Pythagorean Hodograph Quintic Trigonometric Bezier Transtion Curve

Pythagorean Hodograph (PH) quintic transition curves are normally constructed because it is polynomial and has attractive properties, which is its arc-length is a polynomial of its parameter, and the formula for its offset is a rational algebraic expression. Pythagorean Hodograph is very important in formulating efficient real-time interpolator algorithm for CNC machines, suitable for rounding corners and blending smooth transition between two circles. By reinstating quintic Bezier curve with quintic trigonometric Bezier curve with two shape parameters, it will provide more flexibility to construct curves and surfaces. This new type of Pythagorean Hodograph will be more practical for curve designing especially in the computer aided geometric design of consumer products and useful for other computer graphics for designing highways.