Geometry for naval architects [electronic book] / Adrian Biran.

By: Biran, Adrian [author].

Material type: materialTypeLabel

BookPublisher: Oxford, UK : Butterworth Heinmann, [2019]Copyright date: ©2019Description: online resource (xxiv, 501 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9780081003282 (paperback); 9780081003398 (e-book).Subject(s): Naval architecture -- Mathematics

| Geometry

DDC classification: 516 Online resources: E-book

Contents:

Traditional Methods -- Differential Geometry -- Computer Methods -- Applications in naval architecture.

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e-BOOK	MTU National Maritime College of Ireland Library eBook	516 (Browse shelf(Opens below))	Not for loan

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Enhanced descriptions from Syndetics:

Geometry for Naval Architects is the essential guide to the principles of naval geometry. Formerly fragmented throughout various sources, the topic is now presented in this comprehensive book that explains the history and specific applications of modern naval architecture mathematics and techniques, including numerous examples, applications and references to further enhance understanding. With a natural four-section organization (Traditional Methods, Differential Geometry, Computer Methods, and Applications in Naval Architecture), users will quickly progress from basic fundamentals to specific applications.

Careful instruction and a wealth of practical applications spare readers the extensive searches once necessary to understand the mathematical background of naval architecture and help them understand the meanings and uses of discipline-specific computer programs.

Includes bibliographical references and index

Traditional Methods -- Differential Geometry -- Computer Methods -- Applications in naval architecture.

Electronic reproduction.: ProQuest LibCentral. Mode of access: World Wide Web.

Table of contents provided by Syndetics

About the Author (p. xv)
Preface (p. xvii)
The Organization of the Book (p. xix)
Software (p. xx)
Notation (p. xxi)
Acknowledgements (p. xxiii)
Part 1 Traditional Methods
1 Elements of Descriptive Geometry (p. 3)
1.1 Introduction (p. 4)
1.2 Notations (p. 6)
1.3 How We See - The Central Projection (p. 6)
1.4 Central Projection (p. 8)
1.4.1 Definition (p. 8)
1.4.2 Properties (p. 9)
1.4.3 Vanishing Points (p. 14)
1.4.4 Conclusions on Central Projection (p. 17)
1.5 A Note on Stereoscopic Vision (p. 17)
1.6 The Parallel Projection (p. 19)
1.6.1 Definition (p. 19)
1.6.2 A Few Properties (p. 19)
1.6.3 The Concept of Scale (p. 20)
1.7 The Orthogonal Projection (p. 21)
1.7.1 Definition (p. 21)
1.7.2 The Projection of a Right Angle (p. 23)
1.8 The Method of Monge (p. 25)
1.9 Points (p. 27)
1.10 Straight Lines (p. 29)
1.10.1 The Projections of a Straight Line (p. 29)
1.10.2 Intersecting Lines (p. 31)
1.11 Planes (p. 32)
1.12 An Example of Plane-Faceted Solid - The Cube (p. 35)
1.13 A Space Curve - The Helix (p. 37)
1.14 The Cylinder (p. 38)
1.15 The Cone (p. 41)
1.15.1 Introduction (p. 41)
1.15.2 Points on the Cone Surface (p. 42)
1.16 Conic Sections (p. 44)
1.16.1 Introduction (p. 44)
1.16.2 The Circle (p. 45)
1.16.3 The Ellipse (p. 46)
1.16.4 The Parabola (p. 48)
1.16.5 The Hyperbola (p. 50)
1.17 What Is Axonometry (p. 52)
1.17.1 The Law of Scales (p. 54)
1.17.2 Isometry (p. 56)
1.17.3 An Ambiguity of the Isometric Projection (p. 60)
1.18 Developed Surfaces (p. 61)
1.18.1 What Is a Developed Surface (p. 61)
1.18.2 The Development of a Cylindrical Surface (p. 62)
1.18.3 The Development of a Conic Surface (p. 63)
1.19 Summary (p. 64)
1.20 Exercises (p. 66)
Appendix 1.A The Connection to Linear Algebra and MATLAB (p. 70)
Appendix 1.B First Steps in MultiSurf (p. 75)
2 The Hull Surface - Graphic Definition (p. 81)
2.1 Introduction (p. 81)
2.2 The Lines Drawing (p. 86)
2.2.1 A Simple, Idealized Hull Surface (p. 86)
2.3 Main Dimensions and Coefficients of Form (p. 89)
2.4 Systems of Coordinates (p. 94)
2.5 The Hull Surface of a Real Ship (p. 95)
2.6 Consistency and Fairness of Ship Lines (p. 96)
2.7 Drawing Instruments (p. 102)
2.8 Table of Offsets (p. 103)
2.9 Shell Expansion and Wetted Surface (p. 104)
2.10 An Example in MultiSurf (p. 108)
2.11 Summary (p. 115)
2.12 Exercises (p. 118)
3 Geometric Properties of Areas and Volumes (p. 121)
3.1 Introduction (p. 122)
3.2 Change of Coordinate Axes (p. 123)
3.2.1 Translation of Coordinate Axes (p. 123)
3.2.2 Rotation of Coordinate Axes (p. 124)
3.3 Areas (p. 125)
3.3.1 Definitions (p. 125)
3.3.2 Examples (p. 127)
3.3.3 Examples in Naval Architecture (p. 130)
3.4 First Moments and Centroids of Areas (p. 131)
3.4.1 Definitions (p. 131)
3.4.2 Examples (p. 132)
3.4.3 Examples in Naval Architecture (p. 133)
3.5 Second Moments of Areas (p. 134)
3.5.1 Definitions (p. 134)
3.5.2 Parallel Translation of Axes (p. 136)
3.5.3 Rotation of Axes (p. 137)
3.5.4 The Tensor of Inertia (p. 140)
3.5.5 Radius of Gyration (p. 141)
3.5.6 The Ellipse of Inertia (p. 142)
3.5.7 A Problem of Eigenvalues (p. 143)
3.5.8 Examples (p. 146)
3.5.9 Examples in Naval Architecture (p. 155)
3.6 Volume Properties (p. 156)
3.6.1 Definitions (p. 156)
3.6.2 Examples (p. 156)
3.6.3 Moments and Centroids of Volumes (p. 159)
3.7 Mass Properties (p. 161)
3.8 Green's Theorem (p. 163)
3.9 Hull Transformations (p. 169)
3.9.1 Numerical Calculations (p. 170)
3.9.2 The 'One Minus Prismatic' Method (p. 172)
3.9.3 Swinging the Curve (p. 174)
3.9.4 Lackenby's General Method (p. 176)
3.10 Applications (p. 177)
3.10.1 The planimeter (p. 177)
3.10.2 A MATLAB Digitizer (p. 182)
3.11 Summary (p. 183)
3.12 Exercises (p. 188)
Part 2 Differential Geometry
4 Parametric Curves (p. 197)
4.1 Introduction (p. 197)
4.2 Parametric Representation (p. 198)
4.3 Parametric Equation of Straight Line (p. 201)
4.4 Curves in 3D Space (p. 204)
4.4.1 The Straight Line (p. 204)
4.4.2 Working With Parametric Equations (p. 205)
4.4.3 The Helix (p. 207)
4.5 Derivatives of Parametric Functions (p. 207)
4.6 Notation of Derivatives (p. 209)
4.7 Tangents (p. 210)
4.8 Arc Length (p. 210)
4.9 Arc-Length Parametrization (p. 211)
4.10 The Curve of Centres of Buoyancy (p. 213)
4.10.1 Parametric Equations (p. 213)
4.10.2 A Theorem on the Axis of Inclination (p. 216)
4.10.3 The Tangent and the Normal to the B-Curve (p. 217)
4.10.4 Parametric Equations for Small Angles of Inclination (p. 217)
4.11 Summary (p. 219)
4.12 Exercises (p. 220)
5 Curvature (p. 223)
5.1 Introduction (p. 223)
5.2 The Definition of Curvature (p. 224)
5.2.1 Curvature in Explicit Representation (p. 225)
5.2.2 Curvature in Parametric Representation (p. 226)
5.3 Osculating Circle (p. 227)
5.3.1 Definition (p. 227)
5.3.2 Definition 1 detailed (p. 227)
5.3.3 Definition 2 Detailed (p. 228)
5.3.4 Definition 3 Detailed (p. 230)
5.3.5 Centre of Curvature in Parametric Representation (p. 231)
5.4 An Application in Kinematics - The Centrifugal Acceleration (p. 233)
5.4.1 Position (p. 233)
5.4.2 Velocity (p. 234)
5.4.3 Acceleration (p. 235)
5.5 Another Application in Mechanics - The Elastic Line (p. 236)
5.6 An Application in Naval Architecture - The Metacentric Radius (p. 238)
5.7 Differential Metacentric Radius (p. 239)
5.8 Curves in Space (p. 239)
5.9 Evolutes (p. 241)
5.10 A Lemma on the Normal to a Curve in Implicit Form (p. 242)
5.11 Envelopes (p. 244)
5.12 The Metacentric Evolute (p. 246)
5.13 Curvature and Fait Lines (p. 249)
5.14 Examples (p. 249)
5.15 Summary (p. 252)
5.16 Exercises (p. 254)
Appendix 5.A Curvature in MultiSurf (p. 255)
6 Surfaces (p. 259)
6.1 Introduction (p. 259)
6.2 Parametric Representation (p. 260)
6.3 Curves on Surfaces (p. 266)
6.4 First Fundamental Form (p. 267)
6.5 Second Fundamental Form (p. 270)
6.6 Principal, Gaussian, and Mean Curvatures (p. 275)
6.7 Ruled Surfaces (p. 278)
6.7.1 Cylindrical Surfaces (p. 279)
6.7.2 Conic Surfaces (p. 280)
6.7.3 Surfaces of Tangents (p. 281)
6.7.4 A Doubly-Ruled Surface, the Hyperboloid of One Sheet (p. 282)
6.8 Geodesic Curvature (p. 283)
6.9 Developable Surfaces (p. 285)
6.10 Geodesics and Plate Development (p. 288)
6.11 On the Nature of Surface Curvature (p. 290)
6.12 Summary (p. 293)
6.13 Exercises (p. 296)
Appendix 6.A A Few MultiSurf Tools for Working With Surfaces (p. 298)
Part 3 Computer Methods
7 Cubic Splines (p. 305)
7.1 Introduction (p. 305)
7.2 Cubic Splines (p. 307)
7.3 The MATLAB Spline (p. 308)
7.4 Working With Parametric Splines (p. 310)
7.5 Space Curves (p. 312)
7.6 Chord-Length Parametrization (p. 314)
7.7 Centripetal Parametrization (p. 316)
7.8 Summary (p. 317)
7.9 Exercises (p. 318)
Appendix 7.A MultiSurf - Cubic Spline, Polycurve (p. 321)
8 Geometrical Transformations (p. 325)
8.1 Introduction (p. 325)
8.2 Transformations in the Plane (p. 328)
8.2.1 Translation (p. 328)
8.2.2 Rotation Around the Origin (p. 329)
8.2.3 Rotation About an Arbitrary Point (p. 330)
8.2.4 Reflection (p. 332)
8.2.5 Isometries (p. 332)
8.2.6 Shearing (p. 334)
8.2.7 Scaling About the Origin (p. 334)
8.2.8 Affine Transformations (p. 335)
8.2.9 Homogeneous Coordinates (p. 337)
3.3 Transformations in 3D Space (p. 340)
3.4 Perspective Projections (p. 342)
8.4.1 The Projection Matrix (p. 342)
8.4.2 Ideal and Vanishing Points (p. 345)
8.4.3 The Vanishing Line (p. 347)
8.4.4 The Orthographic Projection as Limit of Perspective Projection (p. 347)
8.5 Affine Combinations of Points (p. 348)
8.5.1 Affine Combination of Two Points - Collinearity (p. 348)
8.5.2 Alternative Proof of Collinearity (p. 350)
8.5.3 Affine Combination of Three Points - Coplanarity (p. 351)
8.6 Barycentres (p. 353)
8.7 Summary (p. 354)
8.8 Exercises (p. 356)
9 Bézier Curves (p. 361)
9.1 Introduction (p. 361)
9.2 The First-Degree Bézier Curves (p. 363)
9.3 The Second-Degree Bézier Curves (p. 363)
9.4 The Third-Degree Bézier Curves (p. 364)
9.5 The General Definition of Bézier Curves (p. 365)
9.6 Interactive Manipulation of Bézier Curves (p. 367)
9.7 De Casteljau's Algorithm (p. 368)
9.8 Some Properties of Bézier Curves (p. 371)
9.8.1 The First and the Last Point of the Curve (p. 371)
9.8.2 End Tangents (p. 372)
9.8.3 Convex Hull (p. 372)
9.8.4 Variance Diminishing Property (p. 373)
9.8.5 Invariance Under Affine Transformations (p. 373)
9.9 Joining Two Bézier Curves (p. 375)
9.10 Moving a Control Point (p. 376)
9.11 Rational Bézier Curves (p. 376)
9.12 Summary (p. 380)
9.13 Exercises (p. 381)
10 B-Splines and NURBS (p. 387)
10.1 Introduction (p. 387)
10.2 B-Splines (p. 388)
10.3 Quadratic B-Splines (p. 389)
10.4 Moving a Control Point (p. 392)
10.5 A Cubic B-Spline (p. 392)
10.6 Phantom Points (p. 394)
10.7 Some Properties of the B-Splines (p. 395)
10.8 Nurbs (p. 397)
10.9 Summary (p. 403)
10.10 Exercises (p. 405)
Appendix 10.A A Note on B-Splines and NURBS in MultiSurf (p. 408)
11 Computer Representation of Surfaces (p. 411)
11.1 Introduction (p. 411)
11.2 Bézier Patches (p. 412)
11.2.1 A Bilinear Patch (p. 413)
11.2.2 Curve on Surface (p. 419)
11.3 Bicubic Bézier Patches (p. 420)
11.4 Joining Two Bézier Patches (p. 425)
11.5 Swept Surfaces (p. 428)
11.6 Lofted Surfaces (p. 430)
11.7 Computer-Aided Design of Hull Surfaces (p. 433)
11.8 Summary (p. 435)
11.9 Exercises (p. 436)
Appendix 11.A A Note on Surfaces in MultiSurf (p. 438)
Part 4 Applications in Naval Architecture
12 Hull Transformations by Computer Software (p. 441)
12.1 Introduction (p. 441)
12.2 Affine Hulls (p. 442)
12.3 A Note on Lackenby's Transformation (p. 446)
12.4 Affine Combinations of Offsets (p. 446)
12.5 Morphing (p. 447)
12.6 Non-Linear Transformations (p. 450)
12.7 Summary (p. 450)
12.8 Exercises (p. 451)
13 Conformal Mapping (p. 453)
13.1 Introduction (p. 453)
13.2 Working With Complex Variables (p. 454)
13.3 Conformal Mapping (p. 457)
13.4 Lewis Forms (p. 459)
13.5 Summary (p. 468)
13.6 Exercises (p. 469)
Bibliography (p. 471)
Answers, to Selected Exercises (p. 479)
Index (p. 495)

Author notes provided by Syndetics

Adrian Biran received a Diplomat Engineer degree from Bucharest Polytechnic, and MSc and DSc degrees from Technion - Israel Institute of Technology. He worked extensively in design in Romania at IPRONAV-The Institute of Ship Projects, Bucharest Studios, and IPA-The Institute of Automation Projects, and at the Israel Shipyards and the Technion Research and Development Foundation. Dr. Biran has also worked as a project instructor at the Technical Military Academy in Romania and at Ben Gurion University in Israel. At Technion he taught Machine Design, Engineering Drawing, and Naval Architecture. He has written papers on computational linguistics, computer simulations of marine systems and ship design. Dr. Biran is the author or first coauthor of books on MATLAB that have been translated into several languages, and Ship Hydrostatics and Stability, 2supnd/sup Edition (97800880982878).