Continuous skeleton computation by Voronoi diagram
CVGIP: Image Understanding
Approximating smooth planar curves by arc splines
Journal of Computational and Applied Mathematics
New algorithm for medial axis transform of plane domain
Graphical Models and Image Processing
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Spiral arc spline approximation to a planar spiral
Journal of Computational and Applied Mathematics
Computational Geometry: Theory and Applications
Voronoi Diagrams for Planar Shapes
IEEE Computer Graphics and Applications
Exploiting curvatures to compute the medial axis for domains with smooth boundary
Computer Aided Geometric Design
The Voronoi Diagram of Curved Objects
Discrete & Computational Geometry
Computation of medial axis and offset curves of curved boundaries in planar domain
Computer-Aided Design
A sweepline algorithm for Euclidean Voronoi diagram of circles
Computer-Aided Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
Medial Axis Transformation of a Planar Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational and structural advantages of circular boundary representation
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Divide-and-conquer for Voronoi diagrams revisited
Proceedings of the twenty-fifth annual symposium on Computational geometry
A symbolic-numerical envelope algorithm using quadratic MOS patches
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Divide-and-conquer for Voronoi diagrams revisited
Computational Geometry: Theory and Applications
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
Exact medial axis computation for triangulated solids with respect to piecewise linear metrics
Proceedings of the 7th international conference on Curves and Surfaces
Exact medial axis computation for circular arc boundaries
Proceedings of the 7th international conference on Curves and Surfaces
Medial axis transform of a planar domain with infinite curvature boundary points
Computer Aided Geometric Design
Efficient offset trimming for planar rational curves using biarc trees
Computer Aided Geometric Design
Generalized Swept Mid-structure for Polygonal Models
Computer Graphics Forum
A fast algorithm for constructing approximate medial axis of polygons, using Steiner points
Advances in Engineering Software
Computer Aided Geometric Design
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We present a simple, efficient, and stable method for computing-with any desired precision-the medial axis of simply connected planar domains. The domain boundaries are assumed to be given as polynomial spline curves. Our approach combines known results from the field of geometric approximation theory with a new algorithm from the field of computational geometry. Challenging steps are (1) the approximation of the boundary spline such that the medial axis is geometrically stable, and (2) the efficient decomposition of the domain into base cases where the medial axis can be computed directly and exactly. We solve these problems via spiral biarc approximation and a randomized divide & conquer algorithm.