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and Lindenmayer, 1990). Related to this is are
p-graphs (prototype graphs) (Lintermann and
Deussen, 1999). The nodes of these directed graphs
reflect the relationship between plant components,
but additionally have attributes encoding shape
parameters.
Such abstract, bottom up approaches can model
the natural growing process, but are non-intuitive and
difficult to control without extensive experience. Ijiri
et. al. have shown that an effective way of creating
realistic flowers is to sketch and edit each individual
flower component (petals, flower head etc), and then
combine them together to form the complete flower
model (Ijiri et al., 2006). In order to make the flower
modeling process more an artistic exercise, it has also
been shown that a user can sketch a plant in its en-
tirety, and then have each of its sketched components
replaced with 3D equivalents (Ijiri et al., 2006).
3 MODELING OF ORCHIDS
3.1 The Anatomy of an Orchid
Orchids differ from most other plants by the complex
structure of their flowers, which generally have three
outer sepals, three inner petals and a single large col-
umn (Fortner, 2007) as illustrated in figure 1:
• Sepals: The glorified remains of the flower bud.
There is usually a dorsal (top) sepal and two lat-
eral sepals.
• Petals: Three petals of which two flank a large and
flamboyant petal called the lip or labellum.
• Column: Unlike other flowers, both the male and
female reproductive organs (stamen and pistil) are
combined into a single column (gynostemium).
• Operculum: The Column is located under the Op-
erculum but is invisible on many orchid species.
For that reason we have ignored this structure so
far in our modeling tool
Orchids are bilaterally symmetrical (left and right half
are symmetrical). The flower will always twist so that
the labellum is pointing downwards (except for those
rare species where the labellum points straight up).
With some orchid species, the lateral sepals fuse to-
gether.
3.2 Modeling Framework
The overall design of our orchid modeler is based on
that by (Ijiri et al., 2005). A complex inflorescence
is designed by constructing each flower component
Figure 1: The prominent parts of an orchid flower.
separately and then combining them to form the final
model. The petals, sepals and stem are constructed
similar to those by Ijiri et al. The labellum requires
specialized techniques explained below. The shapes
can be adjusted using a paper bending metaphor.
The basic building blocks of the modeling process
are the user input strokes, which are a collection of
points converted from screen to world coordinates.
The coordinate transformation is achieved by inter-
secting the lines from the view point to each point
with the canvas plane, which is usually the view plane
(xy-plane). We found that smoothing/filtering of in-
put strokes was unnecessary because they only served
to find the control points for creating bicupic B-spline
surfaces representing the flower components.
3.3 Petals and Sepals
Petals and sepals are geometrically similar and are
constructed using the algorithm explained in the left
image of figure 2. Three strokes define the central
axis and the outline of each of these flower compo-
nents (a). If the strokes don’t meet in one point they
are extrapolated and clipped on the central axis. The
resulting shape is represented by a B-spline surface
(b). The surface can be warped in transverse (c,d) and
longitudinal direction (e,f) using modifier strokes.
The modifier strokes can be placed anywhere
within a sketched shape and define a displacement of
the B-spline surface. The right hand side of figure 2
gives an example. The width modifier stroke defines
the displacement along the cross section where it is
drawn (A) and reduces linearly to zero toward the end
points of the central axis (B). The B-spline surface’s
control points are pulled upwards toward the stroke
(C).
3.4 Labellum
In order to make the modeling of the complex label-
lum surface as easy as possible we define its shape
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