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This paper aims to propose a consistent approach to geometric modeling of optimized lattice structures for additive manufacturing technologies.

The proposed method applies subdivision surfaces schemes to an automatically defined initial mesh model of an arbitrarily complex lattice structure. The approach has been developed for cubic cells. Considering different aspects, five subdivision schemes have been studied: Mid-Edge, an original scheme proposed by the authors, Doo–Sabin, Catmull–Clark and Bi-Quartic. A generalization to other types of cell has also been proposed.

The proposed approach allows to obtain consistent and smooth geometric models of optimized lattice structures, overcoming critical issues on complex models highlighted in literature, such as scalability, robustness and automation. Moreover, no sharp edge is obtained, and consequently, stress concentration is reduced, improving static and fatigue resistance of the whole structure.

An original and robust method for modeling optimized lattice structures was proposed, allowing to obtain mesh models suitable for additive manufacturing technologies. The method opens new perspectives in the development of specific computer-aided design tools for additive manufacturing, based on mesh modeling and surface subdivision. These approaches and slicing tools are suitable for parallel computation, therefore allowing the implementation of algorithms dedicated to graphics cards.

Presents an interpolatory subdivision scheme to generate adaptively refined quadrilateral meshes which approximate a smooth surface of arbitrary topology. The described method differs significantly from classical mesh generation techniques based on spline surfaces or implicit representations since no explicit description of the limit surface is used. Instead, simple affine combinations are applied to compute new vertices if a face of the net is split. These rules are designed to guarantee asymptotic smoothness, i.e. the sequence of refined nets converges to a smooth limit surface. Subdivision techniques are useful mainly in applications where a given quadrilateral net is a coarse approximation of a surface and points on a refined grid have to be estimated. To evaluate the proposed approach, shows examples for FE‐computations on surfaces generated by this algorithm.

Refurbishing may be the most practical approach under the low volume production. This effort aims to achieve robotic laser cladding with the main purpose of achieving maximum processing flexibility, predictably high quality, lower maintenance and operating costs. This study aims to focus on online measurement and cladding path generation toward automatic laser cladding.

Based on the specific requirements of automatic laser cladding, an approach was proposed toward an automatic laser cladding with powder injection for the refurbishment of components with free‐form surfaces. This study assessed the feasibility of integrating a non‐contact free‐form surface measurement system, an industrial robot, and an algorithm for generating cladding tool paths seamlessly.

3D laser scanning and laser cladding systems can be embedded into an existing robot motion control system. Online measurement based 3D surface reconstruction is a practical approach toward cladding tool path generation for on‐site refurbishment.

Robotic laser cladding may be a potential application by integrating other measurement devices, such as temperature sensor based monitoring system.

Refurbishing worn‐out components could have significant economic benefits. This study indicates that robotic laser cladding may potentially facilitate improved refurbishment of oversized components.

Irregularly shaped architectural designs with surfaces curved in multiple directions, known as free-form designs, have gained significant public interest in recent decades. However, it is challenging to convert complex designs into real structures. This paper aims to realize free-form construction by developing a novel workflow in which additively manufactured thermoplastic polyurethane (TPU) molds are used.

The workflow is developed through mechanical tests on additively manufactured TPU specimens, determination of TPU mold design criteria and exploration of mold preparation methods. Two concrete elements with free-form geometries are fabricated using the proposed workflow.

TPU is a thermoplastic elastomer that is strong and inexpensive, making it an ideal mold material for casting complex concrete structures. An innovative workflow is developed in which TPU molds are used, appropriate release agents are selected for different concrete casting conditions and a mold subdivision method is proposed to facilitate the demolding process. Furthermore, the integrity of TPU molds can be maintained by following the proposed workflow, enabling repetitive use of molds. The fabrication of the two free-form structures shows that complex concrete members with high dimensional accuracy and excellent surface quality can be manufactured using the proposed method.

To the best of the authors’ knowledge, this is the first systematic study on using additively manufactured TPU molds for concrete casting of complex structures. The new techniques developed in this research can be applied to large-scale architectural, engineering and construction projects.

The purpose of this paper is to develop a robotic tooth brushing simulator mimicking realistic tooth brushing motions, thereby facilitating greater understanding of the generation of realistic tooth brushing motion for optimal design of toothbrushes.

Tooth brushing motions were measured via a motion capture system. Different motion patterns of brushing were analysed. A series of elliptical motion segments were generated by interpolating ellipse‐like trajectories. Furthermore, a path generation algorithm for brushing simulation was proposed. A path planning system incorporating robot motion control was developed to simulate realistic tooth brushing. The generality and efficiency of the proposed algorithm was demonstrated through simulation and experimental results.

The interpolation of ellipse‐like trajectories can generate elliptical motion segments. Furthermore, realistic tooth brushing can be achieved by integrating the elliptical motion segments into the path generated from the surfaces of teeth. The brushing simulator demonstrated good reproducibility of clinically standardized tooth brushing.

A robotic toothbrush assessment system is a potential application to the robotic tooth brushing simulator by incorporating control of brushing variables, including brushing pressure, speed and temperature.

This study demonstrates the feasibility of using robotic simulation techniques towards improved realistic human tooth brushing motions simulation for optimal design of tooth brushes.

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

Shell structures are highly efficient and are an elegant way of covering large uninterrupted spaces, but their complex geometry is notoriously difficult to model and analyse. This paper aims to describe a novel free-form shell modelling technique based on structural harmonics.

The method builds on work using weighted eigenmodes for three-dimensional mesh modelling in a computer graphics setting and extends it by specifically adapting the technique to an architectural design context. This not only enables the sculpting of free-form architectural surfaces using only a few control parameters but also takes advantage of the synergies between eigenmodes and structural buckling modes, to provide an efficient means of stiffening a shell against failure by buckling.

The result is a flexible free-form modelling tool that not only enables the creation of arbitrary doubly curved surfaces but also allows simultan. The tool helps to assist in the design of shells at the conceptual stage and encourages an interaction between the architect and engineer. A number of initiatives, including a single degree of freedom design, boundary constraints, visualisation aids and guidelines towards specific spatial configurations have been introduced to satisfactorily adapt the method to an architectural context.

The tool helps to assist in the design of shells at the conceptual stage and encourages an interaction between the architect and engineer. A number of initiatives, including a single degree of freedom design, boundary constraints, visualisation aids and guidelines towards specific spatial configurations have been introduced to satisfactorily adapt the method to an architectural context. This paper includes a full case study of the iconic British Museum Great Court Roof to demonstrate the applicability of the developed framework to real-world problems and the software developed to implement the method is available as an open-source download.

This paper reports on the work done to decompose a large sized solid model into smaller solid components for rapid prototyping technology. The target geometric domain of the solid model includes quadrics and free form surfaces.

The decomposition criteria are based on the manufacturability of the model against a user‐defined manufacturing chamber size and the maintenance of geometrical information of the model. In the proposed algorithm, two types of manufacturing chamber are considered: cylindrical shape and rectangular shape. These two types of chamber shape are commonly implemented in rapid prototyping machines.

The proposed method uses a combination of the regular decomposition (RD)‐method and irregular decomposition (ID)‐method to split a non‐producible solid model into smaller producible subparts. In the ID‐method, the producible feature group decomposition (PFGD)‐method focuses on the decomposition by recognising producible feature groups. In the decomposition process, less additional geometrical and topological information are created. The RD‐method focuses on the splitting of non‐producible sub‐parts, which cannot be further decomposed by the PFGD‐method. Different types of regular split tool surface are studied.

Combination of the RD‐method and the ID‐method makes up the proposed volume decomposition process. The user can also define the sequence and priority of using these methods manually to achieve different decomposition patterns. The proposed idea is also applicable to other decomposition algorithm. Some implementation details and the corresponding problems of the proposed methods are also discussed.

This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into three types, namely, orthogonal, perspective and parallel projection.

For parametric surfaces, the computing strategy of the algorithm is to obtain an approximate solution by using a geometric algorithm, then improve the accuracy of the approximate solution using the Newton–Raphson iteration. For perspective projection and parallel projection on an implicit surface, the strategy replaces Newton–Raphson iteration by multi-segment tracing. The implementation takes two mesh objects as an example of calculating an image projected onto parametric and implicit surfaces. Moreover, a comparison is made for orthogonal projections with Hu’s and Liu’s methods.

The results show that the new method can solve the 3D objects projection problem in an effective manner. For orthogonal projection, the time taken by the new method is substantially less than that required for Hu’s method. The new method is also more accurate and faster than Liu’s approach, particularly when the 3D object has a large number of points.

The algorithms presented in this paper can be applied in many industrial applications such as computer aided design, computer graphics and computer vision.

The purpose of this paper is to propose a new way of prototyping surfaces, taking the mathematical background into account, without involving drawing environments.

The authors thicken surfaces from a mathematical point of view to obtain solids. Next they look for an operative procedure to build virtual models and interchange files. The authors build a sample of Enneper thickened surface by fused deposition modelling and verify the prototype by reverse engineering techniques.

The authors provide a formulation able to thicken surfaces in mathematical terms. An operative procedure generates virtual solids and interchange files in the same environment. The approximations necessary for additive fabrication, such as triangulations and mesh geometry, can be chosen at this stage.

The approach is useful at the product/process development stage, in which surfaces are delivered by theoretical analysis. At this stage a prototype can give useful advice permitting functional tests. The limitation is that, when the mathematical formulation is not available, it is difficult to translate a concept without fundamentals of differential geometry.

Approximations of drawing environments typically lead to fault models, not ready for fabrication by additive manufacturing (AM) technologies, needing empiric, not at all obvious and not rapid repair interventions. The authors' approach eliminates this stage, permitting a faster and simple managing of modifications due to functional and technological requirements, that are frequent at concept stage. This leads to a time‐to‐market reduction in the course of product/process development.

This paper extends the capability of a mathematical approach to solve surface prototyping problems. By reducing the required stages, the proposed methodology finds a theoretical and practical shorter route to direct fabrication.