Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Local surface interpolation with Be´zier patches: errata and improvements
Computer Aided Geometric Design
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
An approximately G1 cubic surface interpolant
Mathematical methods in computer aided geometric design II
Design of solids with free-form surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Functional Optimization for Fair Surface Design
Functional Optimization for Fair Surface Design
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Blending, smoothing and interpolation of irregular meshes using N-sided Varady patches
Proceedings of the fifth ACM symposium on Solid modeling and applications
Scattered Data Techniques for Surfaces
Dagstuhl '97, Scientific Visualization
Generating symbolic interpolants for scattered data with normal vectors
Journal of Computer Science and Technology
PNG1 triangles for tangent plane continuous surfaces on the GPU
GI '08 Proceedings of graphics interface 2008
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A survey comparing methods for constructing smooth parametric surfaces to interpolate vertices and normal vectors of a triangulated polyhedron is presented. Particular attention is paid to the quality or fairness of the fit, measured by examining how curvature is distributed over the surface. The methods surveyed all generate surfaces composed of one or more surface patches per triangular facet of the input polyhedron. The approaches require an analysis of the number of constraints versus the number of degrees of freedom. Constraints include not only the interpolation conditions, but also continuity conditions imposed where adjacent surface patches abutt. Once the constraints are satisfied, there are generally surplus degrees of freedom. It is shown that the setting of these remaining free parameters can dramatically affect the shape of the surface, so the various methods are classified according to how they assign values to the free parameters.