An explicit expression for the unique implicitization of any planar rational cubic Bézier curve is presented, the only exception being when the tangents at the ends of the curve are parallel. The representation is in the form of a cubic Bernstein-Bézier triangle and is invariant under affine transformations of the curve. The implicitization degenerates to zero if and only if the curve degenerat...

Based on the technique of C-shape G Hermite interpolation by cubic Pythagorean-Hodograph (PH) curve, we present a simple method for Cshape G Hermite interpolation by rational cubic Bézier curve. The method reproduces a circular arc when the input data come from it. Both the Bézier control points, which have the well understood geometrical meaning, and the weights of the resulting rational cubic...

Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these...

.This paper is concerned with the range restricted interpolation of 'data on rectangular grids. The interpolant is constrained to lie on the same side of the constraint surface as the data. Sufficient non-negativity conditions on the Bezier ordinates are derived to ensure the non-negativity of a bicubic Bezier patch. The method modifies Bezier ordinates locally to fulfill the sufficient non-neg...

This paper proposes a time optimal path planning while considering the physical constraints of wheeled mobile robots along a high curvature Bezier curve. The proposed algorithm overcomes drawbacks of preceding results. A trajectory produced through acceleration limits showed long traveling time, non-uniform sampling time and unsatisfied terminal velocity. A convolution-based method to consider ...

A method is presented to interpolate real affine plane curves with second degree NURBS (Non Uniform Rational Bezier Splines). The curve into object is initially partitioned into an arbitrary number of arcs. Then each arc is approximated with a conic section passing thru its extremes, thru a third intermediate point and being tangent to the arc at the extremes. Each arc is then parameterized by ...

/ = /i$i. Since (to)i = 5ii is in (s), and ni is prime to the order of Si, Si is a power of s. Thus h, as well as t, corresponds to t in the isomorphism of G with G/(s) ; but h and /' are of the same order tii. Every element of G/(s) whose order is a divisor of m/mi corresponds to an element of G whose order is a divisor of m. It follows that t', and hence every element of G/(s) whose order div...

Abstract Bézier splines are widely available in various systems with the curves and surface designs. In general, the Bézier spline can be specified with the Bézier curve segments and a Bézier curve segment can be fitted to any number of control points. The number of control points determines the degree of the Bézier polynomial. This paper presents a method which determines control points for Bé...