Discrete Plane Segmentation and Estimation from a Point Cloud Using Local Geometric Patterns

This paper presents a method for segmenting a 3D point cloud into planar surfaces using recently obtained discretegeometry results. In discrete geometry, a discrete plane is defined as a set of grid points lying between two parallel planes with a small distance, called thickness. In contrast to the continuous case, there exist a finite number of local geometric patterns （LGPs） appearing on discrete planes. Moreover, such an LGP does not possess the unique normal vector but a set of normal vectors. By using those LGP properties, we first reject non-linear points from a point cloud, and then classify non-rejected points whose LGPs have common normal vectors into a planar-surface-point set. From each segmented point set, we also estimate the values of parameters of a discrete plane by minimizing its thickness.

Effect of geometric micro-groove texture patterns on tribological performance of stainless steel

This work describes an experimental investigation into the influence of geometric micro-groove texture patterns on the tribological performance of stainless steel.Five geometries were studied:one with untextured and four with micro-groove textured making parallel,triangular,square and hexagonal patterns.The micro-groove textures were produced using an MFT-20laser system as well as a two-step laser surface texturing(LST)process.Tribological performance was measured using a pin-on-disk tribometer.The investigation showed that the two-step LST process could fabricate high-precision micro-grooves.The experimental data indicated that the micro-groove textured surfaces achieved the lower frictional coefficients than the untextured surface and the geometric patterns had significantly affected the tribological properties of samples in both lubricated and unlubricated states.The results were analyzed from the lubricant supplying and fluid dynamic pressure effect under lubricated conditions as well as abrasive capture and remove under dry friction conditions.

Evolution of Islamic geometric patterns

This research demonstrates the suitability of applying Islamic geometrical patterns （IGPs） to architectural elements in terms of time scale accuracy and style matching. To this end, a detailed survey is conducted on the decorative patterns of 100 surviving buildings in the Muslim architectural world. The patterns are analyzed and chronologically organized to determine the earliest surviving examples of these adorable ornaments. The origins and radical artistic movements throughout the history of IGPs are identified. With consideration for regional impact, this study depicts the evolution of IGPs, from the early stages to the late 18th century.

From Tomar to Angra： Interpretative Hypothesis of Geometric Pattern Morphology

This paper is focused on the study of the urban form of Tomar, which was founded in Portugal by the Order of the Temple during the 12th century. It is centered on the site where the Order of the Temple was created, Jerusalem, and also on the Templar European headquarters, Paris, in Marais neighborhood; as well as on its headquarters in Portugal, Tomar; and finally, on Angra which was set up in Azores at the beginning of the Portuguese discoveries in 1427. While exploring possible Templar principles on setting up medieval geometric cities, the aim of this paper is to expose that Tomar is a truly relevant case on that process and, therefore, that Portugal have had a significant role on medieval geometric urbanism. The achievements of this paper show that the selected territories share common settlement principles which are based on both similar geometric rules and analogous hierarchy schemes. Regarding that, it will be possible to state that cultural and population exchanges with France should not be considered as the sole factor to shape European medieval urbanity. Portugal should have had a role on that process, too. At least, it should be possible to explore other hypothesis on further pieces of research, according to the exposed arguments.

New progress in geometric computing for image and video processing

In recent years, geometry-based image and video processing methods have aroused significant interest. This paper considers progress from four aspects： geometric characteristics and shape, geometric transformations, embedded geometric structure, and differential geometry methods. Current research trends are also pointed out.