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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]