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Geometric functions in computer aided geometric design

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    199_geometric_functions_ueaf
    Geometric functions in computer aided geometric design
    15333
    It is usual that existing material on computer aided geometric design oscillates between over-simplification for programmers and practitioners and over formalism for scientific or academic readers. The first type of publications suppresses the taxonomy and properties of the mathematical concepts discussed when seeking straightforward notation and procedures. The second type of materials in thorough in the mathematical concepts at the expense of increasingly complicated notation and sacrifice of clear procedures for the reader.This book intends to be a compromise between the aforementioned extremes. It recalls basic concepts on functions, relations, transformations, matrices and groups and makes evident their impact in the engineering properties of projections, rotations, translations, perspectives, and so on. The material is of interest for computer scientists and electrical, mechanical, production, mathematical and physics engineers. In particular, it gives valuable insight into robotics, computer vision, design, manufacturing, kinematics and dynamics from a practical point of view while keeping contact whit the underlying decisive mathematical properties of the objects and transformations handled.The exercises and examples discussed in this book were stated, solved, documented and illustrated under the supervision of professors Oscar Ruiz and Carlos Cadavid during the years 2004 to 2007. Scenarios for such a work were the courses introduction to CAD CAM Systems and Geometric Modeling and the activities in the CAD CAM CAE laboratory at EAFIT University.This book intends to be a compromise between the aforementioned extremes. It recalls basic concepts on functions, relations, transformations, matrices and groups and makes evident their impact in the engineering properties of projections, rotations, translations, perspectives, and so on. The material is of interest for computer scientists and electrical, mechanical, production, mathematical and physics engineers. In particular, it gives valuable insight into robotics, computer vision, design, manufacturing, kinematics and dynamics from a practical point of view while keeping contact whit the underlying decisive mathematical properties of the objects and transformations handled.The exercises and examples discussed in this book were stated, solved, documented and illustrated under the supervision of professors Oscar Ruiz and Carlos Cadavid during the years 2004 to 2007. Scenarios for such a work were the courses introduction to CAD CAM Systems and Geometric Modeling and the activities in the CAD CAM CAE laboratory at EAFIT University.The exercises and examples discussed in this book were stated, solved, documented and illustrated under the supervision of professors Oscar Ruiz and Carlos Cadavid during the years 2004 to 2007. Scenarios for such a work were the courses introduction to CAD CAM Systems and Geometric Modeling and the activities in the CAD CAM CAE laboratory at EAFIT University.

    Atributos LU

    AutorÓscar Ruiz
    Tabla de Contenido1 Introduction

    2 Basic concepts. Groups
    2.1 Functions
    2.2 Binary operations and Groups
    2.3 Square matrices
    2.4 The general linear group GL(n, R)
    2.5 The positive linear group (GL+(n,R)
    2.6 The orthogonal group 0(n)
    2.7 The Special orthogonal group SO(n)
    2.8 The group (X, 0)
    2.9 Transformations
    2.10 Affine Transformations
    2.11 Summary

    3 Property Invariance under geometric transformations
    3.1 Introduction
    3.2 Property Preservation in general transformations
    3.3 Property preservation in affine Functions
    3.4 Example. A linear transformation in R2
    3.5 Example. Non-linear transformation R2-R2
    3.6 Proposed exercise. Non linear transformations R2-R2
    3.7 Proposed exercise. Affine transformations R2-R2 Af f(2.R)
    3.8 Solvet exercises. Non-affine transformations R2-R2
    3.9 Homogeneous. Coodinates
    3.10 Coordinate Systems

    4 Rigid transformations in R3
    4.1 Definition- Rigid transformations
    4.2 Pure translations
    4.3 Pure rotations
    4.4 Eigenvalues and eigenvectors of R E SO(3)
    4.5 General rigid transformations using quaternions
    4.6 Solved and proposed exercises

    5 Non-rigid transformations and functions
    5.1 Non-rigid affine transformations
    5.2 Pseudo-affine Geometric –functions. Parallel projections
    5.3 Non-linear non-invertible functions. Perspective projections

    Bibliography
    TipoLibro
    ISXN9789587200164
    Año de Edición2008
    Núm. Páginas128
    Peso (Físico)250
    Tamaño (Físico)17 x 24 cm
    TítuloGeometric functions in computer aided geometric design

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