CS 563 Advanced Topics in Computer Graphics Rendering Plants

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CS 563 Advanced Topics in Computer
GraphicsRendering Plants

• by Cliff Lindsay

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Overview

• Eco Systems LOD 3 (high level)
• Plant Structures LOD 2 (medium level)
• Plant, Light Interaction LOD 1 (close up)

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Prerequisites

• L-Systems
• Terminology
• PDF Probability Density Function
• Self-thinning plant mortality due to
  competition

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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-FF-F
• 1st generation S F-FF-F
• 2nd generation S F-FF-F-F-FF-FF-F-FF-F

Examples from Przem90
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Plant Distributions in Eco Systems

• Positioning
• L systems
• Self-thinning Curve
• Multi-species Competitive Models

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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
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Positioning

• Positioning Improvements
• Clustering using Hopkins Index
• Environmental factors mimicked by Hopkins
• Favorable growth areas
• Seed propagation (seeds fall close to parents)
• Other mechanisms

Brendan02
Brendan02
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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

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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
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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

Brendan02
Brendan02
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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

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Multi-Species Result
Step 1
Step 2
Step 3
Step 4
Brendan02
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Plant Structures

• Components of Plants Models
• Primitives
• Parameters
• Special Cases
• Ideas Based on WEBER95

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Plant Primitives

• Primitives
• Stems
• Curves
• Length
• Splits
• Leaves
• Orientation
• Color
• Shape
• Each Stem has a unique coordinate system

weber02
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Plant Parameters

• Additional Parameters
• Taper
• Split Angle
• Radius

weber02
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Special Parameters

• Special Tree Parameters
• Pruning
• Wind Sway
• Vertical Attraction
• Leaf Orientation

weber02
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Tree Structure Results
Weber95
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Tree Structure Results
Weber95
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Treal Tree Render Demo

• Go To Treal Demo (2-3 minutes)

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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

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What Does ABM Do?

• Computes Light interaction
• Surface Reflectance
• Subsurface Reflectance
• Transmittance
• Absorption
• Incorporates Biological Factors into theses
  computations

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Scattering Probability Functions

• Leaf Model

rays in up direction
rays in down direction
Interface 1
epidermis
mesophyll
2
air
3
epidermis
4
Picture Recreated from Bara97
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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.

Bara97,Bara98
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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

Bara97,Bara98
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Absorption

• Beers 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

• Where
• ? uniform random number ? 0,1
• Ag global absorption coefficient
• ? angle between ray direction normal

Bara97
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Conclusion of Simplified ABM

• Color mapping of CIE XYZ -gt SMPTE
• Comparison from Measured Sample and ABM model
  spectra

Bara97
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Resultant ABM Images
Glad98
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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
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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
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Insights, Future, and Cool Stuff

• Virtual Terrain Project http//www.vterrain.org/Pl
  ants/index.html
• More Research Needed for specific BRDFs of plants
• Treal Tree Render using Jason Weber and Joseph
  Penns tree modelsweber95 and Povray (Demo
  Software) http//members.chello.nl/l.vandenheuvel
  2/Treal/

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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)141150, 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