Download L-systems

CS 563 Advanced Topics in
Computer Graphics
Rendering Plants
by Cliff Lindsay
Overview
 Eco Systems – LOD 3 (high level)
 Plant Structures – LOD 2 (medium level)
 Plant, Light Interaction – LOD 1 (close up)
Prerequisites
 L-Systems
Terminology:
PDF – Probability Density Function
Self-thinning – plant mortality due to competition
L-systems
 String rewriting mechanism that reflects
biological motivation.
L-system Components:
 Alphabet
 Axiom – start string
 Productions
 Example:
 Alphabet: {F, +, -} where “F” = move forward, “+” =
turn  degree, “-” = turn – degrees
 Axiom: F
 Production: F  F-F++F-F
1st generation S = F-F++F-F
2nd generation S = F-F++F-F-F-F++F-F++F-F-F++F-F
Examples from [Przem90]
Plant Distributions
in Eco Systems
 Positioning
 L – systems
 Self-thinning Curve
 Multi-species Competitive Models
Positioning
Initial Task Hierarchy:
 Terrain Generation
 Initial Random Placement
 Plant Ecological Characteristics (growth, reproduction rates,
terrain preferences, light tolerances, etc)
 Grow Plants Iteratively (life cycle)
 Result is a distribution of plants.
[Deussen98]
Positioning
Positioning Improvements:
 Clustering using Hopkins Index
 Environmental factors mimicked by Hopkins:
 Favorable growth areas
 Seed propagation (seeds fall close to parents)
 Other mechanisms
H
min i ( x  pi )
min i ( p j  pi )
[Brendan02]
x
j
[Brendan02]
Scene Modeling
Multi-set L-system (L-system extension):
 Allows for sets of Axioms
 Productions work on Multi-sets of Strings
 Allows for Fragmentation of plant
Why is the extension necessary?:
 Operations for multiple plants at once
 Dynamically add or remove plants (birth, death)
 Communication Between Plants and Environment
Has All The Regular Stuff Too:
 Size
 Position
 Allows for growth
Scene Modeling
 Individual Circles Represent ecological of a Plant
(previous, and next slide)
 Biologically Motivated Rules Govern Outcomes of
interaction Between Circles
 Self-thinning Curve:
[Deussen98]
Self-Thinning
 Competition:
 Among Plants of Same Age & Species
 Limited Resources (water, minerals, light)
 Larger plants dominate smaller
 We need L-system extension to include self-thinning

Axiom{T ( x1 , r1 ) ? E (1),

T ( x2 , r2 ) ? E (1),
 ,
T ( xn , rn ) ? E (1)}

1.T ( x , r ) ? E (c) : c  0  
2.T (x , r ) : r  R  T (x , R)
3.T ( x , r ) ? E (c)  T ( x , r  grow(r , t ))
[Brendan02]
[Brendan02]
Multi-species
Competitive Models
Multi-set L-system:
Additional Parameters
 Parameter For Species
Additional Productions
 Plant Domination, and Competition
 Shading due to Domination
 Reduction of Resources
Multi-Species Result
Step 1
Step 2
Step 3
Step 4
[Brendan02]
Plant Structures
Components of Plants Models:
 Primitives
 Parameters
 Special Cases
 Ideas Based on [WEBER95]
Plant Primitives
Primitives:
 Stems
 Curves
 Length
 Splits
 Leaves
 Orientation
 Color
 Shape
[weber02]
 Each Stem has a unique coordinate system
Plant Parameters
Additional Parameters:
 Taper
 Split Angle
 Radius
[weber02]
Special Parameters
Special Tree Parameters:
 Pruning
 Wind Sway
 Vertical Attraction
 Leaf Orientation
[weber02]
Tree Structure Results
[Weber95]
Tree Structure Results
[Weber95]
Treal Tree Render Demo
 Go To Treal Demo (2-3 minutes)
Light Interaction with
Plant Tissue Models
 ABM – Our Focus
 Plate models
 N-Flux Models
Terminology:
SPF – Scattering Probability Function
ABM – Algorithmic BDF Model
BDF – AKA: BSSDF, Bidirectional Surface-scatering Distribution
Function
Oblate – round or elliptical geometry that is flat at poles
What Does ABM Do?
 Computes Light interaction:




Surface Reflectance
Subsurface Reflectance
Transmittance
Absorption
 Incorporates Biological Factors into theses
computations
Leaf Model
rays in down direction
Scattering Probability
Functions
rays in up direction
Interface:
1
epidermis
mesophyll
2
air
3
epidermis
4
Picture Recreated from [Bara97]
Determine Surface
Reflectance
 e – corresponds to polar angle displacement
 e – corresponds to the Azimutal angle
displacement
 Epidermal Cells With Large oblateness make for a
reflection closer to specular distribution.
( e ,  e )  (arccos[(1  1 )
1
ob1
], 22 )
Where 1, 2 = uniform random numbers  [0, 1]
[Bara97,Bara98]
Subsurface Reflectance
and Transmittance
 m – corresponds to polar angle displacement
 m – corresponds to the Azimutal angle
displacement
 Light passing to the Mesophyll Layer becomes
randomized, thus diffuse
( m ,  m )  (arccos( 1 ), 22 )
Where 1, 2 = uniform random numbers  [0, 1]
[Bara97,Bara98]
Absorption
 Beer’s Law of absorption
 P = path length of ray through cell medium (collision
w/ cell)
 P  tm where tm = thickness of the Mesophyll cells,
ray is absorbed
1
p
ln(  ) cos( )
Ag
Where:
 = uniform random number  [0,1]
Ag = global absorption coefficient
 = angle between ray direction & normal
[Bara97]
Conclusion of Simplified
ABM
 Color mapping of CIE XYZ -> SMPTE
 Comparison from Measured Sample and ABM model
spectra
[Bara97]
Resultant ABM Images
[Glad98]
Plate Models
 Simple Slab(s) of Diffusing and Absorbing Material
 N – plates separated by N-1 air spaces
 Parameters:
 Amount of water and chlorophyll
 # of plates
[Jacq01]
N-Flux Models
 Based on Kubelka-Munk theory of reflectance
 Io = incident light intensity
 Applied to a Single slab of diffuse and absorbing
material
[Jacq01]
Insights, Future, and
Cool Stuff
 Virtual Terrain Project
http://www.vterrain.org/Plants/index.html
 More Research Needed for specific BRDFs of plants
 Treal Tree Render using Jason Weber and Joseph
Penn’s tree models[weber95] and Povray (Demo
Software)
http://members.chello.nl/~l.vandenheuvel2/Treal/
References
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Brendan Lane, Przemyslaw Prusinkiewicz Generating spatial
distributions for multilevel models of plant communities. Proceedings of
Graphics Interface 2002.
Oliver Deussen, Pat Hanrahan, Bernd Lintermann, Radomir Mech,
Matt Pharr, and Przemyslaw Prusinkiewicz. Realistic modeling and
rendering of plant ecosystems. Proceedings of SIGGRAPH 98.
Jason Weber, joeseph Penn, Creation and Rendering of Realstic Trees,
Proceedings of the 22nd annual conference on Computer graphics
and interactive techniques September 1995.
G. V.G. Baranoski, J. G. Rokne, Simplified model For Light
Interaction with Plant Tissue, Proceedings of the Eighth
International Conference on Computer Graphics and Visualization GraphiCon'98 , Moscow, Russia, September, 1998
G. V. G. Baranoski, J. G. Rokne. An algorithmic reflectance and
transmittance model for plant tissue. Computer Graphics Forum
(EUROGRAPHICS Proceedings), 16(3):141–150, September 1997.
S. Jacquemoud, S.L.Ustin (2001), Leaf optical properties: A state of the
art, in Proc. 8th Int. Symp. Physical Measurements & Signatures in Remote
Sensing, Aussois (France), 8-12 January 2001
Przemyslaw Prusinkiewicz, Aristad Lindenmayer, “The Algorithmic
Beauty of Plants”, Springer Verlag, 1990