UID:
almahu_9948621355702882
Format:
XXXIX, 630 p.
,
online resource.
Edition:
1st ed. 2002.
ISBN:
9784431678816
Content:
Computer graphics, computer-aided design, and computer-aided manufacturing are tools that have become indispensable to a wide array of activities in contemporary society. Euclidean processing provides the basis for these computer-aided design systems although it contains elements that inevitably lead to an inaccurate, non-robust, and complex system. The primary cause of the deficiencies of Euclidean processing is the division operation, which becomes necessary if an n-space problem is to be processed in n-space. The difficulties that accompany the division operation may be avoided if processing is conducted entirely in (n+1)-space. The paradigm attained through the logical extension of this approach, totally four-dimensional processing, is the subject of this book. This book offers a new system of geometric processing techniques that attain accurate, robust, and compact computations, and allow the construction of a systematically structured CAD system.
Note:
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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9784431680079
Additional Edition:
Printed edition: ISBN 9784431703402
Additional Edition:
Printed edition: ISBN 9784431678823
Language:
English
DOI:
10.1007/978-4-431-67881-6
URL:
https://doi.org/10.1007/978-4-431-67881-6
