Computer Aided Architectural Design Futures 2005 (eBook)
XII, 482 Seiten
Springer Netherland (Verlag)
978-1-4020-3698-9 (ISBN)
MARTENS Bob and BROWN Andre Co-conference Chairs, CAAD Futures 2005 Computer Aided Architectural Design is a particularly dynamic field that is developing through the actions of architects, software developers, researchers, technologists, users, and society alike. CAAD tools in the architectural office are no longer prominent outsiders, but have become ubiquitous tools for all professionals in the design disciplines. At the same time, techniques and tools from other fields and uses, are entering the field of architectural design. This is exemplified by the tendency to speak of Information and Communication Technology as a field in which CAAD is embedded. Exciting new combinations are possible for those, who are firmly grounded in an understanding of architectural design and who have a clear vision of the potential use of ICT. CAAD Futures 2005 called for innovative and original papers in the field of Computer Aided Architectural Design, that present rigorous, high-quality research and development work. Papers should point towards the future, but be based on a thorough understanding of the past and present.
Table of Contents 5
Foreword 11
ACKNOWLEDGEMENTS 12
Keynote Papers 14
Digitally Sponsored Convergence of Design Education, Research and Practice 15
1 BACKGROUND 15
2. HISTORY 17
3. PRE-DIGITAL INTERVENTION 19
4. DIGITAL INTERVENTION 20
5. BESPOKE SOFTWARE 22
6. TRANSDISCIPLINARY DESIGN COLLABORATION 25
7. POST DIGITAL TRANSDISCIPLINARY DESIGN COLLABORATION: ‘ SHOAL FLY BY’ 28
8. POST DIGITAL TRANSDISCIPLINARY DESIGN COLLABORATION: ‘ THE POLITICS OFWATER’ 32
9. CONCLUDING COMMENTS 33
ACKNOWLEDGEMENTS 34
Space, Time, Mind 35
1 MOTIVATION 35
2 ELEMENTS 37
3 REPRESENTATION 38
3.1 Product and Process 38
3.2 Generation of the Representation 41
3.3 Actualization of the Representation 44
4 CONTROL SEMANTICS 49
5. CONCLUSION 51
ACKNOWLEDGMENT 51
REFERENCES 51
Constructing Complexity 53
Virtual Heritage, Reconstruction and Histories 63
Labyrinthine Digital Histories 65
1 INTRODUCTION 65
2 THE PAST RECLAIMED 66
3 FUTURE OF THE DIGITAL PAST 68
4 INTERPRETIVE DIGITAL RECONSTRUCTIONS 69
4.1 Conceptual Framework 71
5 CONCLUSION 73
ACKNOWLEDGEMENTS 73
REFERENCES 73
A 3D Model of the Inner City of Beijing 75
1 INTRODUCTION 75
2 URBAN SPATIAL STRUCTURE 76
3 3D MODEL OF AN URBAN SPATIAL STRUCTURE 76
3.1 Data Acquisition 77
3.2 Modeling Process 79
3.3 Modelling Results 80
4 APPLICATIONS OF THE DIGITAL MODEL 80
4.1 Spatial-structure Analysis 82
4.2 Contradictions 82
4.3 Future Prediction 83
5 CONCLUSION 83
6 ACKNOWLEDGEMENT 84
REFERENCES 84
A Method Proposed for Adoption of Digital Technology in Architectural Heritage Documentation 85
1 INTRODUCTION 85
2 BACKGROUND 86
2.1 Previous Research Dealing with the Subject 86
2.2 Recording of Architectural Heritage in Poland 87
3 PROJECT DESCRIPTION 89
3.1 Project Principles 89
3.2 Addressed Issues 91
4 CONCLUSIONS 93
REFERENCES 94
From Architectural Intent to Physical Model 95
1 INTRODUCTION 95
2 LASER SCANNING 97
3 GEOMETRIC MODELING 98
4 RAPID PROTOTYPING 101
5 CONCLUSIONS AND POSSIBLE DEVELOPMENTS 103
ACKNOWLEDGMENTS 103
REFERENCES 103
Interactive Visualization of Large-Scale Architectural Models over the Grid 105
1 INTRODUCTION 105
2 RELATED WORK 106
3 A NEWGRID-ENABLED VISUALIZATION INFRASTRUCTURE 107
4 MULTI-STAGE DATA COMPRESSION 110
4.1 Data Pre-Processing 110
4.2 Rendering Stage 111
4.3 Remote Display Stage 112
5 PROTOTYPE DEVELOPMENT 112
6 CONCLUSION 113
ACKNOWLEDGEMENTS 113
REFERENCES 113
Digital Design, Representation and Visualization 115
Townscaping: Development of Dynamic Virtual City Augmented 3D Sketch Design Tools 117
1 INTRODUCTION 117
2 SUCOD: A WEB-BASED PLATFORM FOR GENERATINGUSER- DEFINED 3D CITY MODELS 118
3 TOWNSCAPING: DYNAMIC VIRTUAL CITY AUGMENTED 3D SKETCH DESIGN 120
4 CURRENT IMPLEMENTATION AND A WORKED EXAMPLE 121
5 INITIAL FEEDBACK ON TOWNSCAPING AND TOPICS FOR FURTHER RESEARCH 125
REFERENCES 126
Towards a Virtual Reality Tool for Lighting 127
1 INTRODUCTION 127
2 BACKGROUND 128
2.1 Solar Effects 128
2.2 Virtual reality in architectural and urban field 129
3 EXPERIMENTAL STUDY 130
3.1 Experiment Study Area 131
3.2 Procedure and Tasks 132
4 RESULTS 133
4.1 Subjects’ Judgements Space Division 133
4.2 Evaluation Listing 133
4.3 Conditions of Solar Effects Generation 134
4.4 Discussion 134
5 CONCLUSION 135
REFERENCES 136
A Visual Landscape Assessment Approach for Highdensity Urban Development 137
1 INTRODUCTION 137
2 CONCEPT OF THE METHODOLOGY 138
2.1 Visual Perception and Recourse Qualities 139
2.2 GIS Support 139
3 THE FIRST CASE STUDY 140
3.1 Visual Quality Assessment 140
3.2 Evaluation of Impacts to Surrounding Environment 142
4 DISCUSSION AND FUTURE RESEARCH 144
4.1 Methodological Improvement 144
4.2 Potential Fields of Application 144
5 CONCLUSION 145
REFERENCES 145
Architectural Cinematographer: An Initial Approach to Experiential Design in Virtual Worlds 147
1 INTRODUCTION 147
2 RELATED WORK 149
3 ARCHITECTURAL CONCEPTS AND CINEMATOGRAPHY 149
3.1 Encoding Cinematography 150
3.2 Architectural Concepts 152
4 ARCHITECTURAL CINEMATOGRAPHER 152
4.1 System 152
4.2 Example 153
5 CONCLUSIONS 154
REFERENCES 156
Virtual Environments in Design and Evaluation: 157
1 INTRODUCTION 157
1.1 Home Modification Process 158
1.2 Virtual Reality and Environmental Modification 158
2 HABITEST – DESIGN AND INPLEMENTATION 159
2.1 Selection of the Simulation Platform 159
2.2 HabiTest: Designing the Key-Features 160
3 INITIAL EVALUATION OF “HABITEST” BY USERS 161
3.1 Initial Usability Testing 161
3.2 Ongoing Usability Testing of the HabiTest 162
4 CONCLUSIONS 165
References 166
Do We Need CAD during Conceptual Design? 167
1 INTRODUCTION 167
2 THE NEED FOR EXTERNAL REPRESENTATIONS 168
3 METHOD 169
3.1 Experimental Conditions 170
3.2 Assessment of the Design Outcome 171
4 RESULTS 172
5 IMPLICATIONS FOR CAAD 174
REFERENCES 175
Contemporary Digital Techniques in the Early Stages of Design 177
1 INTRODUCTION 177
2 THE PROJECT 179
2.1 Initial Study 179
2.2 Linked Study 181
2.3 Second Study 183
3 CONCLUSIONS 184
REFERENCES 185
Optimizing Architectural Layout Design via Mixed Integer Programming 187
1 INTRODUCTION 187
2 OPTIMIZATION OF GEOMETRY 188
2.1 Design Variables and Parameters 188
2.2 Objective of Problem 189
2.3 Layout Design Constraints 189
3 SOFTWARE DEVELOPMENT 192
4 EXPERIMENTS 193
4.1 Computation time of GLPK 193
4.2 Layout Design with Multiobjectives 194
4.3 Comparison between MIP and Nonlinear Programming 194
4.4 Practical Case Study 195
5 CONCLUSION 196
REFERENCES 196
Design Methods, Process and Creativity 197
Examining Learning in Multiple Settings 199
1 INTRODUCTION 199
2 LEARNING AND THE DESIGN PROCESS 200
3 CODING SCHEMA 202
3.1 Goldschmidt’s Linkograph and Schön’s “Framingmoving- reflecting” Model 204
3.2 Validation 204
4 RESULTS AND DISCUSSION 205
5 CONCLUSION 207
REFERENCES 207
Using Historical Know-how to Model Design References 209
1 INTRODUCTION 209
2 BACKGROUND 210
2.1 Historical Study 210
2.2 On the Role of References 210
3 COMPUTER APPROACHES TO REFERENCES 212
3.1 Reference Data Bases 212
3.2 Case-based Reasoning (CBR) - Case-based Design 213
3.3 Prototypes 214
4 METHODOLOGY 214
4.1 Modeling the Generating Actions 214
4.2 Models of References 215
4.3 Structure of the Design Pedagogy Assistant 216
5 VALIDATION AND DISCUSSION 217
REFERENCES 218
Semantic Roomobjects for Conceptual Design Support 219
1 INTRODUCTION 219
2 MOTIVATION FOR SEMANTIC MODELLING 220
3 INTEGRATED CONCEPTUAL DESIGN SUPPORT 221
4 KNOWLEDGE REPRESENTATION 224
5 CONSISTENCY ANALYSES 226
6 CONCLUSION 227
REFERENCES 228
Shared Design Space 229
1 INTRODUCTION 229
2 WIKI 230
2.1 Comparison with Web based Threaded Discussion Lists 231
2.2 Examples of Possible Ways to Structure Wiki 231
3 ANALYSIS OF EMAIL 232
3.1 Semantic Convergence 232
3.2 Project Language 232
3.3 Empathetic Conformity and Modal Issues 233
3.4 Targeting Information: Structural and Ontological Links 233
4 EARLY CASE STUDIESWITHWIKI 234
5 FINDINGS 234
6 PROPOSALS TO AUGMENTWIKI 235
7 CONCLUSIONS 236
REFERENCES 237
Knowledge Based Design and Generative Systems 239
Generation of Apparently Irregular Truss Structures 241
1 INTRODUCTION: IRREGULARITY AND ITS COST 241
2 THE BEIJING SWIMMING CENTRE 243
3 BOTTOM-UP: VORONOI-BASED FOAMS 245
4 TOP-DOWN: DERIVATION OF THE OCTET-TRUSS 246
5 INTEGRATING BOTTOM-UP AND TOP-DOWN 247
6 CONCLUSION 249
ACKNOWLEDGEMENTS 250
REFERENCES 250
Dynamic Designs of 3D Virtual Worlds Using Generative Design Agents 251
1 INTRODUCTION: 3D VIRTUAL WORLDS 251
2 AGENT MODELS FOR 3D VIRTUAL WORLDS 252
3 GENERATIVE DESIGN AGENT MODEL 253
4 GENERATIVE DESIGN GRAMMAR 255
4.1 Generative Design Grammar Framework 256
4.2 Generative Design Grammar Application 259
5 CONCLUSION 259
REFERENCES 260
Using Cellular Automata to Generate High-Density Building Form 261
1 THE CHALLENGE OF VARIETY 261
2 GENERATING VARIETY 263
3 CELLULAR AUTOMATA FOR ARCHITECTURE 264
4 DESIGNING WITH CELLULAR AUTOMATA: AN EXAMPLE IMPLEMENTATION 267
5 CONCLUSION 269
REFERENCES 269
Dynamic Generative Modelling System for Urban and Regional Design 271
1 INTRODUCTION 271
2 THE GENERATIVE MODELLING SYSTEM 272
2.1 Datasets 272
2.2 Tasks 273
2.3 Workflow 274
3 INTERACTING TASKS 274
3.1 Macro-Scale 274
3.2 Micro-Scale 275
4 CASE PROJECT 275
4.1 Macro-Scale Tasks 276
4.2 Micro-Scale Tasks 276
4.3 Ordinary Dynamic Scenario 279
5 CONCLUSION 279
REFERENCES 280
Turning the Design Process Downside-up 281
1 INTRODUCTION 281
2 GROWING A FOREST OF COLUMNS 282
2.1 Defining the Task 282
2.2 Designing a Dynamic Model 283
2.3 Programming the Simulation 285
2.4 Letting Loose the Columns 286
2.5 From Generating to Building 287
3 RESULTS 287
3.1 Design for Emergence 288
3.2 Calming the System 288
3.3 Finding the Right Parameter Values 288
3.4 Programming Further Simulations 289
4. CONCLUSION 289
REFERENCES 290
Human-machine Interaction: Connecting the Physical and the Virtual 291
iSphere 293
1 INTRODUCTION 293
2 RELATED WORK 294
3 INTERACTIVE TECHNIQUE 295
3.1 Realistic Interaction 296
3.2 Play and Build 297
4 IMPLEMENTATION 297
5 PILOT EXPERIMENT 298
5.1 Experimental Set-up 298
5.2 Experimental Results and Discussion 300
6 DISCUSSION 301
REFERENCES 302
Learning Design with Digital Sketching 303
1 INTRODUCTION, TECHNOLOGY & PRECEDENTS
1.1 Hypothesis 304
2 RESEARCH METHOD 305
3 DATA 305
3.1 Step-Sequencing Survey 306
3.2 Design Sequence Colour Bars 307
4 ANALYSIS 310
4.1 Step-Sequencing Survey Results 310
4.2 Design Sequence Colour Bar Analysis 310
4.3 Quality Criteria 310
5 CONCLUSIONS 311
REFERENCES 312
Simulating Human Behaviour in Built Environments 313
1 INTRODUCTION 313
2 BEHAVIOUR TRACKING AND ANALYSING 314
3 USABILITY-BASED BUILDING MODEL 315
3.1 Geometry Modelling 316
3.2 Usability Modelling 316
4 AGENT-BASED VIRTUAL USER MODEL 317
4.1 Geometry Modelling 317
4.2 Perception Modelling 318
4.3 Behaviour Modelling 318
5 SIMULATION AND RESULTS 320
5.1 2D Simulation 320
5.2 3D Visualization 320
6 CONCLUSION 321
REFERENCES 321
Resolving some Ambiguities in Real-time Design Drawing Recognition by means of a Decision Tree for Agents 323
1 GRAPHIC REPRESENTATIONS 323
1.1 Basic Assumptions 324
1.2 Graphic Units 325
2 GRAPHIC UNIT RECOGNITION 326
2.1 Multi-agent Approach 326
2.2 Online Recognition 327
2.3 Resolving the Decision Process 328
3 FUTURE WORK 329
REFERENCES 330
Sketching with Digital Pen and Paper 333
1 SKETCHING AND THE COMPUTER 333
2 DIGITAL PEN AND PAPER 335
3 MECHANICAL ASPECTS 336
4 SYNTAGMATIC ASPECTS 338
5 UTILITY AND APPLICABILITY 341
REFERENCES 342
Mindstage: Towards a Functional Virtual Architecture 343
1 INTRODUCTION 343
2 DESIGN 344
2.1 Spatialisation of Knowledge 344
2.2 Look and Feel 345
2.3 Demonstrations 346
2.4 Avatars 347
3 IMPLEMENTATION 347
3.1 Static Objects 348
3.2 Dynamic Objects 348
4 EVALUATION 349
5 CONCLUSION AND FURTHER WORK 350
6 ACKNOWLEDGEMENTS 351
REFERENCES 351
Advanced Ubiquitous Media for Interactive Space 353
1 INTRODUCTION 353
2 UBIQUITOUS MEDIA 354
3 A FRAMEWORK 355
3.1 Physical-Digital Interaction Interfaces 355
3.2 Sensing and Perceptual Technologies 356
3.3 Application and Service Control 357
3.4 Human and Environmental Adaptations 359
4 PUT IT ALL TOGETHER: THE IP PROJECT 360
5 THE APPLICATION: INTERACTIVE MEDIA EXHIBITION 360
6 CONCLUSION 361
ACKNOWLEDGEMENT 362
REFERENCES 362
Hands Free 363
1 BUILDING SURVEYING – THE CURRENT SITUATION 363
2 HANDS FREE – MODULARWEARABLE COMPUTER SYSTEMS FOR BUILDING SURVEYING 364
2.1 The Wearable Computer Platform 365
2.2 A Software Concept Based upon a Portable Computer and Augmented Reality 368
3 CONCLUSION 371
ACKNOWLEDGEMENTS 372
REFERENCES 372
Responsive Sensate Environments: Past and Future Directions 373
1 INTRODUCTION 373
2 RESPONSIVE ENVIRONMENTS 373
2.1 Active and Passive Sensing 374
2.2 Responsive Environment Design Using Sensors 374
2.3 Societal Contexts for Responsive Environments 375
3 TOWARDS AESTHETIC AND ENGAGING AMBIENT DISPLAY 377
3.1 Ambient Display and Ambient Devices 379
4 USINGGESTURAL CONTROLLERS AND SPATIAL INTERACTION TO ENGAGEWITH INFORMATION 380
5 CONCLUSION 380
REFERENCES 381
Form and Fabric: Computer Integrated Construction and Manufacturing 383
The Redefinition of Ornament 385
1 INTRODUCTION 385
2 DIGITAL GENERATION OF SURFACES 386
2.1 Modeled Surfaces 386
2.2 Programmed Surfaces 387
2.3 Image Derived Surfaces 388
3 THE CNC PRODUCTION PROCESS 389
3.1 Generation of the NC Machine Code 390
3.2 Computer Controlled Manufacturing 390
3.3 Materials 391
4 EXAMPLES IN PRACTICE AND RESEARCH 391
4.1 EternitOrnament 391
4.2 The Rustizierer 392
4.3 Historical Building Facade 393
5 CONCLUSIONS 393
REFERENCES 394
Wood Frame Grammar: 395
1 INTRODUCTION 395
2 GRAMMAR FUNCTIONS AND CAD SCRIPTING 396
3 BACKGROUND 397
4 WOOD FRAME SHAPE GRAMMAR 398
5 GENERATING A ROOM 401
6 CONCLUSION 403
REFERENCES 404
Transformations on Parametric Design Models 405
1 INTRODUCTION 405
2 PARAMETRIC MODELS 406
2.1 Instances of a Parametric Model 406
2.2 Scope 406
3 PARAMETRIC MODELS FOR THE COLUMNS OF THE SAGRADA FAMILIA 407
3.1 Generation Procedure 407
3.2 Reconstruction of the Column Model 408
3.3 Parameterization of the Column Model 409
3.4 Transformations of the Parametric Model 410
4 DISCUSSION 411
4.1 Counting New Designs 411
REFERENCES 412
Building Information Modelling and Construction Management 413
Spatial Reasoning for Building Model Reconstruction Based on Sensed Object Location Information 415
1 INTRODUCTION 415
2 TAG-BASED BUILDING REPRESENTATIONS 416
3 CONVERSION FROM TAG-BASED TO BOUNDARYBASED BUILDING REPRESENTATIONS 417
3.1 Space-boundaries 418
3.2 Merge of Space-components 419
3.3 Openings 420
3.4 Infrastructure Objects 421
4 EXAMPLE 422
5 DISCUSSION 422
ACKNOWLEDGMENTS 422
REFERENCES 424
Construction Analysis during the Design Process 425
1 INTRODUCTION 425
2 CONSTRUCTION ALGORITHMS 426
2.1 3D Representations 427
2.2 Object Topology Analysis 427
3 IMPLEMENTATION 429
4 PILOT STUDY 430
4.1 3D CAD Model Preparation 431
4.2 Planning Generation 431
4.3 Planning Comparison 432
5 DISCUSSION 433
REFERENCES 434
A Software Architecture for Self-updating Life-cycle Building Models 435
1 INTRODUCTION 435
2 PROJECT DESCRIPTION 436
2.1 Requirements 436
2.2 Architecture 437
2.3 Initial Implementation 442
3 CONCLUSION 443
ACKNOWLEDGEMENTS 443
REFERENCES 443
Multidisciplinary Design in Virtual Worlds 445
1 INTRODUCTION 445
2 COLLABORATIVE VIRTUAL ENVIRONMENTS AND COLLABORATIVE DESIGNING 446
2.1 Example Problem 446
3 MULTIDISCIPLINARY MODELLING 448
4 THE SYSTEM ARCHITECTURE AND PROTOTYPE IMPLEMENTATION 449
4.1 The Database and Internal Model 449
4.2 The Agent Society 450
4.3 The Virtual Collaborative Environment 451
5 CONCLUSION 453
ACKNOWLEDGEMENTS 453
REFERENCES 454
Linking Education, Research and Practice 455
A Multi-Disciplinary Design Studio using a Shared IFC Building Model 457
1 INTRODUCTION 457
2 RESEARCH CONTEXT 458
3 PROJECT OUTLINE 460
4 OPERATIONAL ISSUES 461
4.1 Building Model Issues 462
4.2 IFC Technology Issues 463
5 CONCLUSION AND FUTURE WORK 464
ACKNOWLEDGEMENTS 465
REFERENCES 465
Case Studies of Web-Based Collaborative Design 467
1 INTRODUCTION 467
2 DATA COLLECTION 468
2.1 Software Description 468
2.2 Case Description 468
3 CONTENT ANALYSIS CODING SCHEMAS 469
4 ANALYSIS RESULTS: CHANGES IN COMMUNICATION PATTERNS 470
4.1 Activity by Location 470
4.2 Coordination versus Collaboration 471
4.3 Information Behaviour 472
4.4 Messages According to Organizational Hierarchy 473
5 IMPLICATIONS AND CONCLUSIONS 474
REFERENCES 476
Interdisciplinary Knowledge Modelling for Free-Form Design – An Educational Experiment 477
1 INTRODUCTION 477
2 DESIGN KNOWLEDGE MODELLING AND REPRESENTATION 479
2.1 BLIP 480
3 EXPERIMENTAL WORKSHOPS 481
3.1 First Workshop 481
3.2 Second Workshop 482
4 DISCUSSION 483
5 CONCLUSION 485
ACKNOWLEDGEMENTS 485
REFERENCES 486
Reviewers 487
Author Index 489
Keyword Index 491
Constructing Complexity (p. 41)
MITCHELL William J.
School of Architecture and Planning, MIT, USA
Keywords: assembly, complexity, construction, fabrication, uniformity, variety
Abstract:
Buildings were once materialized drawings, but now, increasingly, they are materialized digital information – designed and documented on computer-aided design systems, fabricated with digitally controlled machinery, and assembled on site with the assistance of digital positioning and placement equipment. Within the framework of digitally mediated design and construction we can precisely quantify the design content and the t construction content of a project, and go on to define t complexity as the ratio of added design content to added construction content.
This paper develops the definitions of design content, construction content, and complexity, and explores the formal, functional, and economic consequences of varying the levels of complexity of projects. It argues that the emerging architecture of the digital era is characterized by high levels of complexity, and that this enables more sensitive and inflected response to the exigencies of site, program, and expressive intention than was generally possible within the framework of industrial modernism.
Perhaps you have wondered why the shapes of buildings seem to be getting more complex. Conceivably, it could be nothing more profound than an arbitrary flicker of architectural fashion. But it is worth asking whether the difference between, say, Frank Gehry’s Bilbao Guggenheim and the characteristically rectangular slabs and towers of the late twentieth century is due to something more fundamental?
Does the curved shape of London’s Swiss Re Building, the twisted profile of New York’s proposed Freedom Tower, or the non-repetitive roof structure of the British Museum courtyard represent some significant change in the conditions of production of architecture?
The shift, I suggest, is a direct outcome of new conditions created by the digital revolution. Buildings were once materialized drawings, but now, increasingly, they are materialized digital information – designed with the help of computer-aided design systems, fabricated by means of digitally controlled machinery, put together on site with the assistance of digital layout and positioning devices, and generally inseparable from flows of information through global computer networks.
Many architects have simply exploited digital technology to reduce the time and cost of producing buildings in the conventionally modernist mode, much as architects of the early industrial revolution took advantage of mass-production to inexpensively proliferate the ornament that had previously been created by craftsmen. But others have recognized that the digital revolution has opened up new domains of architectural form for exploration, and they have seized the opportunity to produce projects that break the old rules.
To see precisely how new formal possibilities emerge from the interplay of information and materiality, we need to do some numbers. It will be helpful to begin with a homely example that should be familiar to anyone who has ever operated a computer graphics or computer-aided design system. Consider the task of inputting a circle.
You need to give a circle command and specify three numbers – usually an xcoordinate, a y-coordinate, and a radius, though Euclid tells us that there are other, equivalent ways to convey the same information.
Erscheint lt. Verlag | 6.12.2005 |
---|---|
Zusatzinfo | XII, 482 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Themenwelt | Sachbuch/Ratgeber ► Natur / Technik ► Natur / Ökologie |
Schulbuch / Wörterbuch ► Unterrichtsvorbereitung ► Unterrichts-Handreichungen | |
Geisteswissenschaften | |
Mathematik / Informatik ► Informatik ► Grafik / Design | |
Informatik ► Weitere Themen ► CAD-Programme | |
Naturwissenschaften ► Biologie ► Ökologie / Naturschutz | |
Naturwissenschaften ► Geowissenschaften | |
Sozialwissenschaften ► Pädagogik | |
Technik ► Architektur | |
Technik ► Umwelttechnik / Biotechnologie | |
Schlagworte | Architecture • Computer-Aided Design (CAD) • Construction • Design • Form • Foundation • Layout • Model • Modeling • Sketch • sketching • Virtual Reality • Visualization |
ISBN-10 | 1-4020-3698-1 / 1402036981 |
ISBN-13 | 978-1-4020-3698-9 / 9781402036989 |
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