organic modeling using generalised cylinders nina halim supervisor: dr. jon mccormack
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![Page 1: Organic Modeling Using Generalised Cylinders Nina Halim Supervisor: Dr. Jon McCormack](https://reader035.vdocuments.site/reader035/viewer/2022062714/56649d3f5503460f94a190bc/html5/thumbnails/1.jpg)
Organic Modeling Using Generalised Cylinders
Nina Halim
Supervisor: Dr. Jon McCormack
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Outline
Generalised Cylinders Parametric curves
Cross-Section Orientation Frenet Frame Turtle movement
Scaling Generalised Cylinders Models
Results Conclusion References
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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]
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Generalised Cylinders
Trajectory: arbitrary 3 dimensional parametric curve
Cross-Section: arbitrary 2 dimensional parametric curve
Automation: Turtle commands
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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, )()(
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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
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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
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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.
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Frenet Frame and Turtle State
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Cross-Section Orientation: Turtle Movement Turtle Orientation
Frenet Frame Orientation
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Cross-Section Orientation: Turtle Movement Turtle Orientation
Frenet Frame Orientation
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Scaling Cross-Section
Without scaling
With scaling
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Scaling Cross-Section
Linear Interpolation
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Scaling Cross-Section
Parametric curve
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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
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Cross-Section
Open Cross-Section: swept surface Closed Cross-Section: solid object
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Generalised Cylinders Models
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Generalised Cylinders Models
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Generalised Cylinders Models
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Generalised Cylinders Models
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Generalised Cylinders Models
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Further Works
Modelling more complex object by varying cross-section shapes
Adding texture
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Conclusions
Generalised cylinders characteristicsSmooth curvatureCylindrical cross section
Turtle commandsAutomation creation of generalised
cylindersSolution to Frenet Frame problem