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.

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.

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 Bézier 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.

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.

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.

RESUME. L’article presente un systeme qui permet la simulation 3D suivie de son execution sur un plateau d’un mouvement de camera realiste pour la stop motion. Les travaux de recherche portent sur deux points : un etat de l’art des outils actuels pour produire des mouvements de camera en animation stop motion ; les moyens de reproduire sur un plateau de stop motion une animation faite en 3D. Le systeme, en cours de developpement, permettra a terme a la chaine des acteurs impliques dans une animation stop motion de previsualiser et de produire des mouvements de camera realistes en 3D. Ces mouvements, parametrables interactivement grâce a une interface haptique, reproductibles a l’identique et modifiables au cours de la prise de vue, donnent a la mise en scene une liberte accrue. MOTS-CLES : animation, stop motion, mouvement de camera, contraintes, simulation realiste.

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.

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.

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.

The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n 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 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 . For these, it is possible to obtain even better domain bounds at no cost using the quadratic curve (xi, ) directly.

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.

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 Q n := ( x 1 , ..., x n , x 2 1 , ..., x 2 n , x 1 x 2 , ..., x n-1 x n ) by projections. This Bernstein polytope has Θ( 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 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.

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 curve's shape generation process in CAD.

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.

In this paper, we present efficient height/distance field data structures for line-of-sight (LOS) queries on terrains and collision queries on arbitrary 3-D 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 compactly be stored in a wavelet-like 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 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 efficiently be answered.

Haptic applications are difficult to debug due to their high update rate and man yf actors influencing their execution. In this paper ,w ed escribe ap ractical 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 infor- mation and associated data lik eg oal positions and computed feedback forces. Also, there are several options for in detail analysis of the feedback force applied at each time instance. We sho ww ith several use cases taken from practical experience that the system is well suited for locating common and intricate problems of haptic appli- cations.