The hdograph of a plane parametric curve r(t) = (x(t), y(t)f is the locus described by the first parametric derivative r' (t) = (x ' (t), y ' (t)) of that curve. A polynomial parametric curve is saidâ€¦ (More)

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 thisâ€¦ (More)

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 curvesâ€¦ (More)

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 youâ€¦ (More)

We investigate the properties of polynomial space curves r(t) = {x(t), y(t), z(t)} whose hodographs (derivatives) satisfy the Pythagorean condition x'Z(t) + y'Z(t) + z'2(t) crZ(t) for some realâ€¦ (More)

The Bernstein-Brzier curve and surface forms have enjoyed considerable populari ty in computer aided design applications, due to their elegant geometric properties and the simple recursive algorithmsâ€¦ (More)

The problem of exercising the freedoms of reparameterization of polynomial or rational curve segments to achieve a "parametric flow" closest to the unit-speed or arc-length representation isâ€¦ (More)