This paper develops a shape space framework for collision-aware geometric modeling, where basic geometric operations automatically avoid inter-penetration. Shape spaces are a powerful tool for surface modeling, shape analysis, nonrigid motion planning, and animation, but past formulations permit nonphysical intersections. Our framework augments an existing shape space using a repulsive energy such that collision avoidance becomes a first-class property, encoded in the Riemannian metric itself. In turn, tasks like intersection-free shape interpolation or motion extrapolation amount to simply computing geodesic paths via standard numerical algorithms. To make optimization practical, we develop an adaptive collision penalty that prevents mesh self-intersection, and converges to a meaningful limit energy under refinement. The final algorithms apply to any category of shape, and do not require a dataset of examples, training, rigging, nor any other prior information. For instance, to interpolate between two shapes we need only a single pair of meshes with the same connectivity. We evaluate our method on a variety of challenging examples from modeling and animation.

Functionals that penalize bending or stretching of a surface play a key role in geometric and scientific computing, but to date have ignored a very basic requirement: in many situations, surfaces must not pass through themselves or each other. This paper develops a numerical framework for optimization of surface geometry while avoiding (self-)collision. The starting point is the tangent-point energy , which effectively pushes apart pairs of points that are close in space but distant along the surface. We develop a discretization of this energy for triangle meshes, and introduce a novel acceleration scheme based on a fractional Sobolev inner product. In contrast to similar schemes developed for curves, we avoid the complexity of building a multiresolution mesh hierarchy by decomposing our preconditioner into two ordinary Poisson equations, plus forward application of a fractional differential operator. We further accelerate this scheme via hierarchical approximation, and describe how to incorporate a variety of constraints (on area, volume, etc. ). Finally, we explore how this machinery might be applied to problems in mathematical visualization, geometric modeling, and geometry processing.

Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or self-intersections. This article develops efficient algorithms for (self-)repulsion of plane and space curves that are well-suited to problems in computational design. Our starting point is the so-called tangent-point energy , which provides an infinite barrier to self-intersection. In contrast to local collision detection strategies used in, e.g., physical simulation, this energy considers interactions between all pairs of points, and is hence useful for global shape optimization: local minima tend to be aesthetically pleasing, physically valid, and nicely distributed in space. A reformulation of gradient descent based on a Sobolev-Slobodeckij inner product enables us to make rapid progress toward local minima—independent of curve resolution. We also develop a hierarchical multigrid scheme that significantly reduces the per-step cost of optimization. The energy is easily integrated with a variety of constraints and penalties (e.g., inextensibility, or obstacle avoidance), which we use for applications including curve packing, knot untangling, graph embedding, non-crossing spline interpolation, flow visualization, and robotic path planning.

Although the potential of Vehicular Ad-Hoc Networks (VANETS) to improve road safety and traffic efficiency for next-generation vehicular traffic system has been well investigated and proved, the performance of vehicle-to-vehicle (V2V) communication, especially at urban intersections has not been clearly quantified. In this paper, we evaluate the effects of buildings on the vehicle-to-vehicle performance at urban intersections based on a profound simulation campaign. Due to the two-dimensional nature of intersection topologies, we investigate the performance of V2V communication by analyzing packet delivery ratios and packet drop rates with respect to sender and receiver's position under varying node density and intersection layout. While stationary and mobile obstacles considerably attenuate the received signal power, the results reveal that the presence of buildings could in some situations improve the performance of V2V communication by reducing co-channel interference from hidden nodes.

Vehicle-to-Vehicle (V2V) communication is envisioned to enable a vast range of road safety, traffic efficiency and infotainment applications for next-generation vehicular traffic. In this paper, we investigate the effects of vegetation on the performance of V2V communication based on a 5.9GHz measurement campaign conducted at different urban and rural intersections with different types of vegetation under non-line-of-sight (NLOS) conditions. We evaluate received power levels and packet delivery rates under varying conditions with respect to vehicle positioning, intersection layout and vegetation type. To capture the additional signal attenuation caused by foliage, the measurements for each intersection were conducted both in summer and in winter, which allows comparing the impact of leaved and leafless vegetation. Moreover, we derive the additional attenuation caused by vegetation and compare the measurement results with three well-known empirical models for vegetation-induced path loss. Based on the acquired sets of measurement data, we present a simple parametrized model for estimation of path loss caused by vegetation in V2V scenarios.

During the last few years, vehicle-to-vehicle (V2V) wireless communication has become a key objective for enabling future cooperative safety applications, such as intersection collision warning. In this paper, we present the results of a 5.9 GHz V2V performance measurement campaign at four different urban intersections under NLOS conditions using commercial off-the-shelf wireless interface cards which meet the 802.11p and ITS-G5 specifications. Particularly, we quantify the packet delivery ratio (PDR) and received signal strength indication (RSSI) levels associated with different scenario conditions with respect to vehicle positioning, intersection geometry and traffic density. We determine reliable communication ranges which constitute an important metric for V2V collision avoidance applications.

Accompanied by the continuous progression of the maturity of car-to-x communication protocols and corresponding system architectures, the need for integrated network simulation approaches which consider realistic channel modeling on the one hand and appropriate mobility models on the other hand becomes more and more observable. Moreover, in order to analyze the impacts of car-to-x applications on the behavior of vehicles, an interconnection of different simulation tools is needed. In this paper, a concept for the interconnection of network, channel and road traffic simulations is presented. This concept relies on network simulation based on the open source simulator OMNeT++ and the INET Framework, which utilizes a coupling to the well-known road traffic simulator SUMO. In order to characterize the radio channel, an interconnection between OMNeT++ and a ray optical propagation model is being established. Furthermore, some preliminary simulation results are presented which serve as a proof of concept.