Boundary surface recovery from skeleton curves and surfaces
Computer Aided Geometric Design
New algorithm for medial axis transform of plane domain
Graphical Models and Image Processing
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Journal of Computational and Applied Mathematics
Exploiting curvatures to compute the medial axis for domains with smooth boundary
Computer Aided Geometric Design
Medial axis computation for planar free-form shapes
Computer-Aided Design
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
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
Medial axis of a planar region by offset self-intersections
Computer-Aided Design
Divide-and-conquer for Voronoi diagrams revisited
Computational Geometry: Theory and Applications
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
Exact medial axis computation for triangulated solids with respect to piecewise linear metrics
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
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In this paper, we begin our research from the generating theory of the medial axis. The normal equidistant mapping relationships between two boundaries and its medial axis have been proposed based on the moving Frenet frames and Cesaro's approach of the differential geometry. Two pairs of adjoint curves have been formed and the geometrical model of the medial axis transform of the planar domains with curved boundaries has been established. The relations of position mapping, scale transform and differential invariants between the curved boundaries and the medial axis have been investigated. Based on this model, a tracing algorithm for the computation of the medial axis has been generated. In order to get the accurate medial axis and branch points, a Two_Tangent_Points_Circle algorithm and a Three_Tangent_Points_Circle algorithm have been generated, which use the results of the tracing algorithm as the initial values to make the iterative process effective. These algorithms can be used for the computation of the medial axis effectively and accurately. Based on the medial axis transform and the envelope theory, the trimmed offset curves of curved boundaries have been investigated. Several numerical examples are given at the end of the paper.