L-systems in Geometric Modeling

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Recoverable DTN Routing based on a Relay of Cyclic Message-Ferries on a MSQ Network

An interrelation between a topological design of network and efficient algorithm on it is important for its applications to communication or transportation systems. In this paper, we propose a design principle for a reliable routing in a store-carry-forward manner based on autonomously moving message-ferries on a special structure of fractal-like network, which consists of a self-similar tiling of equilateral triangles. As a collective adaptive mechanism, the routing is realized by a relay of cyclic message-ferries corresponded to a concatenation of the triangle cycles and using some good properties of the network structure. It is recoverable for local accidents in the hierarchical network structure. Moreover, the design principle is theoretically supported with a calculation method for the optimal service rates of message-ferries derived from a tandem queue model for stochastic processes on a chain of edges in the network. These results obtained from a combination of complex network science and computer science will be useful for developing a resilient network system.Comment: 6 pages, 12 figures, The 3rd Workshop on the FoCAS(Fundamentals of Collective Adaptive Systems) at The 9th IEEE International Conference on SASO(Self-Adaptive and Self-Organizing systems), Boston, USA, Sept.21, 201

Solid NURBS Conforming Scaffolding for Isogeometric Analysis

This work introduces a scaffolding framework to compactly parametrise solid structures with conforming NURBS elements for isogeometric analysis. A novel formulation introduces a topological, geometrical and parametric subdivision of the space in a minimal plurality of conforming vectorial elements. These determine a multi-compartmental scaffolding for arbitrary branching patterns. A solid smoothing paradigm is devised for the conforming scaffolding achieving higher than positional geometrical and parametric continuity. Results are shown for synthetic shapes of varying complexity, for modular CAD geometries, for branching structures from tessellated meshes and for organic biological structures from imaging data. Representative simulations demonstrate the validity of the introduced scaffolding framework with scalable performance and groundbreaking applications for isogeometric analysis

From approximating to interpolatory non-stationary subdivision schemes with the same generation properties

In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying quite mild assumptions. To achieve this result we extend our previous work [C.Conti, L.Gemignani, L.Romani, Linear Algebra Appl. 431 (2009), no. 10, 1971-1987] to full generality by removing additional assumptions on the input symbols. For the so obtained interpolatory schemes we prove that they are capable of reproducing the same exponential polynomial space as the one generated by the original approximating scheme. Moreover, we specialize the computational methods for the case of symbols obtained by shifted non-stationary affine combinations of exponential B-splines, that are at the basis of most non-stationary subdivision schemes. In this case we find that the associated family of interpolatory symbols can be determined to satisfy a suitable set of generalized interpolating conditions at the set of the zeros (with reversed signs) of the input symbol. Finally, we discuss some computational examples by showing that the proposed approach can yield novel smooth non-stationary interpolatory subdivision schemes possessing very interesting reproduction properties

A Framework for Dynamic Terrain with Application in Off-road Ground Vehicle Simulations

The dissertation develops a framework for the visualization of dynamic terrains for use in interactive real-time 3D systems. Terrain visualization techniques may be classified as either static or dynamic. Static terrain solutions simulate rigid surface types exclusively; whereas dynamic solutions can also represent non-rigid surfaces. Systems that employ a static terrain approach lack realism due to their rigid nature. Disregarding the accurate representation of terrain surface interaction is rationalized because of the inherent difficulties associated with providing runtime dynamism. Nonetheless, dynamic terrain systems are a more correct solution because they allow the terrain database to be modified at run-time for the purpose of deforming the surface. Many established techniques in terrain visualization rely on invalid assumptions and weak computational models that hinder the use of dynamic terrain. Moreover, many existing techniques do not exploit the capabilities offered by current computer hardware. In this research, we present a component framework for terrain visualization that is useful in research, entertainment, and simulation systems. In addition, we present a novel method for deforming the terrain that can be used in real-time, interactive systems. The development of a component framework unifies disparate works under a single architecture. The high-level nature of the framework makes it flexible and adaptable for developing a variety of systems, independent of the static or dynamic nature of the solution. Currently, there are only a handful of documented deformation techniques and, in particular, none make explicit use of graphics hardware. The approach developed by this research offloads extra work to the graphics processing unit; in an effort to alleviate the overhead associated with deforming the terrain. Off-road ground vehicle simulation is used as an application domain to demonstrate the practical nature of the framework and the deformation technique. In order to realistically simulate terrain surface interactivity with the vehicle, the solution balances visual fidelity and speed. Accurately depicting terrain surface interactivity in off-road ground vehicle simulations improves visual realism; thereby, increasing the significance and worth of the application. Systems in academia, government, and commercial institutes can make use of the research findings to achieve the real-time display of interactive terrain surfaces

A combined approximating and interpolating subdivision scheme with C2 continuity

AbstractIn this paper a combined approximating and interpolating subdivision scheme is presented. The relationship between approximating subdivision and interpolating subdivision is derived by directly performing operations on geometric rules. The behavior of the limit curve produced by our combined subdivision scheme is analyzed by the Laurent polynomial and attains C2 degree of smoothness. Furthermore, a non-uniform combined subdivision with shape control parameters is introduced, which allows a different tension value for every edge of the original control polygon