Full Text - Tarım Bilimleri Dergisi
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Full Text - Tarım Bilimleri Dergisi
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: sefa.altikat@igdir.edu.tr, 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: sefa.altikat@igdir.edu.tr, 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 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) 123-131 125 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 A New Approach for Determination of Seed Distribution Area in Vertical Plane, Altıkat et al 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) 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 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 Düşey Düzlemdeki Tohum Dağılım Alanının Belirlenmesinde Yeni Bir Yaklaşım, Altıkat et al 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 üçgenlemasiyleVoronoipoligonları (kesikçizgiler,tümnoktalarıkapsayandışbükey set of Convex Hull points are determined from of the seeds were saved into separate CSV files Another Şekil 4Delaunay üçgenlemasiyleVoronoipoligonları (kesikçizgiler,tümnoktalarıkapsayandışbükey zarf;kesiknoktalıçizgiler, Delaunay üçgenleri;sürekliçizgiler, Voronoipoligonları;daireler,tohumlar) zarf;kesiknoktalıçizgiler, Delaunay üçgenleri;sürekliçizgiler, Voronoipoligonları;daireler,tohumlar) zarf;kesiknoktalıçizgiler,Values Delaunay üçgenleri;sürekliçizgiler, Voronoipoligonları;daireler,tohumlar) 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 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) 123-131 127 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 A New Approach for Determination of Seed Distribution Area in Vertical Plane, Altıkat et al 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 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 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 Seed distribution area (mm2) 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 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) 123-131 129 A New Approach for Determination of Seed Distribution Area in Vertical Plane, Altıkat et al 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 Seed distribution area (mm2) Seed distribution area (mm2) 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 Tractor forward speeds (m (mss-1-1) 47 130 158 0,75 1,25 2,25 Tractor forward speeds (m (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 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 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). 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