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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 FunctionSelf-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-F1st generation S = F-F++F-F2nd 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
jiji
xii
pp
pxH
)(min
)(min
[Brendan02][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
),1(?),({ 11 ErxTAxiom
),1(?),( 22 ErxT
,
0:)(?),(.1 ccErxT
),(:),(.2 RxTRrrxT
)),(,()(?),(.3 trgrowrxTcErxT
)}1(?),( ErxT nn
[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
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
Each Stem has a unique coordinate system
[weber02]
Special Parameters
Special Tree Parameters: Pruning Wind Sway Vertical Attraction Leaf Orientation
[weber02]
Light Interaction with Plant Tissue Models
ABM – Our Focus Plate models N-Flux Models
Terminology:SPF – Scattering Probability FunctionABM – Algorithmic BDF ModelBDF – AKA: BSSDF, Bidirectional Surface-scatering
Distribution FunctionOblate – 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
Scattering Probability Functions
Leaf Model
Interface: 1
2
3
4
epidermis
mesophyll
air
epidermis
rays in down direction
rays in up direction
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.
)2 ],)1(arccos[(),( 21ob
1
1 eeWhere 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
)2 ),(arccos(),( 21 mm
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
)cos()ln(1 gA
p
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]
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
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