This paper deals with the approximate merging problem of multiple adjacent Bézier curves with different degrees by a single Bézier curve, which is a frequently seen problem in modeling. The unified matrix representation for precise merging is presented and the approximate merging curve is further derived based on matrix operation. Continuity at the endpoints of curves is also discussed in the m...

A curvature-based algorithm to simplify a polygonal curve is described, together with its implementation. The so-called SimpliPoly algorithm uses Bézier curves to approximate pieces of the input curve, and assign curvature estimates to vertices of the input polyline from curvature values computed for the Bézier approximations. The implementation of SimpliPoly is interactive and available freely...

This paper deals with the approximate merging problem of multiple adjacent Bézier curves with different degrees by a single Bézier curve, which is a frequently seen problem in modeling. The unified matrix representation for precise merging is presented and the approximate merging curve is further derived based on matrix operation. Continuity at the endpoints of curves is also discussed in the m...

The length Λ of a given rational Bézier curve is efficiently estimated. Since a rational Bézier 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 Λn is investigated. In order to improve the efficiency, adaptivity is used with some length estimator. A rigorous theoretical analysis ...

Accurate modeling of co-articulation, the contextsensitive merging of the boundaries between allophones in continuous speech, is vital for natural sounding speech synthesis. This paper describes initial research investigating the use of Bézier Curves to form models of co-articulation in human speech. A 12th order, pitch synchronous line spectral pair (LSP) [1] analysis is performed on a corpus ...

We constructed a single C-Bézier curve with a shape parameter for G joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bézier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in d...

We present an approach to finding the implicit equation of a planar rational parametric cubic curve, by defining a new basis for the representation. The basis, which contains only four cubic bivariate polynomials, is defined in terms of the Bézier control points of the curve. An explicit formula for the coefficients of the implicit curve is given. Moreover, these coefficients lead to simple exp...

Ball basis was introduced for cubic polynomials by Ball, and was generalized for polynomials of higher degree by Said. An algorithmic approach to degree reduction of interval Said-Ball (SB) curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed SB curves) associated with the original interval SB curve are obtained. These four fixed SB curves are transformed into f...

The Virtex FPGA introduces new features which support the design of large systems using a synthesis flow. With much improved routing, features like clock DLLs and BlockRAM, a rich collection of resources are available to designers. We investigate how synthesis friendly Virtex is by implementing the Bézier function in a variety of ways, making use of BlockRAM, clock DLLs and shift-register LUTs....