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• Beam• Boundary

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

Beam Model – the Math

Beam Model – the Math

• Geometric Compatibility Conditions

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

Beam Model – the Math

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

Beam Model – the Code

• OpenGL– primitives

• triangles shapes• normals lighting

– NeHe credit• responsible for rendering window• nehe.gamedev.net

Beam Model – the Code

• OO programming with C++– Dev-C++

• development environment

– A majority of the classes (objects) • Point• Slice• Beam• Dataset• Model

Beam Model – the Pictures

Beam Model – the Pictures

Beam Model – the Pictures

Beam Model – the Pictures

Beam Model - Vizualization

• 8-29-2006

• 10-27-2006

• Pi

• 2 Pi

Further Investigations

• Joint-Leg-Beam – Extension to triangle and truss

• Energy considerations– Visualizing surface temperature– Visualizing structure destruction

• Other graphical output

Thanks

• Visualization and Digital Imaging Laboratory

• Dr. Zhuangyi Liu

• Dr. Steven Trogdon

• Hans Anderson

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