G 2 PH QUINTIC SPIRAL TRANSITION CURVES AND THEIR APPLICATIONS

A method for family of G 2 Pythagorean hodograph (PH) quintic spiral transition from straight line to circle is discussed in this paper. This method is then extended to a pair of spirals between two straight lines or two circles. We derive a family of quintic transition spiral curves joining them. Due to exibilit y and wide range of shape control parameters, our method can be easily applied for practical applications like high way designing, blending in CAD, consumer products such as ping-pong paddles, rounding corners, or designing a smooth path that avoids obstacles. 1 Introduction and Description of Method A method for smooth G 2 planar PH quintic spiral transition from straight line to circle is developed. This method is then ex- tended to a pair of spirals transition between two circles or between two non-parallel straight lines. We also develop a method for drawing a constrained guided planar spiral curve that falls within a closed boundary. The boundary is composed of straight line segments and circular arcs. Our constrained curve can easily be controlled by shape control parameter. Any change in this shape control parameter does not eect the continuity and neighbor- hood parts of the curve. There are several problems whose solution requires these types of methods. For example