Transcript Leaf surface modelling (or: what I’ve been doing for the

Virtual Plants and
Leaf surface modelling
Birgit Loch
Department of Mathematics and Computing
[email protected]
Overview
• Motivation
– what are virtual plants?
– L-systems – the basics
– examples
• Leaf models
– in the past, and why a new approach was needed
– the process
– application example
• Future work
Motivation – what are virtual plants?
Virtual plants
• capture topological and geometrical information
• simulate structural dynamics
• simulate interaction with environment
• are tools for plant scientists and teachers in
developmental biology, agronomy, pest
management…
L-Systems – the basics
[Modular]
Examples
• L-Studio [pretty_franj] [ButterflySwarm]
[TreeEcosystem] [caterpillar]
(Jim Hanan, Michael Renton)
Locations of Virtual Lab users, from: algorithmicbotany.org
Virtual leaves
• are components of plant models
Leaf surface models
• Simulation of light interception in a canopy to
estimate how much light is captured by a leaf,
effects of shading on photosynthetic activity
• Generation of visually pleasing, realistic models
of leaves as part of larger plant models
Functional leaf models
From Lang, 1973 (top) and Sinoquet et al.1998 (bottom)
Visual leaf models
Lintermann and Deussen 1999
Bloomenthal 1985
Mündermann et al. 2003
L-Studio
Here, the visual aspect is considered; the
generated models may be extended and
used to model functionality.
Why a new approach was needed
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Accuracy / based on data
Level of detail
Realism
Mathematical description of surface
Applications such as droplet running along
surface
The process
• digitising
• surface fitting and visualisation
• (the boundary)
Digitising
Laser scanner
Sonic digitiser
Issues: reflective properties, movement, wind,
magnetic interference, daylight, wilting, …
Examples:
Frangipani
Flame tree
Surface fitting
Scattered data interpolation problem:
Given n scattered data point triples ( xi, yi, zi), i  1..n,
find an interpolant f : R^ 2  R satisfying
f ( xi, yi )  zi.
n may be small (sonic digitiser) or large (laser
scanner)
• One function over the whole domain or
several functions?
• FEM: triangulation
nodes
polynomials
• Need to find a function on each triangle
• Simple finite element: linear triangle (3 nodes)
• Result: piecewise linear surface
• If we want C1 continuity we need at least 21
nodes (quintic triangle)
• Or: split triangle into subtriangles, find
piecewise cubic on each triangle and make
sure transitions between subtriangles and
complete triangles are C1
• For example the Clough-Tocher triangle
only needs 12 pieces of information
• The linear triangle (PLM) and the CT
triangle (CTM)
I had the luxury of using a laser scanner –
Is it possible to suggest which points to
digitise with a sonic digitiser?
Are all these points needed? –
Is it possible to reduce without giving up too
much accuracy to the data?
An adaptive approach:
1. Begin with an initial set of data points, for
example some points along the boundary
2. Fit the surface to these points. Calculate how
well the remaining points have been
approximated. Have we reached some error
tolerance limit? If yes then stop.
3. Add one of the remaining points to the set of
interpolated points
4. Go to 2
But which point should be added?
It turns out that the maximum error point is a good
choice, although a better choice may exist.
Accuracy is measured in terms of a maximum
error associated with a fit relative to the
maximum variation in z pointwise
Visualisation
5% PLM 55 pts
1% PLM 323 pts
5% CTM 62 pts
1% CTM 327 pts
5% PLM 55 pts
5% CTM 62 pts
1% PLM 323 pts
1% CTM 327
5% PLM 55 pts
5% CTM 62 pts
1% PLM 323 pts
1% CTM 327 pts
All 10473 pts
5% PLM 127 pts
5% CTM 142 pts
1% PLM 587 pts
1% CTM 607
All 5706 points
So what do we tell the plant scientist with the
sonic digitiser?
• Collect points along major veins
• Collect points along the boundary, particularly if
there is great variation along the edge
• Collect points from peaks and valleys and areas
of high curvature
• Spread remaining points evenly
Visualisation (the boundary)
• GRAPHITE2003 Proceedings p.261-262
Application example
Droplet running along a leaf surface
e.g. to simulate spreading of pathogens
(agents that cause disease) by a droplet, or the
distribution of a pesticide on the leaf surface
Simplified conditions:
• Piecewise linear surface
• negative gradient direction
• The droplet falls off the leaf at the boundary
• The velocity of the droplet is zero as it
crosses from one element to the next
Future work
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integrate in plant models
average models
curled leaves
dynamic model
compare shading results for my models to those
for less detailed models
• functionality
• damage, interaction with environment
• more realistic droplet movement
More information
• Prusinkiewicz and Lindenmayer. (1990) “The
Algorithmic Beauty of Plants”. (“The Bible” in
PAI)
• www.cpai.uq.edu.au (Collaboration for Plant
Architecture Informatics) –
Training course later this year!
• pais.cirad.fr
(Plant Architecture Information
Systems Network)
• algorithmicbotany.org (University of Calgary)
• Phd scholarship for mathematical and computational
methods for modelling the control of plant
development and function
www.uq.edu.au/grad-school/?page=30884
• ACCS Winter School 4-8 July, session and tutorial
on L-systems
www.accs.edu.au/index/winterschool
Magic leaf