G² curve design with planar quadratic rational Bézier spiral segments

Abstract

Spiral segments are useful in the design of fair curves. They are important in computer-aided design (CAD) and manufacturing applications, the design of highway and railway routes, trajectories of mobile robots, and other similar applications. Quadratic rational Bézier curves are often used in CAD applications because they can be used to draw conic sections exactly. This paper shows how curvature continuous curves can be designed using quadratic rational Bézier curve segments of monotone curvature.

Keywords:

• spiral
• rational
• quadratic Bézier
• C-shaped
• fair curve

2000 AMS Subject Classifications:

• 65D17
• 68U07\newline C.R. Categories: I.3.5
• J.6

Acknowledgements

This work was partially supported by the Natural Sciences and Engineering Research Council of Canada. The authors acknowledge the helpful suggestions of the anonymous reviewers which helped to improve the presentation of this paper.