PDGI-BASED REGULAR SWEPT SURFACE EXTRACTION FROM POINT CLOUD

A principal direction Gaussian image （PDGI）-based algorithm is proposed to extract the regular swept surface from point cloud. Firstly, the PDGI of the regular swept surface is constructed from point cloud, then the bounding box of the Gaussian sphere is uniformly partitioned into a number of small cubes （3D grids） and the PDGI points on the Gaussian sphere are associated with the corresponding 3D grids. Secondly, cluster analysis technique is used to sort out a group of 3D grids containing more PDGI points among the 3D grids. By the connected-region growing algorithm, the congregation point or the great circle is detected from the 3D grids. Thus the translational direction is determined by the congregation point and the direction of the rotational axis is determined by the great circle. In addition, the positional point of the rotational axis is obtained by the intersection of all the projected normal lines of the rotational surface on the plane being perpendicular to the estimated direction of the rotational axis. Finally, a pattem search method is applied to optimize the translational direction and the rotational axis. Some experiments are used to illustrate the feasibility of the above algorithm.

On the Downshift of Wave Frequency for Bragg Resonance

For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the peak reflection coefficient is obtained,has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction.It has long been speculated that the downshift may be attributed to higher-order rippled bottom and free-surface boundary effects,but the intrinsic mechanism remains unclear.By a regular perturbation analysis,we derive the theoretical solution of frequency downshift due to third-order nonlinear effects of both bottom and free-surface boundaries.It is found that the bottom nonlinearity plays the dominant role in frequency downshift while the free-surface nonlinearity actually causes frequency upshift.The frequency downshift/upshift has a quadratic dependence in the bottom/free-surface steepness.Polychromatic bottom leads to a larger frequency downshift relative to the monochromatic bottom.In addition,direct numerical simulations based on the high-order spectral method are conducted to validate the present theory.The theoretical solution of frequency downshift compares well with the numerical simulations and available experimental data.

EFFICIENT SPECTRAL METHODS FOR EIGENVALUE PROBLEMS OF THE INTEGRAL FRACTIONAL LAPLACIAN ONABALLOFANYDIMENSION

An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional Laplacian on a unit ball of any dimension is proposed in this paper.The symmetric positive definite linear system is retained explicitly which plays an important role in the numerical analysis.And a sharp estimate on the algebraic system's condition number is established which behaves as N4s with respect to the polynomial degree N,where 2s is the fractional derivative order.The regularity estimate of solutions to source problems of the fractional Laplacian in arbitrary dimensions is firstly investigated in weighted Sobolev spaces.Then the regularity of eigenfunctions of the fractional Laplacian eigenvalue problem is readily derived.Meanwhile,rigorous error estimates of the eigenvalues and eigenvectors are ob-tained.Numerical experiments are presented to demonstrate the accuracy and efficiency and to validate the theoretical results.

ORDER REDUCED METHODS FOR QUAD-CURL EQUATIONS WITH NAVIER TYPE BOUNDARY CONDITIONS

Quad-curl equations with Navier type boundary conditions are studied in this paper.Stable order reduced formulations equivalent to the model problems are presented,and finite element discretizations are designed.Optimal convergence rates are proved.