Bézier and B-spline techniques

Wolfgang Boehm, Hartmut Prautzsch, Marco Paluszny

Publication date: 10 September 2002

Published in: Mathematics and Visualization (Search for Journal in Brave)

interpolation computer-aided geometric design box splines multivariate splines B-spline representation tensor product surfaces simplex splines Bézier representation uniform subdivision Bézier and B-spline curves and surfacse parametric curves and surfaces

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical interpolation (65D05) Spline approximation (41A15) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items

A bounded scheme based on Bézier curves for convection-dominated transport problems, Model-driven identification framework for optimal constitutive modeling from kinematics and rheological arrangement, Parameter estimation for models of chemical reaction networks from experimental data of reaction rates, A fuzzy particle swarm optimization method with application to shape design problem, Geometric Hermite interpolation in \(\mathbb{R}^n\) by refinements, Auxiliary splines space preconditioning for B-splines finite elements: the case of \(\boldsymbol{H}(\boldsymbol{curl},\Omega)\) and \(\boldsymbol{H}(div,\Omega)\) elliptic problems, Surface reconstruction using simplex splines on feature-sensitive configurations, Computational electromagnetism by the method of least action, A family of \(C^1\) quadrilateral finite elements, Infinite Exchangeability for Sets of Desirable Gambles, Minimal bi-6 \(G^2\) completion of bicubic spline surfaces, Refinable \(C^1\) spline elements for irregular quad layout, Non-stationary versions of fixed-point theory, with applications to fractals and subdivision, Gains from switching and evolutionary stability in multi-player matrix games, Generalized \(C^1\) Clough-Tocher splines for CAGD and FEM, A generalized mean value property for polyharmonic functions, Degree reduction of rational Bézier curves by hybrid optimization method, The best uniform quadratic approximation of circular arcs with high accuracy, The conversion matrix between uniform B-spline and Bézier representations, Sleves for planar spline curves, Collisions of electrons with hydrogen atoms II. Low-energy program using the method of the exterior complex scaling, Curve approximation by adaptive neighborhood simulated annealing and piecewise Bézier curves, On multiple roots in Descartes' rule and their distance to roots of higher derivatives, TDHB-splines: the truncated decoupled basis of hierarchical tensor-product splines, Derivatives of isogeometric functions on \(n\)-dimensional rational patches in \(\mathbb R^d\), An approximate characterisation of the set of feasible trajectories for constrained flat systems, Quadratic quadrature formula for curves with third degree of exactness, Overlapping multi-patch structures in isogeometric analysis, Global detection of salient convex boundaries, Exchangeable lower previsions, Biquintic \(G^2\) surfaces via functionals, B-spline-like bases for \(C^2\) cubics on the Powell-Sabin 12-split, Geometric approximation of the sphere by triangular polynomial spline patches, \(h\)-Bernstein basis functions over a triangular domain, Stability results for Gabor frames and the \(p\)-order hold models, Analytical modeling of active magnetic bearing geometry, Construction of Smooth Isogeometric Function Spaces on Singularly Parameterized Domains, A behavioural justification for using sensitivity analysis in imprecise multinomial processes, Shape optimisation with multiresolution subdivision surfaces and immersed finite elements, Probabilistic auto-associative models and semi-linear PCA, Refinable tri-variate \(C^1\) splines for box-complexes including irregular points and irregular edges, Using low-rank approximations of gridded data for spline surface fitting, A local simplex Spline basis for \(C^3\) quartic splines on arbitrary triangulations, Guided spline surfaces, Multidimensional spline integration of scattered data, Existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis, On the complexity of smooth spline surfaces from quad meshes, On transfinite interpolations with respect to convex domains, Polynomial splines as examples of Chebyshevian splines, Exchangeability and sets of desirable gambles, Optimal control of the self-bound dipolar droplet formation process, Subdivision-stabilised immersed b-spline finite elements for moving boundary flows, Learning mixtures of polynomials of multidimensional probability densities from data using B-spline interpolation, The Bernstein polynomial basis: a centennial retrospective, Fair free-form surfaces that are almost everywhere parametrically \(C^2\), Numerical simulation of multiple 3D fracture propagation using arbitrary meshes, Extended SQ-Coons surface and its application on fairing automobile surface design, Isogeometric analysis using T-splines, Strongly stable bases for adaptively refined multilevel spline spaces, Immersed b-spline (i-spline) finite element method for geometrically complex domains, Super-smooth cubic Powell-Sabin splines on three-directional triangulations: B-spline representation and subdivision, Treatment of general domains in two space dimensions in a Partition of Unity Method, A construction of edge B-spline functions for a \(C^1\) polynomial spline on two triangles and its application to Argyris type splines, Smooth multi-patch discretizations in isogeometric analysis, Copula theory and probabilistic sensitivity analysis: is there a connection?, Construction of approximate \(C^1\) bases for isogeometric analysis on two-patch domains, An \(\mathcal{O}(p^3)\) \(hp\)-version FEM in two dimensions: preconditioning and post-processing, An iterative technique for the numerical solution of nonlinear stochastic Itô-Volterra integral equations, Hermite mean value interpolation on polygons, Stable simplex spline bases for \(C^3\) quintics on the Powell-Sabin 12-split, Matrix methods for the tensorial Bernstein form, Dimension of \(C^1\)-splines on type-6 tetrahedral partitions, Calculation of the interface curvature and normal vector with the level-set method, Multi-fidelity deep neural network surrogate model for aerodynamic shape optimization, Set-valued Hermite interpolation, 𝑝-Riesz bases in quasi shift invariant spaces, Polygonal Spline Spaces and the Numerical Solution of the Poisson Equation, Bivariate B-splines from convex configurations, Smooth shapes with spherical topology: beyond traditional modeling, efficient deformation, and interaction, Attractors of trees of maps and of sequences of maps between spaces with applications to subdivision, On estimation and inference in latent structure random graphs, Composite \(\sqrt{2}\) subdivision surfaces, On the completeness of hierarchical tensor-product image-splines, Extracting information about the rotator cuff from magnetic resonance images using deterministic and random techniques, Bounding the influence of domain parameterization and knot spacing on numerical stability in isogeometric analysis, Bayesian Survival Analysis Using Bernstein Polynomials, Non-stationary subdivision schemes: state of the art and perspectives, Modelling orientation trajectories, Fast construction of constant bound functions for sparse polynomials, Adaptive quasi-interpolating quartic splines, Solving Linear Systems with Polynomial Parameter Dependency with Application to the Verified Solution of Problems in Structural Mechanics, An effective bound on the gap between the control polytype and the graph of a real polynomial on a simplex, Construction of \(C^2\) cubic splines on arbitrary triangulations, Quadrilateral orbifold splines, Simplex-splines on the Clough-Tocher split with arbitrary smoothness, THB-spline approximations for turbine blade design with local B-spline approximations, A new hybrid method for shape optimization with application to semiconductor equations, Quasi-interpolation by quadratic piecewise polynomials in three variables, Functional Ross recovery: theoretical results and empirical tests, U-splines: splines over unstructured meshes, An approximate \(C^1\) multi-patch space for isogeometric analysis with a comparison to Nitsche's method, Nonparametric estimation of marginal effects in regression-spline random effects models, Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints, Imprecise Bernoulli Processes, Detecting symmetries in polynomial Bézier curves