A dimensionality paradigm for surface interrogations
Computer Aided Geometric Design
The bisector of a point and a plane parametric curve
Computer Aided Geometric Design
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
Computing Point/Curve and Curve/Curve Bisectors
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
Rational bisectors of CSG primitives
Proceedings of the fifth ACM symposium on Solid modeling and applications
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Three dimensional euclidean Voronoi diagrams of lines with a fixed number of orientations
Proceedings of the eighteenth annual symposium on Computational geometry
IEEE Computer Graphics and Applications
Precise Voronoi cell extraction of free-form rational planar closed curves
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
MOS surfaces: medial surface transforms with rational domain boundaries
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
Automated mixed dimensional modelling from 2D and 3D CAD models
Finite Elements in Analysis and Design
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Given a point and a rational curve in the plane, their bisector curve is rational [Farouki and Johnston 1994a]. However, in general, the bisector of two rational curves in the plane is not rational [Farouki and Johnstone 1994b]. Given a point and a rational space curve, this art icle shows that the bisector surface is a rational ruled surface. Moreover, given two rational space curves, we show that the bisector surface is rational (except for the degenerate case in which the two curves are coplanar).