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Geometric modeling of plants

• "Billboard" texture maps
  • commonly used for years in the Visual Simulation field, a picture of the plant is applied to either 1 or 2 flat polygons
  • the most common case is a 2-polygon "X" configuration (4 triangles)
  • alternately, you can use a single square polygon (2 triangles) and use code to make it turn toward the viewpoint
    • for a technical explanation, see Billboards from SGI's Programming with OpenGL: Advanced Rendering
  • a shadow on the ground under a tree helps a lot in "grounding" it - making it appear to actually be on the ground, not floating above it
    • shadow can be implemented as a black polygon with alpha = 0.5
    • for more realistic shadows, see Creating Shadows (SGI again)
  • creating or acquiring high-quality plant textures can be difficult
• Directional billboards
  • the idea is to use the simple geometry of a billboard, but switch between one of several possible texture maps depending on the direction of view
  • the images can be photographic, pre-rendered, or dynamically created on the fly from a full polygonal model
  • this only works if the plant will not be viewed close up, from above, or below
  • 3D Pipeline TreeFX [http://www.3dpipelinesim.com/tree_fx.html seems to be gone as of late 2005]
    • real-time engine bundled with a library of trees and ground cover
    • claims "fully 3-dimensional branches" - which is actually a fuzzy blend between a set of directional billboard images
    • apparently intended to license to game/vis-sim developers, and required a high-end card for the time (GeForce 2 Ultra)
• Billboards with Normal Maps
  • the tutorial lighting_flat_objects by Olivier Renouard discussed how to use Maya with custom plugins to pre-compute the normals for each texel of a billboard, allowing for dynamic lighting without the polygon count
• Slices
  • Image-Based Vegetation Rendering
    • demo and academic paper by Aleks Jakulin, University of Ljubljana, Slovenia
    • paper: Interactive Vegetation Rendering with Slicing and Blending (pdf), Eurographics 2000
  • going beyond a single billboard polygon, the "fuzzy" parts of the tree are rendered a series of "slices" which are stationary billboards, each containing part of the foliage to provide parallax
  • this still only works if the plant will not be viewed close up, from above, or below
• Hand-modeled plants
  • an intermediate state between a 1-2 polygon billboard and the fully geometry of a plant
  • requires a 3D artist to create each tree individually
  • usually a tree will have a tubular trunk (e.g. 5-6 sides) and each branch will composed of very few polygons, often one billboard for a whole branch
  • currently popular with MMORPGs (massively multiplayer online role-playing games)
• Motivation for using a procedural geometric generation algorithm
  • leverage an large amount of research in the area.
  • provide realistic polygonal models based on real plant data.
  • use stochastic models to provide variety among different instances of the same plant species.
• Przemyslaw Prusinkiewicz (Dr. P)
  • the most well-known researcher in plant generation research
  • Dr. P belongs to the Biological Modeling and Visualization department at the University of Calgary
• L-systems
  • developed by Aristid Lindenmayer in the late 1960's
  • L-systems are rule-based productions based on Chomsky string replacing grammars where the productions are are applied in parallel. The grammar used in L-systems are typically interpreted as Turtle Graphics commands. The resulting images are fractal-like expanding on the concept that simple rules when recursively applied can create complex structures (ala Chaos/Complexity theory).
  • systematically extended to provide greater flexibility and more accurate plant models.
    • Context-free vs. Context-sensitive L-systems to model signals in plants and handle more sophisticated branching structures.)
    • Open L-systems to model external forces (light, gravity, resources, etc.).
    • Stochastic L-systems to model different instances of a plant species by allowing controllably random application of productions.
    • dL-systems are used to model growth through application of PODE's (partial ordinary differential equations) to productions.
    • Spiral Phyllotaxis is used to model complex plant organs such as as seeds and flower petals that correspond to a regular arrangement of lateral organization (related to the packing problem). Examples: Sunflowers - Roses - Tulips.
  • the challenge is finding L-systems that correspond to higher plants
    • this is known as the inference problem
• Voxels
  • there has even been one experiment in using an L-system in voxel space to model plants.
• Higher-level Procedural Systems
  • many plant software tools e.g.. Xfrog
  • see other systems such as Texture-Lobes on Plant Papers

• Plants in Games
  • as of 2005, despite the availability of sophisticated plant rendering engines such as SpeedTree, nearly all realtime games were still using either billboards or hand-modelled plants
  • as of 2006, SpeedTree has numerous licensees in the commercial game world, although there is still nothing usable in the open software field besides classic billboards and hand-modelled plants
• Plant LOD
  • important since they can be polygon heavy when close, yet are well approximated by very simple primitives from a distance.
  • possible distance grouping: assuming a 1024-pixel-width window and a 90° FOV, for a tree that is 10m tall:

    distance (m)	screen size (pixels)	how to draw	# of tris
    5 - 40	1024 - 128	full geometry	up to 6000
    40 - 100	128 - 50	geometry for trunk, 1-poly texture branches	up to 400
    100 - 1km	50 - 5	1-2 poly texture billboard	2 or 4
    1km - 5km	5 - 1	line, if possible	0
    > 5km	< 1 pixel	don't draw, part of texture map	0

  • what poly count does this lead to in a real-world case?
    • assume trees at a ground spacing of 25m apart = .0016 trees/m²
    • full geometry for 40² m² = 1600 m² = average of 2.5 trees
    • trunk geometry for for 100²-40² m² = 8400 m² = average of 13.4 trees
    • single poly for 1000²-100² m² = 990000 m² = average of 1584 trees
    • total = (2.5 * 6000) + (13.4 * 400) + (1584 * 2) = 15000 + 5360 + 3168 = 23528
• Hugo Elias describes a simpler approach to tree modelling
• Grass
  • grass does not lend itself to the same kind of spatial representation as larger plants, since it does not grow so much as individual specimens, but instead as a "coverage" of an area
  • GrassTest by Don Williamson [no longer online as of 2008]
    • a DX-based elastic grass demo, with source code
    • "a spring-mass system running through a verlet integrator"
  • NVIDIA Grass Technical Demo
    • "demonstrates an extremely fast and accurate way to display realtime 3D grass" using a GeForce256 and DX7
    • it looks very fake
  • Frank Perbet - animating prairies in real-time