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

P1

P2

P3

P4

P1

P2

P3

P4

n

iini uJPuQ

0, )()(

Cross-Section Orientation: Frenet Frame

Disadvantages e2 and e3 become

undefined at point which its 2nd derivative is undefined

Worse, directions of e2 and e3 swap at point of infection

|'|

'1

t

te

|'''|

'''

|''1|

''13

tt

tt

te

tee

|'''||'|

')'''(''|'|132

2

ttt

ttttteee

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 1st 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

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Series1

Series2

Cross-Section

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

Generalised Cylinders Models

Generalised Cylinders Models

Generalised Cylinders Models

Generalised Cylinders Models

Generalised Cylinders Models

Further Works

Modelling more complex object by varying cross-section shapes

Adding texture

Conclusions

Generalised cylinders characteristicsSmooth curvatureCylindrical cross section

Turtle commandsAutomation creation of generalised

cylindersSolution to Frenet Frame problem