Quadratic Bezier Curve Research Articles

Redundancy and Criticality based Scheduling in Wireless Video Sensor Networks for Monitoring Critical Areas

Applications for monitoring critical areas, based on Wireless Video Sensor Networks (WVSN), require simultaneously good level of coverage of the entire region of deployment, high frame capture speed and low power consumption in order to increase network lifetime. The question is how to find a tradeoff between these requirements. In this paper, we first propose two new approaches based on the cover set concept to help a node to find its redundancy level which is defined by the cardinality of its cover set. Then, thanks to a model based on behavior functions modeled by quadratic Bezier curves, we link the frame capture speed of video node to its redundancy level and to its criticality which is assigned to a node according to its position in the network. Border node has high criticality while interior one has low criticality. To identify boundary nodes, we propose an algorithm based on Greedy Perimeter Stateless Routing protocol (GPSR). Then, we propose an algorithm to schedule the activity of sensor nodes according to the redundancy level and criticality of each node. Finally, we introduce a new concept called backward border surveillance based on the cover set approach. Simulation results are presented to show performances of the two proposed approaches in terms of percentage of coverage, number of nodes with cover set, size of this latter, the impact of our scheduling algorithm on network lifetime and the incidence of backward border surveillance concept on quality of surveillance.

Continuous tow shearing for manufacturing variable angle tow composites

Automated fibre placement (AFP) is the key technology for manufacturing variable angle tow (VAT) composites with tailored fibre paths. Although it was developed in the 1980s, much research still focuses on the minimization of the process-induced defects because the fundamental principle has not been changed. In this work, a novel fibre placement technique using the shear deformation characteristic of dry tow has been developed, which was named ‘Continuous Tow Shearing (CTS)’. Through the prototype tests, it is shown that CTS could significantly reduce process-induced defects such as fibre wrinkling, resin rich areas and fibre discontinuity. Also, an intuitive notation for defining a curved tow path using piecewise quadratic Bezier curve is developed.

Extension of ALE methodology to unstructured conical meshes

We propose a bi-dimensional finite volume extension of a continuous ALE method on unstructured cells whose edges are parameterized by rational quadratic Bezier curves. For each edge, the control point possess a weight that permits to represent any conic (see for example [LIGACH]) and thanks to [WAGUSEDE,WAGU], we are able to compute the exact area of our cells. We then give an extension of scheme for remapping step based on volume fluxing [MARSHA] and self-intersection flux [ALE2DHAL]. For the rezoning phase, we propose a three step process based on moving nodes, followed by control point and weight re-adjustment. Finally, for the hydrodynamic step, we present the GLACE scheme [GLACE] extension (at first-order) on conic cell using the same formalism. We only propose some preliminary first-order simulations for each steps: Remap, Pure Lagrangian and finally ALE (rezoning and remapping).

Transformation of the Glyph Curve in Map Publishing

In the case of complete information, it is of great significance that use cubic Bezier curves which used as primitive form standard in graphic system to express the spatial data for data processing and transmission. In the text fonts of map, it is customary to use straight lines and the set of quadratic Bezier curves to describe the glyph outlines,but it is inconvenient in the process because the quadratic Bezier curves are non-standard curves. Based on this situation, in this paper,it is proposed the method of quadratic curves fitting using cubic Bezier curves and derive corresponding computing formula. The method is that remove the characters glyph outlines which are described by curve edges from the font and fit the curve edges with quadratic Bezier curves, finally the curve edges are fitted by cubic Bezier curves segment by segment. Through the result of the experiment, it proves that the differences between fitted cubic Bezier curves and quadratic Bezier curves to be fitted are small. The text graphics curves expressed by the method represent the geographical features effectively and provide an effective way of the transformation from font text to the map text.

A new method for video data compression by quadratic Bézier curve fitting

This paper presents a new and efficient method for video data compression using quadratic Bezier curve fitting. The method treats the luminance or color variations of a spatial location in a sequence of frames as input points in Euclidean space R 1 or R 3. The input points are approximated using quadratic Bezier least square fitting. The output data consists of quadratic Bezier control points and difference between original and fitted data. Video data compression is the main application of proposed method. It is shown that entropy of output data is significantly less than the entropy of input data. The method can be applied to 1-D space like luminance and chrominance components separately or 3-D color spaces such as RGB and YC b C r .

Automatic recognition of midline shift on brain CT images

Midline shift is one of the most important quantitative features clinicians use to evaluate the severity of brain compression by various pathologies. It can be recognized by modeling brain deformation according to the estimated biomechanical properties of the brain and the cerebrospinal fluid spaces. This paper proposes a novel method to identify the deformed midline according to the above hypothesis. In this model, the deformed midline is decomposed into three segments: the upper and the lower straight segments representing parts of the tough dura mater separating two brain hemispheres, and the central curved segment formed by a quadratic Bezier curve, representing the intervening soft brain tissue. The deformed midline is obtained by minimizing the summed square of the differences across all midline pixels, to simulate maximal bilateral symmetry. A genetic algorithm is applied to derive the optimal values of the control points of the Bezier curve. Our algorithm was evaluated on pathological images from 81 consecutive patients treated in a single institute over a period of one year. Our algorithm is able to recognize the deformed midlines in 65 (80%) of the patients with an accuracy of 95%, making it a useful tool for clinical decision-making.

Carving surface modeling of images based on quadratic Bezier curved surface

Carving surface was directly modeled using the quadratic Bezier curve surface according to the grey or color pixels information of the image with clear texture and simple construction.This method segmented the image,analyzed and computed the pixel values and their position parameters for the sub-images,and used those values as feature parameters for constructing the surface patches of the model.The modeling was implemented by limited smooth connection of surface patches.The established surface model can describe the basic structure characteristics of the original objects in the image,and satisfy the requirements of digital carving processing.It has low complexity and strong practicability.

Parametric curve interpolation by combination of two conic sections

The problem of constructing a parametric cubic rational curve to interpolate a set of distinct data points is discussed. Unlike the existing methods which include the determination of knots, the new method constructs parametric curve without the process of determining knots. For each point, a quadratic rational Bezier curve is constructed by the five convex data points. For the data point, if there is no five convex data points, the quadratic rational Bezier curve is constructed with four or three points under a constraint. Between each pair of the two adjacent points, a parametric cubic rational curve is constructed by the combination of the two quadratic rational Bezier curves. The constructed cubic rational curve reproduces a conic section exactly if the given data points are taken from the conic section. The comparison of the new method with other ones is included.

Real-time rendering of textures with feature curves

The standard bilinear interpolation on normal maps results in visual artifacts along sharp features, which are common for surfaces with creases, wrinkles, and dents. In many cases, spatially varying features, like the normals near discontinuity curves, are best represented as functions of the distance to the curve and the position along the curve. For high-quality interactive rendering at arbitrary magnifications, one needs to interpolate the distance field preserving discontinuity curves exactly. We present a real-time, GPU-based method for distance function and distance gradient interpolation which preserves discontinuity feature curves. The feature curves are represented by a set of quadratic Bezier curves, with minimal restrictions on their intersections. We demonstrate how this technique can be used for real-time rendering of complex feature patterns and blending normal maps with procedurally defined profiles near normal discontinuities.

Solving Kepler’s Equation using Bézier curves

This paper presents a non-iterative approach to solve Kepler’s Equation, M = E − e sin E, based on non-rational cubic and rational quadratic Bezier curves. Optimal control point coordinates are first shown to be linear with respect to orbit eccentricity for any eccentric anomaly range. This property yields the development of a piecewise (e.g., 3, 4) solving technique providing accuracies better than 10−13 degree for orbit eccentricity e ≤ 0.99. The proposed method does not require large pre-computed discretization data, but instead solves a cubic/quadratic algebraic equation and uses a single final Halley iteration in only a few lines of code. The method still provides accuracies better than 10−5 degree for the near parabolic worst case (e = 0.9999) with very small mean anomalies (M < 0.0517 deg). The complexity of the proposed algorithm is constant, independent of the parameters e and M. This makes the method suitable for extensive orbit propagations.

TRACING THE DEFORMED MIDLINE ON BRAIN CT

Midline shift (MLS) is the most important quantitative feature clinicians use to evaluate the severity of brain compression by various pathologies. We proposed a model of the deformed midline according to the biomechanical properties of different types of intracranial tissue. The model comprised three segments. The upper and lower straight segments represented parts of the tough meninges separating two hemispheres, and the central curved segment, formed by a quadratic Bezier curve, represented the intervening soft brain tissue. For each point of the model, the intensity difference was calculated over 48 adjacent point pairs at each side. The deformed midline was considered ideal as summed square of the difference across all midline points approaches global minimum, simulating maximal bilateral symmetry. Genetic algorithm was applied to optimize the values of the three control points of the Bezier curve. Our system was tested on images containing various pathologies from 81 consecutive patients treated in a single institute over one-year period. The deformed midlines itself as well as the amount of midline shift were evaluated by human experts, with satisfactory results.

Quadratic approximation to plane parametric curves and its application in approximate implicitization

Expressing complex curves with simple parametric curve segments is widely used in computer graphics, CAD and so on. This paper applies rational quadratic B-spline curves to give a global C1 continuous approximation to a large class of plane parametric curves including rational parametric curves. Its application in approximate implicitization is also explored. The approximated parametric curve is first divided into intrinsic triangle convex segments which can be efficiently approximated with rational quadratic Bezier curves. With this approximation, we keep the convexity and the cusp (sharp) points of the approximated curve with simple computations. High accuracy approximation is achieved with a small number of quadratic segments. Experimental results are given to demonstrate the operation and efficiency of the algorithm.

A Bidirectional Generating Algorithm for Rational Parametric Curves

A generating algorithm for rational quadratic Bezier curves is provided. In the algorithm, we find the recurrence relation to get every pixel along the curve, using the bidirectional strategy for rendering and the forward and backward difference method for computing. The algorithm has a fast generating speed, and the curves keep a reasonable rendering accuracy. This algorithm can easily be generalized to render higher-degree rational Bezier curves and other rational parametric curves; it has broad applications. Source code is available online at the website listed at the end of this paper.

Geometric meanings of the parameters on rational conic segments

Using algebraic and geometric methods, functional relationships between a point on a conic segment and its corresponding parameter are derived when the conic segment is presented by a rational quadratic or cubic Bezier curve. That is, the inverse mappings of the mappings represented by the expressions of rational conic segments are given. These formulae relate some triangular areas or some angles, determined by the selected point on the curve and the control points of the curve, as well as by the weights of the rational Bezier curve. Also, the relationship can be expressed by the corresponding parametric angles of the selected point and two endpoints on the conic segment, as well as by the weights of the rational Bezier curve. These results are greatly useful for optimal parametrization, reparametrization, etc., of rational Bezier curves and surfaces.

The relationship between projective geometric and rational quadratic b-spline curves

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four collinear points are represented: which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the two curves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Bezier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray’s location is showed. Also another cross ratio of the following four collinear points are suggested, i. e. one vertex, the points that the ray from the initial vertex intersects respectively with the curve segment, the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only with the ray’s location, but not with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.

２次有理Ｂｅｚｉｅｒ曲線および２次ＮＵＲＢＳの同次表現について

２次有理Ｂｅｚｉｅｒ曲線および２次ＮＵＲＢＳの同次表現について

A global collision-free path planning using parametric parabola through Geometry Mapping of obstacles in robot work space

In this paper, a new algorithm for palnning collision-free path connecting from start to target point is developed using Bezier curve of order two. The control point, i. e. the mid-point of quadratic Bezier curve, determines the shape of parabola and constitutes the Control Point Space, and this process is difined a Geometry Mapping. After Geometry Mapping of all obstacles, the clear area of CPS, an area not occupied by obstacle images, identifies collision-free path. The path planning algorithm, heance, transform path planning problem in Euclidian Space to point selection problem in CPS. The calculations involved in the algorithm do not require iterative procedures and all the formulas of the solution are derived in closed form. A CPS completely filled with obstacle images indicates that path planning based on parabola is not possible and requires higher order curve with more than one control point.

CONSTRAINING A QUADRATIC RATIONAL BEZIER TO BE AN ELLIPTICAL ARC

Analytic constraint solvers have a limited set of available geometries, typically lines and circles. This paper examines a method for constraining the control net of a rational quadratic Bezier curve so that it is always an elliptical arc.

Representing of contour lines by turning point preserving quadratic splines

AbstractTerrain data obtained from satellite imagery or by scanning existing contour maps is in raster mode. Such data may be compressed by detecting and storing the critical points of contour lines. When hand digitising a contour map, a trained digitiser operator would usually select points which visually appear to be critical points. Existing interpolation techniques often fail to restore the critical points, including turning points, to their original positions. This article illustrates the use of splines composed of quadratic Bezier curves with monotone curvature for rendering contour lines which are represented only by their turning and end points, such that the positions of the turning points are preserved.

An integrated approach to structural shape optimization of linearly elastic structures. Part II: Shape definition and adaptivity

In this paper we initially study how the number of design variables used affects the final optimum shape of the structure when employing two different types of curves to describe the boundary of the structure, i.e. quadratic Bezier and cubic B-spline curves. The advantage of using better shape definition is highlighted with several examples. An adaptive mesh refinement (AMR) procedure using six-node triangular elements is adopted in the structural shape optimization process. The procedure makes use of an h-version adaptive refinement technique based on error estimates determined from either best-guess stress values or residual terms in the governing equation. An example is presented to illustrate the performance of these error estimators with respect to their convergence, accuracy and cost of computation. Different strategies for the inclusion of AMR procedures in the shape optimization process are also proposed. Anomalies in predicting the optimum shape due to discretization errors are demonstrated using several examples.