Approximation of TAP Curve Segment by Rational Cubic Bézier Curve

Abstract

Designing aesthetically appealing models is vital for the marketing success of industrial products. Tangential Angle Parameterization Curves (TAP Curves) are new curves having both position control and the curvature control. TAP curves in its quadrature form are not compatible with current CAD systems. In this paper, we present a method that approximates one TAP curve segment by one rational cubic Bézier curve segment. We have analyzed the behavior of approximate errors when the radius of curvature of the TAP curve has changed. We have implemented our algorithm and verified that one TAP curve segment can be approximated by on rational Bézier curve segment when the change of tangential angle is less than 90 deg.