Urban Building Mesh Polygonization Based on 1-Ring Patch and Topology Optimization

With the development of UAV and oblique photogrammetry technology, the multi-view stereo image has become an important data source for 3D urban reconstruction, and the surface meshes generated by it have become a common way to represent the building surface model due to their high geometric similarity and high shape representation ability. However, due to the problem of data quality and lack of building structure information in multi-view stereo image data sources, it is a huge challenge to generate simplified polygonal models from building surface meshes with high data redundancy and fuzzy structural boundaries, along with high time consumption, low accuracy, and poor robustness. In this paper, an improved mesh representation strategy based on 1-ring patches is proposed, and the topology validity is improved on this basis. Experimental results show that our method can reconstruct the concise, manifold, and watertight surface models of different buildings, and it can improve the processing efficiency, parameter adaptability, and model quality.

Methods for anchoring boundary nodes when smoothing a triangular surface mesh

In numerical modeling tasks that use surface meshes, remeshing is often required. However, while remeshing, distortion can occur. The accumulation of distortions can lead to the collapse of the solution. Smoothing algorithms are used to maintain the quality of the mesh during the calculation. When performing smoothing using methods that shift the mesh nodes, the border nodes are usually fixed to avoid distortion. However, simply fixing the nodes can lead to more severe distortion. This paper presents methods for working with boundary nodes to control such nodes during the smoothing process. Algorithms for working with pseudo-3D surface meshes, which are of particular interest, are also considered.

Extrusioncutter : a novel system for generating interactive context-preserving cutaways of anatomical surface meshes

This thesis presents ExtrusionCutter - a novel 3D visualization tool that enables users to create complex, context-preserving cutaways of anatomical surface meshes. To accomplish this, a "paint-roller" interaction metaphor has been developed that allows users to extrude an editable cutting mesh along the natural geometry of an occluding surface. This virtual analogy of a familiar real-world action not only facilitates the removal of occluding surfaces, but also creates a user-defined region parameterization which makes it possible to also generate an effective contextual outline view of the removed material. This thesis will demonstrate how the paint roller interaction metaphor has been implemented to facilitate the creation of multiple editable cutaway types on 3D anatomical surface meshes. Additionally, it will show that the resulting cutaway views are capable of exposing occluded parts while still maintaining their context in the visualization.

Extrusioncutter : a novel system for generating interactive context-preserving cutaways of anatomical surface meshes

This thesis presents ExtrusionCutter - a novel 3D visualization tool that enables users to create complex, context-preserving cutaways of anatomical surface meshes. To accomplish this, a "paint-roller" interaction metaphor has been developed that allows users to extrude an editable cutting mesh along the natural geometry of an occluding surface. This virtual analogy of a familiar real-world action not only facilitates the removal of occluding surfaces, but also creates a user-defined region parameterization which makes it possible to also generate an effective contextual outline view of the removed material. This thesis will demonstrate how the paint roller interaction metaphor has been implemented to facilitate the creation of multiple editable cutaway types on 3D anatomical surface meshes. Additionally, it will show that the resulting cutaway views are capable of exposing occluded parts while still maintaining their context in the visualization.

A Clustering-Based Bubble Method for Generating High-Quality Tetrahedral Meshes of Geological Models

High-quality mesh generation is critical in the finite element analysis of displacements and stabilities of geological bodies. In this paper, we propose a clustering-based bubble method for generating high-quality tetrahedral meshes of geological models. The proposed bubble method is conducted based on the spatial distribution of the point set of given surface meshes using the clustering method. First, the inputted geological models consisting of triangulated surface meshes are divided into several parts based on spatial distribution of point set, which can be used for the determination of the positions and radii of initial bubbles. Second, a procedure based on distance of nearby bubbles is used to obtain the initial size of bubbles. Third, by enforcing the forces acting on bubbles, all bubbles inside the 3D domain reach an equilibrium state by the motion control equations. Finally, the center nodes of the bubbles can form a high-quality node distribution in the domain, and then the required tetrahedral mesh is generated. Comparative benchmarks are presented to demonstrate that the proposed method is capable of generating highly well-shaped tetrahedral meshes of geological models.

Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes

Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces.

Adaptive Surface Mesh Reconstruction for Computed Tomography Images

In medical applications, it is important to reconstruct surface meshes from Computed Tomography (CT) images. Surface mesh reconstruction of biological tissues actually suffers from staircase artifacts, due to anisotropic CT data. To solve this problem, this paper proposes an adaptive surface mesh reconstruction method. We convert the contour pixels of medical image to contour points and exploit the adaptive spherical cover to produce an approximating surface based on the contour points. Due to the reconstruction quality depending on the accurate normal estimation, computing the normal vectors from the negative gradient based on 3D binary volume data instead of classical principal component analysis (PCA), and then covering contour points by adaptive spheres, linking the auxiliary points in the spheres for reconstructing adaptive triangular meshes. The presented method has been used in CT images of the first cervical vertebrae (C1), scapula, as well as the third lumbar vertebrae (L3) and the results are analyzed regarding their smoothness, accuracy and mesh quality. The results show that our method can reconstruct smooth, accurate and high-quality adaptive surface meshes.

Laplacian-based 3D mesh simplification with feature preservation

We propose a novel Laplacian-based algorithm that simplifies triangle surface meshes and can provide different preservation ratios of geometric features. Our efficient and fast algorithm uses a 3D mesh model as input and initially detects geometric features by using a Laplacian-based shape descriptor (L-descriptor). The algorithm further performs an optimized clustering approach that combines a Laplacian operator with K-means clustering algorithm to perform vertex classification. Moreover, we introduce a Laplacian weighted cost function based on L-descriptor to perform feature weighting and error statistics comparison, which are further used to change the deletion order of the model elements and preserve the saliency features. Our algorithm can provide different preservation ratios of geometric features and may be extended to handle arbitrary mesh topologies. Our experiments on a variety of 3D surface meshes demonstrate the advantages of our algorithm in terms of improving accuracy and applicability, and preserving saliency geometric features.