CS 563 Advanced Topics in Computer Graphics Rendering

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 1 st generation S = F-F++F-F 2 nd generation S = F-F++F-F-F-F++F-F-F++F-F Examples from [Przem 90]

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. [Deussen 98]

Positioning Improvements: § Clustering using Hopkins Index § Environmental factors mimicked by Hopkins: § Favorable growth areas § Seed propagation (seeds fall close to parents) § Other mechanisms [Brendan 02]

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: [Deussen 98]

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 [Brendan 02]

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 [Brendan 02]

Plant Structures Components of Plants Models: § Primitives § Parameters § Special Cases § Ideas Based on [WEBER 95]

Plant Primitives: § Stems § Curves § Length § Splits § Leaves § Orientation § Color § Shape [weber 02] § Each Stem has a unique coordinate system

Plant Parameters Additional Parameters: § Taper § Split Angle § Radius [weber 02]

Special Parameters Special Tree Parameters: § Pruning § Wind Sway § Vertical Attraction § Leaf Orientation [weber 02]

Tree Structure Results [Weber 95]

Tree Structure Results [Weber 95]

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 [Bara 97]

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. Where 1, 2 = uniform random numbers [0, 1] [Bara 97, Bara 98]

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 Where 1, 2 = uniform random numbers [0, 1] [Bara 97, Bara 98]

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 Where: § = uniform random number [0, 1] §Ag = global absorption coefficient § = angle between ray direction & normal [Bara 97]

Conclusion of Simplified ABM § Color mapping of CIE XYZ -> SMPTE § Comparison from Measured Sample and ABM model spectra [Bara 97]

Resultant ABM Images [Glad 98]

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 [Jacq 01]

N-Flux Models § Based on Kubelka-Munk theory of reflectance § Io = incident light intensity § Applied to a Single slab of diffuse and absorbing material [Jacq 01]

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[weber 95] and Povray (Demo Software) http: //members. chello. nl/~l. vandenheuvel 2/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 22 nd 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 Graphi. Con'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. 8 th 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