Piecewise-circular curves for geometric modeling
IBM Journal of Research and Development
The use of Cornu spirals in drawing planar curves of controlled curvature
Journal of Computational and Applied Mathematics
Proceedings on Mathematics of surfaces II
Computational geometry: curve and surface modeling
Computational geometry: curve and surface modeling
Locally controllable conic splines with curvature continuity
ACM Transactions on Graphics (TOG)
Curved surface machining through circular arc interpolation
Computers in Industry
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Approximating smooth planar curves by arc splines
Journal of Computational and Applied Mathematics
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
Generating curves and swept surfaces by blended circles
Computer Aided Geometric Design
ACM Transactions on Mathematical Software (TOMS)
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Planar G2 Hermite interpolation with some fair, C-shaped curves
Journal of Computational and Applied Mathematics
An arc spline approximation to a clothoid
Journal of Computational and Applied Mathematics
Technical section: A controlled clothoid spline
Computers and Graphics
High accuracy geometric Hermite interpolation
Computer Aided Geometric Design
The family of biarcs that matches planar, two-point G1 Hermite data
Journal of Computational and Applied Mathematics
Technical Section: Generating fair, C2 continuous splines by blending conics
Computers and Graphics
Improvement construction for planar g2 transition curve between two separated circles
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
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Arc splines are G^1 continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route planners as a natural curve along which to plan the centre line of a road. In this paper, it is shown how to increase the smoothness of a planar arc spline by replacing parts of it and thus to create a G^2 continuous curve. The replacement parts are low-degree NURBS curves: cubic Bezier curves and quadratic rational Bezier curves.