A remark on cubic parabolic curve

A remark on parameterizing nonsingular cubic surfaces

Article history: Received 13 June 2008 Received in revised form 29 May 2009 Accepted 2 June 2009 Available online 6 June 2009 Extending a geometric construction due to Sederberg and to Bajaj, Holt, and Netravali, an algorithm is presented for parameterizing a nonsingular cubic surface by polynomials of degree three. The fact that such a parametrization exists is classical. The present algorithm...

A Public Key Cryptosystem Based on Singular Cubic Curve

An efficient and semantically secure public key cryptosystem based on singular cubic curve is proposed in this paper. It is about two times faster than the cryptosystem of David at the same security label and more efficient than the Koyama scheme at high security level. Further, the partially known plaintext attack and the linearly related plaintext attacks are analyzed and concluded that those...

A Cubic Curve Connected with Two Triangles

/ = /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...

Cubic Bézier approximation of a digitized curve

In this paper we present an efficient technique for piecewise cubic Bézier approximation of digitized curve. An adaptive breakpoint detection method divides a digital curve into a number of segments and each segment is approximated by a cubic Bézier curve so that the approximation error is minimized. Initial approximated Bézier control points for each of the segments are obtained by interpolati...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem