| Popis: |
In this paper, we present the geometric Hermite interpolation for planar Pythagorean-hodograph cubics for some general Hermite data. curve ro(t) = r(t) + dn(t) at a xed distance d from a given polynomial curve r(t), in the direction of its unit normal vector n(t), is an important problem in computer aided geometric design. The oset ro(t) is not, in general, a rational curve. Thus we need some approximation schemes to deal with osets of a polynomial curves. However, if the speed function of a given polynomial curve is a polynomial, then an oset curve can be expressed in a rational parametrization. For this reason, the Pythagorean-hodograph (PH) curves, whose speed function is a polynomial, were introduced by Farouki and Sakkalis ((6)). Since then, there have been vast researches on this class of curves by themselves and others ((1), (2), (3), (4), (5), and (11)). A PH curve r(t) = (x(t);y(t)) means a special polyno- mial curve which is characterized by the algebraic property that its hodograph r 0 (t) = (x 0 (t);y 0 (t)) satises the Pythagorean condition, that is, x 02 (t) +y 02 (t) = 2 (t) for some polynomial (t). So, the arc-length function and the osets |
