Geometry processing is a software technology that facilitates the appropriate and efficient conversion and processing of digital geometric data, including sampled points, curves, surfaces, images, and volumetric data, based on the intended application. It is a versatile technology and is increasingly adopted in diverse fields that rely on digital technologies and for the popularization of digital transition. Geometry processing is based on a robust and extensive mathematical framework that has been extensively investigated. As the scope of potential applications expands, the practical applications of these theories have increased accordingly. Geometry processing is currently employed for shape acquisition, analysis, design, and inspection in various fields, such as manufacturing, social infrastructure, medicine, natural science, and art. As the range of applications expands, several issues have emerged that require further investigation, such as increasing the accuracy and managing large-scale data.

The objective of this special issue is to provide new insights into geometric-processing capabilities. This issue comprises five papers that present novel aspects of this technology and two comprehensive reviews pertaining to aesthetic curves and related topics, as well as the applications of X-ray computed tomography (CT) in manufacturing. The papers included in this issue are as follows:

- Aesthetic curves and related geometries

- Object recognition from laser-scanned point cloud

- CAD data compression via wavelet transform

- Application of structure-from-motion

- Image analysis using Delaunay graphs

- Surface extraction from X-ray CT scan data

- Automation of manufacturing using X-ray CT scanning

The data types and methods used for geometry processing are diverse and depend on the scenarios. In this issue, we present a diverse range of studies pertaining to geometry processing that encompasses both fundamental concepts and applied studies.

We are grateful to all the contributors, reviewers, and editorial staff for their dedication and support in realizing this issue.

This paper delves into the recent advancements of log-aesthetic curves (LAC), a family of curves for industrial design. Recently it has been redefined in the context of similarity geometry, a branch of Klein geometry. Building upon the work of Miura and Gobithaasan [1], the paper explores LAC properties, delves into the connection with similarity geometry (as detailed in Inoguchi et al. [2-5]), and examines extensions of LACs, including the σ-curve [6] and τ-curve [7].

The reflected ceiling plan (RCP) is a two-dimensional drawing of facilities with ceiling equipment, such as lighting, fire alarms, sprinklers, and inspection holes. The RCP is often created from existing facilities for safety standard verification, renovation, and inspection. However, the creation of RCPs of large-scale facilities requires significant time and effort. In this study, a method for extracting ceiling equipment information from point clouds acquired using a terrestrial laser scanner (TLS) was developed for RCP creation. The proposed method is based on footprint detection for ceiling equipment and involves three steps. First, circular and quadrilateral footprints of the ceiling equipment from point clouds of each scan are detected. Next, the footprints are merged for multiple scans and clustered using their dimensions and point distributions. Finally, the labels of pieces of equipment are interactively assigned to each cluster. The performance of the proposed method was evaluated for four facilities using TLS point clouds. The experimental results showed that the detection rates of footprints (recall) exceeded 90% within a scan distance of 6 m, and the labeling accuracy was also more than 90%. For 79 scans (point clouds) of a facility, the time for extracting 80% of equipment information for RCP creation was approximately 25 min, which corresponds to 2% of the manual RCP creation time of the facility. This demonstrates that the proposed method achieves efficient RCP creation.

We propose an algorithm for lossy compression of computer-aided design models in Z-map representation. Our method employs Daubechies wavelet functions, which are smoother than those of the Haar wavelet used in a previous work for the lossy compression of shape models. A significant reduction in the amount of data of the compressed shape model was achieved using the proposed lossy in which the least significant coefficients of the wavelet synopsis were deleted. The nonlinear filtering of coefficients was based on the quickselect algorithm, which was seven to ten times faster than a normal quicksort algorithm and allowed us to accelerate the entire process. We conducted a series of experiments using shape models with 512 × 512–8192 × 8192 resolutions to evaluate our technique using various wavelet functions. The proposed method performed the process in 50–90 ms for the models at 1024 × 1024 resolution and reduced the output binary size by 75%–90% compared with those compressed using a previous method. Some Daubechies wavelets, such as D4 and D6, were found superior in lossy compression using nonlinear filtering based on the order of magnitude of wavelet coefficients.

Unmanned aerial vehicle (UAV)-based photogrammetry that employs structure from motion (SfM) and multi-view stereo (MVS) has been widely used in many disciplines, particularly in topographic surveying. However, several factors can affect the accuracy and precision of these techniques, including the analysis settings of the SfM process. In this study, we evaluated the robustness of SfM accuracy and precision against the non-optimal analysis settings by employing 750 analysis settings of SfM for 15 sets of images taken at five different pitch angles and three distinct ground sample distances. Flights were performed over a 100×100 m² flat surface using the constant-pitch flight design. The results demonstrated the robustness of 20° and 30° pitch angles against non-optimality in SfM settings, producing relatively small root mean square errors for validation points (no larger than 0.056 m). This indicates that using these pitch angles for the flight design helps avoid concern over the SfM settings. Conversely, constant-pitch shooting with a 10° pitch angle was found to be insufficient for accurate estimation of camera intrinsic parameters (focal length f), and shooting with a 40° pitch angle showed a high risk of pose estimation failure, depending on the analysis settings. These findings can be useful for practitioners and researchers to improve their future applications of UAV-based photogrammetry.

Topological data analysis (TDA) based on persistent homology (PH) has become increasingly popular in automation technology. Recent advances in imaging and simulation techniques demand TDA for 3D binary images, but it is not a trivial task in practice, especially in terms of the computational speed of PH. This paper proposes a simple and efficient computational framework to extract topological features of 3D binary images by estimating persistence diagrams (PDs) for 3D binary images. The proposed framework is based on representing a 3D binary image by constructing a topological Delaunay graph with distance edge weights as a Rips complex, and it utilizes PD computation libraries for the constructed graph. The vertices, edges, and edge weights of the proposed graph correspond to connected-components (CCs) in the 3D binary image, Delaunay edges of the generalized Voronoi diagram for the CC boundaries, and minimum distances between adjacent CCs, respectively. Thus, the number of elements required to compute PD is significantly reduced for large objects in 3D binary images compared with conventional representations such as cubical complexes, which results in efficient topological feature estimations.

In recent years, active research has been conducted on X-ray computed tomography (CT) scans for observing and analyzing the internal structures and defects of products. High-precision is often required for products with primitive shapes, such as X-ray rotating ellipsoidal focusing mirrors, which are used for high-resolution observations. However, the CT reconstruction algorithm can cause blurring and artifacts in the CT volume, thereby complicating the accurate determination of the surface position. To address this issue, we propose an algorithm for high-precision surface extraction from the CT volume of primitive shapes. To accurately determine the surface position on the CT volume influenced by partial volume effects, we introduce three methods for primitive fitting. The first method approximates the boundary between the mirror and air in each cross-section with a line. The second method uses a local cylindrical approximation for the boundary, whereas the third method locally fits the primitive shape to the mirror for each cross-section. By comparing the outcomes of the proposed algorithm with those of conventional surface extraction algorithms, we demonstrate the superior accuracy of our approach and discuss the characteristics of various methods. Overall, the algorithm contributes toward enhancing the accuracy of internal structure analysis and defect detection in industrial components, potentially reducing manufacturing errors and improving product quality.

X-ray computed tomography (CT) is a technology that can non-destructively acquire volumetric images of objects. It is the only commercialized and practical measurement of the inner geometry of objects with micrometer-order accuracy. Microfocus X-ray CT scanners have been widely used in several manufacturing industries. The main applications range from typical observation and inspection to precision measurement and geometry acquisition. They are expanding beyond manufacturing (e.g., science, archeology, and food industries). This review describes the requirements for the use of X-ray CT scanners in the manufacturing industry and their modeling techniques. Recently, there have been growing expectations for the introduction of CT scanners for the high-accuracy acquisition of geometry and inline inspection for manufacturing automation. This requires quality and fast measurement data generation and scan data processing methods. Therefore, this paper presents attempts in the field of modeling for this purpose. The latest topics will also be covered, including large-scale CT and 4DCT.

The current rehabilitation evaluation methods for patients with hand dysfunction face issues such as inconsistent standards and incomplete quantification processes. To address these challenges, this paper introduces a rehabilitation evaluation system that integrates various rehabilitation training modes and leverages an exoskeleton finger rehabilitation robot. This system is carefully designed and thoroughly analyzed based on the diverse training modes offered by the rehabilitation robot. Twenty stroke patients and six healthy subjects were recruited to perform grasping of static objects and gesture movement experiments, which were evaluated by Brunnstrom’s motor evaluation and rehabilitation evaluation tests, respectively, and the results were compared. The experimental results showed that the results of the robotic rehabilitation evaluation of the 20 patients were consistent with the clinical Brunnstrom motor grades, which verified the accuracy of the rehabilitation evaluation system that was designed in this study.

This paper describes a method for generating toolpaths based on machining strategies for five-axis controlled machining using special tools. Traditionally, most toolpath generation studies focused on ball-end mills, proposing strategic methods to achieve high-quality machining while avoiding tool interference. Recently, special finishing tools with large cutting edge radii have gained interest for achieving higher machining efficiency. These special tools can produce smooth finished surfaces even with large pick-feed widths, leading to higher productivity. However, unlike conventional machining with ball-end mills, five-axis controlled machining using special tools lacks standardized work design procedures. This study proposes a generic tool-geometry data format for defining special tool geometries and a method for generating toolpaths using this data format. This method strategically treats special tools as conventional ball-end mills. Consequently, five-axis controlled machining for new tool geometries can be achieved using existing operational procedures. To generate toolpaths, this study utilizes a two-dimensional configuration space (C-Space). For special tools with multiple cutting edge radii, the relationship between the tool posture and cutting edge contact point is clarified by mapping the cutting edge radius information onto the C-Space. By employing this mapped cutting edge information, we can determine the interference-free tool posture corresponding to the chosen cutting edge section based on the machining strategy. Finally, the paper presents machining simulations and experiments conducted to confirm the effectiveness of the proposed method.

Wire arc additive manufacturing (WAAM), based on gas metal arc welding, is ideal for fabricating components with sizeable geometries and moderate structural intricacies. However, the electric arc introduces a heat source and directional heat dissipation during deposition, resulting in undesired microstructural characteristics, such as columnar dendritic structures, which lead to variations in hardness across the printed component. Our previous research introduced the friction stir burnishing (FSB) tool integrated with WAAM using a hybrid approach called simultaneous processing. This method suppressed dendrite formation and enhanced the microstructure within WAAM. This approach directly correlates process dynamics, force dynamics, and temperature control, facilitating efficient plastic deformation. This research investigates the relationship between process parameters and microhardness within the combined manufacturing systems of WAAM and FSB tools. The study primarily focuses on using SUS 316L austenitic stainless steel wire material for WAAM and examines how simultaneous operation with the FSB tool impacts microstructure and microhardness. The investigation emphasizes three key parameters: the distance between the welding torch and the FSB tool, tool rotational speed, and machine feed speed. Comprehensive experimentation, including Taguchi analysis, determines optimal values for these parameters. Results indicate that torch-to-tool distance and machine feed speed significantly influence microhardness, while tool rotational speed shows minimal impact. The most effective combination for enhancing microhardness was a torch-to-tool distance of 20 mm, a machine feed speed of 528 mm/min, and a tool rotational speed of 1900 rpm. This combination induced a plastic deformation transformation effect, contributing to the overall improvement in microhardness. Additionally, the optimal parameters for achieving a smaller grain size were a torch-to-tool distance of 17 mm, a machine feed speed of 356 mm/min, and a tool rotational speed of 1900 rpm, as indicated by the average grain size. Furthermore, this study shows significant improvements in microstructure and hardness within 50–200 µm depth from the surface. Comparative analysis between FSB tool-processed and non-processed samples indicates a 22.51% increase in microhardness, with the grain size of the simultaneous process being 7 µm compared to 11.55 µm. Optimizing the process parameters of simultaneous processing achieves superior microhardness and microstructural refinement. Additionally, it highlights the need for further material development to address challenges associated with tool durability, paving the way for advancements in simultaneous processes.

The current badminton shuttlecock products are highly ineffective. The bird feather shuttlecocks used in official competitions have an unsustainably high change count due to rapid breakage from repeated racquet strikes. Meanwhile, the current synthetic shuttlecocks lack the structural properties of their feather counterparts to produce the desired aerodynamics as a projectile. This study discusses two material testing methods: the feather compression and hysteresis test, which can provide relevant mechanical data to be incorporated into the manufacturing process of future synthetic shuttlecocks. The compressive moduli from six feather shuttlecock products (four goose and two duck) were compared using the proposed methods at the strain rate of 1.15 mm/60 s. Subsequently, a three-cycle hysteresis test was conducted at an increasing strain rate of 1.15 mm/120 s, 1.15 mm/80 s, and 1.15 mm/60 s. The compression results were comparable to those from previous studies; however, there are currently no hysteresis data of shuttlecock feathers were available for comparison. The proposed methods have the potential to provide vital mechanical data that should be taken into account for future synthetic shuttlecock designs.

Continuous carbon fiber-reinforced polymer (CFRP) can be used in material extrusion-based additive manufacturing (AM). By appropriately arranging and orienting the continuous fibers, lightweight or high-strength mechanical parts and structures with complex deformation behavior and locally modified stiffness can be fabricated. Although many studies have been conducted to optimize the arrangement of continuous fibers fabricated using CFRP in AM, most of them have focused on the mechanical properties of the fabricated object in the lamination plane. This focus is due to the characteristics of AM, in which continuous fibers are placed in a plane and then layered, allowing for optimization at a relatively low computational cost. However, the computational cost of targeting mechanical properties outside the fabrication plane is enormous, making optimization design difficult. Furthermore, if the fiber material is arranged discontinuously, a process to cut the fibers is required during fabrication, resulting in decreased productivity and fabrication accuracy. Therefore, it is necessary to optimize the fiber arrangement, considering the continuity of the fiber material. To address these problems, this study aims to propose an efficient fiber arrangement optimization method, considering the continuity of the fiber material. For efficient stiffness optimization, the stiffness is represented by a combination of lamination parameters that have been used in the lamination design of CFRP sheets. A genetic algorithm was employed as the optimization algorithm. The proposed method using lamination parameters was implemented, and a case study of fiber arrangement optimization was performed on a simple structure. In addition, a full search was performed to evaluate all possible fiber arrangements for the target structure. The results of the proposed method and the full search confirmed the reliability of the proposed method, which achieved results that were equivalent to the best results obtained in the full search. In addition, a conventional method that directly optimizes the fiber arrangement as a design parameter was implemented. This result was compared with that of the proposed method. For a simple structure with a small number of layers, averaged over 20 runs, the conventional method converged faster than the proposed method, but the convergence speed worsened as the number of layers increased. Moreover, the fiber arrangement obtained by the conventional method was less continuous than the result of the proposed method. These results confirm the usefulness of the proposed method.