il¡.q ,ota( Geometric Typed Feature Structures: Toward design spüce loration Teng-Wen Chang Dissertation Submitted in fultilment of the requirements for the degree of Doctor of Philosophy School of Architecture, Landscape Architecture and Urban Design The University of Adelaide 12 August 1999 copy right O 1999 by Teng-Wen Chang All rights reserved Table of Contents 0.1 Abstract .1 0.2 Statement .2 0.3 Acknowledgements .5 I Introduction and Background 7 1 Introduction 9 1.1 Overview of dissertation 11 1.2 Organisation of dissertation 12 2 Background: From design to exploration 15 2.1 Views on Design t6 2.2 State space search is a useful view 27 3 Directly Supporting explorationlesign space explorers 35 3.1 Components of design space explorers 35 3.2 Several implementations of design space explorers ............39 3.3 Summary ....................78 ll Theories and Algorithms 81 4 Domain objects: the SEED knowledge level 83 4.1, The knowledge level concepts 84 4.2 Realisation of the SEED knowledge level 9l 5 Representation of the knowledge level using Ïlped Feature Structures 93 5.1 Three Components ............. ............94 5.2 Three Algorithms ........98 5.3 A representation using Typed Feature Structures ..............100 5.4 Toward representing geometric information ...................... 103 6 Geometric Tlped Feature Structures 105 6.1 The characteristics of Order Types ,....108 6.2 Order Type Models ..................... .....113 6.3 Representing Order Types .....116 6.4 Order Types canying geometric information .....154 6.5 Summary .....180 lll lmplementation and Examples 181 7 Implementation-Ordering Geometry System 183 7.1 System Integration ..184 7.2 Order Type implementation ..187 7 .3 Two examples of Order Type implementation using C++ .190 7.4 How to specify geometric types in OGS ..205 8 Examples 207 8.1 Single Fronted Cottages 207 8.2 Examples-Building Enclosures 2t3 8.3 Summary 221 It lV Gonclusion 223 9 Conclusion 225 10 Contributions and future work 227 10.1 Contributions 227 10.2 Prospect of future research work 228 Bibliography 231 Appendix 241 Appendix A: The syntax of Kryos descriptions 243 Appendix B: Examples of Order Type Implementation . ...245 Appendix C: Single-Fronted cottage 283 Appendix D: Index of Symbols and Expressions . 287 tv List of Figures FIGURE 1. Interrelationships in the Design Process from Digital Design MedialMitchell and McCullough, 1995b1. 20 FIGURE 2 An Abstract Interpretation of three Phases in the Design Process[Rad- ford and Gero, 19881. 23 FIGURE 3 The Relationships Between Decisions with Constraints and Ideal GoalslRadford and Gero, 19881. 24 FIGURE 4 Possibilities of a Derivation Graph in the Design States[Woodbury, 1991a]. 25 'Woodbury's FIGURE 5 Informal Equation for the Exploration ModellV/oodbury, 19961. 32 FIGURE 6. A Partial Functional Unit Hierarchy for an Insulated Enclosure. 86 FIGURE 7. Abstract Enclosure Elements for (a) Wall Enclosure, (b) Enclosure for the Joint between the Wall and Roof, (c) Ground Enclosure and (d) Roof Enclosure. 8'l FIGURE 8. An Example of a Technology for the Continuous-Support of a V/all Enclosure is shown on the Top. The Partial FU Hierarchy is on the Bottom. 88 FIGURE 9. Left: the Initial Status of Spaces Enclosure. Right: Wall Continuous Support (Membrane) Design Unit (After Applying Technology). 89 FIGURE 10 An Example of Design Spaces Demonstrates the Transformation of Geometry from one State to another. 90 FIGURE 11 Mapping between a Generic Abstract Knowledge System Concept and the Corresponding Representation Scheme[Woodbury et al., 19981. 9l FIGURE 12. Mapping Between the SEED Knowledge Level and its Realisation Concept, 92 FIGURE 13. A Graph Notation of an Inheritance Hierarchy. 94 FIGURE 14. Definition of Appropriateness Specification[Caqpenter, 1992f . 95 FIGURE 15. Definition of a Feature Structure Over Types and Feats[Carpenter, 1992]. 96 FIGURE 16. An Example Feature Structure in Graph Notion. 96 FIGURE 17. Definition of Path Value[Carpenter, 1992]. 97 FIGURE 18. Definition of Description[Carpenter, 1992]. 9'l v FIGURE 19. Definition of Satisfaction[Carpenter, 1992]. 98 FIGURE 20. Definition of Subsumption[Carpenter, 1992]. 99 FIGURE 21. Definition of Unification[Carpenter, 1992]. 100 FIGURE 22. Mapping Between the Abstract System Concepts and the Corre- sponding Typed Feature Structures(TFS) Concepts. 101 FIGURE 23. A Complete Mapping from the Knowledge Level to its Symbol Level Representation. 102 FIGURE 24. A Description of Atomic Values in a Formal System. 103 FIGURE 25. Example of a Complete Partial Order of Three Real Intervals and a Bottom. 106 FIGURE 26 Example of a Succession InheritanceHierarchy. 107 FIGURE 27 Example of an Order Type Hierarchy. 109 FIGURB 28 An Example Represents the Properties of a Cube with a Higher Level Structure (in AVM Notation). 110 FIGURE 29. The Descriptions of Order Types have no Path Values. 111 FIGURE 30. Definition of a Geometric Feature Structure Over Order Types. 111 FIGURE 31. Comparison of Satisfaction of Typed Feature Structures with Satis- faction of Geometric Typed Feature Structures. 112 FIGURE 32. Order Types Need no Constraints. lI2 FIGURE 33. Requirements of a Partial Order Set[Davey and Priestley, 19941. 115 FIGURE 34. A Part of 'Lifted' Reals as an InheritanceHierarchy. l2O FIGURE 35. A Part of 'Lifted' Integers in an InheritanceHierarchy. 123 FIGURE 36. A Pa¡t of 'Lifted' Whole Numbers as an InheritanceHierarchy. 126 FIGURE 37. A Part of Ascending Reals as an InheritanceHierarchy. 129 FIGURE 38. A Part of Descending Reals as an InheritanceHierarchy. I32 FIGURE 39. A Part of Ascending Integers as an InheritanceHierarchy. 135 FIGURE 40. A Part of Descending Integers as an InheritanceHierarchy. 138 FIGURE 41. A Part of Ascending Whole Numbers as an InheritanceHierarchy. l4l FIGURE 42. A Part of Descending Whole Numbers as an InheritanceHierarchy. 144 FIGURE 43 A Part ofReal Intersection Intervals as an InheritanceHierarchy. 147 FIGURE 44. A Part oflnteger Intersection Intervals as an InheritanceHierarchy. 150 FIGURE 45 A Part of Whole Number Intersection Intervals as an InheritanceHierarchy. 154 FIGURE 46. Examples of Cell Complex: a Cell Complex Comprises Multi- Dimensional Cells. 156 FIGURE 47 The Boundary of a Region is Comprised by Cells from Different Dimensions, e.g. the Vertices of the Region Above are 0D Cells. 157 FIGURE 48. The Boundary of an nD Cell Comprises the (n-k)D Cells that Bound it. 157 FIGURE 49. Two Regions: A and B are Part of a Cell Complex C. Each Region Comprises a Set of Cells and two Regions might Share a Set of Cells. 158 FIGURE 50. The Boundary of a Region is Represented as a Region Containing Cells of Lower Dimensionality Than the Given Region. 158 FIGURE 5I. The Cells of a Region do not Maintain their Identities Through the Merge Operation. 159 FIGURE 52. The Point-Set of a Region Remain Invariant Across a Merge Opera- tion, but the Cells it Comprises might Change, e.g. the Cells that Region A Comprises Change After Merge Operation, but the Bound- ary of Region A still Remains Invariant. 159 FIGURE 53. Boolean Ops over Regions are the Set Boolean Ops (After Merging). 160 FIGURE 54. Regions Need not Model Closed Sets. Use two Regions: A and B from Figure 52, the Results of Boolean Ops Over these two Regions are not Closed. 160 FIGURE 55 Example of Point-Set Containing Relation Among Geometry Types. 161 FIGURE 56. A Part of 'Lifted' Point-Set as an InheritanceHierarchy. 165 FIGURE 57. A Part of IPSet as an InheritqnceHierarchy. 168 FIGURE 58. A Part of OPSet as an InheritanceHierarchy. l7l FIGURE 59. Example of Two IOPSets a and b,Such that . 174 FIGURE 60. A Part of IOPSet as an InheritanceHierarchy. 175 FIGURE 61. Example of Two OIPSets a and b,Such That. 178 FIGURE 62. A Part of OIPSet as an InheritanceHierarchy. 179 FIGURE 63. System for a Design Space Explorer Needs to Communicate with Both Typed Feature Structures and Non-Manifold Geometry. 183 FIGURE 64. Implementation of Geometric Typed Feature Structures Comprises Both Kryos and SHAPES (and its Display Library: Viewer). 184 FIGURE 65. A Generic System Design for a Design Space Explorer Requires a DesignRepresentation. 185 FIGURE 66. An Implementation of Representation: Geometric Typed Feature Structures which Contains Typed Feature Structures and Order Types. 185 FIGURE 67 A Proposed System Comprises two External Components: Kryos and SHAPES. 187 FIGURE 68. A 2D Display of the Schematic Layout Generated by OGS. 2ll FIGURE 69. A 3D View of the Abstract Layout: Each Room is Represented as a 3D Region. 212 FIGURETO. Each Room is a Sub-Cell of a Cell-Complex: Cell.¡" ¡our". 213 FIGURE 71. The Wall Continuous Support (Membrane Layer). Outfaces of this 'Wall from the Geometry of DU*". 217 FIGURB 72. A 3D Display of Four Layers of V/all Enclosures: Sun/Rainscreen, Insulation, Air-Banier, and Wall Continuous Support (from Left to Right). 2r9 vlt vlll List of Tables TABLE 1 A complete design space explorer should support representation, rules, memory and policy in both the system and HCI levels. These are examples of questions applied in the following reviews. 40 TABLE 2. LOOS supports exploration in representation, rule, memory and pol- icy in the system level and only supports exploration in representation and rules in the HCI level. 4l TABLE 3 ABLOOS supports exploration in representation, rules, memory and policy in the system level. It supports partially in representation, rules and policy but memory in the HCI level. 45 TABLE 4. DiscoverForm supports exploration in representation, rules and policy in both the system and HCI levels. 49 TABLE 5 GENESIS mainly supports exploration in representation. There are rules in both the system and the HCI levels 53 TABLB 6. Tafan Vy'orlds only supports exploration in representation and rules in the HCI level.