulate and visualize some origami and kirigami models by manipulating a virtual paper, such as origami frogs and butterflies.

In addition to developing KiriSim to manipulate a virtual paper for modeling, an object-space technique rooted in computational geometry for rendering coplanar overlapping polygons in computer graphics applications is proposed and implemented. This method is employed for visualizing paper models, consisting of coplanar overlapping faces, since existing rendering methods that rely on depth buffer values fail to render these coplanar primitives properly.


Sahar Jazebi. Origami, Kirigami, and the Modeling of Leaves: An Interactive Computer Application. M.Sc. thesis, University of Calgary, June 2012.

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