Curves and Surfaces
- 1st Edition - January 1, 1991
- Imprint: Academic Press
- Editors: Pierre-Jean Laurent, Alain Le Méhauté, Larry L. Schumaker
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 3 8 7 - 8
Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and… Read more
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Request a sales quoteCurves 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.
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
ω-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
- Edition: 1
- Published: January 1, 1991
- No. of pages (eBook): 532
- Imprint: Academic Press
- Language: English
- eBook ISBN: 9781483263878
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