Smoothing of polyhedral models
SCG '86 Proceedings of the second annual symposium on Computational geometry
Computer-Aided Design
Piecewise-circular curves for geometric modeling
IBM Journal of Research and Development
Proceedings on Mathematics of surfaces II
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
The displacement method for implicit blending surfaces in solid models
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Modelling rolling ball blends for computer aided geometric design
Computer Aided Geometric Design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Swept volume: a retrospective and prospective view
Neural, Parallel & Scientific Computations - computer aided geometric design
Continuous Skeletons from Digitized Images
Journal of the ACM (JACM)
An augmented Fast Marching Method for computing skeletons and centerlines
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Rapid Generation of C2 Continuous Blending Surfaces
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Applications of Cyclide Surfaces in Geometric Modelling
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
Parametric Blending in a Boundary Representation Solid Modeller
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Twister: a space-warp operator for the two-handed editing of 3D shapes
ACM SIGGRAPH 2003 Papers
Surface Representation Using Second, Fourth and Mixed Order Partial Differential Equations
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Bounded Blending for Function-Based Shape Modeling
IEEE Computer Graphics and Applications
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Generalized sweep templates for implicit modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Efficient and robust computation of an approximated medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Medial axis extraction and shape manipulation of solid objects using parabolic PDEs
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Real-time voxelization of triangle meshes on the GPU
ACM SIGGRAPH 2007 sketches
Branching blend of natural quadrics based on surfaces with rational offsets
Computer Aided Geometric Design
A surface blending approach for displacement features on freeform surfaces
Computer-Aided Design
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Blends of canal surfaces from polyhedral medial transform representations
Computer-Aided Design
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Solid models may be blended through filleting or rounding operations that typically replace the vicinity of concave or convex edges by blends that smoothly connect to the rest of the solid's boundary. Circular blends, which are popular in manufacturing, are each the subset of a canal surface that bounds the region swept by a ball of constant or varying radius as it rolls on the solid while maintaining two tangential contacts. We propose to use a second solid to control the radius variation. This new formulation supports global blending (simultaneous rounding and filleting) operations and yields a simple set-theoretic formulation of the relative blending R"B(A) of a solid A given a control solid B. We propose user-interface options, describe practical implementations, and show results in 2 and 3 dimensions.