The approximation of non-degenerate offset surfaces
Computer Aided Geometric Design
IBM Journal of Research and Development
Box splines
Hermite and Lagrange interpolation by quadratic splines on non-uniform criss-cross triangulations
An international conference on curves and surfaces on Wavelets, images, and surface fitting
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
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
Hermite interpolation by piecewise polynomial surfaces with rational offsets
Computer Aided Geometric Design
Developments in bivariate spline interpolation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Computational Line Geometry
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
C1 Hermite interpolation using MPH quartic
Computer Aided Geometric Design
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
Exploiting curvatures to compute the medial axis for domains with smooth boundary
Computer Aided Geometric Design
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
Error analysis of reparametrization based approaches for curve offsetting
Computer-Aided Design
Rational space curves are not “unit speed”
Computer Aided Geometric Design
Rational hypersurfaces with rational convolutions
Computer Aided Geometric Design
Convolution surfaces of quadratic triangular Bézier surfaces
Computer Aided Geometric Design
Self-intersection detection and elimination in freeform curves and surfaces
Computer-Aided Design
Computing exact rational offsets of quadratic triangular Bézier surface patches
Computer-Aided Design
Mathematics and Computers in Simulation
Branching blend of natural quadrics based on surfaces with rational offsets
Computer Aided Geometric Design
On quadratic two-parameter families of spheres and their envelopes
Computer Aided Geometric Design
Computation of medial axis and offset curves of curved boundaries in planar domain
Computer-Aided Design
On generalized ln-surfaces in 4-space
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
One-sided offset approximation of freeform curves for interference-free NURBS machining
Computer-Aided Design
PN surfaces and their convolutions with rational surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
Medial axis computation for planar free-form shapes
Computer-Aided Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Quadratic spline quasi-interpolants and collocation methods
Mathematics and Computers in Simulation
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
Rational surfaces with linear normals and their convolutions with rational surfaces
Computer Aided Geometric Design
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
Computer Aided Geometric Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
MOS surfaces: medial surface transforms with rational domain boundaries
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Medial Axis Transformation of a Planar Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
Blends of canal surfaces from polyhedral medial transform representations
Computer-Aided Design
Computer Aided Geometric Design
Exact medial axis computation for triangulated solids with respect to piecewise linear metrics
Proceedings of the 7th international conference on Curves and Surfaces
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
Reducibility of offsets to algebraic curves
Computer Aided Geometric Design
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MOS surfaces (i.e., medial surface transforms obeying a sum of squares condition) are rational surfaces in R^3^,^1 which possess rational envelopes of the associated two-parameter families of spheres. Moreover, all offsets of the envelopes admit rational parameterizations as well. Recently, it has been proved that quadratic triangular Bezier patches in R^3^,^1 are MOS surfaces. Following this result, we describe an algorithm for computing an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in R^3^,^1. The paper focuses mainly on the geometric aspects of the algorithm. Since these patches are capable of producing C^1 smooth approximations of medial surface transforms of spatial domains, we use this algorithm to generate rational approximations of envelopes of general medial surface transforms. One of the main advantages of this approach to offsetting is the fact that the trimming procedure becomes considerably simpler.