88
J. Fan et al.
s(p sj ) − s(p si ) = πB
l(p sj ) − l(p si )
= πB
2
κ(p sj ) − κ(p si )
,
(11)
and extract the scaling factor:
B =
s(p sj ) − s(p si )
π
κ(p sj ) − κ(p si )
> 0.
(12)
The clothoid approximation of the shape is then obtained by interpolating
with the points of each obtained segment by Eq. 9, with successive rotation and
translation to extract the final clothoid points approximating the curling shape.
3 Results and Analysis
We evaluate the accuracy and performance of the proposed method by analysing
a set of configurations of a natural tendril captured in 2D RGB images (digital camera Canon EOS 550D with Lens Canon EF-S 18–55 mm f/3.5–5.6 IS
II) extracted from the Supplementary Video
2 which records the changes in the
morphology of a passionflower tendril, taken place in about 4 min, after being
stimulated with a wooden stick for about 1 min.
From the whole frames sequence, we choose four representative images and
we analyzed the morphologies. Figure 5 shows the arclength-curvature relation
established for each point of the skeleton (second row) and the minimum segments (third row) obtained by our program.
We adopt R
2 to quantify the curve fitting error, with R
2 = 1 expressing the
best fitting. Our approach demonstrated to be highly accurate for the analysis
of curling shape morphologies, all the results show R
2 > 0.994, even with the
minimum retrieved number of N = 4 segments.
Our approach can then be purposely adopted to analyze the changes over
time in the morphology of continuum adaptive structures, like living growing
tendrils. Figure 6 shows an example of such analysis for the morphological evolution of our passionflower tendril after the induced stimulation. It can be noted
there is a portion of the tendril that does not change curvature in time, even
though previously stimulated (see Supplementary Video(see footnote 2)), while
the most apical region is more dynamic in curvature variation. This result might
suggest a well-localized zone for coil actuation, independent from the region
of stimulation. However, deeper and focused analysis is worth to establish the
relation between the provided stimulus and connected behaviour.
4 Discussion and Future Works
In this work, we present an image-based reconstruction method based on 2D
piece-wise clothoid model. We used this method to describe and analyse the
different morphologies assumed by a natural tendril after mechanical stimuli.
2 Video link: https://youtu.be/DmbInPlpT1U .
J. Fan et al.
s(p sj ) − s(p si ) = πB
l(p sj ) − l(p si )
= πB
2
κ(p sj ) − κ(p si )
,
(11)
and extract the scaling factor:
B =
s(p sj ) − s(p si )
π
κ(p sj ) − κ(p si )
> 0.
(12)
The clothoid approximation of the shape is then obtained by interpolating
with the points of each obtained segment by Eq. 9, with successive rotation and
translation to extract the final clothoid points approximating the curling shape.
3 Results and Analysis
We evaluate the accuracy and performance of the proposed method by analysing
a set of configurations of a natural tendril captured in 2D RGB images (digital camera Canon EOS 550D with Lens Canon EF-S 18–55 mm f/3.5–5.6 IS
II) extracted from the Supplementary Video
2 which records the changes in the
morphology of a passionflower tendril, taken place in about 4 min, after being
stimulated with a wooden stick for about 1 min.
From the whole frames sequence, we choose four representative images and
we analyzed the morphologies. Figure 5 shows the arclength-curvature relation
established for each point of the skeleton (second row) and the minimum segments (third row) obtained by our program.
We adopt R
2 to quantify the curve fitting error, with R
2 = 1 expressing the
best fitting. Our approach demonstrated to be highly accurate for the analysis
of curling shape morphologies, all the results show R
2 > 0.994, even with the
minimum retrieved number of N = 4 segments.
Our approach can then be purposely adopted to analyze the changes over
time in the morphology of continuum adaptive structures, like living growing
tendrils. Figure 6 shows an example of such analysis for the morphological evolution of our passionflower tendril after the induced stimulation. It can be noted
there is a portion of the tendril that does not change curvature in time, even
though previously stimulated (see Supplementary Video(see footnote 2)), while
the most apical region is more dynamic in curvature variation. This result might
suggest a well-localized zone for coil actuation, independent from the region
of stimulation. However, deeper and focused analysis is worth to establish the
relation between the provided stimulus and connected behaviour.
4 Discussion and Future Works
In this work, we present an image-based reconstruction method based on 2D
piece-wise clothoid model. We used this method to describe and analyse the
different morphologies assumed by a natural tendril after mechanical stimuli.
2 Video link: https://youtu.be/DmbInPlpT1U .