ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Gn-1-functional splines for interpolation and approximation of curves, surfaces and solids
Computer Aided Geometric Design
Cyclides in computer aided geometric design
Computer Aided Geometric Design
Blending of implicit surfaces with functional splines
Computer-Aided Design
Algebraic surface design with Hermite interpolation
ACM Transactions on Graphics (TOG)
Cyclides in computer aided geometric design II
Computer Aided Geometric Design
Computing rational parametrizations of canal surfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Results on nonsingular, cyclide transition surfaces
Computer Aided Geometric Design
Blending two cones with Dupin cyclides
Computer Aided Geometric Design
On blending of several quadratic algebraic surfaces
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Gn-continous connections between normal ringed surfaces
Computer Aided Geometric Design
Blending quadric surfaces with piecewise algebraic surfaces
Graphical Models
Constructive modeling of G1 bifurcation
Computer Aided Geometric Design
G1-smooth branching surface construction from cross sections
Computer-Aided Design
Branching blend of natural quadrics based on surfaces with rational offsets
Computer Aided Geometric Design
Functional splines with different degrees of smoothness and their applications
Computer-Aided Design
Constructive G1 connection of multiple freeform pipes in arbitrary poses
Computer Aided Geometric Design
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First presented by Hartmann, closings (implicit surfaces sealing the inlets or outlets of pipes) can bridge the gap between parametric pipe surfaces and implicit functional splines (a powerful tool for blending several implicit surfaces). This paper proposes auxiliary spheres instead of the initial pipe surfaces as the base surfaces in constructing closings, so that the closing based algorithm of two steps (constructing a closing for each pipe and blending the closings) can G^1-continuously connect multiple parametric normal ringed surfaces with freeform directrices and variable radii. The basic theory of an auxiliary sphere tangent to the normal ringed surface is addressed. Either one or two (yielding more design parameters) auxiliary spheres can be added. How the parameters influence the closing configuration is discussed. In addition, the blending shape can be optimized by genetic algorithm after assigning some fiducial points on the blend. The enhanced algorithm is illustrated with four practical examples.