Skinning techniques for interactive B-spline surface interpolation
Computer-Aided Design
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
The NURBS book
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Interpolating nets of curves by smooth subdivision surfaces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Recursive subdivision of polygonal complexes and its applications in computer-aided geometric design
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Dynamic Catmull-Clark Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
Generating subdivision surfaces from profile curves
Computer-Aided Design
SMI 2012: Full Interpolating an arbitrary number of joint B-spline curves by Loop surfaces
Computers and Graphics
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This paper presents a novel method for defining a Loop subdivision surface interpolating a set of popularly-used cubic B-spline curves. Although any curve on a Loop surface corresponding to a regular edge path is usually a piecewise quartic polynomial curve, it is found that the curve can be reduced to a single cubic B-spline curve under certain constraints of the local control vertices. Given a set of cubic B-spline curves, it is therefore possible to define a Loop surface interpolating the input curves by enforcing the interpolation constraints. In order to produce a surface of local or global fair effect, an energy-based optimization scheme is used to update the control vertices of the Loop surface subjecting to curve interpolation constraints, and the resulting surface will exactly interpolate the given curves. In addition to curve interpolation, other linear constraints can also be conveniently incorporated. Because both Loop subdivision surfaces and cubic B-spline curves are popularly used in engineering applications, the curve interpolation method proposed in this paper offers an attractive and essential modeling tool for computer-aided design.