Abstract: Bezier curves have useful properties for path
generation problem, for instance, it can generate the reference
trajectory for vehicles to satisfy the path constraints. Both algorithms
join cubic Bezier curve segment smoothly to generate the path. Some
of the useful properties of Bezier are curvature. In mathematics,
curvature is the amount by which a geometric object deviates from
being flat, or straight in the case of a line. Another extrinsic example
of curvature is a circle, where the curvature is equal to the reciprocal
of its radius at any point on the circle. The smaller the radius, the
higher the curvature thus the vehicle needs to bend sharply. In this
study, we use Bezier curve to fit highway-like curve. We use
different approach to find the best approximation for the curve so that
it will resembles highway-like curve. We compute curvature value by
analytical differentiation of the Bezier Curve. We will then compute
the maximum speed for driving using the curvature information
obtained. Our research works on some assumptions; first, the Bezier
curve estimates the real shape of the curve which can be verified
visually. Even though, fitting process of Bezier curve does not
interpolate exactly on the curve of interest, we believe that the
estimation of speed are acceptable. We verified our result with the
manual calculation of the curvature from the map.
Abstract: We present a trigonometric scheme to approximate a
circular arc with its two end points and two end tangents/unit
tangents. A rational cubic trigonometric Bézier curve is constructed
whose end control points are defined by the end points of the circular
arc. Weight functions and the remaining control points of the cubic
trigonometric Bézier curve are estimated by variational approach to
reproduce a circular arc. The radius error is calculated and found less
than the existing techniques.
Abstract: The length of a given rational B'ezier curve is
efficiently estimated. Since a rational B'ezier function is nonlinear,
it is usually impossible to evaluate its length exactly. The
length is approximated by using subdivision and the accuracy
of the approximation n is investigated. In order to improve
the efficiency, adaptivity is used with some length estimator.
A rigorous theoretical analysis of the rate of convergence of
n to is given. The required number of subdivisions to
attain a prescribed accuracy is also analyzed. An application
to CAD parametrization is briefly described. Numerical results
are reported to supplement the theory.
Abstract: The motion planning procedure described in this paper has been developed in order to eliminate or reduce the residual vibrations of electromechanical positioning systems, without augmenting the motion time (usually imposed by production requirements), nor introducing overtime for vibration damping. The proposed technique is based on a suitable choice of the motion law assigned to the servomotor that drives the mechanism. The reference profile is defined by a Bezier curve, whose shape can be easily changed by modifying some numerical parameters. By means of an optimization technique these parameters can be modified without altering the continuity conditions imposed on the displacement and on its time derivatives at the initial and final time instants.
Abstract: The distance between two objects is an important
problem in CAGD, CAD and CG etc. It will be presented in this paper
that a simple and quick method to estimate the distance between a
point and a Bezier curve on a Bezier surface.
Abstract: In this work a software simulation model has been
proposed for two driven wheels mobile robot path planning; that can
navigate in dynamic environment with static distributed obstacles.
The work involves utilizing Bezier curve method in a proposed N
order matrix form; for engineering the mobile robot path. The Bezier
curve drawbacks in this field have been diagnosed. Two directions:
Up and Right function has been proposed; Probability Recursive
Function (PRF) to overcome those drawbacks.
PRF functionality has been developed through a proposed;
obstacle detection function, optimization function which has the
capability of prediction the optimum path without comparison
between all feasible paths, and N order Bezier curve function that
ensures the drawing of the obtained path.
The simulation results that have been taken showed; the mobile
robot travels successfully from starting point and reaching its goal
point. All obstacles that are located in its way have been avoided.
This navigation is being done successfully using the proposed PRF
techniques.
Abstract: Arbitrarily shaped video objects are an important
concept in modern video coding methods. The techniques presently
used are not based on image elements but rather video objects having
an arbitrary shape. In this paper, spatial shape error concealment
techniques to be used for object-based image in error-prone
environments are proposed. We consider a geometric shape
representation consisting of the object boundary, which can be
extracted from the α-plane. Three different approaches are used to
replace a missing boundary segment: Bézier interpolation, Bézier
approximation and NURBS approximation. Experimental results on
object shape with different concealment difficulty demonstrate the
performance of the proposed methods. Comparisons with proposed
methods are also presented.
Abstract: In image processing and visualization, comparing two
bitmapped images needs to be compared from their pixels by matching
pixel-by-pixel. Consequently, it takes a lot of computational time
while the comparison of two vector-based images is significantly
faster. Sometimes these raster graphics images can be approximately
converted into the vector-based images by various techniques. After
conversion, the problem of comparing two raster graphics images
can be reduced to the problem of comparing vector graphics images.
Hence, the problem of comparing pixel-by-pixel can be reduced to
the problem of polynomial comparisons. In computer aided geometric
design (CAGD), the vector graphics images are the composition of
curves and surfaces. Curves are defined by a sequence of control
points and their polynomials. In this paper, the control points will be
considerably used to compare curves. The same curves after relocated
or rotated are treated to be equivalent while two curves after different
scaled are considered to be similar curves. This paper proposed an
algorithm for comparing the polynomial curves by using the control
points for equivalence and similarity. In addition, the geometric
object-oriented database used to keep the curve information has also
been defined in XML format for further used in curve comparisons.
Abstract: The Prediction of aerodynamic characteristics and
shape optimization of airfoil under the ground effect have been carried
out by integration of computational fluid dynamics and the multiobjective
Pareto-based genetic algorithm. The main flow
characteristics around an airfoil of WIG craft are lift force, lift-to-drag
ratio and static height stability (H.S). However, they show a strong
trade-off phenomenon so that it is not easy to satisfy the design
requirements simultaneously. This difficulty can be resolved by the
optimal design. The above mentioned three characteristics are chosen
as the objective functions and NACA0015 airfoil is considered as a
baseline model in the present study. The profile of airfoil is
constructed by Bezier curves with fourteen control points and these
control points are adopted as the design variables. For multi-objective
optimization problems, the optimal solutions are not unique but a set
of non-dominated optima and they are called Pareto frontiers or Pareto
sets. As the results of optimization, forty numbers of non- dominated
Pareto optima can be obtained at thirty evolutions.
Abstract: The PH curve can be constructed by given parameters, but the shape of the curve is not so easy to image from the value of the parameters. On the contract, Bézier curve can be constructed by the control polygon, and from the control polygon, we can image the figure of the curve. In this paper, we want to use the hodograph of Bézier curve to construct PH curve by selecting part of the control vectors, and produce other control vectors, so the property of PH curve exists.