Last edited by Kazile
Sunday, July 12, 2020 | History

6 edition of Designing Fair Curves and Surfaces found in the catalog.

Designing Fair Curves and Surfaces

Shape Quality in Geometric Modeling and Computer-Aided Design (Geometric Design Publication)

by Nickolas S. Sapidis

  • 70 Want to read
  • 24 Currently reading

Published by Society for Industrial Mathematics .
Written in English

    Subjects:
  • Algebraic geometry,
  • Mathematical modelling,
  • Mathematics for scientists & engineers,
  • General,
  • Curves, Algebraic,
  • Art & Art Instruction,
  • Computer Books: General,
  • Surfaces,
  • Design - General,
  • Computers / Computer Graphics / General,
  • Computer-aided design,
  • Data processing

  • The Physical Object
    FormatPaperback
    Number of Pages330
    ID Numbers
    Open LibraryOL8271789M
    ISBN 100898713323
    ISBN 109780898713329

      In order to construct more general curves and surfaces well, Li et al. also proposed a curve and surface fitting method based on the homogeneous linear differential system with variable coefficient matrix A(t) to be determined, i.e., (3) {d . Representation of Curves and Surfaces We first introduce three forms to represent geometric objects mathematically. They are the parametric, implicit and explicit forms. Implicit and explicit forms are often referred to as nonparametric forms. Then we briefly review the representation of curves and surfaces in Bézier and B-spline form and.

    Chapter 1 Parametrized curves and surfaces In this chapter the basic concepts of curves and surfaces are introduced, and examples are given. These concepts will be described as subsets of R2 or R3 with a given parametrization, but also as subsets defined by equations. The connection from equations to parametrizations is drawn by means of the. Geometry of Curves. Before a discussion of surfaces, curves in three dimensions will be covered for two reasons: surfaces are described by using certain special curves, and representations for curves generalize to representations for surfaces. Curves can be represented in three forms: implicit, explicit, and parametric.

    Sánchez-Reyes J and Chacón J () Hermite approximation for free-form deformation of curves and surfaces, Computer-Aided Design, , (), Online publication date: 1-May Wang D, Zhang W, Yang J and Wang Z () A virtual punching method for shape optimization of openings on curved panels using CAD-based Boolean operations. The use of curvature plots for the design of curves that have to meet aesthetic requirements is discussed. The aim is to emphasize the usefulness of curvature as a measure for curve fairness.


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Designing Fair Curves and Surfaces by Nickolas S. Sapidis Download PDF EPUB FB2

This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design.

This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design.

The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee. Designing Fair Curves and Surfaces: This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design.

in computer-aided graphic design and some knowledge of differential. Book Code: OT Pages: Buy the Print Edition. Fair curve and surface design system using tangent control. Proceedings Pacific Graphics ' Sixth Pacific Conference on Computer Graphics and Applications (Cat.

NoEX). Fast and Local Fairing of B-Spline Curves and Surfaces. Advances in Geometric Modeling and Processing, Designing Fair Curves and Surfaces > /ch5 Designing Fair Curves and Surfaces.

Most commercial surface modelers used today employ four-sided patches joined together in what is topologically equivalent to a rectangular grid (e.g., Catia™, Geomod™, Euclid™, STRIM™, etc.). This is due primarily to the convenience of generalizing curve definitions by incorporating two orthogonal parameters into one surface.

Designing Fair Curves and Surfaces Next Chapter > Table of Contents. Abstract; PDF Front Matter. This Chapter Appears in.

Title Information. Published: ISBN: eISBN: Book Code: OT Series: Other Titles in Applied Mathematics. Pages: Buy the Print Edition. The front matter includes the title page.

Creating aesthetically pleasing, fair curves and surfaces is a principal issue of Computer Aided Geometric Design (CAGD). It is especially so for automo-biles and other consumer goods, such as household appliances, where sales largely depend on the appearance of the products.

Using today's technol. A leading expert in CAGD, Gerald Farin covers the representation, manipulation, and evaluation of geometric shapes in this the Third Edition of Curves and Surfaces for Computer Aided Geometric Design.

The book offers an introduction to the field that emphasizes Bernstein-Bezier methods and presents subjects in an informal, readable style. In all other respects, it is, thankfully, the same. This means you get the informal, friendly style and unique approach that has made Curves and Surfaces for CAGD: A Practical Guide a true classic.

The book's unified treatment of all significant methods of curve and surface design is heavily focused on the movement from theory to application. *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis.

ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Sederberg T, Lin H and Li X () Curvature of singular Bézier curves and surfaces, Computer Aided Geometric Design,(), Online publication date: 1-May Walton D and Meek D Cubic Bézier spiral segments for planar G curve design Proceedings of the 7th International Conference on Computer Graphics, Virtual Reality.

Purchase Curves and Surfaces for Computer-Aided Geometric Design - 3rd Edition. Print Book & E-Book. ISBNThis volume contains recent results and new NURBS techniques and developments--the most important being curve/surface from the CAD/CAM industry.

The book has been carefully refereed. Researchers, system programmers, and graduate students in CAGD, CAD/CAM and computer graphics will find this book uniquely suited to their field of work. Get this from a library. Designing fair curves and surfaces: shape quality in geometric modeling and computer-aided design.

[Nickolas S Sapidis;]. Next: Bernstein polynomials Up: 1. Representation of Curves Previous: Analytic representation of Contents Index Bézier curves and surfaces Good introductory books on Bézier/B-spline curves and surfaces are provided by Faux and Pratt [], Mortenson [], Ding and Davies [75], Rogers and Adams [], Beach [21], Nowacki et al.

[] and Lee. of polynomial curves and surfaces is captured by the three words: Polarize,homogenize,tensorize. We will be dealing primarily with the following kinds of problems: • Approximating a shape (curve or surface).

We will see how this can be done using polynomial curves or surfaces (also called B´ezier curves or surfaces), spline curves or surfaces. When a book of any kind warrants a fifth edition, there must be more than just a few things right about it.

In the case of Curves and Surfaces for CAGD (Computer Aided Graphics and Design), Gerald Farin has written and maintained a definitive work on computer graphics and graphics programming. The fourth edition of this work was published in Reviews: 4. A plane curve is called fair if three conditions are satisfied: (1) the curve is of GC 2 –continuity, (2) there are no unwanted inflection-points on the curve, and (3) the curvature of the curve varies in an even manner.

The geometric spline and its approximate linearization of the first order, that is, the local cubic spline—including the. NURB Surface Curve With Faired Overlaid Curvature Curve. The top surface curve in figure 16 was faired to within units over a length of units.

This means that the user can accurately see changes in the curvature curve when the surface curve is moved by units. It first defines a base algorithm for fairing curves, which is then extended to the surface case, where the isocurves of the surface are faired.

The curve fairing process involves the discrete integration of a pseudo-arc-length parameterization of B-spline curves, with a blending and fitting phase concluding the algorithm.Definition of Bézier curve and its properties Algorithms for Bézier curves.

Bézier surfaces B-spline curves and surfaces B-splines B-spline curve Algorithms for B-spline curves. B-spline surface. Generalization of B-spline to NURBS2. Differential Geometry of Curves Arc length and tangent vector.A curve fairing method utilizing curvature plots is discussed.

Curvature analysis for surfaces is used to determine the fairness of surfaces and to measure the effects of different choices of twists for bicubic patches. Surface-surface intersections of parametric patches is an important topic in geometric modelling.