2 edition of Approximation of curves and surfaces by algebraic curves and surfaces. found in the catalog.
Approximation of curves and surfaces by algebraic curves and surfaces.
Paul Althaus Smith
Written in English
Reprinted from the Annals of Mathematics, Vo. 27, No. 3, p. 224-244, 1926
|The Physical Object|
|Number of Pages||21|
Approximation of curves and surfaces is a basic problem in many areas such as simulation, computer graphics and geometric modeling. The approximate surface is often a triangulated surface, also known as a mesh. See the recent book  for an algorithmic perspective on meshing problems; chapter 5 in particular is a survey of meshing Size: 2MB. 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 File Size: 1MB.
Computer Aided Geometric Design 8 () 97 North-Holland Geometric Hermite approximation of surface patch intersection curves Thomas W. Sederberg and Tomoyuki Nishita Engineering Computer Graphics Lab., Brigham Young Universitv, Provo, UT , USA Received April Revised March Abstract Sederberg, T.W. and T. Nishita, Geometric Hermite approximation of surface Cited by: We introduce a new method that can be used for interpolation and approximation of curves, surfaces, and solids, as well as for blending and filling of surface holes. This procedure does not use parametric curves or surfaces, but algebraic or transcendental curves and surfaces.
Riemann Surfaces and Algebraic Curves - by Renzo Cavalieri September Email your librarian or administrator to recommend adding this book to your organisation's collection. Riemann Surfaces and Algebraic Curves. Renzo Cavalieri, Eric Miles; Online ISBN: Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category.
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APPROXIMATION OF CURVES AND SURFACES. in R', while the real part of the curve Pn (x, y) = 0 in R consists of a non-singular oval in (1,1) continuous correspondence with J, the distance between corresponding points being.
: Geometry and Interpolation of Curves and Surfaces (): McLeod, Robin J. Y., Baart, M. Louisa: BooksCited by: Therefore, many examples of algebraic curves are presented in the first chapters.
In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic by: In curve and surface fitting it can be essential to use the principle of uniform (Chebyshev) approximation.
We discuss the general problem of approximation by a parameterized curve, the special case of approximation by a straight line and as a generalization the approximation. algebraic curve of arbitrary degree is given by the Cayley-Riemanncriterion: a curve is rational ifand only if 9 = 0, where g, the genus ofthe curve is a measure of the deficiency of the curve's singularities from its maximum allowable limit .
The Problem Here we wish to consider all algebraic curves, and specifically of genus higher than zero. For. Therefore, many examples of algebraic curves are presented in the first chapters.
In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category.
Approximation of curves and surfaces is a basic problem in many areas such as simulation, computer graphics and geometric modeling. The approximate surface is often a triangulated surface, also known as a mesh.
See the recent book  for an algorithmic perspective on meshing problems. We focus on curves. Algebraic Geometry, book in progress This book covers the following topics: Elementary Algebraic Geometry, Dimension, Local Theory, Projective Geometry, Affine Schemes and Schemes in General, Tangent and Normal Bundles, Cohomology, Proper Schemes and Morphisms, Sheaves and Ringed Spaces.
Computing with Plane Algebraic Curves and Riemann Surfaces: The Algorithms of the Maple Package “Algcurves” Bernard Deconinck, Matthew S. Patterson Pages In this way, the book begins as a primer on Riemann surf The author of this monograph argues that algebraic curves are best encountered for alvebraic first time over the complex numbers, where the reader’s classical intuition about surfaces, integration, and.
Approximation of 3D surface-to-surface intersection curves. which involve free-form surfaces. This book provides the mathematical fundamentals as well as algorithms for various shape.
Algebraic Curves and Riemann Surfaces in Matlab DOI: /_3. In book: where the coefficients in the algebraic equation defining the curve are floating point numbers. Computational Methods for Algebraic Spline Surfaces ESF Exploratory Workshop.
Authors (view affiliations) A Recursive Taylor Method for Algebraic Curves and Surfaces. Huahao Shou, Ralph Martin, Guojin Wang, Adrian Bowyer, Irina Voiculescu Algebra Algebraic Geometry Approximation Theory Computer Aided Geometric Design Invariant Numerical.
Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann The author of this monograph argues that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts /5.
That is, they describe how to generate an ordered sequence of points along the curve or surface. We describe them as a mapping from the 1D or 2D parametric domain into the 2D or 3D affine space in which the curve or surface lies.
The general form for algebraic and parametric representations of curves and surfaces is summarized in the table below. Riemann Surfaces and Algebraic Curves A First Course in Hurwitz Theory. Get access. geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics.
This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Cited by: 6. Algebraic curves and compact Riemann surfaces comprise the most developed and arguably the most beautiful portion of algebraic geometry.
However, the majority of books written on the subject discuss algebraic curves and compact Riemann surfaces separately, as parts of. Rick Miranda's Algebraic Curves and Riemann Surfaces is a great place to look for a more complex analytic point of view. I think it starts from very little and only asks you know a bit of complex analysis.
See here for a review of this book by Gunning. As David Lehavi has already recommended in the comments, Herbert Clemens's A Scrapbook of Complex Curve Theory is a beautiful panorama into. The fitting of curves and surfaces through point clouds is discussed in the following papers: Best-Fit of Implicit Surfaces and Plane Curves by Ahn, Rauh, and Warnecke; A Scattered Data Approximation Scheme for the Detection of Fault Lines by Allasia, Besenghi, and De Rossi; Approximation Semi-Structured Data with Different Errors Using Support.
This text is an introduction to the theory of algebraic curves defined over the complex numbers. It begins with the definitions and first properties of Riemann surfaces, with special attention paid to the Riemann sphere, complex tori, hyperelliptic curves, smooth plane curves, and projective curves.
tion of implicit curves and surfaces, that is isotopic to the curve or surface itself. The algorithm is sim-ple and fast, and is among the rst to guarantee isotopy for implicit surface meshing. 1 Introduction Implicit functions provide a convenient repre-sentation of smooth surfaces.
However, piece-wise linear approximations are often required.Curves and surfaces: introduction Surfaces: implicit expression Like for curves, it is sometimes possible to deﬁne a surface by an equationF(x,y,z)=c. For example, the unit sphere of example 3 is given by the equationx2+y2+z2 =1and the cylinder of example 2 given byx2+y2 =1.
For curves like for surfaces, it will beFile Size: 1MB.+ of curves and surfaces , since it forms the basis for the new approx-imation technique. In section 3, the new concept is out-lined for curve approximation and applied to degree reduc-tion and offset approximation.
In section 4, we describe surface approximation and present some examples. Section 5 deals with curves on surfaces. It is.