Computer-Aided Geometric Design: A Totally Four-Dimensional Approach

ISBN-13: 9784431703402 / Angielski / Twarda / 2002 / 630 str.

S. A. Gureev; F. Yamaguchi

Opis

Euclidean processing provides the basis for the computer-aided design systems that have become increasingly useful in computing. This book looks at n-space problems and four-dimensional processing, presenting a system of geometric processing techniques.

Spis treści

I Problem Definitions.- 1 Problems of Euclidean Approach.- 2 Homogeneous Coordinates.- 3 Classical Projective Space.- 4 Two-Sided Space.- 5 Processing in Projective Spaces.- 6 Transformations.- II Presentation of a Solution-Four-dimensional Processing-Four-dimensional Processing-.- 7 A Solution.- 8 Geometric Definitions in General.- 9 Geometric Element Definitions.- 10 Homogeneous Curves.- 11 Homogeneous Surfaces.- 12 Basic Intersections.- 13 4 × 4 Determinant Methods.- 14 The Homogeneous Determinant Method.- 15 Geometric Newton-Raphson Method.- 16 Exact Arithmetic.- 17 Fundamentals of Topology.- 18 Data Structures.- 19 Euclidean and Affine.- 20 Set Operations.- 21 Polyhedron Subdivisions.- 22 Reconstruction of 3-D Points.- 23 Display Process.- 24 Classical or Two-Sided ?.- III Test Results.- 25 Various Tests.- IV Conclusions.- 26 Evaluations.- 27 Role of Division Operations.- 28 Various Interpretations.- Afterword.- A Fundamentals on Euclidean Processing.- A.1.- A.2.- A.3.- A.4.- B Various Geometries.- C Plane Determinant Method.- C.1.- C.2.- C.3.- C.4.- C.5.- C.5.1.- C.5.2.- D Analytical Geometry in Vector Space.- D.1.- D.1.1.- D.1.2.- D.1.3.- D.2.- D.2.1.- E Proofs for Chapter 16.- E.1.- E.2.