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The paper discusses an integrated methodology to implement an interactive augmented reality 3D modelling environment with natural interaction, empowered by real-time gesture recognition. The methodology is developed from a geometry-sculpting algorithm based on the use of the subdivision surfaces approach to combine the ease and versatility of interactive modelling even of complex shapes, while maintaining high geometric continuity and smoothness. The interaction with the deformable elements of the geometry's control cage to be divided uses an optimised version of the Grasp Active Feature/Object Active Feature algorithm developed from hand tracking and gesture recognition based on zero-invasive stereo-infrared techniques. Modelling, combined with an augmented reality environment, allows the modification of geometries having real objects as a reference and, in any case, a general spatial awareness during activities. The methodology was implemented and tested using an advanced mixed-reality headset, the Varjo XR-4, with hi-resolution pass-through and a second-generation Ultraleap for accurate and precise hand tracking. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer-Aided Design & Computer Graphics / Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We propose an efficient method with energy constraints for constructing a Catmull–Clark surface that interpolates a given mesh. We approximate the surface energy of Catmull–Clark surfaces near extraordinary points by summing their finite subpatches and then represent the energy of the subpatches as linear combinations of the vertices of control mesh. By minimizing the surface energy as a constraint, we generate a new control mesh whose limit surfaces interpolate a given mesh. Numerous examples and comparisons demonstrate that our method has the following characteristics: (1) The limit surfaces are fairer, reducing unnecessary undulations and having minimal surface energy, and (2) the approximation process is simple and intuitive, requiring only a small number of computational steps and avoiding complex parameterization processes. [ABSTRACT FROM AUTHOR]

The paper discusses an integrated methodology to implement an interactive augmented reality 3D modelling environment with natural interaction, empowered by real-time gesture recognition. The methodology is developed from a geometry-sculpting algorithm based on the use of the subdivision surfaces approach to combine the ease and versatility of interactive modelling even of complex shapes, while maintaining high geometric continuity and smoothness. The interaction with the deformable elements of the geometry’s control cage to be divided uses an optimised version of the Grasp Active Feature/Object Active Feature algorithm developed from hand tracking and gesture recognition based on zero-invasive stereo-infrared techniques. Modelling, combined with an augmented reality environment, allows the modification of geometries having real objects as a reference and, in any case, a general spatial awareness during activities. The methodology was implemented and tested using an advanced mixed-reality headset, the Varjo XR-4, with hi-resolution pass-through and a second-generation Ultraleap for accurate and precise hand tracking.

We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces. The existing structural optimization methods mainly contain shape and topology schemes, with the former changing the surface geometric profile of the structure and the latter changing the material distribution topology or hole topology of the structure. In the present acoustic performance optimization, the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure, the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter, and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge. The topology and shape sensitivities of the approach are calculated using the adjoint variable method, which ensures the efficiency of the optimization. The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization. Numerical examples are given to validate the effectiveness of the presented optimization approach. [ABSTRACT FROM AUTHOR]

A new general contact model is proposed for preventing inter‐leaflet penetration of bio‐prosthetic heart valves (BHV) at the end of the systole, which has the advantage of applying kinematic constraints directly and creating smooth free edges. At the end of each time step, the impenetrability constraints and momentum exchange between the impacting bodies are applied separately based on the coefficient of restitution. The contact method is implemented in a rotation‐free, large deformation, and thin shell finite‐element (FE) framework based on loop's subdivision surfaces. A nonlinear, anisotropic material model for a BHV is employed which uses Fung‐elastic constitutive laws for in‐plane and bending responses, respectively. The contact model is verified and validated against several benchmark problems. For a BHV‐specific validation, the computed strains on different regions of a BHV under constant pressure are compared with experimentally measured data. Finally, dynamic simulations of BHV under physiological pressure waveform are performed for symmetrical and asymmetrical fiber orientations incorporating the new contact model and compared with the penalty contact method. The proposed contact model provides the coaptation area of a functioning BHV during the closing phase for both of the fiber orientations. Our results show that fiber orientation affects the dynamic of leaflets during the opening and closing phases. A swirling motion for the BHV with asymmetrical fiber orientation is observed, similar to experimental data. To include the fluid effects, fluid–structure interaction (FSI) simulation of the BHV is performed and compared to the dynamic results. [ABSTRACT FROM AUTHOR]

Coarse meshes can be recursively subdivided into denser and denser meshes by dividing their faces into several smaller faces and repositioning the vertices according to carefully designed subdivision rules. This process leads to smooth surfaces, such as in the case of Catmull-Clark or Loop subdivision, but often suffers from shading artifacts near extraordinary points due to the lower quality of the normal field there, typically corresponding to only tangent-plane (and not higher) continuity at these points. The idea of subdivision shading is to apply the same subdivision rules that are used to subdivide geometry to also subdivide the normals associated with mesh vertices. This leads to smoother normal fields, which can be used for shading purposes, and this in turn removes the shading artifacts. However, the original subdivision shading method does not support sharp and semi-sharp creases, which are desired ingredients in subdivision surface modelling. We present two approaches to extending subdivision shading to work also on models with (semi-)sharp creases, and demonstrate this in the cases of Catmull-Clark as well as Loop subdivision. [ABSTRACT FROM AUTHOR]

Methods from the field of computer graphics are the foundation for the representation of geological structures in the form of geological models. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered, and the capacities and limitations of different algorithms are not always evident. In this work, we therefore review surface-based geological modelling methods from both a geological and computer graphics perspective. Specifically, we investigate the use of NURBS (non-uniform rational B-splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of the two approaches. Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention—even if subdivision surfaces support arbitrary topologies and watertight boundary representation, two aspects that make them an appealing choice for complex geological modelling. It is worth mentioning that watertight models are an important basis for subsequent process simulations. Many complex geological structures require a combination of smooth and sharp edges. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterise the resistance of a mesh structure to the subdivision procedure. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology, is described. Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison with the complex geological structure. [ABSTRACT FROM AUTHOR]

The state of the art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low-frequency breakdown, dense-discretization breakdown, preconditioning, and so on. Likewise, the community has seen extensive investment in the development of methods for higher order analysis, in both geometry and physics. Unfortunately, these standard geometric descriptors are continuous, but their normals are discontinuous at the boundary between triangular tessellations of control nodes, or patches, with a few exceptions; as a result, one needs to define additional mathematical infrastructure to define physical basis sets for vector problems. In stark contrast, the geometric representation used for design is second order differentiable almost everywhere on the surfaces. Using these descriptions for analysis opens the door to several possibilities, and is the area we explore in this article. Our focus is on loop subdivision-based isogeometric methods. In this article, our goals are twofold: 1) development of computational infrastructure for isogeometric analysis of electrically large simply connected objects, and 2) introduction of the notion of manifold harmonic transforms and its utility in computational electromagnetics. Several results highlighting the efficacy of these two methods are presented. [ABSTRACT FROM AUTHOR]

Convolutionalneural networks (CNNs) have made great breakthroughs in two-dimensional (2D) computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this article presents SubdivNet, an innovative and versatile CNN framework for three-dimensional (3D) triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from nearby faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g., variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we make use of pooling layers that uniformly merge four faces into one and an upsampling method that splits one face into four. Thereby, many popular 2D CNN architectures can be easily adapted to process 3D meshes. Meshes with arbitrary connectivity can be remeshed to have Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Extensive evaluation and various applications demonstrate SubdivNet's effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

Coarse meshes can be recursively subdivided into denser and denser meshes by dividing their faces into several smaller faces and repositioning the vertices according to carefully designed subdivision rules. This process leads to smooth surfaces, such as in the case of Catmull-Clark or Loop subdivision, but often suffers from shading artifacts near extraordinary points due to the lower quality of the normal field there, typically corresponding to only tangent-plane (and not higher) continuity at these points. The idea of subdivision shading is to apply the same subdivision rules that are used to subdivide geometry to also subdivide the normals associated with mesh vertices. This leads to smoother normal fields, which can be used for shading purposes, and this in turn removes the shading artifacts. However, the original subdivision shading method does not support sharp and semi-sharp creases, which are desired ingredients in subdivision surface modelling. We present two approaches to extending subdivision shading to work also on models with (semi-)sharp creases, and demonstrate this in the cases of Catmull-Clark as well as Loop subdivision.

A novel boundary element method based on subdivision surfaces is applied to simulate wave scattering problems governed by the Helmholtz equation. The Loop subdivision scheme widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The novelty of this work is that it is the first time to apply the fast multipole method for subdivision surface boundary element method to accelerate the solution of the system of equations. It is demonstrated that the subdivision surfaces boundary element method based on the Loop subdivision scheme performs well in terms of accuracy, and automatically provides multiresolution subdivision hierarchy models to meet the requirements of different precision. This approach is then applied to several real-world applications to illustrate the potential for integrated engineering analysis. [ABSTRACT FROM AUTHOR]

Bidirectional path tracing (BPT) with multiple importance sampling (MIS) is a popular technique for rendering realistic images. Recently, it has been shown that BPT can be improved by preparing multiple light sub-paths and by resampling a small number of light sub-paths from them to generate full paths with large contribution. Traditionally, for MIS weights, the balance heuristic has widely been used to minimize the upper bound of variance, where each full path is weighted in proportion to the probability of the path. Although the probability of the path can change due to the resampling process, the weighting functions used in the previous methods remain unaffected by the change in probability, resulting in less efficiency. To address this problem, we propose new weighting functions for BPT with multiple light sub-paths. Our main contribution is a precise formulation of the variance and the derivation of the weighting functions that can appropriately treat the change in probability. We demonstrate that our weighting functions significantly improve the image quality. We will release a simple version of our implementation as open source to ensure reproducibility. [ABSTRACT FROM AUTHOR]

We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities, bridging the mixed finite-element representation with discrete exterior calculus. By commuting with differential operators, our subdivision is structure preserving: it reproduces curl-free fields precisely and reproduces divergence-free fields in the weak sense. Moreover, our subdivision scheme directly extends to directional fields with several vectors per face by working on the branched covering space. Finally, we demonstrate how our scheme can be applied to directional-field design, advection, and robust earth mover’s distance computation, for efficient and robust computation. [ABSTRACT FROM AUTHOR]

Motion control in high-speed micromilling processes requires fast, accurate following of a specified curvilinear path. The accuracy with which the path can be followed is determined by the speed at which individual trajectories can be generated and sent to the control system. The time required to generate the trajectory is dependent on the representations used for the curvilinear trajectory path. In this study, we introduce the use of subdivision curves as a method for generating high-speed micromilling trajectories. Subdivision curves are discretized curves which are specified as a series of recursive refinements of a coarse mesh. By applying these recursive properties, machining trajectories can be computed very efficiently. Using a set of representative test curves, we show that with subdivision curves, trajectories can be generated significantly faster than with NURBS curves, which is the most common method currently used in generating high-speed machining trajectories. Trajectories are computed efficiently with subdivision curves as they are natively discretized, and do not require additional evaluation steps, unlike in the case of NURBS curves. The reduced trajectory generation time allows for improved performance in high-speed, high-precision micromilling. We discuss the use of several metrics to quantify the quality of the subdivision interpolation, and apply them in calculating the error during trajectory generation for the test curves.

We present a strategy for performing view-adaptive, crack-free tessellation of Catmull-Clark subdivision surfaces entirely on programmable graphics hardware. Our scheme extends the concept of breadth-first subdivision, which up to this point has only been applied to parametric patches. While mesh representations designed for a CPU often involve pointer-based structures and irregular per-element storage, neither of these is well-suited to GPU execution. To solve this problem, we use a simple yet effective data structure for representing a subdivision mesh, and design a careful algorithm to update the mesh in a completely parallel manner. We demonstrate that in spite of the complexities of the subdivision procedure, real-time tessellation to pixel-sized primitives can be done. Our implementation does not rely on any approximation of the limit surface, and avoids both subdivision cracks and T-junctions in the subdivided mesh. Using the approach in this paper, we are able to perform real-time subdivision for several static as well as animated models. Rendering performance is scalable for increasingly complex models.

We discuss the use of subdivision surfaces in the procedural design of imprint rolls for use in the roller imprinting process. Roller imprinting is being developed for the fabrication of microfluidic devices in polymer substrates. Imprint rolls are modeled using Catmull-Clark subdivision surfaces, and are procedurally designed based on feedback from finite-element simulations of the imprinting process. Microfluidic devices exhibit repeating patterns, and can be modeled using a small set of unique entities (or tiles). Imprint rolls are also modeled as a sum of tiles, and rolls are designed by studying the imprinting behavior of clusters of tiles corresponding to the repeating patterns seen in the device. This approach reduces the roll complexity and analysis time. The rolls need to be described in a sufficiently flexible format for the tile-based analysis to be effective. Conventional model representations are too cumbersome for piecewise iterative refinement as they require the manipulation of a large number of variables to modify surface features while preserving continuity. Subdivision surfaces, on the other hand, are naturally continuous and can be modified by manipulating a small number of variables. The ability to apply rule-based, arbitrary refinement on subdivision surfaces makes them especially suitable. The procedural modeling methodology and the subdivision design representation enable the integrated design, analysis, and manufacturing of imprint rolls, and has proven effective in decreasing the design-to-manufacture time of novel microfluidic technology.

Subdivision surfaces combine smooth spline surfaces and polygonal meshes together, therefore, a smooth design model and discrete machining models may be unified and subdivision surfaces may be used as a common representation for geometric design and machining. Motivated by the idea, this paper presents the study of finish machining of objects represented by subdivision surfaces with emphasis on geometric error control involved in tool-path generation. First, given a design model, chordal error is controlled during finishing model building. A chordal error-driven adaptive subdivision method is used to build finishing models with less data. Second, a surface decomposition machining strategy is used to control the cusp height error. A simple iso-slope curve tracing and surface decomposition algorithm is presented to partition the model into flat and steep regions. Contour-map tool-paths are generated in the steep regions while iso-planar tool-paths are generated in the flat regions. The gouge problem is easily handled through two-dimensional (2D) tool-path correction algorithms. The implementation results demonstrate that subdivision is capable of serving as a unified representation for both geometric modelling and machining. [ABSTRACT FROM AUTHOR]

We present a new construction approach for symmetric lifted B-spline wavelets on irregular polygonal control meshes defining two-manifold topolgies. Polygonal control meshes are recursively refined by stationary subdivion rules and converge to piecewise polynomaial limit surfaces. At every subdivision level, our wavelet transforms provide an efficient way to add geometric details that are expanded from wavelet coefficients. Both wavelet decomposition and reconstruction operations are based on local lifting steps and have linear-time complexity.

We present a segmentation approach to scientific visualization that combines the definition of higher-level data, the efficient extraction of meaningful derived feature-like data from defined properties, and the effective visual representation of the extracted data. Our framework is aimed at multi-valued time-varying data sets, where, for example, grid vertices might have a multitude of associated scalar, vector and tensor quantities. This segmentation approach to massive data set exploration allows the user to focus upon regions, and interactively explore these regions efficiently. The challenge is to generate this segmented data from existing multi-valued data sets, store this data in an efficient scheme, generate the boundaries of each region, and display these boundaries to the user. We present an integrated scheme that allows a common representation for segmentation, allows it to be applied to a number of data types, and allows derived representations to be calculated. We illustrate this framework with examples from scalar-and vector-field visualization.

A method for the morphing of surface/volume meshes suitable to be used in hydrodynamic shape optimization is proposed. Built in the OpenFOAM environment, it relies on a Laplace equation that propagates the modifications of the surface boundaries, realized by applying a free-form deformation to a subdivision surface description of the geometry, into the computational volume mesh initially built through a combination of BlockMesh with cfMesh. The feasibility and robustness of this mesh morphing technique, used as a computationally efficient pre-processing tool, is demonstrated in the case of the resistance minimization of the DTC hull. All the hull variations generated within a relatively large design space are efficiently and successfully realized, i.e., without mesh inconsistencies and quality issues, only by deforming the initial mesh of the reference geometry. Coupled with a surrogate model approach, a significant reduction in the calm water resistance, in the extent of 10%, has been achieved in a reasonable computational time.

We present a new technique for progressive C0-continuous approximation and compression of polygonal objects in images. Our technique uses local parametrizations defined by meshes of convex polygons in the plane. We generalize a lifted biorthogonal wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tesselation rather than a rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.

In the paper we consider a treatment of Bernoulli type shape optimization problems in three dimensions by the combination of the boundary element method and the hierarchical algorithm based on the subdivision surfaces. After proving the existence of the solution on the continuous level we discretize the free part of the surface by a hierarchy of control meshes allowing to separate the mesh necessary for the numerical analysis and the choice of design parameters. During the optimization procedure the mesh is updated starting from its coarse representation and refined by adding design variables on finer levels. This approach serves as a globalization strategy and prevents geometry oscillations without any need for remeshing. We present numerical experiments demonstrating the capabilities of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A sequence of C 2 -connected nested subdivision rings of polynomial degree bi-4 can be made to follow a guide surface and completed by a tiny finite cap to serve as a refinable surface representation for design and analysis (Karčiauskas and Peters, 2018). This raises the question, both of academic and practical interest, how much and at what cost to surface quality can the efficiency be improved by lowering the number of rings and/or the polynomial degree. In a systematic exploration, a new bi-4 construction is discovered that requires half the number of surface rings but matches the quality of (Karčiauskas and Peters, 2018). For this surface quality, numerous trials indicate that this number of surface rings is minimal and that the degree cannot be reduced. Bi-3 constructions with a similar layout have inferior highlight line distributions – although the best of the new bi-3 constructions visibly improve on Catmull–Clark subdivision and its curvature-bounded variants. • A systematic exploration of low-degree C 2 -connected subdivision rings. • A bi-4 subdivision scheme halves the number of surface rings while matching the quality of its best predecessor. • Numerous trials indicate that reducing the number of rings or the degree yield notably worse shape. • Analogous bi-3 constructions have inferior highlight line distributions. • but visibly improve on Catmull–Clark and curvature-bounded variants. [ABSTRACT FROM AUTHOR]

Cloth simulation is an important topic for many applications in computer graphics, animation, and augmented virtual reality. The mechanical behavior of cloth objects can be modeled by the Kirchhoff--Love thin shell equations, which lead to large-scale, nonlinear, ill-conditioned algebraic equations. We propose to solve these nonlinear problems efficiently using the recursive multilevel trust region (RMTR) method. Our multilevel framework for cloth simulations is based on Catmull--Clark subdivision surfaces, which facilitates generation of the mesh hierarchy and also provides the basis for the finite element discretization. The prolongation and restriction operators are similarly constructed based on the subdivision rules. Finally, we leverage a reverse subdivision operator to transfer iterates from fine levels to coarser levels. The novel use of this fine-to-coarse operator provides a computationally efficient alternative to the least-square approach used elsewhere. Using the resulting RMTR variant, we present numerical examples showing a reduction in the number of iterations by several orders of magnitude when compared to a single-level trust region method. [ABSTRACT FROM AUTHOR]

Probabilistic distribution models like Gaussian mixtures have shown great potential for improving both the quality and speed of several geometric operators. This is largely due to their ability to model large fuzzy data using only a reduced set of atomic distributions, allowing for large compression rates at minimal information loss. We introduce a new surface model that utilizes these qualities of Gaussian mixtures for the definition and control of a parametric smooth surface. Our approach is based on an enriched mesh data structure, which describes the probability distribution of spatial surface locations around each vertex via a Gaussian covariance matrix. By incorporating this additional covariance information, we show how to define a smooth surface via a nonlinear probabilistic subdivision operator based on products of Gaussians, which is able to capture rich details at fixed control mesh resolution. This entails new applications in surface reconstruction, modeling, and geometric compression. [ABSTRACT FROM AUTHOR]

The aim of this attempt was to present an efficient algorithm for the evaluation of error bound of triangular subdivision surfaces. The error estimation technique is based on first order difference and this process is independent of parametrization. This technique can be easily generalized to higher arity triangular surfaces. The estimated error bound is expressed in-terms of initial control point sequence and constants. Here, we efficiently estimate error bound between triangular surface and its control polygon after k-fold subdivision and further extended to evaluate subdivision depth of the scheme.

Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are becoming available in a number of geometric modelling systems for engineering design. The subdivision refinement rules are usually adapted from knot insertion rules for splines. The quadrilateral Catmull–Clark scheme considered in this work is equivalent to cubic B-splines away from extraordinary, or irregular, vertices with other than four adjacent elements. Around extraordinary vertices the surface consists of a nested sequence of smooth spline patches which join C 1 continuously at the point itself. As known from geometric design literature, the subdivision weights can be optimised so that the surface quality is improved by minimising short-wavelength surface oscillations around extraordinary vertices. We use the related techniques to determine weights that minimise finite element discretisation errors as measured in the thin-shell energy norm. The optimisation problem is formulated over a characteristic domain and the errors in approximating cup- and saddle-like quadratic shapes obtained from eigenanalysis of the subdivision matrix are minimised. In finite element analysis the optimised subdivision weights for either cup- or saddle-like shapes are chosen depending on the shape of the solution field around an extraordinary vertex. As our computations confirm, the optimised subdivision weights yield a reduction of 50% and more in discretisation errors in the energy and L 2 norms. Although, as to be expected, the convergence rates are the same as for the classical Catmull–Clark weights, the convergence constants are improved. [ABSTRACT FROM AUTHOR]

Abstract: Converting quadrilateral meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distribution of recent G‐spline constructions with the refinability of subdivision surfaces. This avoids the complex refinement of G‐spline constructions and the poor shape of standard subdivision. Guided subdivision can then be used both to generate the surface and hierarchically compute functions on the surface. Specifically, we present a C2 subdivision algorithm of polynomial degree bi‐6 and a curvature bounded algorithm of degree bi‐5. We prove that the common eigenstructure of this class of subdivision algorithms is determined by their guide and demonstrate that their eigenspectrum (speed of contraction) can be adjusted without harming the shape. For practical implementation, a finite number of subdivision steps can be completed by a high‐quality cap. Near irregular points this allows leveraging standard polynomial tools both for rendering of the surface and for approximately integrating functions on the surface. [ABSTRACT FROM AUTHOR]

The restriction of tensor-product B-splines to regular control meshes and thus four-sided surfaces is the reason that hull form modeling is still a challenge. This limitation is addressed by subdivision surfaces as they originate from the idea to define B-spline surfaces on irregular control meshes. Often subdivision is considered as a method to refine polygon meshes, but the linear nature of polygon meshes is generally not qualified for hull form representation. Therefore an introduction to the theory of generalized B-splines is given which employs the notion of subdivision to define smooth B-spline surfaces on irregular control meshes. This article covers the application of generalized B-splines for the representation of hull forms. It is possible to represent hull forms with a single B-spline surface. The main advantage is, however, the ability to use the control mesh for modeling. It is shown that the structure of a control mesh and the principles to define a control mesh are essentially the same as for curve networks which are mostly used to define hull surfaces. In contrast to the common belief in the industry, it is analyzed that the approximation-based definition of a hull surface in terms of a control mesh simplifies modeling and improves the robustness compared to interpolation-based methods such as the commonly found interpolation of curve networks. [ABSTRACT FROM AUTHOR]

Creating immersive interactive virtual worlds not only require plausible visuals, but it is also important to allow the user to interact with the virtual scene in a natural way. While rigid-body physics simulations are widely used to provide basic interaction, realistic soft-body deformations of virtual objects are challenging and therefore typically not offered in multi user environments. We present a web service for interactive deformation which can accurately replicate real world material behavior. Its architecture is highly flexible, can be used from any web enabled client, and facilitates synchronization of computed deformations across multiple users and devices at different levels of detail. [ABSTRACT FROM AUTHOR]

Summary: We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin‐shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff‐Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work, the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the C1 continuity property required for the Kirchhoff‐Love formulation and are highly efficient for the acoustic field computations. We verify the proposed isogeometric formulation through a closed‐form solution of acoustic scattering over a thin‐shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural‐acoustic analysis of shells. [ABSTRACT FROM AUTHOR]