In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and ...In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.展开更多
We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improveme...We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.展开更多
Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving...Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving the two proposed mathematical models in 2D and 3D.In this paper,B´ezier curves play an important role in the design of the letters.Three examples with simply and multiply-connected domains in 2D and 3D are presented to demonstrate the visual effect of the letters in Times Roman font.展开更多
It is important to reconstruct a continuous surface representation of the point cloud scanned from a human body. In this paper a new implicit surface method is proposed to reconstruct the human body surface from the p...It is important to reconstruct a continuous surface representation of the point cloud scanned from a human body. In this paper a new implicit surface method is proposed to reconstruct the human body surface from the points based on the combination of radial basis functions （RBFs） and adaptive partition of unity （PoU）. The whole 3D domain of the scanned human body is firstly subdivided into a set of overlapping subdomalns based on the improved octrees. The smooth local surfaces are then computed in the subdomalns based on RBFs. And finally the global human body surface is reconstructed by blending the local surfaces with the adaptive PoU functions. This method is robust for the surface reconstruction of the scanned human body even with large or non-uniform point cloud which has a sharp density variation.展开更多
根据微分几何斯托克斯定理的散度理论,利用面积分和体积分之间的转换关系,将表面重构问题用求隐函数的特征函数问题实现。调用快速傅立叶变换FFTW(The Fastest Fourier Transform in the West)软件包,根据点的位置和法向量计算傅立叶系...根据微分几何斯托克斯定理的散度理论,利用面积分和体积分之间的转换关系,将表面重构问题用求隐函数的特征函数问题实现。调用快速傅立叶变换FFTW(The Fastest Fourier Transform in the West)软件包,根据点的位置和法向量计算傅立叶系数,通过逆变换求出特征函数,选择合适的阈值提取表面的等值面,对于非均匀采样通过采样密度的加权系数进一步计算合理的阈值。实验表明这种通过隐函数方式实现点云的表面重构取得了良好的结果。展开更多
文摘In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.
文摘We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.
基金the financial support of the Ministry of Science and Technology(MOST),Taiwan,under the recruitment of visiting science and technology personnel with subsidies 110-2811-E-002-518the support of sabbatical leave provided by the University of Southern Mississippi.
文摘Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving the two proposed mathematical models in 2D and 3D.In this paper,B´ezier curves play an important role in the design of the letters.Three examples with simply and multiply-connected domains in 2D and 3D are presented to demonstrate the visual effect of the letters in Times Roman font.
基金the National Natural Science Foundation of China (No. 50575139)the Shanghai Special Fund of Informatization (No. 088)
文摘It is important to reconstruct a continuous surface representation of the point cloud scanned from a human body. In this paper a new implicit surface method is proposed to reconstruct the human body surface from the points based on the combination of radial basis functions （RBFs） and adaptive partition of unity （PoU）. The whole 3D domain of the scanned human body is firstly subdivided into a set of overlapping subdomalns based on the improved octrees. The smooth local surfaces are then computed in the subdomalns based on RBFs. And finally the global human body surface is reconstructed by blending the local surfaces with the adaptive PoU functions. This method is robust for the surface reconstruction of the scanned human body even with large or non-uniform point cloud which has a sharp density variation.
文摘根据微分几何斯托克斯定理的散度理论,利用面积分和体积分之间的转换关系,将表面重构问题用求隐函数的特征函数问题实现。调用快速傅立叶变换FFTW(The Fastest Fourier Transform in the West)软件包,根据点的位置和法向量计算傅立叶系数,通过逆变换求出特征函数,选择合适的阈值提取表面的等值面,对于非均匀采样通过采样密度的加权系数进一步计算合理的阈值。实验表明这种通过隐函数方式实现点云的表面重构取得了良好的结果。
