Geometric Modeling, 3/e (Hardcover)
Michael Mortenson
- 出版商: Industrial Press, Inc.
- 出版日期: 2006-04-15
- 售價: $2,777
- 貴賓價: 9.5 折 $2,638
- 語言: 英文
- 頁數: 452
- 裝訂: Hardcover
- ISBN: 0831132981
- ISBN-13: 9780831132989
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商品描述
Overview
Completely updated to include the most recent developments in the field, the third edition like the two previous editions, emphasizes clarity and thoroughness in the mathematical development of its subjects. It is written in a style that is free of jargon of special applications, while integrating the three important functions of geometric modeling: to represent elementary forms (curves, surfaces, and solids), to shape and assemble these into complex forms, and to determine geometric properties and relationships. With hundreds of illustrations, this unique book appeals to the readers visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. Upper-division and graduate students, teachers, and professionals studying, teaching or practicing geometric modeling, 3D modeling, computational geometry, computer graphics applications, animation, CAD/CAM, and related subjects will find this to be a very valuable reference.
Table of Contents
Introduction
What is Geometric Modeling?
History
The Mathematics
Vectors
Matrices
Conventions and Notation
Curves
Intrinsic Equations of Curves
Explicit and Implicit Equations of Curves
Parametric Equations of Curves
Conic Curves
Points on a Curve
Hermite, Bezier, and B-Spline Curves: An Overview
Hermite Curves
Algebraic and Geomtric Forms
Hermite Basis Functions
Matrix Form
Tangent Vectors
Truncating and Subdividing
Three-Point Interpolation
Four-Point Interpolation
Conic Hermite Curves
Composite Hermite Curve
Bezier Curves
Bezier Basis Functions
Control Points
Truncating and Subdividing
Composite Bezier Curves
Rational Bezier Curves
B-Spline Curves
Nonuniform B-Spline Basis Functions
Uniform B-Spline Basis Functions
Quadratic and Cubic B-Spline Basis Functions
Closed B-Spline Curves
Continuity
Conversion between Basis Functions
Nonuniform Rational B-Spline Curves
Representing Conics with NURBS Curves
Cubic Beta Splines
Surfaces
Explicit and Implicit Equations of Surfaces
Quadric Surfaces
Parametric Equation of Surfaces
Points on a Surface
Curve Nets
Embedded Curves
Hermite, Bezier, and B-Spline Surfaces: An Overview
Bicubic Hermite Surfaces
Algebraic and Geometric Forms
Hermite Patch Basis Functions
Tangent and Twist Vectors
Normals
16-Point Form
Reparameterization of a Patch
Truncating and Subdividing a Patch
Composite Hermite Surfaces
Special Hermite Patches
Bend Surfaces
Bezier Surfaces
The Tensor Product Bezier Patch
The Bicubic Bezier Patch
A 3 x 5 Rectangular Array of Control Points
Converting between Bicubic Bezier and Hermite Forms
Degree Elevation in a Bezier Surface
Composite Bezier Surfaces
Rational Bezier Patch
B-Spline Surfaces
The Tensor Product B-Spline Surface
Matrix Form
Open and Closed B-Spline Surfaces
Nonuniform Rational B-Spline Surfaces
Solids
Parametric Solids
The Tricubic Solid
Curves and Surfaces Embedded in a Solid
Generalized Notation Scheme and Higher-Dimension Elements
Instances and Parameterized Shapes
Sweep Solids
Controlled Deformation Solids
Complex Model Construction
Topology of Models
Graph-Based Models
Boolean Models
Boolean Model Construction
Constructive Solid Geometry
Boundary Models
Geometric Properties
Local Properties of a Curve
Global Properties of a Curve
Global Properties of a Surface
Global Properties of Complex Solids
Relational Properties
Intersections
Answers to Selected Exercises
Index