Computer aided engineering design / Anupam Saxena, Birendra Sahay.

ForewordviiP
refaceix
Acknowledgementsxiii1.
Introduction11.1
Engineering Design 11.2
Computer as an Aid to the Design Engineer 21.2.1
Computer as a Participant in a Design Team 21.3
Computer Graphics 31.3.1
Graphics Systems and Hardware 41.3.2
Input Devices 41.3.3
Display and Output Devices 51.4
Graphics Standards and Software 61.5
Designer-Computer Interaction 71.6
Motivation and Scope 81.7
Computer Aided Mechanism and Machine Element Design 12Exercises 202.
Transformations and Projections232.1Definition 242.2
Rigid Body Transformations 242.2.1
Rotation in Two-Dimensions 252.2.2
Translation in Two-Dimensions: Homogeneous Coordinates 252.2.3
Combined Rotation and Translation 272.2.4
Rotation of a Point Q (xq,yq, 1) about a Point P (p,q, 1) 292.2.5
Reflection 292.2.6Reflection About an Arbitrary Line 302.2.7
Reflection through a Point 312.2.8
A Preservative for Angles! Orthogonal Transformation Matrices 322.3
Deformations 342.3.1
Scaling 342.3.2
Shear 352.4
Generic Transformation in Two-Dimensions 362.5
Transformations in Three-Dimensions 37
2.5.1Rotation in Three-Dimensions 372.5.2
Scaling in Three-Dimensions 402.5.3
Shear in Three-Dimensions 412.5.4
Reflection in Three-Dimensions 412.6
Computer Aided Assembly of Rigid Bodies 442.7
Projections 482.7.1
Geometry of Perspective Viewing 492.7.2
Two Point Perspective Projection 532.8
Orthographic Projections 542.8.1
Axonometric Projections 552.9
Oblique Projections 60Exercises 623.
Differential Geometry of Curves663.1
Curve Interpolation 673.2
Curve Fitting 703.3
Representing Curves 733.4
Differential Geometry of Curves 75
Exercises 824.
Design of Curves844.1
Ferguson’s or Hermite Cubic Segments 874.1.1
Composite Ferguson Curves 894.1.2
Curve Trimming and Re-parameterization 944.1.3
Blending of Curve Segments 964.1.4
Lines and Conics with Ferguson Segments 974.1.5
Need for Other Geometric Models for the Curve 1004.2
Three-Tangent Theorem 1014.2.1
Generalized de Casteljau’s Algorithm 1014.2.2
Properties of Bernstein Polynomials 1034.3
Barycentric Coordinates and Affine Transformation 1064.4
Bézier Segments 1074.4.1Properties of Bézier Segments 1094.4.2
Subdivision of a Bézier Segment 1134.4.3
Degree-Elevation of a Bézier Segment 1164.4.4
Relationship between Bézier and Ferguson Segments 1174.5
Composite Bézier Curves 1184.6
Rational Bézier Curves 121Exercises 1275.
Splines1305.1Definition 1305.2
Why Splines? 1325.3
Polynomial Splines 1325.4B-
Splines (Basis-Splines) 1365.5
Newton’s Divided Difference Method 1385.5.1
Divided Difference Method of Compute B-Spline Basis Functions 1415.6
Recursion Relation to Compute B-Spline Basis Functions 1435.6.1
Normalized B-Spline Basic Functions 145

xviCONTENTS
5.7Properties of Normalized B-Spline Basis Functions 1465.8B-
Spline Curves: Definition 1515.8.1
Properties of B-Spline Curves 1525.9
Design Features with B-Spline Curves 1555.10
Parameterization 1585.10.1 Knot Vector Generation 1595.11
Interpolation with B-Splines 1605.12
Non-Uniform Rational B-Splines (NURBS) 161Exercises 1626.
Differential Geometry of Surfaces1656.1Parametric Representation of Surfaces 1666.1.1
Singular Points and Regular Surfaces 1686.1.2
Tangent Plane and Normal Vector on a Surface 1696.2
Curves on a Surface 1716.3
Deviation of the Surface from the Tangent Plane: Second Fundamental Matrix 1736.4
Classification of Points on a Surface 1756.5
Curvature of a Surface: Gaussian and Mean Curvature 1786.6
Developable and Ruled Surfaces 1816.7
Parallel Surfaces 1856.8
Surfaces of Revolution 1886.9
Sweep Surfaces 1906.10
Curve of Intersection between Two Surfaces 193
Exercises 1977.
Design of Surfaces2017.1
Tensor Product Surface Patch 2027.1.1
Ferguson’s Bi-cubic Surface Patch 2037.1.2
Shape Interrogation 2067.1.3
Sixteen Point Form Surface Patch 2107.1.4
Bézier Surface Patches 2117.1.5
Triangular Surface Patch 2167.2
Boundary Interpolation Surfaces 2187.2.1
Coon’s patches 2197.3
Composite Surfaces 2267.3.1
Composite Ferguson’s Surface 2267.3.2
Composite Bézier Surface 2297.4B-
Spline Surface Patch 2417.5
Closed B-Spline Surface 2437.6
Rational B-spline Patches (NURBS) 244Exercises 2458.
Solid Modeling2478.1Solids 2478.2
Topology and Homeomorphism 2498.3
Topology of Surfaces 2518.3.1
Closed-up Surfaces 2518.3.2
Some Basic Surfaces and Classification
252CONTENTSxvii
8.4Invariants of Surfaces 2548.5
Surfaces as Manifolds 2558.6
Representation of Solids: Half Spaces 2568.7
Wireframe Modeling 2578.8Boundary Representation Scheme 2598.8.1
Winged-Edge Data Structure 2598.8.2
Euler-Poincaré Formula 2618.8.3Euler-Poincaré Operators 2638.9
Constructive Solid Geometry 2658.9.1Boolean Operations 2678.9.2
Regularized Boolean Operations 2688.10 Other Modeling Methods 2698.11
Manipulating Solids 271Exercises 2739. Computations for Geometric Design2759.1
Proximity of a Point and a Line 2759.2Intersection Between Lines 2779.2.1
Intersection Between Lines in Three-dimensions 2799.3Relation Between a Point and a Polygon 2809.3.1
Point in Polygon 2809.4
Proximity Between a Point and a Plane 2829.4.1
Point within a Polyhedron 2859.5
Membership Classification 2869.6
Subdivision of Space 2869.6.1
Quadtree Decomposition 2879.7
Boolean Operations on Polygons 2909.8
Inter Section Between Free Form Curves 292Exercises 29310.
Geometric Modeling Using Point Clouds29510.1
Reverse Engineering and its Ap
plications 29510.2
Point Cloud Acquisition 29610.3
Surface Modeling from a Point Cloud 29710.4
Meshed or Faceted Models 29810.5
Planar Contour Models 29910.5.1
Points to Contour Models 29910.6
Surface Models 30110.6.1
Segmentation and Surface Fitting for Prismatic Objects 30310.6.2
Segmentation and Surface Fitting for Freeform Shapes 30510.7
Some Examples of Reverse Engineering 30811.
Finite Element Method30911.1 Introduction 30911.2
Springs and Finite Element Analysis 31011.3
Truss Elements 31311.3.1
Transformations and Truss Element
315xviiiCONTENTS
11.4 Beam Elements 31811.5
Frame elements 32211.5.1
Frame Elements and Transformations 32411.6
Continuum Triangular Elements 32511.7
Four-Node Elements 331Exercises 33612.
Optimization33912.1 Classical Optimization 33912.2
Single Variable Optimization 33912.2.1
Bracketing Methods 34012.2.2
Open Methods 34512.3
Multivariable Optimization 34812.3.1
Classical Multivariable Optimization 34812.3.2
Constrained Multivariable Optimization 34912.3.3
Multivariable Optimization with Inequality Constraints 35312.3.4
Karush-Kuhn-Tucker (KKT) Necessary Conditions for Optimality 35512.4
Linear Programming 35912.4.1 Simple Method 36012.5
Sequential Linear Programming (SLP) 36312.6
Sequential Quadratic Programming (SQP) 36412.7
Stochastic Approaches (Genetic Algorithms and Simulated Annealing) 365Exercises 368
Appendix: Mesh Generation370
Suggested Projects378
Bibliography385
Index389
CONTENTS xix

Includes bibliographical references and index.