Overview • Motivation: The History of Origami • Motivation: The History of Origami • • Previous Research Previous Research • The Objective • The Objective Ori • • Data Structures and Operations Data Structures and Operations An Interactive Paper Folding • Implementation Issues • Implementation Issues Simulation • • Demo Demo Purdue University CS 490T • Conclusion Tim Thirion, Darin Rajan, and Jennifer Lin • Conclusion History Previous Research • • Originated in Japan several hundred years ago Originated in Japan several hundred years ago • Mathematical Research Mathematical Research • • The practice of paper folding was divided into: • The practice of paper folding was divided into: • Huzita’s Huzita’s Axioms: Provide a generic Axioms: Provide a generic • mathematical framework that describe all mathematical framework that describe all • Recreational • Recreational origam i folds. origam i folds. • Erik Demaine (MIT) Erik Demaine (MIT) – – Developed several Developed several • • Ceremonial Ceremonial • theorems related to paper folding and theorems related to paper folding and cutting. cutting. • • Protein folding in Protein folding in biochem istry. biochem istry. • • The name origami was coined in 1880 from the The name origami was coined in 1880 from the words words oru oru (to fold) and (to fold) and kami kami (paper). Previously, the (paper). Previously, the art was called art was called orikata orikata ("folded shapes"). ("folded shapes"). • • Interactive Origami Simulations Interactive Origami Simulations • Very few (is this a warning?) Very few (is this a warning?) • • Today, hobbyists and professional paper folders are • Today, hobbyists and professional paper folders are • • Only a 2D application could be found Only a 2D application could be found spread throughout the world spread throughout the world Objective Goal • • To create a system that allows the user to To create a system that allows the user to • • Starting with a square of virtual paper, the Starting with a square of virtual paper, the create simple, 3D origam i objects using an create simple, 3D origam i objects using an user interactively folds until forming a user interactively folds until forming a intuitive interface. intuitive interface. symbolic or representative object. symbolic or representative object. • • The goal is to design a system such that basic The goal is to design a system such that basic folds are immediately available and complex folds are immediately available and complex folds can be added. folds can be added. 1
Data Structures and Operations Connectivity • How do we represent an origam i • Observation: An origam i is highly Observation: An origam i is highly • How do we represent an origam i • computationally? connected. computationally? connected. • • Many different ways to do it Many different ways to do it • It has three data components: • It has three data components: • • Vertex Vertex – – A point in space A point in space • Essentially an origam i is a set of polygons • Essentially an origam i is a set of polygons • • Edge Edge – – A connection between two A connection between two vertices vertices • • Trees and lists are two ways of storing the Trees and lists are two ways of storing the polygons. polygons. • • Face Face – – A sequence of edges that form a A sequence of edges that form a closed polygon closed polygon • This is a tough decision… This is a tough decision… • • • An origam i is then approximated by a set of An origam i is then approximated by a set of faces. faces. Conceptual E xamples The Three Core Operations • • A sequence of simple bends: A sequence of simple bends: • • Make a fold line to divide a face into two. Make a fold line to divide a face into two. • • Select a vertex and use it to label all of the Select a vertex and use it to label all of the vertices as being either fixed or moving. vertices as being either fixed or moving. • • Also, vertices keep track of the edges that are Also, vertices keep track of the edges that are incident upon it. incident upon it. • Rotate interactively all of the “moving” • Rotate interactively all of the “moving” • • Edges keep track of the faces to the left and to Edges keep track of the faces to the left and to vertices about the fold line. vertices about the fold line. the right. the right. • • • • A “Winged Edge Boundary Representation” A “Winged Edge Boundary Representation” Complexity Issues Complexity Issues Complexity Issues Complexity Issues • It is difficult to determ ine if the sequence • Implementation of visual effects • It is difficult to determ ine if the sequence • Implementation of visual effects produced a fold acceptable to the rules of produced a fold acceptable to the rules of • Advanced lighting, advanced shading, and • Advanced lighting, advanced shading, and origam i: origam i: shadowing were completely dependent on shadowing were completely dependent on the origam i data structure. the origam i data structure. • It cannot self • It cannot self- - intersect. intersect. • • As the data structure changed, the As the data structure changed, the algorithm for these effects had to change algorithm for these effects had to change • It cannot be cut. • It cannot be cut. • Many are tough to find and rem edy. • Many are tough to find and rem edy. • Many other constraints… • Many other constraints… • • Because of this, the sim ulation is often easily Because of this, the sim ulation is often easily broken. broken. • • A few degenerate sequences can be A few degenerate sequences can be determ ined from the input sequence and state determ ined from the input sequence and state • • Undo and Redo help tremendously when this Undo and Redo help tremendously when this of the data structures. of the data structures. occurs. occurs. 2
Demo Conclusion • Research in origami is geared toward producing mathematical theorems, not interactive simulations. • For our system, simple folds are easy; sequences of simple folds are difficult. • Trying to catch degenerate cases is difficult. • Debugging involves tracing through the entire structure and discerning the unique circumstances that caused the crash. Questions, Comments, Rotten Fruit? • tthirion@purdue.edu • rajand@purdue.edu • linjs@purdue.edu 3
Recommend
More recommend