PARAMETERIZATION OF COMPLEX CULTURAL HERITAGE SHAPES FOR ONLINE VIEWING AND INTERACTIVE PRESENTATION AND PROCESSING

[EN] We have developed algorithms and programs capable of efficiently parameterizing complex cultural heritage shapes including texture, which significantly reduces the data-set size. This is potentially significant for online viewing and interactive presentation and processing. The proposed approach is based on Non-uniform rational B-splines (NURBS) mathematical model which is also by itself suitable for analysis, especially of different artistic techniques.Ćurković, M.; Vučina, D. (2016). PARAMETERIZATION OF COMPLEX CULTURAL HERITAGE SHAPES FOR ONLINE VIEWING AND INTERACTIVE PRESENTATION AND PROCESSING. En 8th International congress on archaeology, computer graphics, cultural heritage and innovation. Editorial Universitat Politècnica de València. 105-110. https://doi.org/10.4995/arqueologica8.2015.3510OCS10511

Finite element analysis enhanced with subdivision surface boundary representations

In this work we develop a design-through-analysis methodology by extending the concept of the NURBS-enhanced finite element method (NEFEM) to volumes bounded by Catmull-Clark subdivision surfaces. The representation of the boundary as a single watertight manifold facilitates the generation of an external curved triangular mesh, which is subsequently used to generate the interior volumetric mesh. Following the NEFEM framework, the basis functions are defined in the physical space and the numerical integration is realized with a special mapping which takes into account the exact definition of the boundary. Furthermore, an appropriate quadrature strategy is proposed to deal with the integration of elements adjacent to extraordinary vertices (EVs). Both theoretical and practical aspects of the implementation are discussed and are supported with numerical examples.</p

A locally based construction of analysis-suitable G1G^1 multi-patch spline surfaces

Analysis-suitable $G^1$ (AS-$G^1$) multi-patch spline surfaces [4] are particular $G^1$-smooth multi-patch spline surfaces, which are needed to ensure the construction of $C^1$-smooth multi-patch spline spaces with optimal polynomial reproduction properties [16]. We present a novel local approach for the design of AS-$G^1$ multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS-$G^1$ multi-patch spline surface by approximating a given $G^1$-smooth but non-AS-$G^1$ multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS-$G^1$ multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, over them

Three-dimensional virtual microstructure generation of porous polycrystalline ceramics

Various numerical methods have been recently employed to model microstructure of ceramics with different level of accuracy. The simplicity of the models based on regular morphologies results in a low computational cost, but these methods produce less realistic geometries with lower precision. Additional methods are able to reconstruct irregular structures by simulating the grain-growth kinetics but are restricted due to their high computational cost and complexity. In this paper, an innovative approach is proposed to replicate a three-dimensional (3D) complex microstructure with a low computational cost and the realistic features for porous polycrystalline ceramics. We present a package, written in MATLAB, that develops upon the basic Voronoi tessellation method for representing realistic microstructures to describe the evolution during the solid-state sintering process. The method is based on a cohesive prism that links the interconnect cells and thus simulates the neck formation. Spline surfaces are employed to represent more realistic features. The method efficiently controls shape and size and is able to reconstruct a wide range of microstructures composed of grains, grain boundaries, interconnected (open) and isolated (closed) pores. The numerical input values can be extracted from 2D imaging of real polished surfaces and through theoretical analysis. The capability of the method to replicate different structural properties is tested using some examples with various configurations

Creases and boundary conditions for subdivision curves

AbstractOur goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points.The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points