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.

FEATURES
Describes and compares all the important mathematical methods for modeling curves, surfaces,
             and solids.
Prepares the reader for more advanced topics, such as 3D modeling, CAD/CAM, animation,
              and scientific visualization.
Incorporates references throughout the text to direct the reader to more specialized
               treatments of the subjects.
Carefully designed illustrations and exercises support each mathematical concept presented.
  Offers hundreds of exercises to test the readers comprehension.

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

Please Send Your Order To: R Krishnan

Manager (Information Products)

Allied Publishers Pvt Limited

751 Anna Salai, Chennai 600 002

Email: alliedpublishers@vsnl.com