Visualization Terrain Data Using Cubic Ball Triangular Patches

Abstract

Scattered data technique is important to visualize the geometrical images of the surface data especially for terrain, earthquake, geochemical distribution, rainfall etc. The main objective of this study is to visualize the terrain data by using cubic Ball triangular patches. First step, the terrain data is triangulated by using Delaunay triangulation. Then partial derivative will be estimated at the data points. Sufficient condition for C1 continuity will be derived for each triangle. Finally, a convex combination comprising three rational local scheme is used to construct the surface. The scheme is tested to visualize the terrain data collected at central region of Malaysia.

Construction of new cubic Bézier-like triangular patches with application in scattered data interpolation

“…Considering numerical results, the results are almost the same as by using cubic Bézier triangular patches except that the computation is less by 7% by using cubic Ball triangular [14,15]. Karim and Saaban [21] have proved that the scheme of Said and Rahmat [29] is not producing C 1 surface everywhere in the given triangular domain. Karim et al [20] discussed spatial interpolation for rainfall scattered data by extending the results from Chan and Ong [3].…”

“…The direction vectors e i , i = 1, 2, 3, on the side opposite to the vertex V i are given as Fig. 5 [21]). The directional derivatives for P(u, v, w) on the direction z = (z 1 , z 2 , z 3 ), where z 1 + z 2 + z 3 = 0, are given as…”

“…5, the directional derivatives at V 1 i.e. along the edges e 2 and e 3 are calculated as follows: Vertices and edges of the triangle from [21] where F(V 1 ) = b 300 , F x (V 1 ) and F y (V 1 ) are given at the vertex V 1 . Similarly, we can obtain that F(V 2 ) = b 030 , F x (V 2 ) and F y (V 2 ) and F(V 3 ) = b 003 , F x (V 3 ) and F y (V 3 ).…”

Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation

“…Most researchers have investigated surface interpolation based on triangulations of scattered data and there are several scattered data fitting techniques, such as the Delaunay triangulation method [1], radial basis function (RBF) [2], and moving least square (MLS) [3]. Very recently, new techniques for interpolating scattered data have been developed [1,4,5], which can be implemented in fast algorithms [6].…”

“…The property of shape preserving interpolation is an important technique usually applied in curve and surface modeling. Several research papers [2,[7][8][9][10][11][12][13] have been published on shape preservation in the last couple of years. Ibraheem et al [14] proposed a scheme that is suitable for surface reconstruction and deformation.…”