Last edited by Mahn
Saturday, August 1, 2020 | History

3 edition of An algorithm for surface smoothing with rational splines found in the catalog.

An algorithm for surface smoothing with rational splines

# An algorithm for surface smoothing with rational splines

Subjects:
• Splines.,
• Spline theory.

• Edition Notes

The Physical Object ID Numbers Statement James R. Schiess. Series NASA technical paper -- 2708. Contributions United States. National Aeronautics and Space Administration. Scientific and Technical Information Office. Format Microform Pagination 1 v. Open Library OL14663390M

arbitrary k, and use B-spline patches with degree which increases rapidly with k. Instead of specifying a continuity class (and letting degree adapt as necessary), Prautzsch [] also described a ‘midpoint’ scheme which can generate B-spline patches of a speciﬁed degree. The rules for this scheme generalize the averaging algorithm described. The remaining chapters discuss the principles of multiresolution analysis, NURBS, offsets, radial basis functions, rational splines, robotics, spline and Bézier methods for curve and surface modeling, subdivision, terrain modeling, and wavelets. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

This paper is to provide literature review of the Non Uniform Rational B-Splines (NURBS) formulation in the curve and surface constructions. NURBS curves and surfaces have a wide application in Computer Aided Geometry Design (CAGD), Computer Aided Design (CAD), image processing and etc. The formulation of NURBS showing that NURBS curves and surfaces requires three important parameters . An Expansion of the Derivation of the Spline Smoothing Theory Alan Kaylor Cline The classic paper "Smoothing by Spline Functions", Numerische Mathema () by Christian Reinsch showed that natural cubic splines were the solutions to a novel formulation of the data smoothing .

Splines are smooth piecewise polynomials that can be used to represent functions over large intervals, where it would be impractical to use a single approximating polynomial. The spline functionality includes a graphical user interface (GUI) that provides easy access to functions for creating, visualizing, and manipulating splines. Non-uniform rational Basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces. It offers great flexibility and precision for handling both analytic (surfaces defined by common mathematical formulae) and modeled shapes. NURBS are commonly used in computer-aided design (CAD), manufacturing (CAM), and engineering .

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### An algorithm for surface smoothing with rational splines Download PDF EPUB FB2

Non-uniform rational basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces. It offers great flexibility and precision for handling both analytic (surfaces defined by common mathematical formulae) and modeled are commonly used in computer-aided design (), manufacturing (), and engineering.

Get this from a library. An algorithm for surface smoothing with rational splines. [James R Schiess; United States. National Aeronautics and Space Administration.

An algorithm for surface smoothing with rational splines [microform] / James R. Schiess National Aeronautics and Space Administration, Scientific and Technical Information Office ; For sale by the National Technical Information Service] [Washington, D.C.]: [Springfield, Va Australian/Harvard Citation.

Schiess, James R. & United States. It describes a numerical algorithm utilizing Non-Uniform Rational B-Splines (NURBS) surfaces to generate smooth triangulated surface patches for topologically simple holes on discrete surface.

The book focuses on the core concepts of Computer-aided Geometric Design (CAGD) with the intent to provide a clear and illustrative presentation of the basic principles as well as a treatment of advanced material, including multivariate splines, some subdivision techniques and constructions of arbitrarily smooth free-form surfaces.

Smoothing Splines The intuition behind smoothing splines is to cut Y’s domain into partitions over which the algorithm computes a spline, which are joined at intersections called knots. These splines are piecewise polynomials that are typically restricted to being smooth at these knots such that the “knotty-ness” is unobservable to the.

A paper of mine, presented during the Summer of at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design.

For many, B-splines, rational B-splines, and NURBS have been a. An arc spline is formed from straight line segments and circular arcs [4, 6, 8]. In ] a quadratic NURBS (nonuniform rational B-spline) curve is approximated by an arc spline. In this paper, the problem of approximating a segment of a more general smooth curve is discussed.

A smooth curve will be taken to mean a curve with continuous third. A Bézier curve (/ ˈ b ɛ z. eɪ / BEH-zee-ay) is a parametric curve used in computer graphics and related fields. The curve, which is related to the Bernstein polynomial, is named after Pierre Bézier, who used it in the s for designing curves for the bodywork of Renault cars.

Other uses include the design of computer fonts and animation. Bézier curves can be combined to form a. Frequently, computational inefficiencies are accepted if the resulting algorithm more closely follows the discussion in the text. An example is the B-spline surface algorithm bsplsurf.c.

In the C implementation given below, the B-spline basis functions for each parameter value are calculated inside the main loop. This reduces memory requirements.

B-spline: Knot Sequences • Even distribution of knots – uniform B-splines – Curve does not interpolate end points • first blending function not equal to 1 at t=0 • Uneven distribution of knots – non-uniform B-splines – Allows us to tie down the endpoints by repeating knot values (in Cox-deBoor, 0/0=0).

“NURBS” are currently seen as the most promising curve- and surface-form in CAD/CAM-applications. Rational Bezier-surfaces are special non-uniform rational B-Splines.

In this paper we describe a calculus of variation approach to design the weights of a rational surface in a way to achieve a smooth surface in the sense of an energy integral.

As an example, the geometric points of five representative sections of the roadarm (Figure c) are selected and fitted with B-spline curves (Figure ).Following the surface skinning technique (Tang and Chang ), an outer polygon surface formed by 6 × 5 control points and the enclosed B-spline surface are created (Figure a).).

Similarly, an inner B-spline surface (4 × 3. A smooth rational spline for visualizing monotone data. IEEE International Conference on Information Visualization (Cat.

PR), Rational spline interpolation preserving the shape of the monotonic data. Tiller has generalized this algorithm to rational B-spline curves in a way that preserves the simplicity of the algorithm but does not guarantee that the surface will be as smooth as the generator.

B-splines 60 A recursive deﬁnition of B-splines 61 The de Boor algorithm 63 The main theorem in its general form 65 Derivatives and smoothness 67 B-spline properties 68 Conversion to B-spline form 69 The complete de Boor algorithm 70 Conversions between B´ezier and B-spline representations Fast Compact Algorithms and Software for Spline Smoothing investigates algorithmic alternatives for computing cubic smoothing splines when the amount of smoothing is determined automatically by minimizing the generalized cross-validation score.

These algorithms are based on Cholesky factorization, QR factorization, or the fast Fourier transform. Spline screw payload fastening system [microform] / inventor, John M.

Vranish Two-dimensional splines [microform] / by Florencio I. Utreras An algorithm for surface smoothing with rational splines [microform] / James R. Schiess.

Spline; de Boor's algorithm; Subdivision surface; Triangle mesh; Point cloud; Rational Motion References. Les Piegl & Wayne Tiller: The NURBS Book, Springer-Verlag – (2nd ed.).

The main reference for Bézier, B-Spline and NURBS; chapters on mathematical representation and construction of curves and surfaces, interpolation, shape. Paul Dierckx, A Fast Algorithm for Smoothing Data on a Rectangular Grid while Using Spline Functions, SIAM Journal on Numerical Analysis, /, 19, 6, (), ().

Crossref M. Casey, Numerical analysis of X-ray texture data: An implementation in fortran allowing triclinic or axial specimen symmetry and most crystal symmetries. The structure and usage of these libraries is discussed in the final chapter, and the book is invaluable for the user of these libraries.

Most of the work is based on the use of standard B-splines to fit to data sets, using least squares and smoothing algorithms. () Smoothing scattered data with a monotone Powell-Sabin spline surface. Numerical Algorithms() Curve interpolation with constrained length. The second approach is based on scheduling the spline parameter to accurately yield the desired arc displacement (hence feed rate), either by approximation of the relationship between the arc length and the spline parameter with a feed correction polynomial, or by solving the spline parameter iteratively in real-time at each interpolation step.