scholarly journals Visualization Terrain Data Using Cubic Ball Triangular Patches

2018 ◽  
Vol 225 ◽  
pp. 06023 ◽  
Author(s):  
Samsul Ariffin Bin Abdul Karim ◽  
Azizan Saaban
Keyword(s):  
Delaunay Triangulation ◽  
Central Region ◽  
Partial Derivative ◽  
Convex Combination ◽  
Scattered Data ◽  
Sufficient Condition ◽  
Surface Data ◽  
Data Points ◽  
Local Scheme

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.

Triangulation Method of 3D Scattered Data Points Based on CAD Model

2011 ◽  
Vol 52-54 ◽  
pp. 139-143
Author(s):  
Shao Ke Chen ◽  
Hui Qun Chen
Keyword(s):  
Delaunay Triangulation ◽  
Large Scale ◽  
Scattered Data ◽  
Divide And Conquer ◽  
Cad Model ◽  
Nurbs Surface ◽  
Object Shape ◽  
3D Mesh ◽  
3D Data ◽  
Data Points

A new method of triangulation for large scale scattered 3D points is proposed. This method is based on the available CAD model, with the thought of DC(divide and conquer).Alignment between the data and the CAD model, registration which establishes correspondence between the data points and those on the CAD trimmed NURBS surface entities;2D-Delaunay triangulation, performed on the corresponding points in the parametric domains(u, v)of each entity, application of the connectivity structure to the 3D data points for each mesh patch; Elimination of redundant triangles of each 3D mesh patch and stitching of patches together. Unlike many other methods, it is not constrained by certain types of measurement distribution or object shape. The experimental results testify that the approach is feasible and efficient.

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

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 159 ◽  
Author(s):  
Fatin Amani Mohd Ali ◽  
Samsul Ariffin Abdul Karim ◽  
Azizan Saaban ◽  
Mohammad Khatim Hasan ◽  
Abdul Ghaffar ◽  
...  
Keyword(s):  
Convex Combination ◽  
Scattered Data ◽  
Coefficient Of Determination ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Digital Elevation ◽  
Standard Set ◽  
C1 Continuity ◽  
Local Schemes ◽  
Corrected Scheme

This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R2). The higher R2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown’s validation.

Triangulated Surface Construction From Scattered 3-D Points

1992 ◽  
Author(s):  
Sridhar Vajapeyam ◽  
Michael Keefe
Keyword(s):  
Mechanical Design ◽  
Three Dimensional ◽  
Scattered Data ◽  
Three Dimensions ◽  
Triangulated Surface ◽  
Biological Surfaces ◽  
Gabriel Graph ◽  
Mri Scans ◽  
Data Points ◽  
Delaunay Triangles

Abstract A three-dimensional analog to the Gabriel Graph structure is defined and an algorithmic procedure for the construction of a triangulated surface from scattered data points in three dimensions is developed based on the concept on three-dimensional Gabriel Graphs. The algorithm does not require the points to be in the form of a grid or on contours. The closest point 3-D Delaunay triangulation of the points is first constructed and the Delaunay triangles that satisfy the Gabriel Graph criterion are identified. From this set of triangles, extraneous triangles are removed, resulting in a triangulated open surface passing through all the given data points. This surface can then be subjected to smoothing algorithms if necessary and a smooth surface of the desired continuity can be constructed using available interpolation techniques. The algorithm can be used for constructing surfaces from scattered data in mechanical design, geographic terrain modeling and modeling biological surfaces from CT scans and MRI scans.

2-D Imaging of Concealed Objects using Circular Co-Arrays at MM Wave Frequencies: Simulation and Experimental Results

2015 ◽  
Vol 65 (5) ◽  
pp. 372
Author(s):  
Rajendra Prasad Dixit
Keyword(s):  
Image Reconstruction ◽  
Data Acquisition ◽  
Central Region ◽  
Scattered Data ◽  
Experimental Results ◽  
Simulation Program ◽  
Single Target ◽  
Quality Image

Simulation and experimental results at 35 GHz, for a single target of unit reflectivity, a concrete pillar and a gun shaped object placed in the central region  of 2-D scene , have been presented using circularly co-located transmit and receive co-arrays. Simulation program has been written in MATLAB to reconstruct the raw image using an improvised algorithm. Simulation and experimental results confirm the method of reconstruction of image. Reconstruction of a Gun-shaped object has also been shown with help of simulation and experimental results. Reconstruction of image has been performed using post data acquisition processing on the received scattered data. Experimental results confirm that the method can be used to reconstruct quality image for detection of concealed metallic objects using MM wave frequencies.

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