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Joint-Leg-Beam Viz

Joint-Leg-Beam Viz. Andrew Larson Mathematics. Context. Trusses Bridges Cranes Houses. Context. Rigidizable Structures http://exploration.nasa.gov/programs/station/RIGEX.html What are they? Space Applications Trusses Antennas Satellites. Context. Ground work Model Joint Leg

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Joint-Leg-Beam Viz

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  1. Joint-Leg-Beam Viz Andrew Larson Mathematics

  2. Context • Trusses • Bridges • Cranes • Houses

  3. Context • Rigidizable Structures • http://exploration.nasa.gov/programs/station/RIGEX.html • What are they? • Space Applications • Trusses • Antennas • Satellites

  4. Context • Ground work • Model • Joint • Leg • Beam • Boundary

  5. My Motivation? • Learn OpenGL • collection of graphic primitives • used for rendering graphics • found on graphics cards and in video games • Use CS degree • Master’s Project

  6. Beam Model – the Math

  7. Beam Model – the Math • Geometric Compatibility Conditions

  8. Beam Model – the Math w1(si,t) w2(si,t) u1(si,t) u2(si,t) x(t) y(t) θ1(t) θ2(t) displacement of beam1 displacement of beam2 length of beam1 length of beam2 X coordinate of joint Y coordinate of joint angular displacement of leg1 angular displacement of leg2

  9. Beam Model – the Math

  10. Beam Model – the Code • The pieces • MatLab • solves system of equations for specified parameters and initial conditions • C++ • application core used to interface with MatLab and render in OpenGL • OpenGL • renders solution obtained from MatLab

  11. Beam Model – the Code • OpenGL • primitives • triangles  shapes • normals  lighting • NeHe credit • responsible for rendering window • nehe.gamedev.net

  12. Beam Model – the Code • OO programming with C++ • Dev-C++ • development environment • A majority of the classes (objects) • Point • Slice • Beam • Dataset • Model

  13. Beam Model – the Pictures

  14. Beam Model – the Pictures

  15. Beam Model – the Pictures

  16. Beam Model – the Pictures

  17. Beam Model - Vizualization • 8-29-2006 • 10-27-2006 • Pi • 2 Pi

  18. Further Investigations • Joint-Leg-Beam • Extension to triangle and truss • Energy considerations • Visualizing surface temperature • Visualizing structure destruction • Other graphical output

  19. Thanks • Visualization and Digital Imaging Laboratory • Dr. Zhuangyi Liu • Dr. Steven Trogdon • Hans Anderson

  20. References • Burns, J.A., Cliff, E.M., Liu, Z., & Spies, R.D. (2005). “On Coupled Transversal and Axial Motions of Two Beams with a Joint” • Burns, J.A., Cliff, E.M., Liu, Z., & Spies, R.D. (2006). “Results on Transversal and Axial Motion of a System of Two Beams Coupled to a Joint Through Two Legs” • OpenGL – NeHe • nehe.gamedev.net • www.opengl.org • Coding Resource • www.cplusplus.com • www.bloodshed.net/devcpp.html • notepad-plus.sourceforge.net

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