Filling polygonal holes with rectangular patches
Theory and practice of geometric modeling
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Computer Aided Geometric Design
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
Triangular G1 interpolation by 4-splitting domain triangles
Computer Aided Geometric Design
Are isophotes and reflection lines the same?
Computer Aided Geometric Design - Pierre Bézier
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
C2 free-form surfaces of degree (3,5)
Computer Aided Geometric Design
Computer Aided Geometric Design
A geometric criterion for smooth interpolation of curve networks
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Bicubic G1 interpolation of irregular quad meshes using a 4-split
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Constraints on curve networks suitable for G2 interpolation
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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We present a new method for generating a G^n-surface from a triangular network of compatible surface strips. The compatible surface strips are given by a network of polynomial curves with an associated implicitly defined surface, which fulfill certain compatibility conditions. Our construction is based on a new concept, called bubble patches, to represent the single surface patches. The compatible surface strips provide a simple G^n-condition between two neighboring bubble patches, which are used to construct surface patches, connected with G^n-continuity. For n@?2, we describe the obtained G^n-condition in detail. It can be generalized to any n=3. The construction of a single surface patch is based on Gordon-Coons interpolation for triangles. Our method is a simple local construction scheme, which works uniformly for vertices of arbitrary valency. The resulting surface is a piecewise rational surface, which interpolates the given network of polynomial curves. Several examples of G^0, G^1 and G^2-surfaces are presented, which have been generated by using our method. The obtained surfaces are visualized with reflection lines to demonstrate the order of smoothness.