Computer Aided Geometric Design - Special issue: Topics in CAGD
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Approximation of logarithmic spirals
Computer Aided Geometric Design
Circular arc approximation by quintic polynomial curves
Computer Aided Geometric Design
The generalised Cornu spiral and its application to span generation
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Geometric Continuity of Parametric Curves: Three Equivalent Characterizations
IEEE Computer Graphics and Applications
G2 curve design with a pair of Pythagorean Hodograph quintic spiral segments
Computer Aided Geometric Design
Transition between concentric or tangent circles with a single segment of G2 PH quintic curve
Computer Aided Geometric Design
Sketch-Based Interfaces and Modeling (SBIM): Sketching piecewise clothoid curves
Computers and Graphics
Smooth polynomial approximation of spiral arcs
Journal of Computational and Applied Mathematics
A note on quintic polynomial approximation of generalized Cornu spiral segments
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
Within Computer Aided Design (CAD) there is a need to construct fair curves. The Generalised Cornu Spirals (GCSs) are a set of curves with a monotonic curvature profile and are hence considered fair but implementation in current CAD systems is not straightforward, partly due to not being in the usual polynomial form. A method to approximate a GCS using a quintic polynomial curve is presented. The method seeks to interpolate the GCS to satisfy the G^3 constraints at the end points with a quintic Bezier, leaving two degrees of freedom. An initial approximation is shown to be effective for the majority of GCS curves. Moreover, it is possible to determine when an initial approximation is likely to be poor. If this approximation does not meet the tolerance required, a search involving two parameters is performed. Characteristics of the search domain are used to establish a suitable starting value.