1 / 18

Rigid Origami Simulation

Rigid Origami Simulation. Tomohiro Tachi The University of Tokyo http://www.tsg.ne.jp/TT/. About this presentation. For details, please refer to Tomohiro Tachi, "Simulation of Rigid Origami" in Origami^4 : proceedings of 4OSME (to appear). 1. Introduction. Rigid Origami?.

msikorski
Download Presentation

Rigid Origami Simulation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Rigid Origami Simulation Tomohiro Tachi The University of Tokyo http://www.tsg.ne.jp/TT/

  2. About this presentation For details, please refer to • Tomohiro Tachi, "Simulation of Rigid Origami" in Origami^4 : proceedings of 4OSME (to appear)

  3. 1 Introduction

  4. Rigid Origami? • rigid panels + hinges • simulates 3 dimensional continuous transformation of origami • →engineering application: deployable structure, foldable structure

  5. Rigid Origami Simulator • Simulation system for origami from general crease pattern. • 3 dimensional and continuous transformation of origami • Designing origami structure from crease pattern.

  6. Software and galleries Software is available: http://www.tsg.ne.jp/TT/software/ flickr:tactom YouTube:tactom

  7. 2 Kinematics Single-vertex model Constraints Kinematics

  8. r 2 r 3 l 2 l 3 r 1 l 1 l 4 r 4 Model • Rigid origami model (rigid panel + hinge) • Origami configuration is represented by fold angles denoted as r between adjacent panels. • The configuration changes according to the mountain and valley assignment of fold lines. • The movement of panels are constrained around each vertex.

  9. r C ( ) 2 2 r C ( ) 3 3 B l 2 23 B 12 l 3 r C ( ) 1 1 l B 1 34 B 41 l 4 r C ( ) 4 4 Constraints of Single Vertex • single vertex rigid origami[Belcastro & Hull 2001] • equations represented by 3x3 rotating matrix

  10. Derivative of the equation 3x3=9 equations for each vertex F is orthogonal matrix: 3 of 9 equations are independent (6 is redundant)

  11. r 2 r 3 l 2 l 3 r 1 l 1 l 4 r 4 3 independent equations Derivative of orthogonal matrix F at F=I is skew-symmetric.Let denote direction cosine of li, then

  12. Constraints matrix constraints around vertex kis, For the entire model,

  13. Constraints of multi-vertex (general) origami single vertex: M vertex model: Iff N>rank(C), the model transforms, and the degree of freedom is N- rank(C) (If not singular, rank(C)=3M)

  14. Kinematics Constraints: When the model transforms, the equation has non-trivial solution.   represents the velocity of angle change when there are no constraints.

  15. numerical integration Euler integration >Accumulation of numeric error • Use residual of F corresponding to the global matrix elements.

  16. Euler Integration + Newton method Ideal trajectory Euler method + Newton method The solution is, Rawangle change Constrained angle change

  17. 3 System

  18. System • Input is 2D crease pattern in dxf or opx format • Real-time calculation of kinematics • Conjugate Gradient method • Runs interactively to • Local collision avoidance • penalty force avoids collision between adjacent facets • Implementation • C++, OpenGL, ATLAS • now availablehttp://www.tsg.ne.jp/TT/software/

More Related