1. L-System Tree Hugger Project Bauhaus University Weimar
Hasibullah Sahibzada 25-Nov-2013
2. Agenda L-System algorithm and its variations Axial Tree
Brief on Related works ( plastic trees) Brief on Plastic trees
3. L-System Lindenmayer systems (L-systems) createdAristid
Lyndenmeyerhttp://www.avatar.com.au/courses/Lsystems/References.html#ref004Developmental
systems were introduced (Lindenmayer, 1968, 1971) in order to model
morphogenetic (pattern-generating) processes in growing,
multicellular, filamentous organisms. The emphasis was on plant
topology , on the spatial relations between cells or larger plant
modules. To model multicellular plant growth. They did not include
enough detail to allow for comprehensive modeling of higher
plants.-- original work
4. L System Theory L-Systems are mathematical models to
describe the development of plants in a visually convincing way.
This method is preferable to 3D geometry modelling as it requires
much less human interaction and often produces more convincing
results in modeling the small, next to unnoticed details that a
human often would not bother to model. Central Concept of L-System
is that of Re-writing. Rewriting is a technique for defining
complex objects by successively replacing Snowflaks parts of a
simple initial object using a set of rewriting rules or
productions. Classical Example from Von Koch snowflake1: One begins
with two shapes, an initiator and a generator. 2: The latter is an
oriented broken line made up of N equal sides of length r. 3: Thus
each stage of the construction begins with a broken line and
consists in replacing each straight interval with a copy of the
generator, reduced and displaced so as to have the same end points
as those of the interval being replaced. B. B. Mandelbrot. The
fractal geometry of nature. W. H. Freeman, San Francisco,
1982.
5. Re-writing Many Examples are done based on rewriting
technique.1: Rewriting systems on graphs 2: Rewriting systems on
rectangular arrays and matrices ( Cellular automata) 3: Rewriting
systems on character strings History Begin 19th century: Thue
provided first formal definition of a string rewriting system (srw)
1960: Backus and Naur used rewriting notation in the definition of
programming language ALGOL 1968 the biologist A. Lindenmayer
introduced L-Systems to model multicellular plant growth S.
Ginsburg and H. G. Rice. Two families of languages related to
ALGOL. J. ACM, 9(3):350371, 1962.
6. L-System (DOL) Simplest class of L-systems, those which are
deterministic and context-free, called DOL- systems.Development of
a filament of the bacteria Anabaena catenula 1: The symbols a and b
represent cytological states of the cells 2: The subscripts l and r
indicate cell polarity, specifying the positions in which daughter
cells of type a and b will be produced. L-system describes
development startsAxiom(distinguished string) ar p1:aralbr
p2:alblar p3:brar p4:blal Under a microscope, the filaments appear
as a sequence of cylinders of various lengths, with a-type cells
longer than btype cells.Graphical modeling using L-systems
7. Turtle interpretation 1: A state of the turtle is defined as
a triplet (x, y, ) 2: the Cartesian coordinates (x, y) represent
the turtles position, and the angle , called the heading, is
interpreted as the between lines) Gets more complicated ( space
direction in which the turtle is facing. 3: Given the step size d
and the angle increment , the turtle can respond commands
represented by the following symbols Approximations of the
quadratic Koch island taken from Mandelbrots book [95, page
51].
8. Video http://www.youtube.com/watch?v=fq9kx0hjx-UTurtle
Examplehttp://www.youtube.com/watch?v=xTepbIRGn6oDOL Example
9. Axial Trees A rooted tree has edges that are labeled and
directed.An axial tree is a special type of rooted tree 1: At each
of its nodes, it has most one outgoing straight segment. 2: All
remaining edges are called lateral or side segments. 3: A sequence
of segments is called an axis, if:Sub-treea: the first segment in
the sequence originates at the root of the tree or as a lateral
segment at some node, b: each subsequent segment is a straight
segment. c: the last segment is not followedby any straight segment
in the tree.Sample tree generated using a method based on Horton
Strahler analysis of branching patterns
10. L System Model (Ijiri_wiss2005)Sketching L-System:
Interface for designing Flactal Stractures by drawing Axis
11. L-System Summary L-Systems are based on string rewriting
using production rules ( graph grammars) Turtle graphics give them
a graphical interpretationL-Systems serve as models of development
in biology, but also in other areas. Small changes of rules have
often surprisingly large impact. Axial trees are important
branching structures in nature (rivers, botanical trees,
12. Related Work Early Plant Models growthProcedural
approachEarly models of plants were based on procedural approaches
that replicated growth byrepetitive application of a small set of
rules to an initial structure to yield very complex
results.Captured Internal properties of treesbranching anglebranch
length
13. Procedural Approach The forms of nature based on spirals
and ramification are generated not through the use of object data
calculated by measurement, but through the use of an algorithmic
structure based on the laws of nature. Explained Processes of
recreating some forms of nature, including shells, horns, tusks,
claws, and spiral plants.KAWAGUCHI, Y. 1982. A morphological study
of the form of nature. In SIGGRAPH 82: Proceedings of the 9th
annual conference on Computer graphics and interactive techniques,
ACM Press, New York, NY, USA, 223232.3-D Shapes Spiral Shells
Spiral Growth into Tendrils HornMouth of shell Young plant
14. Procedural Approach The whole form of actual
trees,therefore, was speculated to be affected also by their
branching angle and relative ratio of their branch lengths HONDA,
H. 1971. Journal of Theoretical Biology 31, 331338.Problemviews of
trees or their crown1: Pattern-recognition. How Define a specie
from the various forms (same crown ) 2: Morphogenesis. ( Gens
specify the form of tree)Described erect trees as repeated
branching structures. The whole form of actual trees seems to be
determined by a great many factors, (branching angles and relative
ratios of branch lengths)
15. Textures The present work seeks to model trees with
sufficient realism that they may be the subject of animation,
rather than simple elements of the landscape. The model should have
a well-defined structure; beneath the bark the limb should be
smooth: leaves should be properly attached to twigs. Several spline
segments interpolate the data points (asterisks) with C2
continuity. A strobe captures a disk as it passes along the
curve.SurfacesOrder of creation of limbs (red, then orange, yellow,
green, blue, and white)BLOOMENTHAL, J. 1985. Modeling the mighty
maple. SIG- GRAPH Computer Graphics 19, 3, 305311.
16. Textures Resolution Issues A tree tends to maximize its
surface area to volume ratio. If the viewpoint is close to a limb,
a large number of limbs will be off-screen. Thus, a method is
desired for polygonizing limbs that varies the axial and
circumferential(enclosing boundry) resolutions according to the
projection of the limb onto the screen and that culls off-screen
limb sections.Verisimilar BarkX-rayingSurface plasterMappingLeaves
by Camera Movable JointsBLOOMENTHAL, J. 1985. Modeling the mighty
maple. SIG- GRAPH Computer Graphics 19, 3, 305311.
17. Botanical Structure & Development DE REFFYE, P.,
EDELIN, C., FRANON, J., JAEGER, M., AND PUECH, C. 1988. Plant
models faithful to botanical structure and development. In
Proceedings of SIGGRAPH 88, 151158.Concern here is the faithfulness
of the models to the botanical nature of trees and plants. In the
model They Integrated Botanical Knowledge of tree architecture
Growth Mechanism to Occupy space Location of Leaves, flowers and
fruits Important ThingTime Integration Viewing the aging of a
treeDifferent Pictures Simulation of death of leaves and branches
Wind and insects
18. Botanical Structure & Dev DE REFFYE, P., EDELIN, C.,
FRANON, J., JAEGER, M., AND PUECH, C. 1988. Plant models faithful
to botanical structure and development. In Proceedings of SIGGRAPH
88, 151158.MeristemsFound in zones of a plant where growth Take
place. Functionality 1: Growth Time 2: Ramification Diversions from
small to big3: Mortality. Each Bud is given two
probabilitiesBreak/abortRamification
19. Botanical Structure & Dev DE REFFYE, P., EDELIN, C.,
FRANON, J., JAEGER, M., AND PUECH, C. 1988. Plant models faithful
to botanical structure and development. In Proceedings of SIGGRAPH
88, 151158.
20. Botanical Structure & Dev DE REFFYE, P., EDELIN, C.,
FRANON, J., JAEGER, M., AND PUECH, C. 1988. Plant models faithful
to botanical structure and development. In Proceedings of SIGGRAPH
88, 151158.Growth Simulation Bellow Parameters should be given -the
age, - the clocks or growth speeds of the axes, - the number of
possible buds at each node, as a function of order,- the
probabilities of death, pause, ramification and reiteration By
experiment Mathematical Law
21. Botanical Tree Model Dynamic Modeling Technique Dynamic
modeling and representation technique for trees that aims at
incorporating aspects of the trees genotype into our models to
allow them to react to the environment. Dependency of
modelEndogenousExogenous
22. Botanical Tree Model 1: Exogenous ( Environment )
23. Related Works B: user-assisted plant modeling 1: complex
parametric model. Weber and Penn [1995]2: introduce decomposition
graphs [Boudon et al. 2003]3: Xfrog modeling technique Lintermann
and Deussen [1999]which combines rule-based and procedural modeling
and also allows for creating animated models.Not possible for
models to dynamically react to their environment.
24. Related Works C: Image-based techniques 1:Register Input
Images to reconstruct the 3D shape While Reche-Martinez et al.
[2004]2: loosely arranged images Neubert et al. [2007]The main
branches are determined by the user and the static model is
constructed using a particle flow system and some botanic
heuristics.D: sketch-based technique1: Combination of rule-based
and image-based techniques on procedural made trees Ijiri et al.
[2006] and Zakaria and Shukri [2007]2: 2D-3DChen et al.
[2008]Bringing Set of biologically motivated branching rules to
infer the 3D structure of the tree from a given2D sketch.
25. Related Works E: Environment Modification of the
environment itself can be used as a way of controlling
theprocedural model.2: Climbing of plants that grow on support
structures and are influenced by the light density.Arvo and Kirk
[1988], Greene [1989], and later Benes and Millan [2002]F:
Computing light Method 1: Simplified, technique proposed by Rudnick
et al. [2007]. 2: Radiant energy transfer[Soler et al. 2003].
26. Plastic Trees Trees reaction in Environment changes:Studied
1: Geometrical 2: Topological1: Study the environmental
conditionsSelf Shadowing2: Natural morphological properties. 3:
Construct a procedural model .Isolated spaceBehavior of branch
Controllable by environmental parameters Morphological
parametersSelf Shadowing
27. Branch Age FactorGrowth rate of entire tree.Growth rate in
a branch The growth rate of an individual branch is determined by
how many internodes (segments without buds) a given branch produces
in one season.ButNodes Depends on resources Branch Age =>>
Internode length and growth rate Distance from a given segment to
its furthest leaf node,Threshold dt = 0.2drDistance from the root
of the tree to its furthest leaf node.Branch age Growth
rateDistance from the segment to the root of the tree Minimum
growth rate(all)Absolute growth rateLength of internodeLength of
branch segment Parent age
28. Temporal Light Conditions Simulate effect for each leaf
Leaf Cluster cast shadowShadow calculated by Shadow volume that is
attached to shadow casterpointLeaf translucencyAmount of
lightNormalization constant [0,1] == in coming lightVisibility of
hemisphere From P
29. Inverse Tropism A tropism is the tendency of the branches
to grow towards or away from some entity.Need to know Environmental
changes + different stages of tree development Influence of
tropisms on tree growth and shape. unit direction of the
tropismtropismTropism strengthTropism 1: Phototropism 2:
Gravitropism
30. Phototropism The tendency of a given branch to grow towards
the light direction. Calculated on All branches using Temporal
Light Model
31. Gravitropism Gravitropism controls bending of the branches
either away from or towards gravitySet the angle of
branchesTropismNew DirectionLinear combination of all
tropismsNormalized directionweightsweight of the original direction
of branch segmentBranch segment lenght
32. Inverse tropism To Compute the effect of tropism on a input
tree.Inverse tropismd0
33. Pruning estimation Natural pruning influences the tree
structure Apical meristematic cells in a bud produce wood or plant
organsIf no light then dieSum of Leaf node distances Resource by
their child leave cluster
34. Pruning estimationUser controllable parameter = 0.8 Local
pruning Factor 5th percentile of local pruning factortopiary
35. Dynamic Interaction After growth behavior and
pruningLearn1: Amount of changes in environment. 2: Tree response
according to the changes1: Tree Graph transformation 2: Modeling of
leaf-Clusters 3: Types of Interaction
36. Tree Graph Transformation Changes in tree growth
accordingAge, Light conditions1: binding 2: Rotation of a branch
=== > transferred to parent 3: Leaf Cluster changes ( shadow )
4: Pruning
37. Modeling a leaf cluster 1: Response to light Amount of
lighta. Branch creation, and branchlets ( Cluster Density ) b.
Branch orientation c. Number of leaves per branchInitial
densityNormalize density For leaf clusterIncoming light
38. Modeling a leaf cluster 1: Response to
ObstaclesIntersection of leaf New treeoverlapCollide and then
pruned. Hull cluster1Black = input tree color Red=binding Blue =
pruned Exception for small branches2
39. Types of Interaction As seen before interactionA:
Tree-Obstacle B: Tree-Tree A: Global LightComputation of
transformation
40. Implementation and Results Tree Modelings main focus is on
the branches rather then leaf clusterThickness Threshold
setBigRendered LOD ( Level of Detail) technique is createdThe
amount of produced geometery Cluster Size Light situation LOD stage
Depends on Camera Location too.SmallLeaf Cluster
41. Implementation and Results Main branching structure
StoredTree self similarities Branchlets ( patches)CPU Mem Mapped
GPU / VBOTexture buffer GPU
42. Results Models from 1: Xfrog 2: Open L-System 3:
LiDarPlastic Tree: 1: Representation Model 2: Interaction model 3:
Influence in tropism Limitation: 1: Prodxuction of new branches 2:
Soil change effect. 3: Influence in tropism
43. References HONDA, H. 1971. Journal of Theoretical Biology
31, 331338.Ijiri_wiss2005 Sketching L-System: Interface for
designing Flactal Stractures by drawing Axis R. E. Horton.
Hypsometric (area-altitude) analysis of Erosional topology. Bull.
Geol. Soc. America, 63:11171142, 1952. OPPENHEIMER, P. E. 1986.
Real time design and animation of fractal plants and trees.
SIGGRAPH Comput. Graph. 20, 4, 55 64. BOUDON, F., PRUSINKIEWICZ,
P., FEDERL, P., GODIN, C., AND KARWOWSKI, R. 2003. Interactive
design of bonsai tree mod- els. Computer Graphics Forum.
Proceedings of Eurographics 22, 3, 591599. DE REFFYE, P., EDELIN,
C., FRANON, J., JAEGER, M., AND PUECH, C. 1988. Plant models
faithful to botanical structure and development. In Proceedings of
SIGGRAPH 88, 151158. KAWAGUCHI, Y. 1982. A morphological study of
the form of nature. In SIGGRAPH 82: Proceedings of the 9th annual
conference on Computer graphics and interactive techniques, ACM
Press, New York, NY, USA, 223232. BLOOMENTHAL, J. 1985. Modeling
the mighty maple. SIG- GRAPH Computer Graphics 19, 3,
305311.http://www.avatar.com.au/courses/Lsystems/References.html#ref004