Interpolation by Piecewise Quadric Polynomial to Scattered Data Points

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.

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Fitting scattered data points with ball B-Spline curves using particle swarm optimization

Computers & Graphics ◽

10.1016/j.cag.2018.01.006 ◽

2018 ◽

Vol 72 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

Zhongke Wu ◽

Xingce Wang ◽

Yan Fu ◽

Junchen Shen ◽

Qianqian Jiang ◽

...

Keyword(s):

Particle Swarm Optimization ◽

Particle Swarm ◽

Scattered Data ◽

Swarm Optimization ◽

B Spline ◽

Spline Curves ◽

Data Points

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A Technology to Multi-Resolution Surface Reconstruction

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.805-806.1933 ◽

2013 ◽

Vol 805-806 ◽

pp. 1933-1936

Author(s):

Tong Tong Zhu ◽

Gang Xu ◽

Ming Cong Ma ◽

Xing Ye Liu

Keyword(s):

Surface Reconstruction ◽

Characteristic Curve ◽

Scattered Data ◽

Subdivision Surfaces ◽

Texture Characteristic ◽

Reconstruction Process ◽

Mesh Model ◽

Data Points ◽

Image Edge ◽

Short Time

An approach is presented based on scattered data points subdivision surfaces to achieve multi-resolution surface reconstruction techniques. In the surface reconstruction process, based on gray-scale image edge detection ideological eigenvalues scattered data analysis, these features will generate texture characteristic curve values tessellation, thus forming a multi-resolution mesh model structure; After testing, the technology is not only surface reconstruction short time, while the constructed subdivision surfaces can reflect the characteristics of the original details of the data.

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