Local smooth surface interpolation: A classification

DOI10.1016/0167-8396(90)90030-UzbMath0713.65003MaRDI QIDQ750074

Jörg Peters

Publication date: 1990

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

zbMATH Keywords

algorithmsweight functionspiecewise polynomialssplitting approachblending approachoriented tangent plane continuitysingle patch approachsmooth interpolating surfacesvertex enclosure problem

Mathematics Subject Classification ID

Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05)

Related Items

Degenerate polynomial patches of degree 4 and 5 used for geometrically smooth interpolation in \(\mathbb{R}^ 3\), Surface deformation with differential geometric structures, Constructive \(G^1\) connection of multiple freeform pipes in arbitrary poses, Unnamed Item, Reconstruction of quasi developable surfaces from ribbon curves, RAGS: rational geometric splines for surfaces of arbitrary topology, A weighted bivariate blending rational interpolation based on function values, Minimal energy surfaces using parametric splines, Recursive \(G^{k}\) transformations between adjacent Bézier surfaces, Smoothing of free-form surfaces with Bézier patches, Biquadratic G-spline surfaces, Construction of a VC1 interpolant over triangles via edge deletion, Point-normal interpolation schemes reproducing spheres, cylinders and cones, Smooth interpolation of a mesh of curves, Degenerate polynomial patches of degree 11 for almost \(GC^ 2\) interpolation over triangles, On degenerate surface patches

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Smooth interpolation in triangles
• Closed surfaces defined from biquadratic splines
• Smooth mesh interpolation with cubic patches
• Nonrectangular surface patches with curvature continuity
• A pentagonal surface patch for computer aided geometric design
• Piecewise algebraic surface patches
• Smooth closed surfaces with discrete triangular interpolants
• A modified Clough-Tocher interpolant
• \(G^ 1\) interpolation of generally unrestricted cubic Bézier curves
• Local surface interpolation with Bézier patches
• A \(C^ 2\) polygonal surface patch
• \(GC^ 1\) continuity conditions between adjacent rectangular and triangular Bézier surface patches
• The side-vertex method for interpolation in triangles
• Bicubic patches for approximating non-rectangular control-point meshes
• g-splines
• Piecewise Quadratic Approximations on Triangles