A Robust Fast Bridging Algorithm for Laser Cutting

Bridging the different parts together is considered a simple but effective strategy to reduce the number of piercing operations during laser cutting. However, fast bridging is never an easy task. In this paper, we present a near-linear bridging algorithm for the input parts with the shortest total bridge length. At first, the input part contours are discretized into a point cloud, then the point cloud is triangulated with the Delaunay standard. The shortest line segments between any two adjacent parts are found in the triangles connecting the two parts. These segments are finally extended into bridges. To solve the problem of the damages to the contour characteristics caused by the bridges, some restrictions are set on the screening of the discrete point cloud and the Delaunay triangles. This algorithm not only ensures the minimum total distance of all bridges, but also avoids the problem of generating bridge loops. Computational experiments show that the proposed bridging algorithm is much faster than that in existing commercial software. The feasibility and superiority of the algorithm are verified by actual lasering cutting experiments.

Accurate Volume Calculation Driven by Delaunay Triangulation for Coal Measurement

Volume calculation from 3D point cloud is widely used in engineering and applications. The existing methods either have large errors or are time-consuming. This paper focuses on the coal measurement. Based on the triangular mesh generated from the point cloud, each triangle is projected downward to the base plane to form a voxel. We derive the calculation formula of voxel by an integral method, which is more efficient than the method of decomposing voxel into tetrahedrons and more accurate than slicing methods. Furthermore, this paper proposes a Delaunay triangulation-driven volume calculation (DTVC) method. DTVC does not preserve the Delaunay triangles but directly calculates the volume in the process of triangulation. It saves memory and running time. Experimental results show that DTVC has achieved a good balance between error and efficiency.

A Zonal Displacement Approach via Grid Point Weighting in Building Generalization

When generalizing a group of objects, displacement is an essential operation to resolve the conflicts arising between them due to enlargement of their symbol sizes and reduction of available map space. Although there are many displacement methods, most of them are rather complicated. Therefore, more practical methods are still needed. In this article, a new building displacement approach is proposed. For this purpose, buildings are grouped and zones are created for them in the blocks via Voronoi tessellation and buffering. Linear patterns are then detected through buffer analyses and the respective zones are narrowed to be able to preserve these patterns. After all the buildings are displaced inside their zones, grid points are generated and then weighted through kernel density estimation and buffer analyses to find suitable locations. Accordingly, the buildings are displaced toward the computed locations iteratively. The proposed approach directly enforces minimum distance and positional accuracy constraints while several indirect mechanisms are used for preserving spatial patterns and relationships. For the quality evaluation of the displacement, the angle, length and shape comparison measures are introduced, computed based on the (Delaunay) triangles or the azimuth comparison measure of the connection lines, generated for the buildings. The quality evaluation criteria are yielded according to the visual assessment of the displacement quality and the quantitative analysis of the measures. The findings demonstrate that the proposed approach is quite effective and practical for zonal building displacement.

Faulted geological contacts: constraining uncertainty of discontinuities orientation using triangulation and combinatorial algorithm

<p>Subsurface information is usually a limited resource in geological modelling. This is not the case, however, for the Kraków-Silesian Homocline in central Poland. It was subject to rapid exploitation of ore-bearing clays in the second half of the 20<sup>th </sup>century. Exhaustive geological documentation remained after this activity had ceased and it contains thousands of borehole records. A small part of this resource has recently been incorporated to propose a new method for determining the dominant orientation of a selected geological contact. This new method regarded Delaunay triangles as source of local orientations that were then analyzed on stereonets. The geological contacts in this region are inclined gently towards NE, but they are also faulted and indicate some stratigraphic noise which makes the extraction of dominant orientation a challenging task.</p><p>It is still unknown, however, to which extent the proposed modelling approach is capable of detecting faults and calculating their orientation. This is particularly important for the introduction of a new method for the recognition of faults based on investigating spatial distribution of orientation patterns. This expert-guided methodology assumes to relate orientation trends with genetic trends and investigate them on 2D maps.</p><p>In this research, we built synthetic models of faulted contacts to observe the behaviour of triangles intersecting the fault surface. To observe the variability of the orientation at larger scale, and perhaps to constrain it at the same time, we applied a combinatorial algorithm for creating all three-element subsets from an n-element set. The employment of this combinatorial approach allowed to achieve a better clustering effect around the expected orientation. The limitation of the proposed approach can be attributed to some unexpected and unintuitive orientations. Compared to previous studies these singularities seem to be geometrical and not numerical in nature.</p>

Application of Tessellation in Architectural Geometry Design

Tessellation plays a significant role in architectural geometry design, which is widely used both through history of architecture and in modern architectural design with the help of computer technology. Tessellation has been found since the birth of civilization. In terms of dimensions, there are two- dimensional tessellations and three-dimensional tessellations; in terms of symmetry, there are periodic tessellations and aperiodic tessellations. Besides, some special types of tessellations such as Voronoi Tessellation and Delaunay Triangles are also included. Both Geometry and Crystallography, the latter of which is the basic theory of three-dimensional tessellations, need to be studied. In history, tessellation was applied into skins or decorations in architecture. The development of Computer technology enables tessellation to be more powerful, as seen in surface control, surface display and structure design, etc. Therefore, research on the application of tessellation in architectural geometry design is of great necessity in architecture studies.

ADAPTIVE HIERARCHICAL DENSE MATCHING OF MULTI-VIEW AIRBORNE OBLIQUE IMAGERY

Traditional single-lens vertical photogrammetry can obtain object images from the air with rare lateral information of tall buildings. Multi-view airborne photogrammetry can get rich lateral texture of buildings, while the common area-based matching for oblique images may lose efficacy because of serious geometric distortion. A hierarchical dense matching algorithm is put forward here to match two oblique airborne images of different perspectives. Based on image hierarchical strategy and matching constraints, this algorithm delivers matching results from the upper layer of the pyramid to the below and implements per-pixel dense matching in the local Delaunay triangles between the original images. Experimental results show that the algorithm can effectively overcome the geometric distortion between different perspectives and achieve pixel-level dense matching entirely based on the image space.