Applied & computational complex analysis: power series integration conformal mapping location of zero
Geometric concepts for geometric design
Geometric concepts for geometric design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Inflection points and singularities on planar rational cubic curve segments
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Computer Aided Geometric Design
Curvature extrema of planar parametric polynomial cubic curves
Journal of Computational and Applied Mathematics
Interpolation with cubic spirals
Computer Aided Geometric Design
Geometric modeling: techniques, applications, systems and tools
Geometric modeling: techniques, applications, systems and tools
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
Transition between concentric or tangent circles with a single segment of G2 PH quintic curve
Computer Aided Geometric Design
Geometric Hermite interpolation with circular precision
Computer-Aided Design
A smooth spiral tool path for high speed machining of 2D pockets
Computer-Aided Design
Technical section: Rational cubic spline interpolation with shape control
Computers and Graphics
A further generalisation of the planar cubic Bézier spiral
Journal of Computational and Applied Mathematics
Lagrange geometric interpolation by rational spatial cubic Bézier curves
Computer Aided Geometric Design
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This paper finds reachable regions for a single segment of parametric rational cubic Bezier spiral matching G^2 Hermite data. First we derive spiral conditions for rational cubics and then we use a free parameter to find the admissible region for a spiral segment with respect to the curvatures at its endpoints under the fixed positional and tangential end conditions. Spirals are curves of constant sign monotone curvature and therefore have the advantage that the minimum and maximum curvatures are at their endpoints only.