Filling polygonal holes with rectangular patches
Theory and practice of geometric modeling
On the G2 continuity of piecewise parametric surfaces
Mathematical methods in computer aided geometric design II
Joining smooth patches around a vertex to form a Ck surface
Computer Aided Geometric Design
Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Curvature continuous interpolation of curve meshes
Computer Aided Geometric Design
G2 interpolation of free form curve networks by biquintic Gregory patches
Computer Aided Geometric Design - Special issue: in memory of John Gregory
Geometric criteria on the higher order smoothness of composite surfaces
Computer Aided Geometric Design
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
Computer Aided Geometric Design
A geometric criterion for smooth interpolation of curve networks
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
G2 tensor product splines over extraordinary vertices
SGP '08 Proceedings of the Symposium on Geometry Processing
A geometric constraint on curve networks suitable for smooth interpolation
Computer-Aided Design
| Hi-index | 0.00 |
Prescribing a network of curves to be interpolated by a surface model is a standard approach in geometric design. Where n curves meet, even when they afford a common normal direction, they need to satisfy an algebraic condition, called the vertex enclosure constraint, to allow for an interpolating piecewise polynomial C^1 surface. Here we prove the existence of an additional, more subtle constraint that governs the admissibility of curve networks for G^2 interpolation. Additionally, analogous to the first-order case but using the Monge representation of surfaces, we give a sufficient geometric, G^2 Euler condition on the curve network. When satisfied, this condition guarantees existence of an interpolating surface.