Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
The adaptive pyramid: a framework for 2D image analysis
CVGIP: Image Understanding
An algorithm for constructing the convex hull of a set of spheres in dimension d
Computational Geometry: Theory and Applications
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Collision detection for volumetric objects
VIS '97 Proceedings of the 8th conference on Visualization '97
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Computer representation of planar regions by their skeletons
Communications of the ACM
Sphere-tree construction using dynamic medial axis approximation
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Multiresolution Representation and Visualization of Volume Data
IEEE Transactions on Visualization and Computer Graphics
Efficient collision detection of complex deformable models using AABB trees
Journal of Graphics Tools
Adaptive medial-axis approximation for sphere-tree construction
ACM Transactions on Graphics (TOG)
Inclusion-Exclusion Formulas from Independent Complexes
Discrete & Computational Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
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In discrete geometry, the Distance Transformation and the Medial Axis Extraction are classical tools for shape analysis. In this paper, we present a Hierarchical Discrete Medial Axis, based on a pyramidal representation of the object, in order to efficiently create a sphere-tree, which has many applications in collision detection or image synthesis.