اسم المؤلف
Anupam Saxena, Birendra Sahay
التاريخ
25 يونيو 2019
المشاهدات
257
التقييم
(لا توجد تقييمات)

Computer Aided Engineering Design
Anupam Saxena, Birendra Sahay
Department of Mechanical Engineering
Indian Institute of Technology Kanpur, India
Contents
Foreword vii
Preface ix
Acknowledgements xiii
1. Introduction 1
1.1 Engineering Design 1
1.2 Computer as an Aid to the Design Engineer 2
1.2.1 Computer as a Participant in a Design Team 2
1.3 Computer Graphics 3
1.3.1 Graphics Systems and Hardware 4
1.3.2 Input Devices 4
1.3.3 Display and Output Devices 5
1.4 Graphics Standards and Software 6
1.5 Designer-Computer Interaction 7
1.6 Motivation and Scope 8
1.7 Computer Aided Mechanism and Machine Element Design 12
Exercises 20
2. Transformations and Projections 23
2.1 Definition 24
2.2 Rigid Body Transformations 24
2.2.1 Rotation in Two-Dimensions 25
2.2.2 Translation in Two-Dimensions: Homogeneous Coordinates 25
2.2.3 Combined Rotation and Translation 27
2.2.4 Rotation of a Point Q (xq, yq, 1) about a Point P (p, q, 1) 29
2.2.5 Reflection 29
2.2.6 Reflection About an Arbitrary Line 30
2.2.7 Reflection through a Point 31
2.2.8 A Preservative for Angles! Orthogonal Transformation Matrices 32
2.3 Deformations 34
2.3.1 Scaling 34
2.3.2 Shear 35
2.4 Generic Transformation in Two-Dimensions 36
2.5 Transformations in Three-Dimensions 372.5.1 Rotation in Three-Dimensions 37
2.5.2 Scaling in Three-Dimensions 40
2.5.3 Shear in Three-Dimensions 41
2.5.4 Reflection in Three-Dimensions 41
2.6 Computer Aided Assembly of Rigid Bodies 44
2.7 Projections 48
2.7.1 Geometry of Perspective Viewing 49
2.7.2 Two Point Perspective Projection 53
2.8 Orthographic Projections 54
2.8.1 Axonometric Projections 55
2.9 Oblique Projections 60
Exercises 62
3. Differential Geometry of Curves 66
3.1 Curve Interpolation 67
3.2 Curve Fitting 70
3.3 Representing Curves 73
3.4 Differential Geometry of Curves 75
Exercises 82
4. Design of Curves 84
4.1 Ferguson’s or Hermite Cubic Segments 87
4.1.1 Composite Ferguson Curves 89
4.1.2 Curve Trimming and Re-parameterization 94
4.1.3 Blending of Curve Segments 96
4.1.4 Lines and Conics with Ferguson Segments 97
4.1.5 Need for Other Geometric Models for the Curve 100
4.2 Three-Tangent Theorem 101
4.2.1 Generalized de Casteljau’s Algorithm 101
4.2.2 Properties of Bernstein Polynomials 103
4.3 Barycentric Coordinates and Affine Transformation 106
4.4 Bézier Segments 107
4.4.1 Properties of Bézier Segments 109
4.4.2 Subdivision of a Bézier Segment 113
4.4.3 Degree-Elevation of a Bézier Segment 116
4.4.4 Relationship between Bézier and Ferguson Segments 117
4.5 Composite Bézier Curves 118
4.6 Rational Bézier Curves 121
Exercises 127
5. Splines 130
5.1 Definition 130
5.2 Why Splines? 132
5.3 Polynomial Splines 132
5.4 B-Splines (Basis-Splines) 136
5.5 Newton’s Divided Difference Method 138
5.5.1 Divided Difference Method of Compute B-Spline Basis Functions 141
5.6 Recursion Relation to Compute B-Spline Basis Functions 143
5.6.1 Normalized B-Spline Basic Functions 145
xvi CONTENTS5.7 Properties of Normalized B-Spline Basis Functions 146
5.8 B-Spline Curves: Definition 151
5.8.1 Properties of B-Spline Curves 152
5.9 Design Features with B-Spline Curves 155
5.10 Parameterization 158
5.10.1 Knot Vector Generation 159
5.11 Interpolation with B-Splines 160
5.12 Non-Uniform Rational B-Splines (NURBS) 161
Exercises 162
6. Differential Geometry of Surfaces 165
6.1 Parametric Representation of Surfaces 166
6.1.1 Singular Points and Regular Surfaces 168
6.1.2 Tangent Plane and Normal Vector on a Surface 169
6.2 Curves on a Surface 171
6.3 Deviation of the Surface from the Tangent Plane: Second Fundamental Matrix 173
6.4 Classification of Points on a Surface 175
6.5 Curvature of a Surface: Gaussian and Mean Curvature 178
6.6 Developable and Ruled Surfaces 181
6.7 Parallel Surfaces 185
6.8 Surfaces of Revolution 188
6.9 Sweep Surfaces 190
6.10 Curve of Intersection between Two Surfaces 193
Exercises 197
7. Design of Surfaces 201
7.1 Tensor Product Surface Patch 202
7.1.1 Ferguson’s Bi-cubic Surface Patch 203
7.1.2 Shape Interrogation 206
7.1.3 Sixteen Point Form Surface Patch 210
7.1.4 Bézier Surface Patches 211
7.1.5 Triangular Surface Patch 216
7.2 Boundary Interpolation Surfaces 218
7.2.1 Coon’s patches 219
7.3 Composite Surfaces 226
7.3.1 Composite Ferguson’s Surface 226
7.3.2 Composite Bézier Surface 229
7.4 B-Spline Surface Patch 241
7.5 Closed B-Spline Surface 243
7.6 Rational B-spline Patches (NURBS) 244
Exercises 245
8. Solid Modeling 247
8.1 Solids 247
8.2 Topology and Homeomorphism 249
8.3 Topology of Surfaces 251
8.3.1 Closed-up Surfaces 251
8.3.2 Some Basic Surfaces and Classification 252
CONTENTS xvii8.4 Invariants of Surfaces 254
8.5 Surfaces as Manifolds 255
8.6 Representation of Solids: Half Spaces 256
8.7 Wireframe Modeling 257
8.8 Boundary Representation Scheme 259
8.8.1 Winged-Edge Data Structure 259
8.8.2 Euler-Poincaré Formula 261
8.8.3 Euler-Poincaré Operators 263
8.9 Constructive Solid Geometry 265
8.9.1 Boolean Operations 267
8.9.2 Regularized Boolean Operations 268
8.10 Other Modeling Methods 269
8.11 Manipulating Solids 271
Exercises 273
9. Computations for Geometric Design 275
9.1 Proximity of a Point and a Line 275
9.2 Intersection Between Lines 277
9.2.1 Intersection Between Lines in Three-dimensions 279
9.3 Relation Between a Point and a Polygon 280
9.3.1 Point in Polygon 280
9.4 Proximity Between a Point and a Plane 282
9.4.1 Point within a Polyhedron 285
9.5 Membership Classification 286
9.6 Subdivision of Space 286
9.7 Boolean Operations on Polygons 290
9.8 Inter Section Between Free Form Curves 292
Exercises 293
10. Geometric Modeling Using Point Clouds 295
10.1 Reverse Engineering and its Applications 295
10.2 Point Cloud Acquisition 296
10.3 Surface Modeling from a Point Cloud 297
10.4 Meshed or Faceted Models 298
10.5 Planar Contour Models 299
10.5.1 Points to Contour Models 299
10.6 Surface Models 301
10.6.1 Segmentation and Surface Fitting for Prismatic Objects 303
10.7 Some Examples of Reverse Engineering 308
11. Finite Element Method 309
11.1 Introduction 309
11.2 Springs and Finite Element Analysis 310
11.3 Truss Elements 313
11.3.1 Transformations and Truss Element 315
xviii CONTENTS11.4 Beam Elements 318
11.5 Frame elements 322
11.5.1 Frame Elements and Transformations 324
11.6 Continuum Triangular Elements 325
11.7 Four-Node Elements 331
Exercises 336
12. Optimization 339
12.1 Classical Optimization 339
12.2 Single Variable Optimization 339
12.2.1 Bracketing Methods 340
12.2.2 Open Methods 345
12.3 Multivariable Optimization 348
12.3.1 Classical Multivariable Optimization 348
12.3.2 Constrained Multivariable Optimization 349
12.3.3 Multivariable Optimization with Inequality Constraints 353
12.3.4 Karush-Kuhn-Tucker (KKT) Necessary Conditions for Optimality 355
12.4 Linear Programming 359
12.4.1 Simple Method 360
12.5 Sequential Linear Programming (SLP) 363
12.6 Sequential Quadratic Programming (SQP) 364
12.7 Stochastic Approaches (Genetic Algorithms and Simulated Annealing) 365
Exercises 368
Appendix: Mesh Generation 370
Suggested Projects 378
Bibliography 385
Index
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