Spline approximation of offset curves
Computer Aided Geometric Design
Offset approximation of uniform B-splines
Computer-Aided Design
On the computational geometry of pocket machining
On the computational geometry of pocket machining
An algorithm for generating NC tool paths for arbitrarily shaped pockets with islands
ACM Transactions on Graphics (TOG)
Offset approximation improvement by control point perturbation
Mathematical methods in computer aided geometric design II
Offsets of polynomial Be´zier curves: Hermite approximation with error bounds
Mathematical methods in computer aided geometric design II
Polynomial/rational approximation of Minkowski sum boundary curves
Graphical Models and Image Processing
Curve offsetting based on Legendre series
Computer Aided Geometric Design
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Approximation of circular arcs and offset curves by Bézier curves of high degree
Journal of Computational and Applied Mathematics
Offsets of Two-Dimensional Profiles
IEEE Computer Graphics and Applications
Computing exact rational offsets of quadratic triangular Bézier surface patches
Computer-Aided Design
Hermite interpolation by hypocycloids and epicycloids with rational offsets
Computer Aided Geometric Design
Computing offsets of freeform curves using quadratic trigonometric splines
ROCOM'10 Proceedings of the 10th WSEAS international conference on Robotics, control and manufacturing technology
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This paper proposes an error analysis of reparametrization based approaches for planar curve offsetting. The approximation error in Hausdorff distance is computed. The error is bounded by O(rsin^2@b), where r is the offset radius and @b is the angle deviation of a difference vector from the normal vector. From the error bound an interesting geometric property of the approach is observed: when the original curve is offset in its convex side, the approximate offset curve always lies in the concave side of the exact offset, that is, the approximate offset is contained within the region bounded by the exact offset curve and the original curve. Our results improve the error estimation of the circle approximation approaches, as well as the computation efficiency when the methods are applied iteratively for high precision approximation.