Planar spirals that match G2 Hermite data
Computer Aided Geometric Design
A shape controlled fitting method for Be´zier curves
Computer Aided Geometric Design
Spiral arc spline approximation to a planar spiral
Journal of Computational and Applied Mathematics
Designing Bézier conic segments with monotone curvature
Computer Aided Geometric Design
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Planar G2 transition with a fair Pythagorean hodograph quintic curve
Journal of Computational and Applied Mathematics
Non-linear subdivision using local spherical coordinates
Computer Aided Geometric Design
Interpolation with cubic spirals
Computer Aided Geometric Design
A generalisation of the Pythagorean hodograph quintic spiral
Journal of Computational and Applied Mathematics
On PH quintic spirals joining two circles with one circle inside the other
Computer-Aided Design
G2 Pythagorean hodograph quintic transition between two circles with shape control
Computer Aided Geometric Design
G2 curve design with a pair of Pythagorean Hodograph quintic spiral segments
Computer Aided Geometric Design
Computer-Aided Design
An involute spiral that matches G2 Hermite data in the plane
Computer Aided Geometric Design
Normal based subdivision scheme for curve design
Computer Aided Geometric Design
Incenter subdivision scheme for curve interpolation
Computer Aided Geometric Design
Using a biarc filter to compute curvature extremes of NURBS curves
Engineering with Computers
Geometric conditions for tangent continuity of interpolatory planar subdivision curves
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
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Spirals are curves with single-signed, monotone increasing or decreasing curvature. A spiral can only interpolate certain G^2 Hermite data that is referred to as admissible G^2 Hermite data. In this paper we propose a biarc-based subdivision scheme that can generate a planar spiral matching an arbitrary set of given admissible G^2 Hermite data, including the case that the curvature at one end is zero. An attractive property of the proposed scheme is that the resulting subdivision spirals are also offset curves if the given input data are offsets of admissible G^2 Hermite data. A detailed proof of the convergence and smoothness analysis of the scheme is also provided. Several examples are given to demonstrate some excellent properties and practical applications of the proposed scheme.