Computer Aided Geometric Design
Design of an n-sided surface patch from Hermite boundary data
Computer Aided Geometric Design
Survey and new results in n-sided patch generation
Proceedings on Mathematics of surfaces II
A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Generalized B-spline surfaces of arbitrary topology
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Overlap patches: a new scheme for interpolating curve networks with n-sided regions
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
A Practical Implementation of Vertex Blend Surfaces using an n-Sided Patch
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Transfinite Surface Interpolation
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Computer Aided Geometric Design
ACM SIGGRAPH 2003 Papers
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
Some negative results in N sided patches
Computer-Aided Design
Pointwise radial minimization: Hermite interpolation on arbitrary domains
SGP '08 Proceedings of the Symposium on Geometry Processing
Design-driven quadrangulation of closed 3D curves
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Transfinite surface interpolation with interior control
Graphical Models
Technical note: A technical note on the geometric representation of a ship hull form
Computer-Aided Design
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Transfinite surface interpolation is a classic topic of computer-aided geometric design (CAGD), and many non-quadrilateral schemes are known. Surfaces defined solely by means of their boundary curves and cross-tangent functions are needed, for example, in three-dimensional curve network-based design, and to fill complex irregular holes such as in vertex blending. This paper deals with interpolating so-called tangential ribbons. Former schemes are enhanced and extended in order to minimize shape artifacts and to provide a more natural patch interior. The proposed representation is based on irregular convex domains that correspond to the lengths and orientations of the boundary curves. The mapping of the individual ribbons within the n-sided domain is calculated by focused parameterization methods that ensure a balanced orientation related to the center of the domain and avoid parametric shearing. Distance-based blending functions ensure that modifying or inserting a small edge will have only a local effect over the n-sided patch. Constructions to create one-sided or two-sided patches are also presented. Examples and open research topics conclude the paper.