CONTENTS Foreword 1 Acknowledgements 3 Author's note 5 1 Introduction 7 2 What is parametric modeling? 11 3 How designers use parameters 23 3.1 Conventional and parametric 23 3.2 New skills 24 3.2.1 Conceiving data flow 24 3.2.2 Dividing to conquer 27 3.2.3 Naming 29 3.2.4 Thinking with abstraction 30 3.2.5 Thinking mathematically 33 3.2.6 Thinking algorithmically 34 3.3 New strategies 35 3.3.1 Sketching 35 3.3.2 Throw code away 36 3.3.3 Copy and modify 37 3.3.4 Search for form 39 3.3.5 Use mathematics and computation to understand design 39 3.3.6 Defer decisions 43 3.3.7 Make modules 45 3.3.8 Help others 46 3.3.9 Develop your toolbox 47 4 Programming 49 4.1 Values 50 4.2 Variables 50 4.3 Expressions 51 4.4 Statements 51 4.5 Control statements52 4.6 Functions. 53 4.7 Types 54 4.8 Objects, classes & methods 56 4.9 Data structures, viz. lists 57 4.10 Conventions for this book 59 4.11 It's more than writing code 60 4.12 Parameter + Algorithm 62 4.13 End-user programming 65 5 The New Elephant House 69 5.1 Introduction 69 5.2 Capturing design intent70 5.3 The torus 71 5.4 Structure generator72 5.5 Frit generator 74 5.6 Conclusions 78 6 Geometry 81 6.1 Vectors and points 86 6.1.1 Points 86 6.1.2 Vectors 87 6.1.3 Vectors and points are different 87 6.1.4 The arithmetic of vectors 89 6.1.5 The arithmetic of points 92 6.1.6 Combining vectors 92 6.1.7 Length and distance94 6.1.8 Bound and free vectors94 6.1.9 The scalar product 95 6.1.10 Projecting one vector onto another 96 6.1.11 Converse projection97 6.2 Lines in 2D 98 6.2.1 Explicit equation 98 6.2.2 Implicit equation 98 6.2.3 Line operator 99 6.2.4 Normal-point equation 100 6.2.5 Parametric equation . 101 6.2.6 Projecting a point to a line 102 6.3 Lines in 3D 103 6.4 Planes103 6.4.1 Normal vector103 6.4.2 Implicit equation 103 6.4.3 Normal-point equation 104 6.4.4 Plane operator104 6.4.5 Parametric equation 105 6.4.6 Projecting a point onto a plane 105 6.5 Coordinate systems = frames 106 6.5.1 Generating frarftes: the cross product 108 6.5.2 Representing frames111 6.5.3 Matrices as representations113 6.5.4 Matrices as mappings114 6.5.5 Matrices as transformations 116 6.6 Geometrically significant vector bases 116 6.7 Composing vector bases120 6.7.1 Which comes first? Translation or rotation? 121 6.8 Intersections 123 6.8.1 Do two objects intersect? 124 6.8.2 Generate an object lying on another object 128 6.8.3 Intersect two objects 129 6.8.4 Closest fitting object 132 6.9 Curves134 6.9.1 Conic sections 135 6.9.2 When conic sections are not enough 135 6.9.3 Interpolation versus approximation 137 6.9.4 Linear interpolation = tweening 138 6.9.5 Parametric curve representations 138 6.9.6 Relating objects to curves 139 6.9.7 Continuity: when curves join 144 6.9.8 Bezier curves - the most simple kind of free-form curve . 146 6.9.9 Order and degree 149 6.9.10 Bezier curve properties. 149 6.9.11 Joining Bezier curves 154 6.9.12 B-Spline curves 155 6.9.13 Non-uniform rational B-Sphne curves 166 6.9.14 The rule of four and five 167 6.10 Parametric surfaces 168 7 Geometric gestures 171 7.1 Geometrical fluidity: White Magnolia Tower 172 7.2 Designing with bits: Nanjing South Station 178 7.3 Alternative design thinking 183 8 Patterns for parametric design 185 8.1 The structure of design patterns 187 8.2 Learning parametric modeling with patterns 188 8.3 Working with design patterns 188 8.4 Writing design patterns 189 8.5 CLEAR NAMES 190 8.6 CONTROLLER 191 8.7 JIG 201 8.8 INCREMENT 207 8.9 POINT COLLECTION 212 8.10 PLACE HOLDER 218 8.11 PROJECTION 223 8.12 REACTOR 230 8.13 REPORTER 236 8.14 SELECTOR 245 8.15 MAPPING 252 8.16 RECURSION 260 8.17 GOAL SEEKER 269 9 Design space exploration 275 9.1 Introduction275 9.1.1 Design space276 9.1.2 Alternatives and variations 277 9.2 Hysterical space278 9.2.1 Recorder pattern 278 9.2.2 Hysterical State pattern280 9.3 Case study . 282 9.4 Representing the hysterical space 285 9.5 Visualizing the hysterical space 285 9.6 Conclusion 287 Contributor biographies 288 Bibliography 289 Trademark notices 295 Index 297