The Construction Of Quartic Pythagorean Hodograph Curve

The Pythagorean hodograph curves(PH curves) are curves (x(t),y(t)),whose hodograph components satisfy the Phythagorean condition for x'2(t)+y'2(t)=σ2(t) some polynomialσ(t). The distinct chatacteristic of PH curves is to have exact rational offset curves. Offset curves are also called parallel curves, and defined as locus of the points which are at constant d along the normal from the generator curves. They have been one of the most important geometric operations in CAD/CAM systems over the past years.In the thesis, quartic PH curves, which belong to PH curves of even degrees, are presented. Emphatically, based on the research of odd number PH curves and the parametric research of rational offset curves (OR curves). By adjusting the inner controlling parameter, curves are regulated effectively, which make them serve the human being more effectively. In this thesis, Quartic PB curves and quartic parabolic. PH interpolation Hermite curves are mainly researched, and their geometric and algebraic character is also analysed. In general, there are always four distinct interpolants and at least one has acceptable geometric shape characteristics. The obtained curve can be directly applied in the area of industry product design and milling machines. The constructing process not only is easy and flexible to satisfy different designed requirements, but also provides a convenient means of controlling curve shape for engineer in CAGD.