Curves and Surfaces

Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation.

Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Other chapters consider a nonparametric technique for estimating under random censorship the amplitude of a change point in change point hazard models. This book discusses as well the algorithm for ray tracing rational parametric surfaces based on inversion and implicitization. The final chapter deals with the results concerning the norm of the interpolation operator and error estimates for a square domain.

This book is a valuable resource for mathematicians.

Inhalt

Preface

Contributors

Parametrization for Data Approximation

A Vector Spline Approximation with Application to Meteorology

Kernel Estimation in Change-Point Hazard Rate Models

Spline Manifolds

Use of Simulated Annealing to Construct Triangular Facet Surfaces

G1 and G2 Continuity Between (SBR) Surfaces

Ray Tracing Rational Parametric Surfaces

Energy-Based Segmentation of Sparse Range Data

Error Estimates for Multiquadric Interpolation

A Geometrical Analysis for a Data Compression of 3D Anatomical Structures

Ck Continuity of (SBR) Surfaces

A Note on Piecewise Monotonie Bivariate Interpolation

Real-Time Signal Analysis with Quasi-Interpolatory Splines and Wavelets

Polynomial Expansions for Cardinal Interpolants and Orthonormal Wavelets

Realtime Pipelined Spline Data Fitting for Sketched Curves

Remarks on Digital Terrain Modelling Accuracy

Convexity and Bernstein-Bézier Polynomials

How to Draw a Curve Using Geometrical Data

The Generation of an Aerodynamical Propeller Using Partial Differential Equations

Fast Computation of Cross-Validated Robust Splines and Other Non-linear Smoothing Splines

Szasz-Mirakyan Quasi-Interpolants

Statistical Check on the Smoothing Parameter of a Method for Inversion of Fourier Series

A General Method of Treating Degenerate Bézier Patches

G1 Smooth Connection Between Rectangular and Triangular Bézier Patches at a Common Corner

Regularity Conditions for a Class of Geometrically Continuous Curves and Surfaces

Splines and Digital Signal Processing

B-Rational Curves and Surfaces, N-Rational Splines

Reparametrizations of Polynomial and Rational Curves

Numerical Stability of Geometric Algorithms

Solving Implicit ODEs by Simplicial Methods

On the Power of a posteriori Error Estimation for Numerical Integration and Function Approximation

Using the Refinement Equations for the Construction of Pre-Wavelets II: Powers of Two

Elastica and Minimal-Energy Splines

A Distributed Algorithm for Surface/Plane Intersection

Construction of Exponential Tension B-Splines of Arbitrary Order

On the Almost Sure Limit of Probabilistic Recovery

A New Curve Tracing Algorithm and Some Applications

Pseudo-Cubic Weighted Spline Can Be C2 or G2

Composite Cr-Triangular Finite Elements of PS Type on a Three Direction Mesh

Dynamic Segmentation: Finding the Edge with "Snake Splines"

Recent Developments in the Strang-Fix Theory for Approximation Orders

Aligning Frames with the Tangent Curve of a B-Spline Curve

Error Estimates for Interpolation by Generalized Splines

Varying the Shape Parameters of Rational Continuity

Detecting Cusps and Inflection Points in Curves

Image-Like Surfaces: Parallel Least Squares Approximation Methods

Local Kriging Interpolation: Application to Scattered Data on the Sphere

Best Approximation of Circle Segments by Quadratic Bézier Curves

A Procedure for Determining Starting Points for a Surface/Surface Intersection Algorithm

Norms of Inverses for Matrices Associated with Scattered Data

2D Sampling in Tomography

Subdividing Multivariate Polynomials over Simplices in Bernstein-Bézier Form Without de Casteljau Algorithm

Geometrically Smooth Interpolation by Triangular Bernstein-Bézier Patches with Coalescent Control Points

Curve Fitting Using NURBS

Univariate Multiquadric Interpolation: Some Recent Results

Periodic Spline Interpolation of Functions of Bounded Variation

Least Squares Fitting by Linear Splines on Data Dependent Triangulations

How to Build Quasi-Interpolants: Application to Polyharmonic B-Splines

Algorithms for Local Convexity of Bézier Curves and Surfaces

Polynomial N-Sided Patches

Cubic Recursive Division with Bounded Curvature

-Convergence, A Criterion for Linear Approximation

Bernstein-Type Quasi-Interpolants

Extension of the Problem of Best Interpolating Parametric Curves to L-Splines

Adaptive G1 Approximation of Range Data Using Triangular Patches

Universal Splines and Geometric Continuity

Procedural Construction of Patch-Boundary Curves

Efficient Computation of Multiple Knots Nonuniform Spline Functions

Chebyshev Approximation in Rn by Curves and Linear Manifolds

A Building Method for Hierarchical Covering Spheres of a Given Set of Points

The Variational Approach to Shape Preservation

Spline Fitting Numerous Noisy Data with Discontinuities

B-Spline Surfaces for Real-time Shape Design

Conversion of a Composite Trimmed Bézier Surface into Composite Bézier Surfaces

Multivariate Model Building with Additive, Interaction and Tensor Product Thin Plate Splines

Recursion Relations for 4x4 Determinants Related to Rational Cubic Bézier Curves

Lagrange Interpolation by Quadratic Splines on a Quadrilateral Domain of R2