NURBS Model Research Articles

Built forms and underlying geometries in 20th century architecture: Muuratsalo House and Leicester Engineering Department Building

By starting from the notions of rhythm, rule, and the analogy between architecture and music, the research focuses on the analysis and the representation of architecture and, in particular, of facades by comparing two case studies: Muuratsalo House by Alvar Aalto (1952-53) and the Leicester Engineering Department Building by James Stirling and James Gowan (1959-63). The methodology is based on the comparison among some specific facade categories: texture, basic compositional signs (connection to the ground, windows, connection to the sky), and geometries. The operating methodology follows these phases: i) the analysis of project drawings and photographic documentation; ii) two-dimensional reconstruction in CAD of plans, fronts, and sections; iii) NURBS modeling. By analyzing Muuratsalo House’s facades through 2D representations and 3D models, the research highlights the proportional and compositional relationship between walls and openings as a leading principle. The study on the patio’s fronts shows how this association gets more complex because the textures, rhythm, and geometry of the materials become the main elements in the compositional grammar of the house. In the case of the Leicester Engineering Department, the model allows the understanding of the general volumetric articulation. The whole configuration is characterized by the juxtaposition of multiple volumes, which impacts the facades, whose openings direct rhythms, textures, and geometries.

3D Modelling: A Review

Three-dimensional (3D) modeling is a transformative process in the digital realm that involves the creation of virtual representations of objects, environments, or characters. This multifaceted discipline plays a pivotal role across diverse industries, encompassing animation, gaming, virtual reality, architecture, product design, and more. The fundamental components of 3D modeling include vertices, edges, and faces, forming meshes that define the object's geometry. Techniques such as polygonal modeling, NURBS modeling, and subdivision surfaces offer varying approaches to sculpting digital forms. UV mapping ensures precise texture application, while rigging and animation breathe life into models through skeletal structures and movement. The integration of textures, materials, and lighting enhances the realism of rendered images or animations. Computer-Aided Design (CAD) modeling caters to engineering precision, and sculpting tools enable intricate detailing for characters or organic shapes. As technology advances, 3D modeling continues to evolve, influencing the way we visualize, design, and interact with virtual worlds. This abstract provides an overview of key concepts in 3D modeling, highlighting its significance in shaping digital experiences and pushing the boundaries of creative expression and technical innovation.

The Frinco Castle: From an Integrated Survey to 3D Modelling and a Stratigraphic Analysis for Helping Knowledge and Reconstruction

The Frinco Castle (AT-Italy) was the focus of a critical requalification and restoration project and historical knowledge. The initial medieval nucleus was modified and enriched by other architectural parts giving the current shape over the centuries. These additions gave the castle its actual internal and external complexity and an extreme structural fragility: in 2014, a significant portion collapsed. The main objective of this work was to obtain 3D metric documentation and a historical interpretation of the castle for reconstruction and fruition purposes. The local administration has planned knowledge processes from 2021: an integrated 3D geodetic survey of the entire castle and stratigraphic investigations of masonries. Both surveys were essential for understanding the architectural composition as well as the historical evolution of the court. NURBS modelling and a stratigraphic analysis of masonries allowed for the implementation of 3D immersion related to the historical interpretation. Furthermore, this modelling choice was essential for virtually reconstructing the collapsed area and helping the restoration phase.

T-Splines for Isogeometric Analysis of the Large Deformation of Elastoplastic Kirchhoff–Love Shells

In this paper, we develop a T-spline-based isogeometric method for the large deformation of Kirchhoff–Love shells considering highly nonlinear elastoplastic materials. The adaptive refinement is implemented, and some relatively complex models are considered by utilizing the superiorities of T-splines. A classical finite strain plastic model combining von Mises yield criteria and the principle of maximum plastic dissipation is carefully explored in the derivation of discrete isogeometric formulations under the total Lagrangian framework. The Bézier extraction scheme is embedded into a unified framework converting T-spline or NURBS models into Bézier meshes for isogeometric analysis. An a posteriori error estimator is established and used to guide the local refinement of T-spline models. Both standard T-splines with T-junctions and unstructured T-splines with extraordinary points are investigated in the examples. The obtained results are compared with existing solutions and those of ABAQUS. The numerical results confirm that the adaptive refinement strategy with T-splines could improve the convergence behaviors when compared with the uniform refinement strategy.

Improved Dexel Representation: A 3-D CNN Geometry Descriptor for Manufacturing CAD

In this article, we present a novel 3-D descriptor, improved dexel representation (IDR), which assists to input holistic information from an engineering computer-aided design (CAD) model to convolutional neural network (CNN) based manufacturing applications. The IDR carries the model’s position, size, and surface information, which not only provides high resolution to small-scale local (machining) features, but also has the potential to reconstruct the original CAD model. Data conversion algorithms between IDR and other CAD models (mesh and NURBS model) are efficient. CNNs with IDR input can largely improve the prediction accuracy compared to other 3-D descriptors, which reaches 98.8% in the modified machining-process-identifier dataset and 100% on the FeatureNet style 3-class dataset. IDR benefits both the manufacturing industry and other CAD-related deep learning applications in engineering fields.

Web-system for modeling surfaces based on Catmull-Rom patches

Today, surfaces play an important role in the work of designers, scientists, artists, sur-geons and other professionals involved in creating innovative products. Development of uten-sils, furniture, automobile chassis, phones, clothes, buildings, even human bodies involves geometrical modeling of surfaces. NURBS modeling is the technology of non-uniform rational B-splines creating smooth forms and models that have no sharp edges. The characteristic makes NURBS as the analytical model of choice in Autodesk 3ds Max, Blender, Autodesk Ma-ya, ZBrush, and other modeling systems. A generalizing characteristic of the given software systems is the use of a monolithic architectural style of software development, which is typical for desktop applications. Desktop software systems require installation on a local computer, which in turn binds the user to a specific operating system. NURBS accurately describe conical surfaces. Although each control has its own weight, and each weight has a local effect on the surface, a change in the weight of one vertex leads to a change in the entire surface. One of the main requirements for 3D object modeling software is the ability to change the shape of the surface freely as it passes through all control points. An algorithmic model of the Hermit surface construction under the Catmull-Rom condition and nonzero surface torsion vectors is obtained. It is shown that the Catmull-Rom condition makes it possible to glue individual patches with first-order smoothness, which is a guarantee of ergonomic surfaces. It is shown that a single control point has a local effect on the surface, namely on the 12 sur-rounding patches. The development of a software system for modeling the surfaces of objects with the client part in the form of a web application, which is based on the architectural style of SPA, showed that the user experience of such an application is close to the experience of using a desktop program. At the same time, the SPA application does not require installation and successfully runs on both stationary and mobile devices.

Delaunay Meshing and Repairing of NURBS Models

AbstractCAD models represented by NURBS surface patches are often hampered with defects due to inaccurate representations of trimming curves. Such defects make these models unsuitable to the direct generation of valid volume meshes, and often require trial‐and‐error processes to fix them. We propose a fully automated Delaunay‐based meshing approach which can mesh and repair simultaneously, while being independent of the input NURBS patch layout. Our approach proceeds by Delaunay filtering and refinement, in which trimmed areas are repaired through implicit surfaces. Beyond repair, we demonstrate its capability to smooth out sharp features, defeature small details, and mesh multiple domains in contact.

Research on the design and Creation of contemporary Powder enamel based on NURBS modeling method

as an important discovery of ceramic design, contemporary ceramic design must be able to keep pace with the development of the times, learn to actively introduce new elements into the creation. This paper attempts to carry out the research of contemporary ceramic design and creation based on NURBS modeling, which is to integrate digital technology into the traditional ceramic design, and use NURBS modeling to innovate the decoration design of contemporary Famile-rose porcelain, so that the pastel porcelain works have a stronger sense of the times.

A CAD-free methodology for volume and mass properties computation of 3-D lifting surfaces and wing-box structures

The geometry, volume, and mass properties (GVM) of lifting surfaces and wing box structures play an important role in aircraft design and optimization. Commercial Computer-Aided-Design packages can be employed to determine these features; however, they are difficult to embed in multidisciplinary frameworks because of their limited scripting capabilities and their black-box structure. In this context, the present work introduces an open-source, fully scriptable, high fidelity, and low computational demanding methodology to compute the volume and mass properties of lifting surfaces and wingbox structures using their three-dimensional geometric definition. NURBS modeling is employed to generate the 3-D geometry and derive the vertex representation of the lifting surface. The volume computation is based on the Divergence Theorem and employs a structured triangulation approach, tailored for lifting surfaces and their cross sections. The mass properties (i.e. center of mass and moments of inertia) are calculated as a system of mass particles. For this, a mass distribution model, based on the thickness and chord distribution throughout the lifting surface, has been elaborated. The methodology for volume computation and the mass distribution model has been validated analytically using a simple polytope that resembles to a lifting surface. The convergence and the robustness of the methodology has been evaluated for a straight tapered lifting surface. The results indicate a maximum error, compared with a commercial CAD software, of 0.3% and 0.5% for the volume and mass properties computation, respectively. In addition, to assess its suitability for complex lifting surfaces, the NASA Common Research Model aircraft (NASA-CRM) has been used as case of study. To summarize, the main contribution of this work lies on the development of an open-source and fully scriptable methodology, which can be easily implemented in any computational environment for aircraft design and optimization.

Splipy: B-Spline and NURBS Modelling in Python

Splipy is a pure Python library for the creation, evaluation and manipulation of B-spline and NURBS geometries. It supports n-variate splines of any dimension, but emphasis is placed on the use of curves, surfaces and volumes. The library is designed primarily for analysis use, and therefore allows fine-grained control over many aspects which cannot be achieved with conventional CAD tools. It is packaged and distributed through Python Package Index: PyPi which gives easy installation.

Ball End Mill—Tool Radius Compensation of Complex NURBS Surfaces for 3-Axis CNC Milling Machines

In order to extend the 2D-TRC (tool radius compensation) function of 3-axis CNC milling machines to ball end mills (BEMs), a new TRC named BEM-TRC is proposed to achieve successful milling of complex surfaces without over-cut. The implementation of the BEM-TRC for complex surfaces depicted in NURBS model is divided into three steps. The first one is to search the cutting point (CP) on a NURBS surface using equi-arc length interpolation in u or v direction. The second one is to accomplish BEM-TRC at the CP through offsetting the CP to the cutter center point (CCP) of a BEM along the normal vector at CP. The third one is to compute the cutter location point (CLP) of the BEM according to the BEM-CCP. The simulation and experiment verifies that the BEM-TRC is feasible and effective, and can avoid over-cut phenomenon successfully. The BEM-TRC extends the ability of the traditional 2D-TRC function, and makes 3-axis CNC milling machines to accomplish the milling process of complex NURBS surfaces.

Closed T-Spline Surface Reconstruction from Medical Image Data

The reconstruction from medical image data to CAD model is an essential process of Bio-medical engineering. So far, it is still challenging to create medical model which is suitable for both design and manufacturing. This paper introduces a process of constructing a single-patched closed T-spline surface model based on medical image data. The image data is first converted into triangular mesh and then parameterized onto a rectangular domain. An iterative least-squares fitting process is proposed to finally obtain the T-spline surface model with a user-specified tolerance. In this fitting process, the smoothing part of the algorithm is redesigned, considering the flexible structure of T-mesh and the geometric complexity of the T-spline surface. Local smoothness weighting factors are introduced to the fitting formula to locally adjust the smoothness of the surface. An adaptive smoothness checking points distribution method is proposed to reduce the computational cost. These algorithms are easy to implement and the obtained model is simple in form. Compared with the STL and NURBS model, the T-spline surface model requires less storage space and can be easily modified. The obtained model is suitable for Bio-medical engineering applications like bone scaffolds design, surgical planning and related manufacturing process.

Analysis of terahertz scattering from electrically large scatterer with NURBS modeling

A novel expression based on conventional Non-Uniform Rational B-Splines surfaces is proposed to model a scatterer, which can be used to overcome the deficiencies of conventional modeling method and can also be combined perfectly with the stationary phase method (SPM). Furthermore, we propose a fast and accurate algorithm to locate inner critical points and boundary critical points of physical optics (PO) integrals, as well as to locate stationary points of edge-diffracted integrals. The terahertz (THz) scattering field from an electrically large scatterer is evaluated by the physical theory of diffraction and SPM (PTD-SPM), which consists of four parts, including the PO scattering field from inner critical points, boundary critical points, corner points of PO integrals, and edge-diffracted field from the stationary points of edge-diffracted integral. Moreover, the order of magnitude of each part contribution is derived. Numerical results demonstrate that PTD-SPM is a valid and efficient algorithm for analyzing THz scattering from an electrically large scatterer.

Numerical Simulation of cracked orthotropic materials using extended isogeometric analysis

In the present study, extended isogeometric analysis (XIGA) is used to analyse cracks in orthotropic media. NURBS and T-splines geometric technologies are used to define the geometry and the solution. Knot insertion and order elevation are used in NURBS models, while a new local refinement algorithm is applied to T-spline models. In XIGA, the basic idea of the extended finite element method (X-FEM) is used along with isogeometric analysis for modelling discontinuities by including enrichment functions. Special orthotropic crack tip enrichments are used to reproduce the singular fields near a crack tip, and fracture properties of the models are defined by the mixed mode stress intensity factors (SIFs), which are obtained by means of the interaction integral (M-integral). Results of the proposed method are compared with other available results.

Fast Evaluation of Minimum Zone form Errors of Freeform NURBS Surfaces

Nowadays freeform components are more and more commonly employed in precision engineering and it is crucial to evaluate their form qualities. The widely adopted PV parameters for form errors need to be evaluated in the sense of minimum zone, which is a non-differentiable optimization problem, and very difficult to be solved. Currently NURBS has become a ubiquitous data format in computer aided design and manufacturing. However, little can be found concerning the minimum zone fitting between the NURBS surfaces and measured data, due to the mathematical complexity of this problem. A fast evaluation strategy is proposed in this paper. It is implemented in three stages. The NURBS model is decomposed into Bezier patches first and the iterative closest point matching is implemented. And then the relative position is refined by the orthogonal distance least squares fitting. Finally the minimum zone fitting is carried out by the primal-dual interior point method. The solutions are recursively updated by line search until the Karush-Kuhn-Tucker conditions are satisfied. Numerical experiments proved that the proposed method is capable of minimum zone fitting for freeform NURBS surfaces with very high accuracy and efficiency.

Evaluation of a Mixed CAD Gear Modeling from Time and Precision Point of View

Abstract The aim of the paper is to present an evaluation of a new mixed CAD modeling method, capable to universally build surfaces and solid models of gears. The proposed CAD solution builds gear models, primary not for a visual simulation of the gearing processes, but for complex gearing- and FEA studies in virtual environment. Localization of the contact paths of gear pairs, virtual kinematic evaluations, rapid verification of newly developed gear types and FEA analysis requires satisfactorily precise surface and solid models. The known NURBS modeling methods are mainly based on the analytical equations of the flanks of the teeth surfaces. The bottom and tip surfaces of the teeth, are very important in meshing and FEA studies, and generally cannot be built from the meshing equations. As the new mixed modeling method proposes a simplified and quick CAD modeling procedure, with flexible modeling options like rapid tool profile modifications, an evaluation of the obtained models must be made, from both: generating time and precision point of view. For this purpose, a model of a spur cylindrical gear (generated by a convolute helical hob) is built using the Solid Boolean Subtraction method and is compared with the gear generating process using a new mixed CAD method.

Free-form surface machining error compensation applying 3D CAD machining pattern model

The article presents a methodology for compensating for systematic influences of computer numerical control (CNC) machining processes on free-form surfaces. The proposed procedure is performed off-line by introducing corrections compensating for these influences to machining programs. The effect of systematic influences of machining are deterministic deviations of surfaces. CAD models of these deviations, averaged for a number of surfaces machined under repeatable conditions, represent a machining pattern model (MPM) which serves as the basis for performing compensation. The basis for developing such models is surface deviations determined during coordinate measurements carried out along a regular grid of points. For estimating surface MPMs, a methodology is proposed in which regression analysis, spatial statistics methods, an iterative procedure, and NURBS modeling are applied. An MPM with the opposite sign was used for compensating systematic influences of the ball-end milling process by modifying the nominal geometry data and correcting the machining program. The results of machining error compensation carried out on the basis of a previously developed MPM were compared to the results of compensation performed on the basis of raw measurement data as well as to the results these after compensation on the basis of a model of deterministic deviations for the surface under study.

Turbine Blade CNC Machining Simulation Analysis Based on MATLAB and UG

As a key component of turbine, the surface of turbine blade is usually designed to distorted variable cross-section surface, and the shape is very complex. This paper combines NURBS modeling theory and NC machining method, and use NC machining trajectory generation and simulation analysis by means of UG software. The results show that the method is effective for blade processing, and have a guiding role to the industrial production.

The Use of NURBS Modeling in the Ceramic Design

NURBS is a great modeling method which is supported in all the advanced three-dimensional softwares. With NURBS, people can create the lively and vivid models on the computer. And it plays a role on the model designing of chinas.combining with the experience of practices, the dissertation will analyze with cases to curved surface model of the china’s style designs and mainly study NURBS curved surface modeling taking the method of ceramic design.

Research of Model-Constructing Method for Bulldozer Case Based on NURBS

Using NURBS modeling method can construct more realistic and vivid 3D models, because it has a remarkable ability to control the curves of the model surface than the traditional grid modeling method. Therefore, on analysis of the primary principles of NURBS, this paper adopted professional modeling software 3DS MAX to explore the methods and techniques of NURBS in the complex surface building process. And then, the techniques and methods were applied to construct practical engineering machinery, completing the 3D model of bulldozer case.