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 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

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

Each Stem has a unique coordinate system

[weber02]

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 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]

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

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