Geometric Simplifications of Natural Caves in Ray-Tracing-Based Propagation Modelling

Natural caves show some similarities to human-made tunnels, which have previously been the subject of radio-frequency propagation modelling using deterministic ray-tracing techniques. Since natural caves are non-uniform because of their inherent concavity and irregular limestone formations, detailed 3D models contain a large number of small facets, which can have a detrimental impact on the ray-tracing computational complexity as well as on the modelling accuracy. Here, we analyse the performance of ray tracing in repeatedly simplified 3D descriptions of two caves in the UK, i.e., Kingsdale Master Cave (KMC) Roof Tunnel and Skirwith Cave. The trade-off between the size of the reflection surface and the modelling accuracy is examined. Further, by reducing the number of facets, simulation time can be reduced significantly. Two simplification methods from computer graphics were applied: Vertex Clustering and Quadric Edge Collapse. We compare the ray-tracing results to the experimental measurements and to the channel modelling based on the modal theory. We show Edge Collapse to be better suited for the task than Vertex Clustering, with larger simplifications being possible before the passage becomes entirely blocked. The use of model simplification is predominantly justified by the computational time gains, with the acceptable simplified geometries roughly halving the execution time given the laser scanning resolution of 10 cm.

3D mesh simplification with feature preservation based on Whale Optimization Algorithm and Differential Evolution

Large-scale 3D models consume large computing and storage resources. To address this challenging problem, this paper proposes a new method to obtain the optimal simplified 3D mesh models with the minimum approximation error. First, we propose a feature-preservation edge collapse operation to maintain the feature edges, in which the collapsing cost is calculated in a novel way by combining Gauss curvature and Quadratic Error Metrics (QEM). Second, we introduce the edge splitting operation into the mesh simplification process and propose a hybrid ‘undo/redo’ mechanism that combines the edge splitting and edge collapse operation to reduce the number of long and narrow triangles. Third, the proposed ‘undo/redo’ mechanism can also reduce the approximation error; however, it is impossible to manually choose the best operation sequence combination that can result in the minimum approximation error. To solve this problem, we formulate the proposed mesh simplification process as an optimization model, in which the solution space is composed of the possible combinations of operation sequences, and the optimization objective is the minimum of the approximation error. Finally, we propose a novel optimization algorithm, WOA-DE, by replacing the exploration phase of the original Whale Optimization Algorithm (WOA) with the mutate and crossover operations of Differential Evolution (DE) to compute the optimal simplified mesh model more efficiently. We conduct numerous experiments to test the capabilities of the proposed method, and the experimental results show that our method outperforms the previous methods in terms of the geometric feature preservation, triangle quality, and approximation error.

Edge collapse and subsequent longitudinal accretion in filament S242

Filament S242 is 25 pc long with massive clumps and YSO clusters concentrated in its end regions; it is considered a good example of edge collapse. We mapped this filament in the 12CO(1–0) and 13CO(1–0) lines. A large-scale velocity gradient along filament S242 has been detected; the relative velocity between the two end-clumps is ~3 km s−1, indicating an approaching motion between them. These signatures are consistent with the filament S242 being formed through the collapse of a single elongated entity, where an effect known as “gravitational focusing” drives the ends of the filament to collapse (edge collapse). Based on this picture, we estimate a collapse timescale of ~4.2 Myr, which is the time needed for a finite and elongated entity evolving to the observed filament S242. For the whole filament, we find that increases in surface densities lead to increases in velocity dispersion, which can be consistently explained as the result of self-gravity. We also calculated the contribution of longitudinal collapse to the observed velocity dispersion and found it to be the dominant effect in driving the gas motion near the end-clumps. We propose that our filament S242 is formed through a two-stage collapse model, where the edge collapse of a truncated filament is followed by a stage of longitudinal accretion toward the dense end-clumps.

Mesh simplification algorithm based on edge curvature metrics and local optimization

Aiming at the problem that the mesh simplification algorithm loses the geometric features of the model in large-scale simplification, an improved half-edge collapse mesh simplification algorithm is proposed. The concept of approximate measurement of edge curvature is introduced, and the edge curvature is added to the error measure, so that the order of half-edge collapse of the mesh is changed, and the simplified details of the mesh model can be preserved accurately. At the same time, by analyzing the quality of simplified triangular mesh, optimizing triangular mesh locally, reducing the amount of narrow triangles, the quality of the simplified model is improved. The proposed algorithm was tested on Cow model, Car model and Bunny model, and compared with another three algorithms, one of them is a classical mesh simplification algorithm based on edge collapse, the other is an improved algorithm of the classical one. The experimental results show that the improved algorithm can better retain the detail features of the original model at the same reduction ratio, and has reasonable mesh allocation, fast execution speed and small error.

Continuous-Scale 3D Terrain Visualization Based on a Detail-Increment Model

Triangulated irregular networks (TINs) are widely used in terrain visualization due to their accuracy and efficiency. However, the conventional algorithm for multi-scale terrain rendering, based on TIN, has many problems, such as data redundancy and discontinuities in scale transition. To solve these issues, a method based on a detail-increment model for the construction of a continuous-scale hierarchical terrain model is proposed. First, using the algorithm of edge collapse, based on a quadric error metric (QEM), a complex terrain base model is processed to a most simplified model version. Edge collapse records at different scales are stored as compressed incremental information in order to make the rendering as simple as possible. Then, the detail-increment hierarchical terrain model is built using the incremental information and the most simplified model version. Finally, the square root of the mean minimum quadric error (MMQE), calculated by the points at each scale, is considered the smallest visible object (SVO) threshold that allows for the scale transition with the required scale or the visual range. A point cloud from Yanzhi island is converted into a hierarchical TIN model to verify the effectiveness of the proposed method. The results show that the method has low data redundancy, and no error existed in the topology. It can therefore meet the basic requirements of hierarchical visualization.