Loop detection in surface patch intersections
Computer Aided Geometric Design
Fat arcs: a bounding region with cubic convergence
Computer Aided Geometric Design
Curve intersection using Be´zier clipping
Computer-Aided Design - Special Issue: Be´zier Techniques
Planar spirals that match G2 Hermite data
Computer Aided Geometric Design
A shape controlled fitting method for Be´zier curves
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Computer-Aided Design
Bézier clipping is quadratically convergent
Computer Aided Geometric Design
Log-aesthetic space curve segments
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Computer Aided Geometric Design
Applying inversion to construct planar, rational spirals that satisfy two-point G2 Hermite data
Computer Aided Geometric Design
3D Euler spirals for 3D curve completion
Proceedings of the twenty-sixth annual symposium on Computational geometry
From spiral to spline: optimal techniques in interactive curve design
From spiral to spline: optimal techniques in interactive curve design
Fat arcs for implicitly defined curves
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Efficient point-projection to freeform curves and surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
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A bounding region for spiral curve segments shaped by two circular arcs, parts of the osculating circles at the spiral's endpoints, and two lines is introduced. This bounding region, denoted spiral fat arc (SFA) is simple to construct and process, and shows a cubic approximation order to a given spiral curve. Given a general planar parametric curve, it can be split at curvature extrema (and inflection points), solving for the parametric locations for which @k'=0 (and @k=0), @k being the signed curvature field, to yield a set of spiral curves. Each of the spirals is then fitted with a bounding SFA. Finding the intersection locations of two free-form planar curves is a fundamental task in geometric computing and computer aided design, and can immediately benefit from this new SFA bounding region. A recursive curve-curve intersection (CCI) algorithm that efficiently computes the intersection location of two parametric curves using SFAs is also introduced.