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- Rida T. Farouki
- Computer Aided Geometric Design
- 2012

One hundred years after the introduction of the Bernstein polynomial basis, we survey the historical development and current state of theory, algorithms, and applications associated with this remarkable method of representing polynomials over finite domains. Originally introduced by Sergei Natanovich Bernstein to facilitate a constructive proof of the… (More)

- Rida T. Farouki, V. T. Rajan
- Computer Aided Geometric Design
- 1988

- HODOGRAPH QUINTICS, Rida T. Farouki, C. Andrew Neff
- 2010

The Pythagorean hodograph (PH) curves are polynomial parametric curves {x(t), y(t)} whose hodograph (derivative) components satisfy the Pythagorean condition x'2(t)+y'2(t) = a2(t) for some polynomial a(t). Thus, unlike polynomial curves in general, PH curves have arc lengths and offset curves that admit exact rational representations. The lowest-order PH… (More)

- Rida T. Farouki
- Geometry and Computing
- 2008

Follow up what we will offer in this article about pythagorean hodograph curves algebra and geometry inseparable. You know really that this book is coming as the best seller book today. So, when you are really a good reader or you're fans of the author, it does will be funny if you don't have this book. It means that you have to get this book. For you who… (More)

- Rida T. Farouki, Mohammad al-Kandari, Takis Sakkalis
- Adv. Comput. Math.
- 2002

The interpolation of first-order Hermite data by spatial Pythagorean-hodograph curves that exhibit closure under arbitrary 3-dimensional rotations is addressed. The hodographs of such curves correspond to certain combinations of four polynomials, given by Dietz et al. [4], that admit compact descriptions in terms of quaternions – an instance of the “PH… (More)

- Rida T. Farouki, John K. Johnstone
- Computer Aided Geometric Design
- 1994

- Rida T. Farouki, V. T. Rajan
- Computer Aided Geometric Design
- 1987

- A. Kaul, Rida T. Farouki
- Int. J. Comput. Geometry Appl.
- 1995

- Rida T. Farouki, Tim N. T. Goodman
- Math. Comput.
- 1996

We show that the Bernstein polynomial basis on a given interval is “optimally stable,” in the sense that no other nonnegative basis yields systematically smaller condition numbers for the values or roots of arbitrary polynomials on that interval. This result follows from a partial ordering of the set of all nonnegative bases that is induced by nonnegative… (More)

- Rida T. Farouki, C. Andrew Neff, M. A. O'Conner
- ACM Trans. Graph.
- 1989

In general, two quadric surfaces intersect in a nonsingular quartic space curve. Under special circumstances, however, this intersection may “degenerate” into a quartic with a double point, or a composite of lines, conics, and twisted cubics whose degrees, counted over the complex projective domain, sum to four. Such degenerate forms are… (More)