Surfaces in computer aided geometric design: A survey with new results

DOI10.1016/0167-8396(85)90002-0zbMath0597.65001OpenAlexW1971409998MaRDI QIDQ1079318

Robert E. Barnhill

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0167-8396(85)90002-0

zbMATH Keywords

interpolationbibliographyapproximationcomputer graphicssurfacescomputer aided geometric designcontouringBézier patchesCoons patchesdesign of surfacesmultidimensional surfacesopen research questionsrepresentation of surfacestriangular patches

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Multidimensional problems (41A63) Spline approximation (41A15) Graphical methods in numerical analysis (65S05)

Related Items (58)

Special issue: Radial basis functions and partial differential equations ⋮ Surfaces in computer aided geometric design: A survey with new results ⋮ Thin plate spline surface approximation using Coons' patches ⋮ Construction of polynomial preserving cochain extensions by blending ⋮ A survey of curve and surface methods in CAGD ⋮ Scattered data interpolation and approximation with error bounds ⋮ Generation of interpolation surfaces with the least strain energy using dynamic programming ⋮ The sphere as a rational Bézier surface ⋮ Interpolation over a sphere based upon a minimum norm network ⋮ Interpolation and approximation of 3-D and 4-D scattered data ⋮ Automatic smoothing with geometric surface patches ⋮ Conversion of a triangular Bézier patch into three rectangular Bézier patches ⋮ \(G^{2}\) interpolation of free form curve networks by biquintic Gregory patches ⋮ Surface design using triangular patches ⋮ Ensuring compatibility of \(G^{2}\)-continuous surface patches around a nodepoint ⋮ Multivariate interpolation of arbitrarily spaced data by moving least squares methods ⋮ Problems with defining barycentric coordinates for the sphere ⋮ Modeling contours of trivariate data ⋮ A trivariate Powell-Sabin interpolant ⋮ Geometric continuous patch complexes ⋮ Unnamed Item ⋮ Surface lofting and smoothing with skeletal-lines ⋮ Shape optimal design using B-splines ⋮ \(h\)-Bernstein basis functions over a triangular domain ⋮ Iterates of \(q\)-Bernstein operators on triangular domain with all curved sides ⋮ Bernstein-type operators on a triangle with all curved sides ⋮ Lupaş type Bernstein operators on triangle with one curve side ⋮ Bernstein-type operators on elliptic domain and their interpolation properties ⋮ On numerical quadrature for \(C^1\) quadratic Powell-Sabin 6-split macro-triangles ⋮ An efficient algorithm for subdividing linear Coons surfaces ⋮ Practical curves and surfaces for a geometric modeler ⋮ A local scheme for bivariate co-monotone interpolation ⋮ Recursive \(G^{k}\) transformations between adjacent Bézier surfaces ⋮ Smoothing of free-form surfaces with Bézier patches ⋮ \(GC^{n}\) continuity conditions for adjacent rational parametric surfaces ⋮ Triangulated Surface Denoising using High Order Regularization with Dynamic Weights ⋮ Interpolation on surfaces using minimum norm network ⋮ Interpolating scattered multivariate data as a function of time ⋮ Fat surfaces: A trivariate approach to triangle-based interpolation on surfaces ⋮ Bernstein-type operators on a triangle with one curved side ⋮ A rectangular \(G^{m}\)-continuous filling surface patch and some improvements at corners ⋮ Phillips-type \(q\)-Bernstein operators on triangles ⋮ A representation of a \(C^ 2\) interpolant over triangles ⋮ Scattered data interpolation based upon generalized minimum norm networks ⋮ Data-dependent triangulations for scattered data interpolation and finite element approximation ⋮ The intersection of a bicubic Bézier patch and a plane ⋮ Bayesian Multiscale Modeling of Closed Curves in Point Clouds ⋮ The convexity of quadratic parametric triangular Bernstein-Bézier surfaces ⋮ Overlap patches: a new scheme for interpolating curve networks with n- sided regions ⋮ Smooth interpolation over hypercubes ⋮ Design techniques for the definition of solid objects with free-form geometry ⋮ Surfaces defined on surfaces ⋮ A new quadratic and biquadratic algorithm for curve and surface estimation ⋮ Algorithms for ordering unorganized points along parametrized curves ⋮ Degree of simultaneous approximation of bivariate functions by Gordon operators ⋮ Smooth closed surfaces with discrete triangular interpolants ⋮ Increasing the smoothness of bicubic spline surfaces ⋮ Approximating potential integrals by cardinal basis interpolants on multivariate scattered data

Uses Software

• pchip

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Smooth interpolation in triangles
• A transfinite \(C^ 2\) interpolant over triangles
• Estimation of gradients from scattered data
• The convexity of Bernstein polynomials over triangles
• Three- and four-dimensional surfaces
• Multistage trivariate surfaces
• Smooth interpolation over hypercubes
• Properties of Shepard's surfaces
• An improved condition for the convexity of Bernstein-Bézier surfaces over triangles
• A trivariate Clough-Tocher scheme for tetrahedral data
• A discrete \(C^ 1\) interpolant for tetrahedral data
• Monotonicity preserving bicubic interpolation: A progress report
• Adaptive contouring of three-dimensional surfaces
• Geometric spline curves
• \(C^ 1\) surface interpolation for scattered data on a sphere
• Interpolation to boundary data on the simplex
• Increasing the smoothness of bicubic spline surfaces
• Derivative generation from multivariate scattered data by functional minimization
• A modified Clough-Tocher interpolant
• Thin plate splines with tension
• Surfaces in computer aided geometric design: A survey with new results
• A bivariate \(C^ 2\) Clough-Tocher scheme
• \(C^ 2\) interpolation over hypercubes
• A survey of curve and surface methods in CAGD
• \(C^ 1\) trivariate polynomial interpolation
• Interpolation remainder theory from Taylor expansions on triangles
• Sard kernel theorems on triangular domains with application to finite element error bounds
• Interpolation to boundary data in tetrahedra with applications to compatible finite elements
• The side-vertex method for interpolation in triangles
• A practical guide to splines
• Polynomial approximation on tetrahedrons in the finite element method
• A geometric interpretation of convexity conditions for surfaces
• Interpolation polynomials on the triangle
• A construction for visualC1 continuity of polynomial surface patches
• Monotone Piecewise Bicubic Interpolation
• Minimum Norm Interpolation in Triangles
• Scattered Data Interpolation: Tests of Some Method
• C1 quintic interpolation over triangles: Two explicit representations
• Piecewise Rational Quadratic Interpolation to Monotonic Data
• Polynomial Interpolation to Boundary Data on Triangles
• Computing Dirichlet Tessellations in the Plane
• Deriving the beta-constraints for geometric continuity of parametric curves
• Blending-Function Methods of Bivariate and Multivariate Interpolation and Approximation
• Interactive Interpolation and Approximation by Bezier Polynomials

This page was built for publication: Surfaces in computer aided geometric design: A survey with new results