Numerical recipes in Pascal: the art of scientific computing
Numerical recipes in Pascal: the art of scientific computing
Numerical control milling machine toolpath generation for regions bounded by free form curves and surfaces
On the computational geometry of pocket machining
On the computational geometry of pocket machining
New algorithm for medial axis transform of plane domain
Graphical Models and Image Processing
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Journal of Computational and Applied Mathematics
Voronoi diagrams and medial axes of planar domains with curved boundaries
Voronoi diagrams and medial axes of planar domains with curved boundaries
Computing Point/Curve and Curve/Curve Bisectors
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
Computer Aided Geometric Design
Computation of medial axis and offset curves of curved boundaries in planar domain
Computer-Aided Design
Computer Aided Geometric Design
Medial axis computation for planar free-form shapes
Computer-Aided Design
A symbolic-numerical envelope algorithm using quadratic MOS patches
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
Computer Aided Geometric Design
Medial axis of a planar region by offset self-intersections
Computer-Aided Design
Computer Aided Geometric Design
Medial axis transform of a planar domain with infinite curvature boundary points
Computer Aided Geometric Design
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In the paper, strong proofs of some basics facts about the medial axis transform of a planar region Ω with smooth boundary curve(s) are given. In particular the decomposition of Choi et al. (1997) is derived from the set of regular disks. Two special algorithms to compute the medial axis are presented. Due to the decomposition, they can be applied to each part of Ω separately. Emphasis is given to the local analysis of the boundary's curvatures. This leads to an interesting connection to the theory of Dupin cyclides. With this mean, a predictor/corrector algorithm (as in the numerical analysis of ODE's) is developed. The examples show that the predictor yields already an excellent approximation; so only a few refining steps of the corrector are necessary.