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Interpolation Using Cubic Bѐzier Triangular Patches

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@article{IJASEIT6780,
   author = {Samsul Ariffin Abdul Karim and Azizan Saaban and Mohammad Khatim Hasan and Jumat Sulaiman and Ishak Hashim},
   title = {Interpolation Using Cubic Bѐzier Triangular Patches},
   journal = {International Journal on Advanced Science, Engineering and Information Technology},
   volume = {8},
   number = {4-2},
   year = {2018},
   pages = {1746--1752},
   keywords = {},
   abstract = {Spatial interpolation is a method that can be used to estimate the unknown value (or parameter) at certain time or location.  Besides of that, shape preserving interpolation especially positivity preserving interpolation play an important role for data visualization where the resulting interpolating surface must be positive everywhere. In this study, we use a triangulation based method consists of positivity preserving cubic Bézier triangular patches to estimate the unknown value of rainfall amount at spatial localization.  This scheme is useful for spatial data interpolation compared to the mesh free methods which are required the optimization technique in order to ensure the positivity of basis functions.The data is triangulated by using Delaunay’s triangulation algorithm and from there the triangular surfaces are constructed piecewisely comprising three local schemes that are blended together via convex combination to form a scattered interpolating surface. Sufficient conditions on Bézier ordinates are derived in order to preserve the positivity of the surface. Validation of the propose schemes are conducted by using well-known test function used in previous researches. Then, the best the scheme is selected to visualize a rainfall data distribution based on secondary data collected at various meteorology stations in Malaysia obtain from Malaysian Meteorology Department.  Finally, we estimate the unknown rainfall amount at certain locations that lies inside the convex hull formed by all given stations. The finding shows that positivity preserving cubic triangular patches is able to preserve the positivity of rainfall distribution surface and has a significant application in estimating the rainfall amount at unallocated meteorology stations in Malaysia.},
   issn = {2088-5334},
   publisher = {INSIGHT - Indonesian Society for Knowledge and Human Development},
   url = {http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=6780},
   doi = {10.18517/ijaseit.8.4-2.6780}
}

EndNote

%A Abdul Karim, Samsul Ariffin
%A Saaban, Azizan
%A Hasan, Mohammad Khatim
%A Sulaiman, Jumat
%A Hashim, Ishak
%D 2018
%T Interpolation Using Cubic Bѐzier Triangular Patches
%B 2018
%9 
%! Interpolation Using Cubic Bѐzier Triangular Patches
%K 
%X Spatial interpolation is a method that can be used to estimate the unknown value (or parameter) at certain time or location.  Besides of that, shape preserving interpolation especially positivity preserving interpolation play an important role for data visualization where the resulting interpolating surface must be positive everywhere. In this study, we use a triangulation based method consists of positivity preserving cubic Bézier triangular patches to estimate the unknown value of rainfall amount at spatial localization.  This scheme is useful for spatial data interpolation compared to the mesh free methods which are required the optimization technique in order to ensure the positivity of basis functions.The data is triangulated by using Delaunay’s triangulation algorithm and from there the triangular surfaces are constructed piecewisely comprising three local schemes that are blended together via convex combination to form a scattered interpolating surface. Sufficient conditions on Bézier ordinates are derived in order to preserve the positivity of the surface. Validation of the propose schemes are conducted by using well-known test function used in previous researches. Then, the best the scheme is selected to visualize a rainfall data distribution based on secondary data collected at various meteorology stations in Malaysia obtain from Malaysian Meteorology Department.  Finally, we estimate the unknown rainfall amount at certain locations that lies inside the convex hull formed by all given stations. The finding shows that positivity preserving cubic triangular patches is able to preserve the positivity of rainfall distribution surface and has a significant application in estimating the rainfall amount at unallocated meteorology stations in Malaysia.
%U http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=6780
%R doi:10.18517/ijaseit.8.4-2.6780
%J International Journal on Advanced Science, Engineering and Information Technology
%V 8
%N 4-2
%@ 2088-5334

IEEE

Samsul Ariffin Abdul Karim,Azizan Saaban,Mohammad Khatim Hasan,Jumat Sulaiman and Ishak Hashim,"Interpolation Using Cubic Bѐzier Triangular Patches," International Journal on Advanced Science, Engineering and Information Technology, vol. 8, no. 4-2, pp. 1746-1752, 2018. [Online]. Available: http://dx.doi.org/10.18517/ijaseit.8.4-2.6780.

RefMan/ProCite (RIS)

TY  - JOUR
AU  - Abdul Karim, Samsul Ariffin
AU  - Saaban, Azizan
AU  - Hasan, Mohammad Khatim
AU  - Sulaiman, Jumat
AU  - Hashim, Ishak
PY  - 2018
TI  - Interpolation Using Cubic Bѐzier Triangular Patches
JF  - International Journal on Advanced Science, Engineering and Information Technology; Vol. 8 (2018) No. 4-2
Y2  - 2018
SP  - 1746
EP  - 1752
SN  - 2088-5334
PB  - INSIGHT - Indonesian Society for Knowledge and Human Development
KW  - 
N2  - Spatial interpolation is a method that can be used to estimate the unknown value (or parameter) at certain time or location.  Besides of that, shape preserving interpolation especially positivity preserving interpolation play an important role for data visualization where the resulting interpolating surface must be positive everywhere. In this study, we use a triangulation based method consists of positivity preserving cubic Bézier triangular patches to estimate the unknown value of rainfall amount at spatial localization.  This scheme is useful for spatial data interpolation compared to the mesh free methods which are required the optimization technique in order to ensure the positivity of basis functions.The data is triangulated by using Delaunay’s triangulation algorithm and from there the triangular surfaces are constructed piecewisely comprising three local schemes that are blended together via convex combination to form a scattered interpolating surface. Sufficient conditions on Bézier ordinates are derived in order to preserve the positivity of the surface. Validation of the propose schemes are conducted by using well-known test function used in previous researches. Then, the best the scheme is selected to visualize a rainfall data distribution based on secondary data collected at various meteorology stations in Malaysia obtain from Malaysian Meteorology Department.  Finally, we estimate the unknown rainfall amount at certain locations that lies inside the convex hull formed by all given stations. The finding shows that positivity preserving cubic triangular patches is able to preserve the positivity of rainfall distribution surface and has a significant application in estimating the rainfall amount at unallocated meteorology stations in Malaysia.
UR  - http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=6780
DO  - 10.18517/ijaseit.8.4-2.6780

RefWorks

RT Journal Article
ID 6780
A1 Abdul Karim, Samsul Ariffin
A1 Saaban, Azizan
A1 Hasan, Mohammad Khatim
A1 Sulaiman, Jumat
A1 Hashim, Ishak
T1 Interpolation Using Cubic Bѐzier Triangular Patches
JF International Journal on Advanced Science, Engineering and Information Technology
VO 8
IS 4-2
YR 2018
SP 1746
OP 1752
SN 2088-5334
PB INSIGHT - Indonesian Society for Knowledge and Human Development
K1 
AB Spatial interpolation is a method that can be used to estimate the unknown value (or parameter) at certain time or location.  Besides of that, shape preserving interpolation especially positivity preserving interpolation play an important role for data visualization where the resulting interpolating surface must be positive everywhere. In this study, we use a triangulation based method consists of positivity preserving cubic Bézier triangular patches to estimate the unknown value of rainfall amount at spatial localization.  This scheme is useful for spatial data interpolation compared to the mesh free methods which are required the optimization technique in order to ensure the positivity of basis functions.The data is triangulated by using Delaunay’s triangulation algorithm and from there the triangular surfaces are constructed piecewisely comprising three local schemes that are blended together via convex combination to form a scattered interpolating surface. Sufficient conditions on Bézier ordinates are derived in order to preserve the positivity of the surface. Validation of the propose schemes are conducted by using well-known test function used in previous researches. Then, the best the scheme is selected to visualize a rainfall data distribution based on secondary data collected at various meteorology stations in Malaysia obtain from Malaysian Meteorology Department.  Finally, we estimate the unknown rainfall amount at certain locations that lies inside the convex hull formed by all given stations. The finding shows that positivity preserving cubic triangular patches is able to preserve the positivity of rainfall distribution surface and has a significant application in estimating the rainfall amount at unallocated meteorology stations in Malaysia.
LK http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=6780
DO  - 10.18517/ijaseit.8.4-2.6780