Organic Modeling Using Generalised Cylinders Nina Halim Supervisor: Dr. Jon McCormack

Outline Generalised Cylinders Parametric curves Cross-Section Orientation Frenet Frame Turtle movement Scaling Generalised Cylinders Models Results Conclusion References

Why Modeling Organic Using Generalised Cylinder?? Different modelling methods, different characteristics Solid Construction Blobby Surface Generalised Cylinders ‘The bodies of multicellular plats and animals are cylindrical in shape’ [Wainwright 1988]

Generalised Cylinders Trajectory: arbitrary 3 dimensional parametric curve Cross-Section: arbitrary 2 dimensional parametric curve Automation: Turtle commands

Parametric Curves Many types of parametric curve, eg. Hermite, Bezier, Splines etc. Bezier Interpolates two end points and approximates two control points P1P1 P2P2 P3P3 P4P4 P1P1 P2P2 P3P3 P4P4

Cross-Section Orientation: Frenet Frame Disadvantages e2 and e3 become undefined at point which its 2 nd derivative is undefined Worse, directions of e2 and e3 swap at point of infection

Turtle State, Movements and Commands State A point represents turtle’s position Three vectors represents its heading, left and up directions Movement and Commands ‘F’ to move forward heading direction ‘+’ to turn left ‘-’ to turn right ‘&’ to pitch down ‘^’ to pitch up ‘/’ to roll left ‘\’ to roll right

More Turtle Commands Parameterize Command F(3.2) +(45) F F ^(30) & F(1.8) Curve generation commands ‘Ts’ to start curve and add 1 st control points ‘Tp’ to add more control point ‘Te’ to add last control point ‘Gs(param)’ to scale cross-section by param unit etc.

Frenet Frame and Turtle State

Cross-Section Orientation: Turtle Movement Turtle Orientation Frenet Frame Orientation

Cross-Section Orientation: Turtle Movement Turtle Orientation Frenet Frame Orientation

Scaling Cross-Section Without scaling With scaling

Scaling Cross-Section Linear Interpolation

Scaling Cross-Section Parametric curve

Scaling Cross Section

Cross-Section Open Cross-Section: swept surface Closed Cross-Section: solid object

Generalised Cylinders Models

Further Works Modelling more complex object by varying cross-section shapes Adding texture

Conclusions Generalised cylinders characteristics Smooth curvature Cylindrical cross section Turtle commands Automation creation of generalised cylinders Solution to Frenet Frame problem