IBM Journal of Research and Development
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
The bisector surface of rational space curves
ACM Transactions on Graphics (TOG)
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Computational Line Geometry
IEEE Computer Graphics and Applications
Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
Computer Aided Geometric Design
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
Computer Aided Geometric Design
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
On quadratic two-parameter families of spheres and their envelopes
Computer Aided Geometric Design
On generalized ln-surfaces in 4-space
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Rational two-parameter families of spheres and rational offset surfaces
Journal of Symbolic Computation
A symbolic-numerical envelope algorithm using quadratic MOS patches
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Blends of canal surfaces from polyhedral medial transform representations
Computer-Aided Design
Algebraic curves of low convolution degree
Proceedings of the 7th international conference on Curves and Surfaces
Research on 3D medial axis transform via the saddle point programming method
Computer-Aided Design
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
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We consider rational surface patches s(u, v) in the four-dimensional Minkowski space IR3,1, which describe parts of the medial surface (or medial axis) transform of spatial domains. The corresponding segments of the domain boundary are then obtained as the envelopes of the associated two-parameter family of spheres. If the Plücker coordinates of the line at infinity of the (two-dimensional) tangent plane of s satisfy a sum-of-squares condition, then the two envelope surfaces are shown to be rational surfaces. We characterize these Plücker coordinates and analyze the case, where the medial surface transform is contained in a hyperplane of the four-dimensional Minkowski space.