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2024

Ch. Fünfzig, R. Wallrath, S. Hubert
Efficient batch assignment for parallel-machine production scheduling, Proc. Int. Conference on Agents and Artificial Intelligence (ICAART), Rome 2024.
In this article, we consider different batch assignment schemes for non-separable, non-preemptive production scheduling on m parallel work stations. Batch assignment is a very important part of production models as batches with identical parameters usually occur in a large number in real-world applications, which causes a large number of symmetric solutions. The common scheme Exactly-n for assignment of n batches to m machines originating from general assignment problems is very inefficient when it comes to scheduling, even with additional ordering for symmetry breaking (Exactly-n Ordered). We define three restricted assignment schemes for the same-parameter batches by forming blocks of size 0\leq z_i \leq n on machine i and ordering them between the different machines. We compute bounds for the number of feasible assignments as a measure for the feasible space and give solving times from our experiments with a boolean inference-based solver like the Google CP-SAT solver. We show that with the proposed restricted assignment schemes, production scheduling models result that solve significantly faster than the models with the common scheme Exactly-n.
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2020

N. Kirchhof, K. Müller, Ch. Fünfzig
Virtual Blox: When Interlockable Blocks Meet the Infinite Possibilities of Virtual Reality, Proc. Conference on Mensch und Computer, Magdeburg 2020.
There are a plethora of brick systems on the market these days. Children and young adults play very creatively with the interlocking bricks. Even adults like the colorful bricks and build models with them quickly and easily. In this paper we present our brick system solution for the virtual world, playable with the HTC Vive and two controllers. For our solution, we transferred the brick properties of the real world into the virtual one. Play patterns like grabbing a brick, connecting it to other bricks or releasing it needed to be converted for the virtual world. Virtual reality is capable of enhancing the play experience in a way that would not be possible in the real world. To support the building process, we implemented several forms of assistance. These were positively evaluated by players.
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2014

Ch. Fünfzig
Parallel Approximate Viewshed Computation, 11th Int. IADIS Conference on Applied Computing, Porto, Portugal 2014.
Visibility computation on height field grids is important for geo information and simulation tasks like signal propagation and flight surveillance. We describe a new parallel primitive to compute an approximate viewshed inside a ray cone given by two point-vector pairs. For a given number of points along the edge, it computes the largest view heights on line segments parallel to the given edge. The primitive is an approximation, as it happens that the selected ray segments are not in a common plane. We analyze and compare the primitive s performance on different OpenCL devices in terms of sampling resolution on the edge and orthogonal to the edge. In applications, the primitive can be used to compute the approximate viewshed of a polygon or candidate viewpoints for covering the polygon.
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2013

Ch. Fünfzig, D. Michelucci, S. Foufou
Reliable Outer Bounds for the Dual Simplex Algorithm with Interval Right-hand Side, 7th Int. Conference on Advanced Engineering Computing and Applications in Sciences (ADVCOMP), Porto, Portugal 2013.
In this article, we describe the reliable computation of outer bounds for linear programming problems occuring in linear relaxations derived from the Bernstein polynomials. The computation uses interval arithmetic for the Gauss-Jordan pivot steps on a simplex tableau. The resulting errors are stored as interval right hand sides. Additionally, we show how to generate a start basis for the linear programs of this type. We give details of the implementation using OpenMP and comment on numerical experiments.
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2012

A. Amresh, J. Femiani, Ch. Fünfzig
Methods for Approximating Loop Subdivision Using Tessellation Enabled GPUs, 8th Int. Symposium on Visual Computing, Rethymnon, Crete, Greece 2012, pp. 115-125.
Subdivision surfaces provide a powerful alternative to polygonal rendering. The availability of tessellation supported hardware presents an opportunity to develop algorithms that can render subdivision surfaces in realtime. We discuss the performance of approximating Loop Subdivision surfaces using tessellation-enabled GPUs in terms of speed and quality of rendering for these methods as well as the implementation strategy. We also propose a novel one pass unified rendering setup for all three methods. Subdivision using the Loop method supports arbitrary triangle meshes and provides for easy transition from polygonal rendering of triangles to the parametric domain. Majority of graphics software applications, especially game engines, render polygons as triangles. The objectives of this paper are to evaluate the performance of smooth rendering algorithms developed to take advantage of tessellator enabled GPUs, provide an easy transition from polygonal to parametric rendering and propose an optimal way to achieve multi-level rendering dependent on performance and visual needs of the application.
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M. Boschiroli, Ch. Fünfzig, L. Romani, G. Albrecht
G1 rational blend interpolatory schemes: a comparative study, Graphical Models 74(2012), Issue 1, pp. 29-49.
Interpolation of triangular meshes is a subject of great interest in many computer graphics related applications, as, for example, gaming and realtime rendering. One of the main approaches to interpolate the positions and normals of the mesh vertices is the use of parametric triangular Bézier patches. As it is well known, any method aiming at constructing a parametric, tangent plane G1 continuous surface has to deal with the vertex consistency problem. In this article, we propose a comparison of three methods appeared in the nineties that use a particular technique called rational blend to avoid this problem. Together with these three methods we present a new scheme, a cubic Gregory patch, that has been inspired by one of them. Our comparison includes an analysis of their computational costs on CPU and GPU, a study of their capabilities of approximating analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use.
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Ch. Fünfzig, D. Michelucci, S. Foufou
Polytope-Based Computation of Polynomial Ranges, Computer Aided Geometric Design 29(2012), Issue 1, pp. 18-29.
Polynomial ranges are commonly used for numerically solving polynomial systems with interval Newton solvers. Often ranges are computed using the convex hull property of the tensorial Bernstein basis, which is exponential size in the number n of variables. In this paper, we consider methods to compute tight bounds for polynomials in n variables by solving two linear programming problems over a polytope. We formulate a polytope defined as the convex hull of the coefficients with respect to the tensorial Bernstein basis, and we formulate several polytopes based on the Bernstein polynomials of the domain. These Bernstein polytopes can be defined by a polynomial number of halfspaces. We give the number of vertices, the number of hyperfaces, and the volume of each polytope for n=1,2,3,4, and we compare the computed range widths for random n-variate polynomials for n<=10. The Bernstein polytope of polynomial size gives only marginally worse range bounds compared to the range bounds obtained with the tensorial Bernstein basis of exponential size.
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2011

K. Müller, L. Heischbourg, Ch. Fünfzig, S. Petsch, H. Hagen
Virtual City Map Generation using Area Subdivision, Pacific Graphics 2011, Kaohsiung, Taiwan, pp. 55-60.
In this paper we present a new approach to build typical street networks for urban and rural areas automatically. Most street networks have a characteristic appearance which is a mixture between a kind of a regular spreading of streets and various perturbations of the regular structure, e.g., caused by the terrain. Our City Map Generation (CMG) algorithm gets as input an height field including watercourses and restricted areas such as nature protection areas or mountain areas. Furthermore, the user can specify the urbanization by the number of city centers or by a density map. The CMG algorithm produces a street map for the given landscape based on rules, which the user can also modify to obtain an individual appearance. Additionally, the regular structure is varied by a set of rules incorporating randomness. The results can be used to generate models for city areas, e.g., in movies and commercials. Depending on the demands, our flexible approach can be adjusted to produce a variety of road maps automatically. We show some examples and demonstrate that our algorithm is easy to implement and to use.
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L. Saini, N. Lissarague, G. Albrecht, L. Romani, Ch. Fünfzig, J.-P. Becar
Animation 3D : mouvements de caméra réalistes pour la stop motion, Proc. Hypertext & Hypermedia, Products, Tools & Methods H2PTM, October 2011, Metz, France.
L article présente un système qui permet la simulation 3D suivie de son exécution sur un plateau d un mouvement de caméra réaliste pour la stop motion. Les travaux de recherche portent sur deux points: un état de l art des outils actuels pour produire des mouvements de caméra en animation stop motion; les moyens de reproduire sur un plateau de stop motion une animation faite en 3D. Le système, en cours de développement, permettra à terme à la chaîne des acteurs impliqués dans une animation stop motion de prévisualiser et de produire des mouvements de caméra réalistes en 3D. Ces mouvements, paramétrables interactivement grâce à une interface haptique, reproductibles à l identique et modifiables au cours de la prise de vue, donnent à la mise en scène une liberté accrue.
The article presents a system, specifically designed for the animation technique of stop motion, that combines 3D simulation and on stage execution of a realistic camera movement. We focus our attention on the following two aspects: firstly we present a state of the art of the existing tools for camera animation for stop motion, and secondly we concentrate on the way to reproduce on a real stop motion stage a 3D computer animation of the camera movement. The system, which is still work in progress, will enable stop motion animators to preview and to produce realistic 3D camera movements. A haptic interface will allow to control these movements which can thus be modified during the shots. The whole process will be reproducible and highly flexible.
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S.E.B. Thierry, P. Schreck, D. Michelucci, Ch. Fünfzig, J.-D. Génevaux
Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems, Computer-Aided Design 43(2011), Issue 10, pp. 1234-1249.
This paper describes new ways to tackle several important problems encountered in geometric constraint solving, in the context of CAD, and which are linked to the handling of under- and over-constrained systems. It presents a powerful decomposition algorithm of such systems. Our methods are based on the witness principle whose theoretical background is recalled in a first step. A method to generate a witness is then explained. We show that having a witness can be used to incrementally detect over-constrainedness and thus to compute a well-constrained boundary system. An algorithm is introduced to check if anchoring a given subset of the coordinates brings the number of solutions to a finite number. An algorithm to efficiently identify all maximal well-constrained parts of a geometric constraint system is described. This allows us to design a powerful algorithm of decomposition, called W-decomposition, which is able to identify all well-constrained subsystems: it manages to decompose systems which were not decomposable by classic combinatorial methods.
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M. Boschiroli, Ch. Fünfzig, L. Romani, G. Albrecht
A comparison of local parametric C0 Bezier interpolants for triangular meshes, Computers & Graphics 35(2011), Issue 1, pp. 20-34.
Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability to effectively represent any surface of arbitrary genus. In this context, continuous curved shape surface schemes using only the information related to the triangle corresponding to the patch under construction, emerged as attractive solutions responding to the requirements of resource-limited hardware environments. In this paper we provide a unifying comparison of the local parametric C0 curved shape schemes we are aware of, based on a reformulation of their original constructions in terms of polynomial Bezier triangles. With this reformulation we find a geometric interpretation of all the schemes that allows us to analyse their strengths and shortcomings from a geometrical point of view. Further, we compare the four schemes with respect to their computational costs, their reproduction capabilities of analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use.
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2010

D. Michelucci, Ch. Fünfzig
Linear Programming for Bernstein Based Solvers, LNCS (Proc. Automated Deduction in Geometry), Volume 6301, Springer.
Some interval Newton solvers rely on tensorial Bernstein bases to compute sharp enclosures of multivariate polynomials on the unit hypercube. These solvers compute all coefficients with respect to tensorial Bernstein bases. Unfortunately, polynomials become exponential size in tensorial Bernstein bases. This article gives the first polynomial time method to solve this issue. A polynomial number of relevant Bernstein polynomials is selected. The non-negativity of each of these Bernstein polynomials gives a linear inequality in a space connected to the monomials of the canonical tensorial basis. We resort to linear programming on the resulting Bernstein polytope to compute range bounds of a polynomial or bounds of the zero set.
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Ch. Fünfzig, D. Michelucci, S. Foufou
Optimizations For Tensorial Bernstein-Based Solvers By Using Polyhedral Bounds, Int. Journal of Shape Modeling 16(2010), Issue 1-2, pp. 109-128.
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3^n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number O(binom(n, 2)) of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a change to the tensorial Bernstein basis for domain reduction. The performance is similar for n = 2 variables but only the solver using linear programming on the Bernstein polytope can cope with a large number of variables. We demonstrate this difference with two formulations of the forward kinematics problem of a Gough-Stewart parallel robot: a direct Cartesian formulation and a coordinate-free formulation using Cayley-Menger determinants, followed by a computation of Cartesian coordinates. Furthermore, we present an optimization of the Bernstein polytope-based solver for systems containing only the monomials xi and xi^2. For these, it is possible to obtain even better domain bounds at no cost using the quadratic curve (xi, xi^2) directly.
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A. Amresh, Ch. Fünfzig
Semi-Uniform, 2-Different Tessellation of Triangular Parametric Surfaces, 6th Int. Symposium on Visual Computing, Las Vegas, Nevada, 2010.
With a greater number of real-time graphics applications moving over to parametric surfaces from the polygonal domain, there is an inherent need to address various rendering bottlenecks that could hamper the move. Scaling the polygon count over various hardware platforms becomes an important factor. Much control is needed over the tessellation levels, either imposed by the hardware limitations or by the application. Developers like to create applications that run on various platforms without having to switch between polygonal and parametric versions to satisfy the limitations. In this paper, we present SD-2 (Semi-uniform, 2-Different), an adaptive tessellation algorithm for triangular parametric surfaces. The algorithm produces well distributed and semi-uniformly shaped triangles as a result of the tessellation. The SD-2 pattern requires new approaches for determining the edge tessellation factors, which can be fractional and change continuously depending on view parameters. The factors are then used to steer the tessellation of the parametric surface into a collection of triangle strips in a single pass. We compare the tessellation results in terms of GPU performance and surface quality by implementing SD-2 on PN patches.
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K. Müller, Ch. Fünfzig, L. Reusche, D. Hansford, G.E. Farin, H. Hagen
Dinus: Double insertion, nonuniform, stationary subdivision surfaces, ACM Transactions on Graphics, Volume 29(2010), Issue 3, pp. 1-21.
The Double Insertion, Nonuniform, Stationary subdivision surface (DINUS) generalizes both the nonuniform, bicubic spline surface and the Catmull-Clark subdivision surface. DINUS allows arbitrary knot intervals on the edges, allows incorporation of special features, and provides limit point as well as limit normal rules. It is the first subdivision scheme that gives the user all this flexibility and at the same time all essential limit information, which is important for applications in modeling and adaptive rendering. DINUS is also amenable to analysis techniques for stationary schemes. We implemented DINUS as an Autodesk Maya plugin to show several modeling and rendering examples.
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D. Michelucci, P. Schreck, S.E.B. Thierry, Ch. Fünfzig, J.-D. Génevaux
Using the witness method to detect rigid subsystems of geometric constraints in CAD, SPM '10: Proceedings of the 14th ACM Symposium on Solid and Physical Modeling, pp. 91-100.
This paper deals with the resolution of geometric constraint systems encountered in CAD-CAM. The main results are that the witness method can be used to detect that a constraint system is over-constrained and that the computation of the maximal rigid subsystems of a system leads to a powerful decomposition method. In a first step, we recall the theoretical framework of the witness method in geometric constraint solving and extend this method to generate a witness. We show then that it can be used to incrementally detect over-constrainedness. We give an algorithm to efficiently identify all maximal rigid parts of a geometric constraint system. We introduce the algorithm of W-decomposition to identify all rigid subsystems: it manages to decompose systems which were not decomposable by classical combinatorial methods.
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Ch. Fünfzig, D. Michelucci, S. Foufou
Optimizations for Bernstein-Based Solvers using Domain Reduction, Int. Symposium on Tools and Methods of Competitive Engineering, Ancona 2010.
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Ch. Fünfzig, D. Michelucci, S. Foufou
Polytope-Based Computation of Polynomial Ranges, ACM Symposium on Applied Computing, Sierre 2010, pages 1248-1253.
Polynomial ranges are commonly used for numerically solving polynomial systems with interval Newton solvers. Often ranges are computed using the convex hull property of the tensorial Bernstein basis, which is exponential size in the number n of variables. In this paper, we consider methods to compute tight bounds for polynomials in n variables by solving two linear programming problems over a polytope. We formulate several polytopes based on the tensorial Bernstein basis, and we formulate a polytope for the quadratic patch Qn := (x_1, . . . , x_n, x_1^2, . . . , x_n^2, x_1x_2, . . . , x_{n-1}x_{n}) by projections. This Bernstein polytope has O(n^2) hyperplanes. We give the number of vertices, the number of hyperplanes, and the volume of each polytope for n = 1,2,3, 4, and we compare the range widths computed with all of them for random n-variate polynomials with n<=10. The Bernstein polytope of polynomial size gives only marginally worse range bounds compared to the range bounds obtained with the tensorial Bernstein basis of exponential size.
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Ch. Fünfzig, P. Thomin, G. Albrecht
Haptic Manipulation of Rational Parametric Planar Cubics Using Shape Constraints, ACM Symposium on Applied Computing, Sierre 2010, pages 1254-1258.
In this paper, we show how to deform a planar rational cubic based on a local interpolation constraint while retaining the qualitative shape of the curve. An impedance-type, parallel haptic device is used to signal changes of the number of inflection points, cusps and loops during the deformation. In this way, the user is provided with an intuitive and natural guidance throughout the curves shape generation process in CAD.
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2009

Ch. Fünfzig, D. Michelucci, S. Foufou
Nonlinear systems solver in floating-point arithmetic using LP reduction, ACM/SIAM Symposium on Solid and Physical Modeling, San Francisco 2009, pages 123-134.
This paper presents a new solver for systems of nonlinear equations. Such systems occur in Geometric Constraint Solving, e.g., when dimensioning parts in CAD-CAM, or when computing the topology of sets defined by nonlinear inequalities. The paper does not consider the problem of decomposing the system and assembling solutions of subsystems. It focuses on the numerical resolution of well-constrained systems. Instead of computing an exponential number of coefficients in the tensorial Bernstein basis, we resort to linear programming for computing range bounds of system equations or domain reductions of system variables. Linear programming is performed on a so called Bernstein polytope: though, it has an exponential number of vertices (each vertex corresponds to a Bernstein polynomial in the tensorial Bernstein basis), its number of hyperplanes is polynomial: O(n2) for a system in n unknowns and equations, and total degree at most two. An advantage of our solver is that it can be extended to non-algebraic equations. In this paper, we present the Bernstein and LP polytope construction, and how to cope with floating point inaccuracy so that a standard LP code can be used. The solver has been implemented with a primal-dual simplex LP code, and some implementation variants have been analyzed. Furthermore, we show geometric-constraint-solving applications, as well as numerical intersection and distance computation examples.
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Ch. Fünfzig, K. Müller, G. Albrecht
Visual Debugger for Single-Point-Contact Haptic Rendering, SE 2009 - Workshop Human-Computer-Interaction and Visualization (HCIV), Achim Ebert and Peter Dannenmann editors, Kaiserslautern, Germany, GI-Lecture Notes in Informatics (LNI) 2009.
Haptic applications are difficult to debug due to their high update rate and many factors influencing their execution. In this paper, we describe a practical visual debugger for single-point-of-contact haptic devices of impedance-type. The debugger can easily be incorporated into the running haptic application. The visualization shows the position trajectory with timing information and associated data like goal positions and computed feedback forces. Also, there are several options for in detail analysis of the feedback force applied at each time instance. We show with several use cases taken from practical experience that the system is well suited for locating common and intricate problems of haptic applications.
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Ch. Fünfzig, T. Ullrich, D.W. Fellner, E.N. Bachelder
Terrain and Model Queries Using Scalar Representations With Wavelet Compression, IEEE Transactions on Instrumentation and Measurement 2009.
In this paper, we present efficient height/distance field data structures for line-of-sight queries on terrains and collision queries on arbitrary 3D models. The data structure uses a pyramid of quad-shaped regions with the original height/distance field at the highest level and an overall minimum/maximum value at the lower levels. The pyramid can be stored compactly in a waveletlike decomposition but using max and plus operations. Additionally, we show how to get minimum/maximum values for regions in a wavelet decomposition using real algebra. For line-of-sight (LOS) calculations, we compare with a kd-tree representation containing the maximum height values. Furthermore, we show that the LOS calculation is a special case of a collision detection query. Using our wavelet-like approach, even general and arbitrary collision detection queries can be answered efficiently.
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2008

Ch. Fünfzig, K. Müller, R. Janetzek, T. Techmann
A versatile hierarchical Mesh for Subdivision Surfaces, IEEE Potentials, September/October 2008.
In this article we present a hierarchical mesh data structure for subdivision surfaces (e.g. Catmull-Clark for quadrangle meshes and Loop for triangle meshes). The mesh is especially suitable for advanced global illumination algorithms, where long light paths with surface reflections and transmissions are simulated.
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Ch. Fünfzig, K. Müller, D. Hansford, and G. Farin
PNG1 Triangles for Tangent Plane Continuous Surfaces on the GPU, Proceedings of Graphics Interface, Windsor, Ontario 2008.
Improving the visual appearance of coarse triangle meshes is usually done with graphics hardware with per-pixel shading techniques. Improving the appearance at silhouettes is inherently hard, as shading has only a small influence there and the geometry must be corrected. With the new geometry shader stage released with DirectX 10, the functionality to generate new primitives from an input primitive is available. Also the shader can access a restricted primitive neighborhood. In this paper, we present a curved surface patch that can deal with this restricted data available in the geometry shader. A surface patch is defined over a triangle with its vertex normals and the three edge neighbor triangles. Compared to PN triangles, which define a curved patch using just the triangle with its vertex normals, our surface patch is G1 continuous with its three neighboring patches. The patch is obtained by blending two cubic Bezier patches for each triangle edge. In this way, our surface is especially suitable for efficient, high-quality tessellation on the GPU. We show the construction of the surface and how to add special features such as creases. Thus, the appearance of the surface patch can be fine-tuned easily. The surface patch is easy to integrate into existing polygonal modeling and rendering environments. We give some examples using Autodesk Maya.
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2007

T. Ullrich, V. Settgast, U. Krispel, Ch. Fünfzig, and D.W. Fellner
Distance Calculation between a Point and a Subdivision Surface, Workshop on Vision, Modeling, and Visualization, Saarbrücken 2007.
This article focuses on algorithms for fast computation of the Euclidean distance between a query point and a subdivision surface. The analyzed algorithms include uniform tessellation approaches, an adaptive evalution technique, and an algorithm using Bezier conversions. These methods are combined with a grid hashing structure for space partitioning to speed up their runtime. The results show that a pretessellated surface is sufficient for small models. Considering the runtime, accuracy, and memory usage an adaptive on-the-fly evaluation of the surface turns out to be the best choice.
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Ch. Fünfzig, T. Ullrich, D.W. Fellner, E.N. Bachelder
Empirical Comparison of Data Structures for Line-Of-Sight Computation, IEEE Workshop on Intelligent Signal Processing 2007, Madrid, Spain.
Line-of-sight (LOS) computation is important for interrogation of heightfield grids in the context of geo information and many simulation tasks like electromagnetic wave propagation and flight surveillance. Compared to searching the regular grid directly, more advanced data structures like a 2.5d kd-tree offer better performance. We describe the definition of a 2.5d kd-tree from the digital elevation model and its use for LOS computation on a point-reconstructed or bilinear-reconstructed terrain surface. For compact storage, we use a wavelet-like storage scheme which saves one half of the storage space without considerably compromising the runtime performance. We give an empirical comparison of both approaches on practical data sets which show the method of choice for CPU computation of LOS.
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T. Ullrich, Ch. Fünfzig, D.W. Fellner
Two Different Views On Collision Detection, IEEE Potentials Volume 26 (2007), Number 1.
The realistic movement of geometry governed by physics is necessary for many applications. Changes of movements occur at events, where geometries collide. For real-time applications the collision detection must be as fast as possible. While conceptually simple, the collision detection excels in its intrinsic complexity. Naive approaches to determine all collisions of n objects require a runtime of O(n2), which will rapidly be too much in practice. Innumerable algorithms with reduced runtime complexity have been developed in the last decades. They can be classified according to different schemes regarding e.g. field of application or solution strategy. This article differentiates by the algorithms’ background: computational geometry or signal processing, and presents a representative of each domain. The main characteristics of both algorithms are simplicity and efficiency.
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2006

Ch. Fünfzig, T. Ullrich, D.W. Fellner
Hierarchical Spherical Distance Fields for Collision Detection, IEEE Computer Graphics and Applications Volume 26 (2006), Number 1.
This article presents a fast collision detection technique for all types of rigid bodies, demonstrated using polygon soups. The new approach uses spherical distance fields, which are stored in a compact representation.
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2005

Ch. Fünfzig
Iconic Drawing of Scenegraph Structure, 31st Annual Conference on Current Trends in Theory and Practice of Informatics (SOFSEM), Liptovsky Jan 2005.
In this paper we consider graph drawing for the application of scenegraphs as encoded by VRML97/X3D. As these formats store the structure and attributes of scenes in a directed acyclic graph, the techniques for drawing rooted trees are suitable but require much drawing space. Therefore we devised a smart, interactive drawing, which uses a detailed view of the current point of interest and an iconic view of subgraphs besides the current point of interest. This interactive method balances detail and overview much better than classic techniques to cope with limited space like fisheye views. Concerning implementation it is easy to implement with a small lines-of-code count (in Java).
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2004

V. Settgast, K. Müller, Ch. Fünfzig, D.W. Fellner
Adaptive Tesselation of Subdivision Surfaces, Computers & Graphics 2004.
For a variety of reasons subdivision surfaces have developed into a prominent member of the family of freeform shapes. Based on a standard polygonal mesh a modeller can build various kinds of shapes using an arbitrary topology and special geometrical features like creases. However, the interactive display of subdivision surfaces in current scenegraph systems based on static levels of detail is unpractical, because of the exponentially increasing number of polygons during the subdivision steps. Therefore, an adaptive algorithm choosing only the necessary quads and triangles is required to obtain high-quality images at high frame rates. In this paper we present a rendering algorithm which dynamically adapts to static surface properties like curvature as well as to view- dependent properties like silhouette location and projection size. Without modifying the base mesh, the method works patchwise and tesselates each patch recursively using a new data structure, called slate. Besides these geometric properties the algorithm can also adapt to the graphics load in order to achieve a desired frame rate in the scenegraph system OpenSG.
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2003

T. Neumann, Ch. Fünfzig, D.W. Fellner
TRIPS - A Scalable Spatial Sound Library for OpenSG, OpenSG Symposium, Darmstadt 2003.
We present a Sound Library that is scalable on several computers and that brings the idea of a self-organized scenegraph to the Sound Library’s interface. It supports the implementation of audio features right from the start at a high productivity level for rapid prototypes as well as for professional applications in the immersive domain. The system is built on top of OpenSG12 which offers a high level of functionality for visual applications and research, but does not come with audio support. We show and compare the effort to implement audio in an OpenSG application with and without TRIPS. Today’s audio systems only accept raw 3D-coordinates and are limited to run on the same computer and the same operating system than the application runs on. Breaking these constraints could give developers more freedom and ease to add high-quality spatial sound to their software. Therefore, users benefit from the promising potential OpenSG offers.
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Ch. Fünfzig, D.W. Fellner
Easy Realignment of k-DOP Bounding Volumes, Graphics Interface, Halifax 2003.
In this paper we reconsider pairwise collision detection for rigid motions using a k-DOP bounding volume hierarchy. This data structure is particularly attractive because it is equally efficient for rigid motions as for arbitrary point motions (deformations). We propose a new efficient realignment algorithm, which produces tighter results compared to all known algorithms. It can be implemented easily in software and in hardware. Using this approach we try to show, that k-DOP bounding volumes can keep up with the theoretically more efficient oriented bounding boxes (OBBs) in parallel-close-proximity situations.
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2002

Ch. Fünfzig
GENVIS - Eine Bibliothek für Räumliche Strukturierungen auf OpenSG, OpenSG Symposium, Darmstadt 2002.
A scene graph for the same scene contents can be structured in different ways depending on the application. In this paper the library GENVIS for spatial structuring and some applications on the scene graph OpenSG is presented. Concerning architecture the flexible and efficient connection with OpenSG is especially important. As examples, k-DOP bounding volume hierarchies and regular spatial grids are covered in detail. Bounding volume hierarchies can be used for collision detection and for a spatialization of the scene contents.
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