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Incremental algorithms are among the most popular approaches for Delaunay triangulation, and the point insertion sequence has a substantial impact on the amount of work needed to construct Delaunay triangulations in incremental algorithm triangulation. In this paper, 2D adaptive Hilbert curve insertion, including the method of dividing 3D multi-grids and adjusting the 3D adaptive Hilbert curve to avoid the “jump” phenomenon, is extended to 3D Delaunay triangulation. In addition, on the basis of adaptive Hilbert curve insertion, we continue to optimize the addition of control points by selecting control points in every order and every grid level. As a result, the number of conflicting elongated tetrahedra that have to be created and deleted multiple times and the number of search steps for positioning inserted points can both be reduced. Lastly, a new comparison method is used in the point location process to solve the precision problem in 3D Delaunay triangulation. As shown by detailed experiments and analysis, compared with previous adaptive Hilbert curve insertion, CGAL, regular grid insertion, multi-grid insertion and random insertion, the proposed 3D Delaunay triangulation is the most efficient for both artificial and real surface sampling point sets.

This paper presents a surface reconstruction algorithm that takes an unoriented point cloud as input and produces an interpolating surface in the form of triangulation. Based on region-growing and Delaunay approaches, this algorithm aims to address the difficulties of reconstruction from point data with imperfections. Starting with a seed triangle from the Delaunay tetrahedron result for input points, the surface is gradually formed by adding the linked Delaunay triangle from the current boundaries one by one. During surface growth, the topology errors and the quantity of the holes generated by adding inappropriate triangles can be reduced by changing the triangle selection criteria and adjusting the addition order of the triangles. We evaluated our method using a wide range of datasets, and this method compares well to popular classic and current algorithms with unoriented input points and triangulated surface output. In addition, to achieve results with a small number of holes on the generated surface, a detection and repair approach is proposed to turn the holes of various shapes into smooth surfaces.

Line integral convolution (LIC) is a useful visualization technique for a vector field. However, the output image produced by LIC has many problems in a marine vector field. We focus on the visual quality improvement when LIC is applied in the ocean steady and unsteady flow field in the following aspects. When a white noise is used as the input in a steady flow field, interpolation is used to turn the discrete white noise into continuous white noise to solve the problem of discontinuity. The “cross” high-pass filtering is used to enhance the textures of streamlines to be more concentrated and continuity strengthened for each streamline. When a sparse noise is used as the input in a steady flow field, we change the directions of background sparse noise according to the directions of vector field to make the streamlines clearer and brighter. In addition, we provide a random initial phase for every streamline to avoid the pulsation effect during animation. The velocities of vector field are encoded in the speed of the same length streamlines so that the running speed of streamlines can express flow rate. Meanwhile, to solve the problem of obvious boundaries when stitching image, we change the streamline tracking constraints. When a white noise is used as an input in an unsteady flow field, double value scattering is used to enhance the contrast of streamlines; moreover, the “cross” high-pass filtering is also adopt instead of two-dimensional high-pass filtering. Finally, we apply the above methods to a case of the surface wave field in typhoon condition. Our experimental results show that applying the methods can generate high-quality wave images and animations. Therefore, it is helpful to understand and study waves in typhoon condition to avoid the potential harm of the waves to people’s lives and property.

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