Bicubic patches for approximating non-rectangular control-point meshes
Computer Aided Geometric Design
G1 interpolation of generally unrestricted cubic Bézier curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Necessary and sufficient conditions for tangent plane continuity of Be´zier surfaces
Computer Aided Geometric Design
A G1 triangular spline surface of arbitrary topological type
Computer Aided Geometric Design
SIAM Journal on Numerical Analysis
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Interactive multiresolution surface viewing
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Interactive multi-resolution modeling on arbitrary meshes
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
Localized-hierarchy surface splines (LeSS)
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Polynomial Surfaces Interpolating Arbitrary Triangulations
IEEE Transactions on Visualization and Computer Graphics
Generating Sharp Features on Non-regular Triangular Meshes
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Generalized hierarchical NURBS for interactive shape modification
VRCAI '08 Proceedings of The 7th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry
High-order approximation of implicit surfaces by G1 triangular spline surfaces
Computer-Aided Design
Local and singularity-free G 1 triangular spline surfaces using a minimum degree scheme
Computing - Geometric Modelling, Dagstuhl 2008
Curvilinear constraints for free form deformations on subdivision surfaces
Mathematical and Computer Modelling: An International Journal
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Smooth parametric surfaces interpolating triangular meshes are very useful for modeling surfaces of arbitrary topology. Several interpolants based on these kind of surfaces have been developed over the last fifteen years. However, with current 3D acquisition equipments, models are becoming more and more complex. Since previous interpolation methods lack a local refinement property, there is no way to locally adapt the level of detail. In this article, we introduce a hierarchical triangular surface model. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent plane continuity. This model enables designers to create a complex smooth surface of arbitrary topology composed of a small number of patches to which details can be added by locally refining the patches until an arbitrary small size is reached. It is implemented as a hierarchical data structure where the top layer describes a coarse, smooth base surface and the lower levels encode the details in local frame coordinates.