Basic Geometric Elements Research Articles

Notas sobre escultura e Notas sobre escultura, parte 2

The articles “Notes on Sculpture” and “Notes on Sculpture, Part 2” by Robert Morris mark a milestone in the history of sculpture, challenging traditional notions of form and function. The emphasis on basic geometric elements and the understanding of sculpture as a spatial event, rather than a static object, transformed artistic discourse. By proposing an approach centered on the viewer’s experience and the work’s interaction with the environment, Morris paved the way for Minimalism. Through his reflections, the artist significantly expanded the possibilities of sculpture, influencing contemporary art production and criticism in a decisive manner.

A Registration Method Based on Planar Features Between BIM Model and Point Cloud

Abstract In the digitization process of the construction industry, it is frequently necessary to use BIM as a digital model carrier, and the registration between BIM and point cloud is a crucial step in BIM applications. Most existing 3D registration methods, such as the ICP algorithm, are capable of aligning point clouds. However, these classical methods are subject to the influence of numerous points contained within the point cloud, relying heavily on point-to-point correlations. Consequently, it is challenging to extend these algorithms to register with other forms of spatial information, such as BIM models, beyond the point cloud. Considering that planes are basic geometric elements in building BIM models, this paper proposes a novel method for aligning BIM models with point clouds by matching planar features. The method extracts planes from point clouds using an enhanced region growing algorithm, directly parsing the planar geometric information from BIM in IFC format. After completing the matching of plane groups, the optimal solution is calculated using a weighted least squares method. The experimental results indicate that the proposed method can achieve successful registration between the BIM model and point cloud, with a lower RMSE of 5.73mm compared to the registration method using RANSAC+ICP on the same dataset.

Auxetic dihedral Escher tessellations

The auxetic structure demonstrates an unconventional deployable mechanism, expanding in transverse directions while being stretched longitudinally (exhibiting a negative Poisson’s ratio). This characteristic offers advantages in diverse fields such as structural engineering, flexible electronics, and medicine. The rotating (semi-)rigid structure, as a typical auxetic structure, has been introduced into the field of computer-aided design because of its well-defined motion patterns. These structures find application as deployable structures in various endeavors aiming to approximate and rapidly fabricate doubly-curved surfaces, thereby mitigating the challenges associated with their production and transportation. Nevertheless, prior designs relying on basic geometric elements primarily concentrate on exploring the inherent nature of the structure and often lack aesthetic appeal. To address this limitation, we propose a novel design and generation method inspired by dihedral Escher tessellations. By introducing a new metric function, we achieve efficient evaluation of shape deployability as well as filtering of tessellations, followed by a two-step deformation and edge-deployability optimization process to ensure compliance with deployability constraints while preserving semantic meanings. Furthermore, we optimize the shape through physical simulation to guarantee deployability in actual manufacturing and control Poisson’s ratio to a certain extent. Our method yields structures that are both semantically meaningful and aesthetically pleasing, showcasing promising potential for auxetic applications.

Design and Development of a Geometric Calculator in CATIA

In this article, an application in the field of engineering graphics is presented for the design of a geometric calculator generated as a macro in CATIA V5. The code of this macro is written in the CATVBA language and utilizes the CATIA internal editor while taking advantage of the capabilities offered by Visual Basic for Applications (VBA). The principal purpose of this application lies in the possibility of creating the three main geometric elements (point, line, and plane) and in solving five types of general geometric problems, and then comparing the results obtained with their equivalent problems from analytical geometry. In particular, within these types of general geometric problems, 34 possible cases are solved: definition of lines (nine cases), definition of planes (12 cases), intersection points (three cases), angles (three cases), and distances (seven cases). These new entities defined with the geometric calculator can serve as support for the generation of new three-dimensional volumes, the creation of auxiliary symmetries, and the dimensioning of various elements. It was verified that the results of the designed macro and the solutions of the analytical equations coincided; therefore, the procedure was validated. Likewise, the module employed herein in the CATIA V5 environment is “Wireframe and Surface Design”, since it enables handling the three basic geometric elements (point, line, and plane), which form the basis of the geometric calculator. Lastly, it is verified how the geometric calculator allows their integration with three-dimensional solids, which represents a notable advance as an aid in its geometric definition.

Interior Soft Decoration Product Design Based on 3D Modeling and Image Processing Technology

In order to solve the problems of the traditional 3D simulation system of indoor soft decoration, such as the lack of effective enrichment, rendering means, and poor authenticity when selecting the geometric modeling method to simulate the effect of indoor soft decoration, this paper proposes a 3D simulation system of indoor soft decoration based on OpenGL and Direct3D. The system uses 3DMAX software to establish the indoor model, imports the model into the OpenGL 3D graphics standard library module, draws the indoor soft decoration scene elements using the basic geometric elements, and constrains the scene elements through the wall, overlap, and size constraint functions, so as to ensure the reasonable layout of the indoor soft decoration agent area and enrich the indoor model. After enrichment, the indoor model is transmitted to the Direct3D rendering engine module transformation unit to implement the soft decoration layout, and the lighting unit and rasterization unit are used to render the indoor after layout so as to obtain the optimal indoor soft decoration effect and output the 3D simulation image of indoor soft decoration. The experimental results show that the favorability, operation sensitivity, design portability, design satisfaction, and soft fitting effect score of the system are higher than those of the Untiy3D system and Smart3D system. The average score of this system is about 95, while the average score of the Untiy3D system is lower than 89, and the average score of the Smart3D system is lower than 85. Conclusion. The three-dimensional simulation effect of indoor soft decoration of this system is good, the design is convenient, the operation is sensitive, and the user satisfaction is high, which provides a reliable analysis basis for indoor design.

A Local Enhancement Method for Large-Scale Building Facade Depth Images using Densely Matched Point Clouds

In recent years, laser scanning systems have been widely used to acquire multi-level three-dimensional spatial objects in real time. The laser scanning system is used to acquire the three-dimensional point cloud data of urban scenes. Due to the large-scale characteristics of urban scenes, and the problems of scanning occlusion, scanning path, and limited scanning laser range, the laser scanning system cannot scan every object in the scene comprehensively, multidirectionally and finely, so the corresponding three-dimensional point cloud data collected by many objects are incomplete, and the data images are relatively sparse and unevenly distributed. The existing point cloud denoising and enhancement algorithms, such as AMLS, RMLS, LOP, and WLOP, all use local information to enhance the missing or sparse parts of the point cloud. This point cloud enhancement method is only limited to a small range and cannot do anything for the larger missing area of the point cloud. Even if it is done reluctantly, the effect is not satisfactory. There are a lot of repetitive and similar features in urban buildings, such as the repetitive areas of floors and balconies in buildings. These repetitive areas are distributed in different positions of point clouds, so the repetitive information has non local characteristics. Based on the nonlocal characteristics of building point cloud data and the repetitive structure of buildings, this article proposes a nonlocal point cloud data enhancement algorithm, which organizes the point cloud data in the repeated area into a set of basic geometric elements (planes). The structures are registered in a unified coordinate system, and the point cloud is enhanced and denoised through two denoising processes, “out-of-plane” and “in-plane.”

Feasibility Study of Performance Assessment Gauge for Freeform Measurement

Recent product components have been designed as a combination of complex forms for advanced functionality. Such high degree-of-freedom forms are shaped by various manufacturing processes. In the industrial supply chain, the deviation of a manufactured form from its designed form must be verified to ensure product quality. Three-dimensional (3D) measuring systems are typically used for verification. To validate the product manufacturing performance accurately, a measurement procedure that can derive the measurands of forms with small measurement uncertainty is necessitated. For simple geometries such as flats, spheres, and cylinders, precise measurement and uncertainty evaluation methods have been established; however, those for complex forms are still being developed. In this study, measurement uncertainty is assessed by measuring a calibrated gauge and comparing the measured with calibrated values. Several gauges configured with basic geometric elements have been proposed as a reference for complex form measurements, and some issues remain. Some of the gauges do not sufficiently simulate the forms of actual product components, whereas other gauges are difficult to calibrate with small uncertainties. Herein, we discuss a possible approach for solving these problems in the metrology of complex forms using 3D measuring systems. First, a new gauge concept is proposed. The gauge is designed by extracting the complex features of the actual product form and segmenting the gauge’s form into various circular arc curvatures. The geometric parameters are well calibrated, and the measurable angular range of the curvature is not limited. A representative gauge based on this concept is described. Next, a robust and small-uncertainty calibration method for complex-form objects is described. The area encompassing the target cross-section is measured, and an envelope is generated on the probe tip mechanical surface from the probe tip centers to determine the measured surface. Finally, the calibration and measurement uncertainty evaluation for the geometric parameters of the new gauge are quantitatively presented. It is verified that the proposed calibration procedure is applicable to freeform measurements, and that both simple and complex forms can be measured within a 1.5 μm uncertainty.

Design Rules for Hybrid Additive Manufacturing Combining Selective Laser Melting and Micromilling.

We report on a comprehensive study to evaluate fundamental properties of a hybrid manufacturing approach, combining selective laser melting and high speed milling, and to characterize typical geometrical features and conclude on a catalogue of design rules. As for any additive manufacturing approach, the understanding of the machine properties and the process behaviour as well as such a selection guide is of upmost importance to foster the implementation of new machining concepts and support design engineers. Geometrical accuracy between digitally designed and physically realized parts made of maraging steel and dimensional limits are analyzed by stripe line projection. In particular, we identify design rules for numerous basic geometric elements like walls, cylinders, angles, inclinations, overhangs, notches, inner and outer radii of spheres, chamfers in build direction, and holes of different shape, respectively, as being manufactured by the hybrid approach and compare them to sole selective laser melting. While the cutting tool defines the manufacturability of, e.g., edges and corners, the milling itself improves the surface roughness to Ra < 2m. Thus, the given advantages of this hybrid process, e.g., space-resolved and custom-designed roughness and the superior geometrical accuracy are evaluated. Finally, we exemplify the potential of this particular promising hybrid approach by demonstrating an injection mold with a conformal cooling for a charge socket for an electro mobile.

The Mathematical Model of Curve-Face Gear and Time-Varying Meshing Characteristics of Compound Transmission

The curve-face gear pair is a new type of gear pair with variable transmission ratio for spatial finite helical motion. In this paper, mathematical models of a new developed curve-face gear were simplified and obtained directly by the standard shaper. The subsequent studies on the curve-face gear compound transmission characteristics were further analyzed by the combinations of the principle of space gearing and screw theory. Firstly, the conjugate tooth surface geometry as well the point contact traces of curve-face gears were derived. Secondly, the geometric relationships between gear pair and the corresponding meshing characteristics were evaluated by several basic geometric elements, including instantaneous screw, axodes, striction curve, and conjugate pitch surface. Based on that analysis, it was found that the tooth contact normal was reciprocal to the instantaneous twist, which demonstrated that the conjugate motion with the desired transmission ratio could be realized in current curve-face gear compound transmission. Moreover, the time-varying slip characteristics of the curve-face gear pair were also revealed, that is, rolling and sliding action coexist at all contact on the tooth surfaces. In brief, this work provided the theoretical basis for following researches on machining curve-face gear with standard shaper.

Geometric considerations for the 3D printing of components using fused filament fabrication

Demand in 3D printing products using fused filament fabrication (FFF) in industry has been growth a lot with 55% in development of prototypes, 43% in production, and 41% in conceptual models for testing. However, information regarding the manufacturing considerations of geometry-restricted components is still an opportunity area, generating printed components with quality defects. This article is aimed to present some characteristics in geometric components that should be considered during the developing process for components to be produced in FFF to avoid in quality defects. The methodology used considers three stages: first, the reproduction of basic geometric elements and a template that integrates elements with software design; second, the component analysis and the template with software for pre-processing of components, and third, the printing of a template for assumption validation identified in stage two. Findings obtained indicate that the spherical components are geometries with the greatest possibility of defect generation during the FFF printing process. The complexity of the template allowed to identify that the template orientation is a factor that generates defects; for example, with 0° orientation regarding the X axis generates 40,008 risk points for defect and for 30° orientation there are 6658 risk point defects. Therefore, it is advisable to consider avoid geometries associated with sphericity and cylindrical characteristics as possible in the design processes, since these geometries require specific processes to achieve the finishing quality.

Criteria for Estimating the Quality of Coordinate Measurements of the Geometric Parameters of Parts in Experimental Pilot-Scale Production

Criteria for estimating the quality of coordinate measurements under the conditions of experimental pilot-scale construction based on the use of modern methods of construction of high-quality measurement systems and traditional methods of estimating the quality of measurements in metrology are considered. The duration of the measurements is proposed as an additional criterion of the quality of measurements. The role of technological inheritance in the analysis of sources of uncertainty of coordinate measurements is noted. It is shown that such characteristics of the form of controlled geometric elements as planeness, roundness, and cylindricity must be taken into account in order to achieve an objective estimate of the quality of coordinate measurements. It is established that decreasing the uncertainty of the initial data and the measurement conditions together with increasing the stability of already solved problems through a well-defined selection of the basic geometric elements (measurement base of the part) is one of the basic methods of reducing the uncertainty of coordinate measurements. A necessary condition for obtaining reliable quality indicators, such as quantitative estimation of conditions and management of the measurement process, is found. It is proposed that analytic dependences needed for quantitative analysis and optimization of the quality indicators of measurements, including measurement time, should be used to schedule and standardize the measurement time.

Surface reconstruction based on CAD model driven priori templates.

In this paper, a method of reconstructing 3D (three dimensional) models from the original scanned point cloud using priori templates is proposed. Different from previous reconstruction methods that triangulate and fit the original scanning point cloud directly, we construct a priori template based on the CAD (computer aided design) model and guide the reconstruction of the original scanning point cloud with the priori template. Given a CAD model, the basic geometric elements are used as the basic units to extract the set elements of 3D shapes. Then the geometric elements are meshed, and the normal vectors at the mesh nodes are extracted. The corresponding point cloud data of each basic element are extracted from the original point cloud. The point cloud data near the normal of the guide point are searched, and the Gaussian weighted average value of the searched point represents the actual geometric parameters of the part at the guide point. Finally, the geometric elements of the basic unit are reconstructed locally by Non-Uniform Rational B-Splines surface fitting, and the complete reconstruction model is obtained by integrating the local reconstruction. Experiments show that our method can solve the problems of high quality reconstruction, sharp feature preservation, and detail recovery in surface reconstruction.

Contact detection between polygonal blocks based on a novel multi-cover system for discontinuous deformation analysis

A novel multi-cover searching (MCS) algorithm is presented to promote the efficiency of contact detection. As simple geometrical entities, covers are built on basic geometrical elements of the boundary of polygonal blocks, promoting the efficiency of rough search. Firstly, blocks possible to contact each other are identified more precisely through intersections between covers. Secondly, when performing contact type identification between two blocks, a full range search between geometrical elements is reduced into several local delicate checks. Moreover, we could embed MCS into many other contact detection methods. Several examples validate its accuracy and improved efficiency over traditional methods.

Criteria for evaluation of the coordinate measurements quality of parts geometric parameters at pilot-experimental production

The criteria of the coordinate measurements quality at pilot-experimental production based on contemporary methods of quality management system and traditional methods of the measurements quality in Metrology are considered. As an additional criterion for quality of measurements, their duration is proposed. Analyzing the problem of assessing the quality of measurements, the authors pay particular attention to the role of technological heredity in the analysis of the sources of uncertainty of coordinate measurements, including not only the process of manufacturing the part, but all stages of the development of design and technological documentation. Along with such criteria as the degree of confidence in the results of measurements; the accuracy, convergence, reproducibility and speed of the results must take into account the correctness of technical specification, and such characteristics of the shape of the geometric elements to be controlled, such as flatness, roundness, cylindrical. It is noted that one of the main methods to reduce the uncertainty of coordinate measurements is to reduce the uncertainty in the initial data and measurement conditions, as well as to increase the stability of the tasks due to the reasonable choice of the basic geometric elements (measuring bases) of the part. A prerequisite for obtaining reliable quality indicators is a quantitative assessment of the conditions and organization of the measurement process. To plan and normalize the time of measurements, the authors propose to use analytical formulas, on the basis of which it is possible to perform quantitative analysis and optimization of quality indicators, including the speed of measurements.

An inspecting method of 3D dimensioning completeness based on the recognition of RBs

The intelligent and automatic inspection of 3D dimensioning completeness plays an important role in 3D CAD/CAM systems. This paper proposes a new inspection method based on the recognition of the rigid body (RB) using the trajectory intersection method. The concept of the positioning element (PE) is introduced, and the selection rules of the PE group are established based on their intersection with the degree of invariance (DOI). Then, by setting the PEs as the datum, the RB recognition method, based on the trajectory intersection method, is proposed. Through adding a virtual dimension to the inner part of a RB, a combination of RBs is achieved by fixing the equivalent PE group. Thereafter, four conditions of dimensioning completeness are analyzed according to the combined RB and dimensional states. Through the differential locus method, the minimum missing dimension extraction process of the basic geometric elements is established. The algorithm for extracting dimensions missing from two related RBs is also carried out. Finally, the validity and stability of the method are verified using two dimensional models, and a prototype system of 3D dimensioning completeness inspection is introduced.

Construction of [formula omitted] conic spline interpolation

In this paper, a new method to interpolate a sequence of ordered points with conic splines is presented. The degree of continuity at the joints of the resulting splines can reach G3; and the splines are faired by decreasing curvature extrema. The construction is not based on parametrization, but based on basic geometric elements, such as the directions of tangents and chord lengths. The weight of Rational Quadratic Bézier Spline is translated into an equivalent form called chord–tangent ratio. The main idea of the new method is converting the geometric construction problem into a conditional extrema problem through representing the curvature and the curvature changing rate at joints with tangent arguments and chord–tangent ratios, and then deriving the unknowns by solving the conditional extremum problem. Experiments show that splines constructed by the new method perform well not only in terms of continuity, but also in smoothness.

A Practice Upon Transformation of Creative Data at Architectural basic Design Education

One of the main aided points in the basic design education is to present different methods and spaces to students to help them develop their thoughts and improve their creativeness. One of the methods which help the designer to generate new forms is using inspiration and interpretations which are the inherent of design to differentiate the way of design to catch new ideas is using generative designs. In the generative design both the nature and the abstracts inspired from the nature are being useful in forming of architectural solutions. During this study by using generative design methods it is aimed for the students to perceive relation between forms better and to improve the creativity of the students to compose integrated approaches. In this respect a two parted case study is done by architecture basic design (first grade students).In the first step it is aimed to design the form itself and also to feel the scale of designs by forming a cube of 2x2 x2 meter using generative design and installation techniques. From half of the students it is asked to form their designs by only using lines and surfaces and basic geometric elements. And from the other half is asked to inspire the patterns of generating in the nature to form non-form shapes and forms to design a place or space. The second step was to compare the works of two groups. In the both groups it is shown that the works which are inspired by nature and used generative methods have been able to be more creative during the process of solving the problem of formation.

An intelligent approach for dimensioning completeness inspection in 3D based on transient geometric elements

Complete dimensioning plays an important role in digital product design. This paper proposes an intelligent reasoning approach to inspect the dimensioning completeness for 3D mechanical parts. Firstly, the problem of inspecting the dimension completeness is transformed into the problem of determining the geometric element (GE) constrained states. Then, 8 types of general geometric elements are decomposed into basic geometric elements (BGE) and basic dimensional elements (BDE), and an intermediate model named transient geometric element (TGE) is proposed to reflect the influences of geometric constraints (GC) on the BGEs. Thereafter, 3 types of complex constraints are decomposed into 6 types of simple constraints, which are then utilized to form the generation rules of the TGEs. Then, an upgrading geometric reasoning method of creating new TGEs is developed to get the BGE’s constrained state and the dimension usage status. Finally, the completeness states of dimensions are acquired according to the dimension usage status and the BGE’s constrained states. The presented approach is tested by a pre-dimensioned mechanical part composed of many typical geometric elements and constraints, and the result demonstrates that the dimensioning completeness states can be successfully inspected.

Development of an Approach for Producing Architectural form in Architectural Design Education

At the early stages of architectural education, it is observed that students have difficulty to produce forms. Students, during the design process, comfortably use basic geometrical elements one by one, however are not able to diversify them by transformation because of the fact that students are not capable enough to transform basic geometrical forms in accordance with arithmetical operations and geometrical transformation. In this study examining the architectural form creation; a three-month case study is conducted with first year students in Department of Architecture through which the software is used. Initially architectural projects of students designed in accordance with traditional methods and it is observed that students are not able to throughly transform the forms. At the second stage, students are expected to develop their projects through sofware transformations. Additionally, a questionaire is also conducted with students in order to define the possitive and negative aspects of forms created with this method.

A model analysis of static stress in the vestibular membranes

BackgroundThe scheme of the core vestibular membranes, consisting of serially connected utricle, ampulla and semicircular canal, first appeared hundreds of millions of years ago in primitive fish and has remained largely unchanged during the subsequent course of evolution. The labyrinths of higher organisms build on this core structure, with the addition of the phylogenetically newer membrane structures, namely, saccule, lagena and cochlea. An analysis of static stress in these core vestibular membranes may contribute to a better understanding of the role of stress in the evolution of derivative membrane structures over the long term as well as the short-term membrane distortions seen in Meniere's disease.MethodsA model of these core vestibular membranes is proposed in order to analyze the distribution of stress in the walls of the component chambers. The model uses basic geometrical elements of hollow cylinders and spheres to emulate the actual structures. These model elements lend themselves to a mathematical analysis of static stress in their membranes.ResultsHoop stress, akin to the stress in hoops used to reinforce barrel walls, is found to be the predominant stress in the model membranes. The level of hoop stress depends not only on pressure but as well on a geometric stress factor that incorporates membrane shape, thickness and curvature. This result implies that hoop stress may be unevenly distributed in the membranes of the several vestibular chambers due to variations in these dimensional parameters. These results provide a theoretical framework for appraising hoop stress levels in any vestibular labyrinth whose dimensions are known.ConclusionStatic hoop stress disparities are likely to exist in the vestibular membranes given their complex physical configurations. Such stress disparities may contribute to the development of membrane pathologies as seen in Meniere's Disease. They may also factor in the evolutionary development of other derivative membrane structures such as the saccule, the lagena, and the cochlea found in higher animals.