Full Text - Tarım Bilimleri Dergisi

Transkript

Journal of Agricultural Sciences
Dergi web sayfası:
www.agri.ankara.edu.tr/dergi
Journal homepage:
www.agri.ankara.edu.tr/journal
Tar. Bil. Der.
A New Approach for Determination of Seed Distribution Area in
Vertical Plane
Sefa ALTIKATa, Alper GÜLBEb, Ahmet ÇELİKc
a
b
c
Iğdır University, Faculty of Agriculture, Department of the Biosystem Engineering, Iğdır, TURKEY
Iğdır University, Technical Sciences Vocational School, Department of Computer Programming, Iğdır, TURKEY
Atatürk University, Faculty of Agriculture, Department of the Agricultural Machinery, Erzurum, TURKEY
ARTICLE INFO
Research Article
Corresponding Author: Sefa ALTIKAT, E-mail: [email protected], Tel: +90 (476) 226 20 12
Received: 14 May 2014, Received in Revised Form: 22 July 2014, Accepted: 20 August 2014
ABSTRACT
The objective of this study was to develop a new method to evaluate the seed distribution area in vertical plane and
compare it with the other methods. For this purpose, the different calculation methods of seed distribution area namely,
standard deviational ellipse, voronoi polygons with delaunay triangulation, integral method, and developed one, the
concave hull algorithm was considered and compared in this study. Three different types of no-till seeders equipped
with hoe (NS1), single disc (NS2) and winged hoe (NS3) type openers were used and operated at three different tractor
forward speeds (0.75 m s-1, 1.25 m s-1 and 2.25 m s-1). According to the results obtained from the study, it was found
that the newly developed seed distribution evaluation procedure, concave hull, provided the smaller area values of the
distributed seeds as compared to others. The influences of seeders were tested and it was found that the no-till seeder
which has disc type furrow opener spread the seeds into larger areas. However, maximum variations of sowing depth
values were observed at the no-till seeder with single disc furrow opener. Increasing tractor forward speeds resulted in
an increased variation of sowing depth.
Keywords: Ellipse; Voronoi; Integral; Concave hull algorithm; No-till seeder; Tractor forward speed
Düşey Düzlemdeki Tohum Dağılım Alanının Belirlenmesinde Yeni Bir
Yaklaşım
ESER BİLGİSİ
Araştırma Makalesi
Sorumlu Yazar: Sefa ALTIKAT, E-posta: [email protected], Tel: +90 (476) 226 20 12
Geliş Tarihi: 14 Mayıs 2014, Düzeltmelerin Gelişi: 22 Temmuz 2014, Kabul: 20 Ağustos 2014
ÖZET
Bu araştırmanın amacı, tohum dağılım alanının değerlendirilmesine yeni bir yaklaşım geliştirmektir. Bu amaçla, standart
sapmalı elips, delaunay üçgenlemesiyle voronoi poligonları ve integral metodu gibi farklı tohum dağılım alanı hesaplama
yöntemleri karşılaştırılmış ve içbükey zarf adı verilen yeni bir yöntem geliştirilmiştir. Araştırmada, çapa (NS1),
TARIM BİLİMLERİ DERGİSİ — JOURNAL OF AGRICULTURAL SCIENCES 21 (2015) 123-131
Tarım Bilimleri Dergisi
A New Approach for Determination of Seed Distribution Area in Vertical Plane, Altıkat et al
tek diskli (NS2) ve kanatlı çapa (NS3) tip gömücü ayaklara sahip üç farklı anıza doğrudan ekim makinası, üç farklı
ilerleme hızında (0.75 m s-1, 1.25 m s-1 ve 2.25 m s-1) kullanılmıştır. Elde edilen sonuçlara göre yeni geliştirilen tohum
dağılımı değerlendirme yönteminin diğerleriyle karşılaştırıldığında daha küçük dağılım alanları verdiği belirlenmiştir.
Gömücü ayakların tohum dağılımına olan etkileri incelendiğinde, tek diskli gömücü ayağa sahip ekim makinasının
tohumları daha geniş alana dağıttığı ve bu makina ile ekim yapılan parsellerde ekim derinliğindeki varyasyonun diğer
makinalara göre daha fazla olduğu belirlenmiştir. Araştırmada traktör ilerleme hızlarının artışına paralel olarak ekim
derinliği varyasyon değerlerinde de artış gözlemlenmiştir.
Anahtar Kelimeler: Elips; Voronoi; İntegral; İç bükey zarf algoritması; Anıza doğrudan ekim; Traktör ilerleme hızı
© Ankara Üniversitesi Ziraat Fakültesi
1. Introduction
Seed distribution as an important factor affecting
seed emergence and productivity is expressed in
lateral and vertical plane during sowing process.
The factors affecting uniform seed distribution in
horizontal plane are the distribution of seed spacing
in a row and deviations from the furrow.
The purpose of sowing is to place seeds into
preferred depth and distance within the row. The
coefficient of variation which is the standard
deviation of the sowing depths expressed as
percentage of the mean seeding depth can be used
to indicate the uniformity of the seeding depth. A
coefficient of variation (CV%) value under 30%
represents acceptable sowing depth (ISO 1984).
Karayel & Özmerzi (2001) have stated that the
seed distribution in vertical plane relevant to seed
distribution area depends on the sowing depth. Besides,
Wilkins et al (1991) have stated that the “Stampede”
peas had yield rise with spacing uniformity but
“Bolero” peas had no sensitivity on uniformity of plant
spacing. That is, some plants require uniform seed
distribution during sowing or planting.
There are three accepted methods to calculate
the seed distribution area; the standard deviational
ellipse (SDE), integral method (IM), voronoi
polygons with delaunay triangulation (VPDT).
Karayel & Özmerzi (2007) used first two methods in
calculation of vertical and lateral seed distribution.
Karayel (2010) used the third method to evaluate
seed distribution in the horizontal plane and plant
growing area for row seeding.
Standard deviational ellipse (SDE) method
forms an ellipse from the standard deviation of seeds
from the row center (Sa) and standard deviation of
124
sowing depth (Sb) and calculates the area of the
seeds distributed with the formula A=Sa·Sb·π.
Integral method divides the seeds into two
groups one on the left of the row and the other
on the right of the row. A cubic function of curve
fitted by least squares estimation for each group is
conducted from the seed coordinates in the groups
and the area between the curves is calculated using
the difference of integrals of both functions. The
ellipse conducted by SDE method and the curved
area by integral method (IM) are imaginary and
may not envelop all the seeds. However Voronoi
polygons with Delaunay triangulation (VPDT)
method encloses all the seeds in a convex polygon
and the voronoi polygons are established. Then,
with delaunay triangulation the polygon is divided
into proper triangles.
New criterion which is presented for evaluation
of seed distribution area in this study is concave
hull method. It resembles to convex hull which it
was derived from. However, Duckham et al (2008)
claimed that the convex hull which voronoi polygons
use can never provide good characterization of the sets
of points with a pronounced non-convex distribution.
Park & Oh (2012) advise to use concave hull for
geometrical evaluation because the convex hull
cannot fully reflect the geometrical characteristics of
a dataset. Srivatsan et al (1998) defined the concave
hull of a set of curves that is the smallest bounding
area envelope that is convex or concave.
The purpose of this study is to add a new and
closer viewpoint to evaluate the seed distribution
area. While presenting concave hull method, it was
compared to three other methods; each experiment
was assessed by four of methods mentioned for
seeder performances and tractor forward speeds.
Ta r ı m B i l i m l e r i D e r g i s i – J o u r n a l o f A g r i c u l t u r a l S c i e n c e s
21 (2015) 123-131
Düşey Düzlemdeki Tohum Dağılım Alanının Belirlenmesinde Yeni Bir Yaklaşım, Altıkat et al
2. Material and Methods
The region where the field experiments took place
displays the characteristics of the continental
climate; winter temperature is cold enough to
support a fixed period of snow and short hot period
during summer. The texture classification of the soil
in the experimental field was loam.
Winter wheat was reaped from the field in
August with a combined harvester which its stubble
height was adjusted to 12 cm, then the field was left
for the winter. Summer vetch was sown on the same
area in April using the no-tillage method. Table 1
illustrates the physical properties of the soil in the
experimental field.
Table 1- Some important soil physical properties in
the experiment area (0-10 cm)
Çizelge 1- Deneme alanı toprağının bazı fiziksel
özellikleri (0-10 cm)
Soil physical properties
Bulk density
Moisture content
Penetration resistance
Field surface stubble covering rate
Stubble height
Soil texture class
Sand
Clay
Silt
Value
1.47 Mg m-3
18.21%
0.89 MPa
90.3%
12 cm
Loam
48.44%
12.06%
39.5%
A randomized complete block design was used
for the layout of the experiment, with a factorial
arrangement of treatments that included three tractor
forward speeds and three different no-till seeders
and at the sowing with three replications. The width
Hoe type furrow opener (NS1)
and length of the one experiment plot were 3 m and
30 m respectively.
Three no-till seeder types used in the experiment
were different from each other for their furrow opener
types; hoe (NS1), single disc (NS2) and winged hoe
(NS3) (Figure 1). Table 2 illustrates some of the
important technical properties of no-till seeders.
Table 2- Some technical properties of no-till seeders
Çizelge 2- Anıza doğrudan ekim makinalarının bazı
teknik özellikleri
Technical properties
Types of furrow opener
Total weight, kg
Number of openers,
Seeder weight per furrow
opener, kg
NS1
Hoe
1400
16
NS2
Disc
1000
15
NS3
Winged hoe
534
8
87.5
66.6
66.7
Tractor forward speeds used in the study were;
V1: 0.75 m s-1, V2: 1.25 m s-1, V3: 2.25 m s-1. Tillage
implements were pulled by a Massey Ferguson 365
S tractor. A True Ground Speed radar and a DJCMS
100 monitor made by Tracktometer were used
to achieve the tractor forward speed. Ebena type
summer vetch was sown for the experiment with
140 kg ha-1 seed rate and at 50 mm sowing depth.
Sowing depth was determined by measuring the
mesocotyl length of summer vetch (Chen et al 2004).
Distances in the transverse direction of plants to a
straight line parallel to the row were measured to
determine lateral seed scatter (Karayel & Özmerzi
2005). Sowing depth and lateral seed scatter of 40
seeds were measured in the field after sowing for all
treatments and replications.
Disc type furrow opener (NS2)
Winged hoe type furrow opener (NS3)
Figure 1- Furrow opener of no-till seeders
Şekil 1- Anıza doğrudan ekim makinalarına ait gömücü ayaklar
21 (2015) 123-131
125
definite integral using following equation. For this purpose a short VBA module
defined function and called to compute the area between curves. Sum of the ar
distribution area evaluated by IM (Karayel& Özmerzi, 2007).
𝑐𝑐
𝑏𝑏
𝑎𝑎3 𝑥𝑥 3 + 𝑎𝑎2 𝑥𝑥 2 +𝑎𝑎1 𝑥𝑥 + 𝑎𝑎0 𝑑𝑑𝑥𝑥 −
= 𝑎𝑎0 − 𝑎𝑎 𝑐𝑐 − 𝑏𝑏 +
𝑎𝑎 1
2
𝑏𝑏
𝑐𝑐 2 − 𝑏𝑏 2 +
𝑎𝑎𝑑𝑑𝑥𝑥
𝑎𝑎 2
3
𝑐𝑐 3 −
Where; a3, a2, a1 and a0 are the coefficients of polynomial function,a is the optim
the leftmost
rightmost
respectively
from the row.
length ofofmajor
axis ofand
ellipse
was seeds
standard
deviation
Four different criteria were used to evaluatethe deviations
of seed distribution areas in this study. These are from row center of seeds and semi-length of minor
At the standard deviational ellipse (SDE) criteria, seed points were plotted on
integral method (IM), standard deviational ellipsefittedaxis
of ellipse was the standard deviation of sowing
into an ellipse (Figure 3). Semi-length of major axis of ellipse was standard d
(SDE), voronoi diagram with delaunay triangulationseedsdepth.
In this criterion
seed
distribution
wasdeviation of sowin
and semi-length
of minorthe
axis
of ellipse
was the area
standard
(VPDT) and concave hull (CH) methods.
as followed
(Karayel
& Özmerzi
2007).
seed calculated
distribution area
was calculated
as followed
(Karayel&
Özmerzi 2007).
In integral criteria, points in every block were
sorted by sowing depth. Then, each set of points
was split into two groups whether below or above
the optimal sowing depth. A cubic polynomial of a
curve fitted by least squares estimate was derived
for each group by using LINEST command of
Microsoft Excel 2013 (Figure 2).
Figure 3- Determination of seed distribution area
using standard deviational ellipse (SDE) criterion.
Figure
3-Determination
seed distribution
area using
with
standard deviational el
Şekil
3- Standart of
sapmalı
elips yöntemine
göre
tohum
Şekil 3-Standartsapmalıelipsyönteminegöretohumdağılımalanınınbelirlenmesi
dağılım alanının belirlenmesi
𝐴𝐴 = 𝑆𝑆𝑎𝑎 ∙ 𝑆𝑆𝑏𝑏 ∙ 𝜋𝜋 (2)
Where; A is seed distribution area (mm2), S is
a
Where; A is seed distribution area (mm2),Sa is standard deviation
from row cente
standard
deviation
deviation
of sowing
depth. from row center of seeds and Sb
is standard deviation of sowing depth.
Figure 2- Polynomial functions derived from two The third method used to calculate the distribution area is, voronoi diagram
The third
method
(VPDT) (Figure
4) (Karayel
2010). used to calculate the
sets of points in a block
distribution area is, voronoi diagram with delaunay
Şekil 2- Bir bloktaki iki nokta kümesinden türetilen triangulation (VPDT) (Figure 4) (Karayel 2010).
polinom fonksiyonları
Areas between each polynomial function
and y=a (line of the optimal sowing depth) were
calculated by definite integral using following
equation. For this purpose a short VBA module was
re 2-Polynomial functions derived from two sets of points in a block
implemented as a user defined function and called to
2- Birbloktakiikinoktakümesindentüretilenpolinomfonksiyonları
compute the area between curves. Sum of the areas
reas between each polynomial function and y=a(line of the optimal sowing depth) were calculated by
were
theForresulting
distribution
area evaluated
ite integral using following
equation.
this purpose seed
a short VBA
module was implemented
as a user
ed function and called to compute the area between curves. Sum of the areas were the resulting seed
by
IM
(Karayel
&
Özmerzi
2007).
bution area evaluated by IM (Karayel& Özmerzi, 2007).
𝑐𝑐
𝑏𝑏
𝑎𝑎3 𝑥𝑥 3 + 𝑎𝑎2 𝑥𝑥 2 +𝑎𝑎1 𝑥𝑥 + 𝑎𝑎0 𝑑𝑑𝑥𝑥 −
= 𝑎𝑎0 − 𝑎𝑎 𝑐𝑐 − 𝑏𝑏 +
𝑎𝑎 1
2
2
𝑐𝑐 − 𝑏𝑏
2
𝑐𝑐
𝑏𝑏
+
𝑎𝑎𝑑𝑑𝑥𝑥
𝑎𝑎 2
3
𝑐𝑐 3 − 𝑏𝑏 3 +
𝑎𝑎 3
4
(1)
𝑐𝑐 4 − 𝑏𝑏 4 (1)
Where; a , a , a and a are the coefficients of
polynomial function, a is the optimal sowing
At the standard deviational
ellipse (SDE)
criteria,
seed the
pointsdeviations
were plotted on of
a chart
their distribution
depth,
b and
c are
theandleftmost
and
into an ellipse (Figure 3). Semi-length of major axis of ellipse was standard deviation from row center of
rightmost
respectively
the row.
s and semi-length of minor
axis of ellipse seeds
was the standard
deviation offrom
sowing depth.
In this criterion the
Where; a3, a2, a1 and a0 are the coefficients3of polynomial
2
1 function,a 0is the optimal sowing depth, b and c are
eviations of the leftmost and rightmost seeds respectively from the row.
distribution area was calculated as followed (Karayel& Özmerzi 2007).
At the standard deviational ellipse (SDE)
criteria, seed points were plotted on a chart and their
distribution fitted into an ellipse (Figure 3). Semi-
126
Figure 4- Voronoi polygons with Delaunay
triangulation (dashed lines, convex hull enclosing
all points; dash-dot lines, Delaunay triangulation;
solid lines, Voronoi polygons; circles, seeds)
Şekil 4- Delaunay üçgenlemesiyle Voronoi poligonları
(kesik çizgiler, tüm noktaları kapsayan dış bükey zarf;
kesik noktalı çizgiler, Delaunay üçgenleri; sürekli
çizgiler, Voronoi poligonları; daireler, tohumlar)
re 3-Determination of seed distribution area using with standard deviational ellipse (SDE) criterion.
3-Standartsapmalıelipsyönteminegöretohumdağılımalanınınbelirlenmesi
𝐴𝐴 = 𝑆𝑆𝑎𝑎 ∙ 𝑆𝑆𝑏𝑏 ∙ 𝜋𝜋
𝑐𝑐
(2)
21 (2015) 123-131
The last method used to compute the seed distribution
Delaunay Triangulation covers all the nodes
with a convex polygon and connects all the nodes area is Concave Hull algorithm. The algorithm uses
with the nearest two neighbors to make up the Convex Hull algorithm to set up the outer layer of bound
oflines,
the convex
points hull
(dashed
linesallinpoints;
Figuredash-dot
6). The points on
smallest
triangle.
The with
3D Delaunay
points obtained
from
Figure
4-Voronoi
polygons
triangulation
(dashed
enclosing
Figure
Figure 4-Voronoi
4-Voronoi polygons
polygons with
with Delaunay
Delaunay triangulation
triangulation (dashed
(dashed lines,
lines, convex
convex hull
hull enclosing
enclosing all
all points;
points; dash-dot
dash-dot
the
outer
layer
are
removed
from
the
original
point list.
the
field
measurements
to
determine
the
location
lines,
Delaunay
triangulation;
solid
lines,Voronoi
polygons;
circles,
seeds)
lines,
Delaunay
triangulation;
solid
lines,Voronoi
polygons;
circles,
seeds)
lines, Delaunay triangulation; solid lines,Voronoi polygons; circles, seeds)
Şekil
4Delaunay
üçgenlemasiyleVoronoipoligonları
(kesikçizgiler,tümnoktalarıkapsayandışbükey
Şekil
4Delaunay
set of Convex Hull points are determined from
of
the seeds
were
saved into
separate CSV files Another
Şekil
4Delaunay
zarf;kesiknoktalıçizgiler,
Delaunay
üçgenleri;sürekliçizgiler,
Voronoipoligonları;daireler,tohumlar)
zarf;kesiknoktalıçizgiler,
Delaunay
zarf;kesiknoktalıçizgiler,Values
Delaunay
the remaining points as the second layer bound (Dash(Comma-Seperated
file
format used by many
dotpolygon
combination
in Figure
6-a).
The with
next the
step is to test
Spreadsheet
and
database
management
software).
Delaunay
Triangulation
covers
all
the
nodes
with
a
convex
and
connects
all
the
nodes
Delaunay
Triangulation
covers
all
aa convex
polygon
and
all
the
nodes
with
Delaunay
Triangulation
covers
all the
the nodes
nodes with
with
convexouter
polygon
and connects
connects
all
theinner
nodesalternatives:
with the
the
connections
with
the
if there
A
Visual
LISP
program
was
implemented
to
read
nearest
two
neighbors
to
make
up
the
smallest
triangle.
The
3D
points
obtained
from
the
field
measurements
to
nearest
nearest two
two neighbors
neighbors to
to make
make up
up the
the smallest
smallest triangle.
triangle. The
The 3D
3D points
points obtained
obtained from
from the
the field
field measurements
measurements to
to
are
smaller
lines
connecting
outer
point
with
an
inner
the
data
into
AutoCAD.
The
average
of
intra-row
determine
the
location
of
the
seedswere
saved
into
separate
CSV
files
(Comma-Seperated
Values
file
format
determine
determine the
the location
location of
of the
the seedswere
seedswere saved
saved into
into separate
separate CSV
CSV files
files (Comma-Seperated
(Comma-Seperated Values
Values file
file format
format
used
by
many
Spreadsheet
and
database
management
software).
A
Visual
LISP
program
was
implemented
to
point
than
a
line
connecting
the
two
nodes
on
the
outer
spacing
values
(y-coordinates)
was
calculated
used
by
many
Spreadsheet
and
database
management
software).
A
Visual
LISP
program
was
implemented
to
used by many Spreadsheet and database management software). A Visual LISP program was implemented to
read
the
data
into
AutoCAD.
The
average
of
intra-rowspacing
values
(y-coordinates)
was
calculated
and
all
the
read
average
of
(y-coordinates)
was
and
hull (The
lines between
Point
3 - Point
4 the
and Point 4 –
and
all
the
y-coordinates
of the
points
were set to values
read the
the data
data into
into AutoCAD.
AutoCAD. The
The
average
of intra-rowspacing
intra-rowspacing
values
(y-coordinates)
was calculated
calculated
and all
all
the
y-coordinates
of
the
points
were
set
to
the
average
value
by
the
program,
so
the
points
were
flattened
to
2D
form.
y-coordinates
of
the
points
were
set
to
the
average
value
by
the
program,
so
the
points
were
flattened
to
2D
form.
y-coordinates
the points
wereprogram,
set to the average
by the program,
so the
pointsthan
werethe
flattened
to 2D form.
Point 5 are
smaller
line between
Point 3 – Point
the
average ofvalue
by the
so thevalue
points
The
points
were
sorted
according
to
the
vertical
coordinates
(z-coordinates).
The
outmost
polygons
covering
all
The
were
according
to
vertical
coordinates
(z-coordinates).
The
covering
all
The points
points
were sorted
sorted
according
to the
the
vertical
coordinates
(z-coordinates).
The outmost
outmost
polygons
covering
all
55).in Figure 6-a).
If therepolygons
exists such
a connection,
then
were
flattened
to 2D
form.
The
points
were
sorted
the
other
points
were
drawn
by
the
Visual
LISP
program
(Figure
the
other
points
were
drawn
by
the
Visual
LISP
program
(Figure
5).
the
other
points
were
drawn
by
the
Visual
LISP
program
(Figure
5).
according to the vertical coordinates (z-coordinates). the larger outer connection (the line connecting Point
The outmost polygons covering all the other points 3 and Point 5 in Figure 6-a) is omitted and two new
connections
lines between Point 3 – Point
were drawn by the Visual LISP program (FigureThe
5).total areasmaller
of the convex
polygon is sum of(the
triangles.
𝑛𝑛 4 and Point 4 – Point 5 in Figure 6-a) are established.
𝐴𝐴 = 𝑖𝑖=1 𝐴𝐴𝑖𝑖 (6)
The encapsulated points are removed from the original
The last method used to compute the seed distribution area is Concave Hull algorithm. The algorithm uses
list
and
put
into
list. lines
After
testing
Convex Hullpoint
algorithm
to set
up the
outer
layer boundary
of bound of the point
points (dashed
in Figure
6). The points on
the outer layer are removed from the original point list. Another set of Convex Hull points are determined from
all
the
connections
the
algorithm
builds
another
inner
the remaining points as the second layer bound (Dash-dot combination in Figure 6-a). The next step is to test
outer connections
withconvex
the inner alternatives:
if therepoints
are smalleras
linesconnecting
outer point
with an inner point
set of
boundary
a third layer
bound
than a lineconnecting the two nodes on the outer hull (The lines between Point 3 - Point 4 and Point 4 – Point 5
are smaller than
the line between
Point 3 – Point 5 in Figure
6-a). If there exists
a connection,
(Dash-dot
combination
in Figure
6-b).suchThen
thethen thelarger
outer connection (the line connecting Point 3 and Point 5 in Figure 6-a) is omittedand two new smaller
carries
on3 building
connections
until
no
connections method
(the lines between
Point
– Point 4 andsmaller
Point 4 – Point
5 in Figure 6-a)
are established.
The
encapsulated points are removed from the original point list and put into boundary point list.After testing all the
other
convex
polygon
exists.
Figure
6-c
and
6-d
show
Figure 5- Convex Hull algorithm for a sample connections
set
the algorithm builds another inner set of convex boundary points as a third layer bound (Dash-dot
combinationthe
in Figure
Then
the method carries
building
connections
no other convex
next6-b).
two
iterations.
Theonarea
is smaller
calculated
asuntil
in the
of 2D points
polygon exists. Figure 6-c and 6-d show the next two iterations. The area is calculated as in the second method
second
method
described
above.
described above.
Şekil 5- İki boyutlu örnek bir nokta kümesi için
dışbükey zarf algoritması
Figure
5-Convex
Hull
algorithm
for
sample
set
of
2D
points
Figure
5-Convex
for
Figure
5-Convex
Hull
algorithm
for aaa sample
sample
set of
of 2D
2D points
points
Finally
the Hull
areaalgorithm
was calculated
by set
AutoCAD’s
Şekil
5-İkiboyutluörnekbirnoktakümesiiçindışbükey
zarf
algoritması
Şekil
Şekil 5-İkiboyutluörnekbirnoktakümesiiçindışbükey
5-İkiboyutluörnekbirnoktakümesiiçindışbükey zarf
zarfalgoritması
algoritması
AREA command. The Delaunay Triangulation
Finally
the
area
was
calculated
by
AutoCAD’s
AREA
command.
The
Delaunay
Triangulation
method
method
with
shortest AREA
side command.
Finally
the
was
calculated
by
AutoCAD’s
Finallyconnects
the area
area the
was points
calculated
bythe
AutoCAD’s
AREA
command. The
The Delaunay
Delaunay Triangulation
Triangulation method
method
connects
the
points
with
the
shortest
side
lengths,
so
the
smallest
angle
values.
connects
with
shortest
side
lengths,
so points
the
smallest
values.
connects the
the
points
with the
theangle
shortest
side lengths,
lengths, so
so the
the smallest
smallest angle
angle values.
values.
(a)
(b)
The area
areaofof
the
i-th
triangle
whose
sides
have i,i, and
method) isis calculated
calculated with
with the
the
The
the
i-th
triangle
whose
sides
have
lengths
i(Heron’s
method)
The
b , and
and ccci(Heron’s
The area
area of
of the
the i-th
i-th triangle
triangle whose
whose sides
sides have
have lengths
lengths aaai,i,, bb
i(Heron’s method) is calculated with the
lengths
abelow:
, bi, and ci (Heron’s method) is calculated i i
equation
equation
i
equation below:
below:
with the equation below:
=
(𝑢𝑢
−
)(𝑢𝑢
−
)(𝑢𝑢
−
(3)
(3)
𝐴𝐴𝐴𝐴
𝐴𝐴𝑖𝑖𝑖𝑖 =
= 𝑢𝑢𝑢𝑢
𝑢𝑢𝑖𝑖𝑖𝑖(𝑢𝑢
(𝑢𝑢𝑖𝑖𝑖𝑖 −
− 𝑎𝑎𝑎𝑎
𝑎𝑎𝑖𝑖𝑖𝑖)(𝑢𝑢
)(𝑢𝑢𝑖𝑖𝑖𝑖 −
− 𝑏𝑏𝑏𝑏
𝑏𝑏𝑖𝑖𝑖𝑖)(𝑢𝑢
)(𝑢𝑢𝑖𝑖𝑖𝑖 −
− 𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖𝑖𝑖))) (3)
(3)
𝑖𝑖
𝑖𝑖
𝑖𝑖
𝑖𝑖
𝑖𝑖
𝑖𝑖
𝑖𝑖
𝑖𝑖
(b)
(d)
+𝑏𝑏𝑖𝑖𝑖𝑖+𝑐𝑐
+𝑐𝑐
𝑎𝑎𝑎𝑎
(4) 6-The first four iterations of the concave hull algorithm for a sample set of points. (dashed lines, convex
𝑎𝑎𝑖𝑖𝑖𝑖+𝑏𝑏
+𝑏𝑏 +𝑐𝑐𝑖𝑖𝑖𝑖 Figure
=
(4)
𝑢𝑢𝑢𝑢
(4)
𝑢𝑢𝑖𝑖𝑖𝑖𝑖𝑖 =
= 𝑖𝑖 222𝑖𝑖 𝑖𝑖
(4)
Figure
6- The
four
iterations
thehullconcave
hull enclosing
all points; dash-dot
lines,first
inner layer
convex
hull; solid lines,of
concave
enclosing all points)
Şekil
6-Örnekbirnoktakümesiiçiniçbükey
zarf
algoritmasının
ilk
dörtötelemesi
hull
algorithm
for
a
sample
set
of
points
(dashed
(kesikçizgilertümnoktalarıkapsayandışbükey
zarf;kesiknoktalıçizgilerdışbükey
zarf
The
sides“a”,
“a”,“b”,
“b”,
and
“c”
are |BC|,
|AC|,
and
|AB|
The
sides
and
“c”
are
|BC|,
|AC|,
and
|AB|
respectively.
lines,
convex
hull
enclosing
all
points;
dash-dot
The
sides
“a”,
“b”,
and
“c”
are
|BC|,
|AC|,
and
|AB|
respectively.
içkatmanı;sürekliçizgilertümnoktalarıkapsayaniçbükey
zarf)
The sides “a”, “b”, and “c” are |BC|, |AC|, and |AB| respectively.
respectively.
lines, inner layer convex hull; solid lines, concave
A Visual LISP program implemented was used to obtain the results. The smallest possible concave hull
22 + (𝑦𝑦
22 + (𝑧𝑧
22 according
enclosing
all points)
tohull
the algorithm
was constructed.
Then the area of the concave polygon was calculated by the
−
−
−
(5)
𝐴𝐴𝐵𝐵
=
(𝑥𝑥
(5)
𝐴𝐴𝐵𝐵
−𝑥𝑥𝑥𝑥
𝑥𝑥𝐵𝐵𝐵𝐵𝐵𝐵)))2 +
+ (𝑦𝑦
(𝑦𝑦𝐴𝐴𝐴𝐴𝐴𝐴 −
− 𝑦𝑦𝑦𝑦
𝑦𝑦𝐵𝐵𝐵𝐵𝐵𝐵)))2 +
+ (𝑧𝑧
(𝑧𝑧𝐴𝐴𝐴𝐴𝐴𝐴 −
− 𝑧𝑧𝑧𝑧𝑧𝑧𝐵𝐵𝐵𝐵𝐵𝐵)))2 AutoCAD’s
(5)
𝐴𝐴𝐵𝐵 =
= (𝑥𝑥
(𝑥𝑥𝐴𝐴𝐴𝐴𝐴𝐴 −
AREA command.
(5)
Şekil 6- Örnek bir nokta kümesi için içbükey zarf
The ANOVA
procedure, appropriate
randomized
complete (kesik
block design,
was the procedure
algoritmasının
ilk fordört
ötelemesi
çizgiler
tüm used to
The total area of the convex polygon is sumanalyze
of
the variance of the obtained data. Means were compared by using Duncan’s multiple range tests.
The total area of the convex polygon is sum of triangles.
noktaları
kapsayan
dış
bükey
zarf;
kesik
noktalı
triangles.
𝐴𝐴 =
𝑛𝑛
𝑖𝑖=1 𝐴𝐴𝑖𝑖 (6)
3. Results çizgiler
and Discussion
dış bükey
(6)
zarf iç katmanı; sürekli çizgiler tüm
noktaları kapsayan iç bükey zarf)
3.1. Sowing uniformity
In measurements conducted in order to ascertain the sowing depth uniformity, deviation amounts of the
The last method used to compute the seed distribution
areaamounts
is Concave
Hullsowing
algorithm.
algorithm
usesof variation is valid only ratio
measured
from the target
depth wereThe
determined.
Coefficient
scale
asthe
which
area values
are stated
sinceinnegative
areas
areThe
meaningless.
When
related to these
Convex
Hull
algorithm
to
set
up
the
outer
layer
of
bound
of
points
(dashed
lines
Figure
6).
points
on the results
21 (2015) 123-131
127
the outer layer are removed from the original point list. Another set of Convex Hull points are determined from
the remaining points as the second layer bound (Dash-dot combination in Figure 6-a). The next step is to test
outer connections with the inner alternatives: if there are smaller linesconnecting outer point with an inner point
than a lineconnecting the two nodes on the outer hull (The lines between Point 3 - Point 4 and Point 4 – Point 5
are smaller than the line between Point 3 – Point 5 in Figure 6-a). If there exists such a connection, then thelarger
outer connection (the line connecting Point 3 and Point 5 in Figure 6-a) is omittedand two new smaller
connections (the lines between Point 3 – Point 4 and Point 4 – Point 5 in Figure 6-a) are established. The
3. Results and Discussion
3.1. Sowing uniformity
In measurements conducted in order to ascertain
the sowing depth uniformity, deviation amounts
of the measured amounts from the target sowing
depth were determined. Coefficient of variation is
valid only ratio scale as which area values are stated
since negative areas are meaningless. When the
results related to these deviation values expressed
as variation coefficient are examined, it is seen that
no-till seeder having hoe furrow openers (NS1) had
the lowest variation coefficient with 13.43% and
Sowing depth (mm)
20
18.29 %
20
4
10
2
0
13.39 %
60
50
14.95 %
14
40
10
8
6
4
42.03 mm
12
43.39 mm
20
Variation coefficient (CV%)
42.63 mm
30
39.25 mm
10
16
Sowing depth (mm)
40
42.82 mm
Variation coefficient (CV%)
13.43 %
50
CV %
17.15 %
18
14.8 %
12
6
The analysis shows that differences of the areas
calculated by four methods are statistically
significant. The difference between SDE and VPDT
methods has no importance. However the area
values of the CH and IM criteria is significantly
different from each other and CH shows similarity
with VPDT (Table 3).
Sowing depth (mm)
60
14
8
3.2. Comparison of methods
CV %
18
16
Karayel (2011) has also shown that increasing
seeder forward speed caused a rise in the precision
for the distribution of seeds along the length of the
row and in the coefficient of variation of depth.
The best emergence values were obtained with
the lowest speed of seeders (Karayel 2009). This
situation bears a resemblance to the results of this
study.
30
20
Sowing depth (mm)
The ANOVA procedure, appropriate for
randomized complete block design, was the
procedure used to analyze the variance of the
obtained data. Means were compared by using
Duncan’s multiple range tests.
this seeder was followed by winged hoe type seeder
with 14.8% and disc type seeder with 18.29%.
The increase of tractor forward speed increased
the variation coefficient of sowing depth as well.
The variation coefficient, being 13.39% in 0.75
ms-1 speed, increased to 17.15% in 2.25 ms-1 speed
(Figure 7).
39.77 mm
A Visual LISP program implemented was used
to obtain the results. The smallest possible concave
hull according to the algorithm was constructed.
Then the area of the concave polygon was calculated
by the AutoCAD’s AREA command.
10
2
NS1
NS2
No till seeders
NS3
0
0
0,75
1,25
2,25
Tractor forward speeds (m
(mss-1-1)
0
Figure 7- Effects of no-till seeders and tractor forward speeds on the sowing uniformity
Şekil 7- Anıza doğrudan ekim makinaları ve tractör ilerleme hızlarının ekim düzgünlüğüne etkileri
128
21 (2015) 123-131
Table 3- Effects of evaluation methods on seed
distribution area
Çizelge 3- Tohum dağılım alanı belirleme yöntemlerinin
etkileri
Average seed
distribution area (mm2)
Integral method (IM)
359.85 a
Standard deviational ellipse (SDE) 256.41 b
Voronoi diagram with delaunay
233.52 bc
triangulation (VPDT)
Concave hull methods (CH)
149.83 c
P: 0.0014
Method
(a, b, c) means with the same letter are not significantly different
From no-till seeder perspective, (NS1) and
(NS3) sprinkled the seeds without distributing into
a large area although (NS2) spread the seeds. For all
the seeders the concave hull method calculated the
smallest seed distribution areas. The NS2 machine
spread the seeds about 3 times with respect to the
other two machines.
All of the methods are dependent on the forward
speed of the tractor. For the VPDT method areaspeed relation seems to be distorted depending
on the large areas produced by NS2 seeder. This
SDE
VPDT
CH
IM
VPDT
CH
IM
NS1
No-till seeders
NS3
484
341
282
191
200
232
243
300
320
400
147
160
137
80
NS2
500
276
300
244
302
400
600
198
176
500
700
111
466
462
600
Seed distribution area (mm2)
658
700
144
102
67
177
SDE
800
800
0
For all the blocks, seeders and speed
combinations, the concave hull algorithm resulted
in the smallest area values. IM raised the widest
areas almost in all blocks. Although in some cases
SDE areas were smaller than the VPDT areas,
VPDT generally brought about second smallest area
values. The definition of concave hull foresees that
area of the concave polygons would be smaller or
equal to the areas of the convex polygons. Figure 10
illustrates some sets of seeds distributed.
900
900
100
Interaction values were given in Figure 9 and
Figure 10. When examining the figures, maximum
seed distribution area values were observed at the
sowing with NS2 no-till seeder and 2.25 ms-1 tractor
forward speed in all of the seed distribution area
calculation methods.
1000
1000
200
method has no filtering mechanism on the areas;
voronoi polygons delaunay triangulation method
tries to find the convex polygon enclosing all the
points. When the seeds are widely spread on both
horizontal and vertical axis, the area of the polygon
will be larger. All of the experiments increasing
the tractor forward speeds were increased seed
distribution area (Figure 8).
100
0
0,75
1,25
2,25
Tractor forwaed speeds (m
(mss-1-1)
Figure 8- Effects of no till seeders and tractor forward speeds on the seed distribution area
Şekil 8- Anıza doğrudan ekim makinaları ve traktör ilerleme hızlarının tohum dağılım alanlarına etkileri
21 (2015) 123-131
129
NS1
NS2
NS3
NS1
1000
Integral (IM) method
700
600
485
500
332
400
300
223
206
200
100
0
900
814
694
800
266
177
900
NS2
NS3
1000
800
Standard deviational ellipse
(SDE) method
700
600
500
583
418
427
400
253
300
200
154
145
100
79
0
0,75
1,25
2,25
(mss-1-1)
47
130
158
0,75
1,25
2,25
(mss-1-1)
Figure 9- Effects of interactions on the seed distribution area for integral and standard deviation ellipse methods
Şekil 9- İntegral ve elips yöntemine göre tohum dağılım alanına interaksiyonların etkileri
VPDT:
CH:
NS1 / V1
40.39 mm2
25.01 mm2
VPDT:
CH:
NS1 / V2
88.75 mm2
58.00 mm2
VPDT:
CH:
NS1 / V3
168.20 mm2
87.79 mm2
VPDT:
CH:
NS2 / V1
337.33 mm2
167.89 mm2
VPDT:
CH:
NS2 / V2
379.05 mm2
248.85 mm2
VPDT:
CH:
NS2 / V3
631.84 mm2
455.82 mm2
VPDT:
CH:
NS3 / V1
128.00 mm2
91.50 mm2
VPDT:
CH:
NS3 / V2
169.54 mm2
98.98 mm2
VPDT:
CH:
NS3 / V3
111.02 mm2
67.34 mm2
Figure 10- Effects of interactions on the seed distribution area for Voronoi and concave hull methods
(dashed lines, convex hull used in VPDT method; continuous lines, concave hull; small circles, seeds)
Şekil 10- Voronoi ve iç bükey zarf algoritması yöntemine göre interaksiyonların tohum dağılım alanına etkileri
(kesik çizgiler Voronoi methoduna göre tohum dağılım alanı; sürekli çizgiler iç bükey zarf algoritması yöntemine
göre tohum dağılım alanı; çemberler, tohumlar)
130
21 (2015) 123-131
4. Conclusions
References
The coefficients of variation of the seeding depths of
the seeders are all in acceptable limits. This means
that No-till seeder with disc type furrow opener has
the highest CV values while no-till seeder with hoe
type furrow opener has the lowest ones. Increase in
the tractor forward speed also causes an increase in
the coefficients of variation of seeding depth.
Chen Y, Monero FV, Lobb D, Tessier S & Cavers C.
(2004). Effects of six tillage methods on residue
incorporation and crop performance in a heavy clay
soil. Transactions of the ASAE 47(4): 1003−1010
No-till seeder with hoe type and winged hoe
type furrow openers produced better results from
the perspective of seed distribution area. Tractor
forward speed also showed an important influence
on seed distribution area; since speed increase
created seed scattering, this rise on velocity raised
area in which seeds distributed.
There exists three methods to evaluate seed
distribution area; IM, SDE and VPDT. This research
tried to show that the characteristic or concave hull
method used in many other fields can be determinant
of seed distribution area. CH method displays
the characteristic of the distribution of points and
the shape of the region and closer approach to
the evaluation of seed distribution area. In the
experiments, CH method produced the smallest
seed distribution area values as expected.
Abbreviations and Symbols
NS1
no-till seeder with hoe type furrow
opener
NS2
no-till seeder with disc type furrow
opener
NS3
no-till seeder with winged hoe type furrow opener
SDE
standard deviational ellipse method
IM
integral method
VPDT
Voronoi polygons with Delaunay triangulation method
CH
concave hull method
Duckham M, Kulik L, Worboys M & Galton A (2008).
Efficient generation of simple polygons for
characterizing the shape of a set of points in the plane.
Pattern Recognition 41: 3224 - 3236
ISO (1984). Sowing equipment, Test methods, Part 1:
Single seed drills
Karayel D & Özmerzi A (2001). Effect of forward speed
and seed spacing on seeding uniformity of a precision
vacuum metering unit for melon and cucumber seeds.
Akdeniz University Journal of Faculty of Agriculture
14(2): 63–67
Karayel D & Özmerzi A (2007). Comparison of vertical
and lateral seed distribution of furrow openers using
a new criterion. Soil & Tillage Research 95: 69–75
Karayel D & Özmerzi A. (2005). Hassas ekimde
gömücü ayakların tohum dağılımına etkisi. Akdeniz
Üniversitesi Ziraat Fakültesi Dergisi 18(1): 139-150
Karayel D (2009). Performance of a modified precision
vacuum seeder for no-till sowing of maize and
soybean. Soil & Tillage Research 104: 121–125
Karayel D (2010). Sıraya Ekimde Yatay Düzlemdeki
Tohum Dağılımı ve Bitki Yaşam Alanının Voronoi
Poligonlarıyla Değerlendirilmesi. Tarım Bilimleri
Dergisi-Journal of Agricultural Sciences 16: 97-103
Karayel D (2011). Direct Seeding of Soybean Using a
Modified Conventional Seeder. Soybean Applications
and Technology, Rijeka - Croatia 3-18
Park J & Oh S (2012). A New Concave Hull Algorithm and
Concaveness Measure for n-dimensional Datasets.
Journal of Information Science and Engineering 28:
587-600
Srivatsan RA, Viswanath AV & Ramanathan M
(1998). Concave hull of freeform planar curves.
Chennai-600036
Wilkins D E, Kraft J M & Klepper B L (1991). Influence
of plant spacing on pea yield. Transactions of the
ASAE 34(5): 1957-1961
21 (2015) 123-131
131

Full Text - Tarım Bilimleri Dergisi

Transkript

Benzer belgeler

2016 Taiwan Economic and Trade Delegation to Turkey Tentative

Abstract

Mustafa Kemal Üniversitesi

Determination of Fatty Acid, C, H, N and Trace Element

regeneration of fertile plants from sunflower - Field

(Glycine max Merril) Genotypes Using SDS-PAGE Technique

HAND GESTURE RECOGNITION

c-dory 19` angler

Silvicultural characteristics and natural regeneration of Pinus brutia

gungor_ingilizce_katalog_20 sayfalik.FH10