Unit quaternion integral curve: A new type of fair free-form curves

This paper proposes a new type of free-form curves for fairness. A unit qua ternion curve is used to specify the tangent of the curve in order to more directly manipulate its curvature and variation of curvature than is possib le for the traditional parametric representations like Bezier and NURBS cur ves. Since the new curve is represented by an integral form of a unit quate rnion curve, it is named a unit quaternion integral: QI curve. It is a gene ralization and an extension of the clothoid into the three dimensional spac e and the norm of its tangent is always equal to 1. Its curvature and varia tion of curvature are given by rather simple expressions. (C) 2000 Elsevier Science B.V. All rights reserved.