An application of techniques is presented to construct G￣1 smooth surfaces by using acombination of the rectangular and triangular Bezier patches of degree as low as possible. TheG￣1 smooth surfaces have the local p...An application of techniques is presented to construct G￣1 smooth surfaces by using acombination of the rectangular and triangular Bezier patches of degree as low as possible. TheG￣1 smooth surfaces have the local property and interpolate the given data and inherit thetopology imposed by the given space convex quadrilateral partition and triangulation. The papergeneralizes current approaches for assembling of rectangular and triangular patches.展开更多
This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with C1 continuity everywhere.We derive the C1 condition on each adjacent triangle.On each triangular patch,we...This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with C1 continuity everywhere.We derive the C1 condition on each adjacent triangle.On each triangular patch,we employ convex combination method between three local schemes.The final interpolant with the rational corrected scheme is suitable for regular and irregular scattered data sets.We tested the proposed scheme with 36,65,and 100 data points for some well-known test functions.The scheme is also applied to interpolate the data for the electric potential.We compared the performance between our proposed method and existing scattered data interpolation schemes such as Powell–Sabin(PS)and Clough–Tocher(CT)by measuring the maximum error,root mean square error(RMSE)and coefficient of determination(R^(2)).From the results obtained,our proposed method is competent with cubic Bézier,cubic Ball,PS and CT triangles splitting schemes to interpolate scattered data surface.This is very significant since PS and CT requires that each triangle be splitting into several micro triangles.展开更多
This paper describes practical approaches on how to construct bounding pyramids and bounding cones for triangular Bezier surfaces. Examples are provided to illustrate the process of construction and comparison is made...This paper describes practical approaches on how to construct bounding pyramids and bounding cones for triangular Bezier surfaces. Examples are provided to illustrate the process of construction and comparison is made between various surface bounding volumes. Furthermore, as a starting point for the construction, we provide a way to compute hodographs of triangular Bezier surfaces and improve the algorithm for computing the bounding cone of a set of vectors. [ABSTRACT FROM AUTHOR]展开更多
A Particle Image Velocimetry (PIV) method based on the image separation andreconstruction with the median filter and triangular Bezier patch was proposed to measure multiplevelocity fields from single-camera images in...A Particle Image Velocimetry (PIV) method based on the image separation andreconstruction with the median filter and triangular Bezier patch was proposed to measure multiplevelocity fields from single-camera images in the present study. The method was examined on syntheticPIV images with the Green-Taylor two-phase vortex flows and the test results showed high accuracyand highly correct tracking percent compared with the exact solution. An experiment of the bubblyjet flow was also conducted as a practical demonstration of the present method. As a result, it isconfirmed from the simulation image examination and the experimental measurement that the proposedmethod shows a good performance in the measurement of bubble and particle phases.展开更多
文摘An application of techniques is presented to construct G￣1 smooth surfaces by using acombination of the rectangular and triangular Bezier patches of degree as low as possible. TheG￣1 smooth surfaces have the local property and interpolate the given data and inherit thetopology imposed by the given space convex quadrilateral partition and triangulation. The papergeneralizes current approaches for assembling of rectangular and triangular patches.
基金This research was fully supported by Universiti Teknologi PETRONAS(UTP)and Ministry of Education,Malaysia through research grant FRGS/1/2018/STG06/UTP/03/1/015 MA0-020(New rational quartic spline interpolation for image refinement)and UTP through a research grant YUTP:0153AA-H24(Spline Triangulation for Spatial Interpolation of Geophysical Data).
文摘This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with C1 continuity everywhere.We derive the C1 condition on each adjacent triangle.On each triangular patch,we employ convex combination method between three local schemes.The final interpolant with the rational corrected scheme is suitable for regular and irregular scattered data sets.We tested the proposed scheme with 36,65,and 100 data points for some well-known test functions.The scheme is also applied to interpolate the data for the electric potential.We compared the performance between our proposed method and existing scattered data interpolation schemes such as Powell–Sabin(PS)and Clough–Tocher(CT)by measuring the maximum error,root mean square error(RMSE)and coefficient of determination(R^(2)).From the results obtained,our proposed method is competent with cubic Bézier,cubic Ball,PS and CT triangles splitting schemes to interpolate scattered data surface.This is very significant since PS and CT requires that each triangle be splitting into several micro triangles.
基金This work was supported by the National Natural Science Foundation of China(Grant No.601 73052)Shandong Province Natural Science Foundation(Grant No.Z2001G01)Doctoral Program of High Education of China(Grant No.20020422030).
基金NKBRSF on Mathematics Mechanics! (grant G1998030600)the National Natural Science Foundation of China! (grants 69603009 and 1
文摘This paper describes practical approaches on how to construct bounding pyramids and bounding cones for triangular Bezier surfaces. Examples are provided to illustrate the process of construction and comparison is made between various surface bounding volumes. Furthermore, as a starting point for the construction, we provide a way to compute hodographs of triangular Bezier surfaces and improve the algorithm for computing the bounding cone of a set of vectors. [ABSTRACT FROM AUTHOR]
文摘A Particle Image Velocimetry (PIV) method based on the image separation andreconstruction with the median filter and triangular Bezier patch was proposed to measure multiplevelocity fields from single-camera images in the present study. The method was examined on syntheticPIV images with the Green-Taylor two-phase vortex flows and the test results showed high accuracyand highly correct tracking percent compared with the exact solution. An experiment of the bubblyjet flow was also conducted as a practical demonstration of the present method. As a result, it isconfirmed from the simulation image examination and the experimental measurement that the proposedmethod shows a good performance in the measurement of bubble and particle phases.
