Parametric Spiral And Its Application As Transition Curve

Lengkung Bezier merupakan suatu perwakilan lengkungan yang paling popular digunakan di dalam applikasi Rekabentuk Berbantukan Komputer (RBK) dan Rekabentuk Geometrik Berbantukan Komputer (RGBK). The Bezier curve representation is frequently utilized in computer-aided design (CAD) and computer-aided geometric design (CAGD) applications. The curve is defined geometrically, which means that the parameters have geometric meaning; they are just points in three-dimensional space

Path Planning Based on Parametric Curves

Parametric curves are extensively used in engineering. The most commonly used parametric curves are, Bézier, B-splines, (NURBSs), and rational Bézier. Each and every one of them has special features, being the main difference between them the complexity of their mathematical definition. While Bézier curves are the simplest ones, B-splines or NURBSs are more complex. In mobile robotics, two main problems have been addressed with parametric curves. The first one is the definition of an initial trajectory for a mobile robot from a start location to a goal. The path has to be a continuous curve, smooth and easy to manipulate, and the properties of the parametric curves meet these requirements. The second one is the modification of the initial trajectory in real time attending to the dynamic properties of the environment. Parametric curves are capable of enhancing the trajectories produced by path planning algorithms adapting them to the kinematic properties of the robot. In order to avoid obstacles, the shape modification of parametric curves is required. In this chapter, an algorithm is proposed for computing an initial Bézier trajectory of a mobile robot and subsequently modifies it in real time in order to avoid obstacles in a dynamic environment

Sketch-based path design

We first present a novel approach to sketching 2D curves with minimally varying curvature as piecewise clothoids. A stable and efficient algorithm fits a sketched piecewise linear curve using a number of clothoid segments with G2 continuity based on a specified error tolerance. We then present a system for conceptually sketching 3D layouts for road and other path networks. Our system makes four key contributions. First, we generate paths with piecewise linear curvature by fitting 2D clothoid curves to strokes sketched on a terrain. Second, the height of paths above the terrain is automatically determined using a new constraint optimization formulation of the occlusion relationships between sketched strokes. Third, we present the break-out lens, a novel widget inspired by break-out views used in engineering visualization, to facilitate the in-context and interactive manipulation of paths from alternate view points. Finally, our path construction is terrain sensitive. ii Acknowledgements I would like to acknowledge the efforts of my supervisor, Karan Singh, and thank him for his guidance over the duration of the Masters program. I learned much from him a

The design and simulation of traffic networks in virtual environments

For over half a century, researchers from a diverse set of disciplines have been studying the behaviour of traffic flow to better understand the causes of traffic congestion, accidents, and related phenomena. As the global population continues to rise, there is an increasing demand for more efficient and effective transportation infrastructures that are able to accommodate a greater number of civilians without compromising travel times, journey quality, cost, or accessibility. With recent advances in computing technology, transportation infrastructures are now typically developed using design and simulation packages that enable engineers to accurately model large-scale road networks and evaluate their designs through visual simulation. However, as these projects increase in scale and complexity, methodologies to intuitively design more complex and realistic simulations are highly desirable. The need of such technology translates across to the entertainment industry, where traffic simulations are integrated into computer games, television, film, and virtual tourism applications to enhance the realism and believability of the simulated scenario. In this thesis two significant challenges related to the design and simulation of traffic networks for use in virtual environments are presented. The first challenge is the development of intuitive techniques to assist the design and construction of high-fidelity three-dimensional road networks for use in both urban and rural virtual environments. The second challenge considers the implementation of computational models to accurately simulate the behaviour of drivers and pedestrians in transportation networks, in real time. An overview of the literature in the field is presented in this work with novel contributions relating to the challenges defined above