Using Google Maps and Spherical Quadrilateral Approach Method for Land Area Measurement Adi Setiawan Eko Sediyono Department of Mathematics Master of Information System Programme Faculty of Science and Mathematics Universitas Kristen Satya Wacana Universitas Kristen Satya Wacana Jl. P. Diponegoro 52-60 Salatiga 50711, Indonesia Jl. P. Diponegoro 52-60 Salatiga 50711, Indonesia Email : [email protected] Abstract— In this paper, we present how to determine the Sjoberg explained how numerical integration is used in the land area measurement by using spherical quadrilateral determination of the area in fields, spheres and ellipsoid [5]. approach method. The proposed method is compared to Likewise, Pedzich and Kuzma presents a method of calculating quadrilateral approach method with the UTM (Universal the area of geodesic polygons used in the Polish region [6]. Transverse Mercator) coordinate system. The spherical quadrilateral approach method delivers in the calculation of the The polygon method and square method are used in the area of DIY and Central Java provinces 3328.2355 km2 and determination of the plantation area of the subdivision of 34978.488 km2, respectively, while the quadrilateral approach Pendowo TBM 2015 PTPN IX Getas, Semarang Regency by method yielded 3613.1760 km2 and 35207.7300 km2. The results considering the land as un contoured land. It is described in obtained by spherical quadrilateral approach method are bigger Alivah et al. [7]. Devi et al. described how the area of land that than the reference areas but less than 10 %. is Semarang regency can also be done using spherical triangle approach method [8]. In addition, Alivah et al. also explained Keywords— Google Maps, Measurement of Land Area, how to determine the area of contoured land with cone and Quadrilateral Approach Method, Spherical Quadrilateral square cone method and it is applied to Gili Trawangan island Approach Method. and plantation land of Afdeling Tembir sub Sembir subdistrict of Pendowo TBM 2015 PTPN IX Getas, Semarang Regency I. INTRODUCTION [9]. Land area measurement is very important in agriculture, plantation and housing. The border of the land are often In this paper, it will be presented how to determine the area irregular and contoured. Determining the coordinates of land of region by using spherical quadrilateral approach method boundaries by using GPS (Global Position System) requires without considering the contour of the region. The borders of field visits to the site of land will be very costly. Today, land can be obtained by using Google Maps. Google Maps provided by Google Inc. is widely used in GIS In this section, it is explained the distance between 2 points (Geographic Information System) e.g. to determine the latitude on the earth that can be considered as an ellipsoid by using and longitude coordinates of location on the surface of the Vincenty formula [10] and [11]. Suppose we have 2 points on earth such that the coordinate of boundary of a region or the earth with coordinate ( ,L ) and ( ,L ) where , are position on the surface of the earth can be determined. More 1 1 2 2 1 2 latitude and L1 and L2 are longitude. In this case, the earth is information of Google Earth can be found in [1] and [2]. considered as an ellipsoid such that a = 6378137.0 meters i.e. Furthermore, the coordinates of the border of the region can be length of semi-major axis of the ellipsoid (radius at equator), used in land area measurement. b = 6356732.314245 meters i.e. length of semi-minor axis of II. LITERATURE REVIEW the ellipsoid (radius at the poles) and f = 1/298.257223563 i.e. flattening of the ellipsoid. Furthermore, it can be used the First, Various methods of land area measurement can be symbols as follows : L = L2 – L1 i.e. the difference in longitude used if the coordinates of the border of the region are known. of two points, Setiawan et al. presented how the circle approach method can U arctan(1 f )tan( ) be used to determine the area of Gili Air island in Lombok 1 1 and West Nusa Tenggara [3]. Devi et al. also explained how the circle approach method is used to determine the area of flat U 2 arctan(1 f ) tan(2 ) region. It was used to determine the football field area at i.e., reduced latitude (latitude on the auxiliary sphere), 1, 2 Universitas Kristen Satya Wacana Salatiga, Rawa Pening Lake i.e. longitude of the points on the auxiliary sphere, 1, 2 i.e. area in Semarang regency and the are of Salatiga City. These forward azimuths at the points, i.e. azimuth at the equator, s three areas are located in Central Java, Indonesia. The concern i.e. ellipsoid distance between the two points. Given the regions can be considered as the surface on the earth coordinates of the two points (1,L1) and (2,L2), the invers considered as an ellipsoid [4]. problem proposed by Vincenty want to find the azimuths and the ellipsoidal distance s. It is calculated U1, U2 and L and set or initial value of -L, then iteratively evaluate the following d (230199.56313373.34)2 (9205585.54 9239273.69)2 equations until converges i.e. 89737.22 meter. That means Vincenty distance is less sin (cosU sin )2 (cosU sinU sinU cosU cos )2 , 2 1 2 1 2 22.587 meter. cos sin U sin U cos U cos U cos , 1 2 1 2 III. RESEARCH METHODS In this research, latitude and longitude coordinates of sin arctan , border of the region are used to determine the land area cos measumerent. The region of concern are the DIY and Central cos U cos U sin Java provinces. A total of 29 points on the top border and 29 sin 1 2 , points on the bottom boder of DIY province are used to sin determine the area of the region. For the province of Central cos 2 1 sin 2 , Java, it is used 45 points on the top border and 45 points on the 2 sin U sin U bottom border. The area is determined by using two spherical 1 2 cos( 2 m ) cos 2 , triangles approach by considering the earth as an ellipsoid. As a cos comparison, the quadrilateral method by using UTM f coordinate system is also used in determining the area of C cos 2 [ 4 f (4 3 cos 2 ) ], 16 concern region using the same points. The results are compared 2 to the area based on the information of Central Bureau of D Csin cos(2 )C cos (12cos (2 )) m m Statistics (BPS - Badan Pusat Statistik) i.e. 3185.80 km2 for the L (1 C ) f sin D . DIY province and 32548 km2 for the Central Java province. When has converged to the desired degrees of accuracy, evaluate the following : IV. RESULTS AND DISCUSSION a 2 b 2 The proposed method is applied to determine the area of u 2 cos 2 , b 2 Central Java province and can be described as follows. Table I 2 presents 5 coordinates of top border and 5 coordinates of u A 1 4096 u 2 [ 768 u 2 (320 175 u 2 )], bottom border respectively A, B, C, D, E and A, B, C, D, E. 16384 Based on Table I, the given coordinates can be conversed in 1 E B [ cos (2 ) (3 4 sin 2 ) (3 4 cos 2 (2 ))], UTM coordinates as presented in Table II. To obtain the UTM 6 m m coordinate system from longitude and latitude coordinate 1 system can be used web based program package. 2 F B [ cos ( 1 2 cos ( 2 m )) E ], 4 B sin ( cos( 2 m ) F ), s b A( ), cos U sin 2 1 arctan , cos U 1 sin U 2 sin U 1 cos U 2 cos cos U sin 1 2 arctan . sin U 1 cos U 2 cos U 1 sin U 2 cos Later, Vincenty formula is modified by using formula : k 2 1 1 4 3 2 A , B k1 1 k1 1 k 1 8 where 1 u 2 1 k 1 . Fig 1. Map of Central Java. 1 u 2 1 To illustrate the use of the Vincenty formula, suppose point A has coordinates (-7,180433, 108,557056) and point B has The area of the spherical quadrilateral region is presented in coordinates (-6,879217, 109,310992). After 5 iterations, will Fig. 1 with the vertices B, C, B and C that are located on the converge such that Vincenty distance between A and B is surface of the earth by considering the earth as an ellipsoid. 89714.636 meter. In UTM coordinate system, point A and B Using the Vincenty formula, the distance c = BC, d = CB, has coordinate (230199.56, 9205585.54) and (313373.34, 9239273.69), respectively. By using UTM coordinate, the e = BC, g = CC are spherical quadrilateral sides where distance between A and B can be found by using Euclide c = 75183.014934, d = 102616.794342, e = 81188.155580, distance : g = 130577.299289 (in meters). Furthermore, it also can be obtained side h = BC = 130577.299289 meters. 2 2 d ( x A x B ) ( y A y B ) d c h 1 1 1 Table I. Latitude and Longitude Coordinate of Border of Central Java. 1 arc cos 0.90212495 , c2 h2 No. Location Latitude Longitude h1 c1d1 1 A -7.180433 108.557056 arc cos 1.62709448. c d 2 B -6.879217 109.310992 2 2 3 C -6.929661 109.989398 In a similar way, 2, , 2 in spherical triangle BCB can also 4 D -6.480940 110.698016 be determined by cosines rule in spherical triangle i.e.