Validation and Verification Using Spatial Logic Framework for Building Layouts By Abhinav Fatehpuria Vineet Gupta 12/ 6/ 2005 ENPM 643 – System Validation & Verification 1
Agenda � Background � Project Description � Floor Plan � Goals � System Requirements � System Structure � Spatial Logic � Overview � Application to Building Layouts � Conclusion � Software Used � References 12/ 6/ 2005 ENPM 643 – System Validation & Verification 2
3 ENPM 643 – System Validation & Verification Background 12/ 6/ 2005
Background – Project Description � Defined and categorized the design requirements of a building from an architectural view point � Prepared the system structure (Class Diagram) at a higher level of abstraction � Defined Validation Parameters � To allow the architect to check potential building designs against the specification � Quickly � Easily � In early phases of the design 12/ 6/ 2005 ENPM 643 – System Validation & Verification 4
Background - Floor Plan F lo o r P la n Vent R e s tR o o m P a s s a g e W a y K itc h e n Window Joint B e d r o o m L iv in g R o o m Window O f f ic e 3 8 4 0 s q . ft . Window Window 12/ 6/ 2005 ENPM 643 – System Validation & Verification 5
Background – Goals – Cont’d 12/ 6/ 2005 ENPM 643 – System Validation & Verification 6
Background–System Requirements � Architectural requirements of one bedroom apartment can be broadly categorized as � Apartment Level: Area of the apartment should be at least 10000 sq units. 1. The apartment should have 1 bedroom, 1 living room, 1 kitchen, 1 2. restroom and one passageway. The apartment should have easy access to exit in case of fire. 3. Room Level: � Occupancy of the bedroom should be two. 4. Bedroom should be adjacent to the restroom. 5. Proximity strength between restroom and bedroom is 1. 6. Bedroom should have air tight and sound proof doors. 7. Orientation of the bedroom should be towards the west. 8. 12/ 6/ 2005 ENPM 643 – System Validation & Verification 7
Background–System Requirements 12/ 6/ 2005 ENPM 643 – System Validation & Verification 8
Background–System Structure � The complete architectural viewpoint is divided in to three sub classes: � Spaces � Dividers � Portals � Relationship � between different rooms - (Association_Rooms) � between rooms and walls (Association_Rooms_Walls) � between walls and portals (Association_Walls_Portals) � The properties of these association classes � Proximity strength - address the proximity issue between different rooms � Access Type – What type of access is available � Access Vent – Is it for ventilation purpose � Access Light – Is it allowing light to pass through i.e. is it transparent � Access admit – Is it allowing people to enter or exit 12/ 6/ 2005 ENPM 643 – System Validation & Verification 9
Background–System Structure G eneric C lass D iagram «bind» A rchitectu re S tru ctu ral P lu m b in g E lectricity V iew P oints 1 1 A ssociatio n _W alls_P o rtals S p aces P o rtals D ivid ers -Inner/O uter -Length -Length -A ccess V ent -B readth -B readth -A ccess Light * -S hape -B ase D istance -A ccess A dm it 1 A sso ciatio n _R o o m _W alls -A ccess A udible 1 * -N o.of P ortals -N um ber of W alls * R o o m s -Length F lo o r -B readth 1 -H eight -O ccupancy -O rientation 1 * W alls -T hickness -Inner/outer * * Living ro o m B ed ro o m P assag e W ay Jo in ts D o o rs A sso ciatio n _R o om s -P roxim ity S trength -A ccess V ent K itch en R estro o m W in d o w s V en t -A ccess Light -A ccess A dm it -A ccess A udible 12/ 6/ 2005 ENPM 643 – System Validation & Verification 10
Spatial Logic & Its Application 12/ 6/ 2005 ENPM 643 – System Validation & Verification 11
Concept of Hyperplanes � A conceptual border that divides two sets of points � Each half forms a halfplane � Mathematically, it can be represented as l U 12/ 6/ 2005 ENPM 643 – System Validation & Verification 12
Half planes � Represents spaces symbolically without any reference to a particular coordinate system � The predicate hp(x) is a general representation of a halfplane, according to its truth value � E.g.. hp(a) a 12/ 6/ 2005 ENPM 643 – System Validation & Verification 13
Halfplanes � U = {p(x, y)} � U always can be divided into exactly two subsets A and B, defined by: � A = { p(x, y) : f(x,y) > 0}, and � B = { p(x, y) : f(x,y) <0} � f(x,y) is a continuous function in U. A and B are non-empty, closed sets. � � Therefore A and B have the following characteristics: � A ∩ B is Ǿ , and U � A U B is U. A B 12/ 6/ 2005 ENPM 643 – System Validation & Verification 14
Defining Regions using Halfplanes -1 � Given n halfplanes, a region R is defined by a conjunctive formula of n hp(x), as R is hp(a 1 ) hp(a 2 ) .. hp(a n ). � Since each halfplane can have truth value True or False, each region is an interpretation of the Formula above. � For our floor plan: → α ∧ β ∧ γ ∧ δ U hp ( ) hp ( ) hp ( ) hp ( ) 12/ 6/ 2005 ENPM 643 – System Validation & Verification 15
Constraints → ¬ � hp(b) hp(c) → ¬ � hp(c) hp(b) → � hp(b) hp(a) ¬ → ¬ � hp(b) hp(a) 12/ 6/ 2005 ENPM 643 – System Validation & Verification 16
Defining Regions using Halfplanes -2 γ → → hp ( ) hp ( b ) hp ( a ) γ → hp ( ) hp ( b ) α → hp ( ) hp ( c ) δ → hp ( ) hp ( d ) U a 2 b c α β R 5 R 4 R 1 1 3 R 2 R 3 γ δ 4 12/ 6/ 2005 ENPM 643 – System Validation & Verification 17
Restroom R1 ∧ ∧ ∧ ¬ hp ( a ) hp ( b ) hp ( d ) hp ( c ) ∧ hp ( a ) hp ( d ) Rest Room hp(a) a hp(a) b hp(d) hp(d) 12/ 6/ 2005 ENPM 643 – System Validation & Verification 18
Bedroom R2 ∧ ∧ ¬ ∧ ¬ hp ( a ) hp ( b ) hp ( d ) hp ( c ) ∧ ¬ hp ( b ) hp ( d ) Bed Room hp(b) hp(b) b hp(d) hp(d) 12/ 6/ 2005 ENPM 643 – System Validation & Verification 19
Living room R3 ¬ ∧ ¬ ∧ ¬ hp ( a ) hp ( b ) hp ( d ) ¬ ∧ ¬ hp ( b ) hp ( d ) Living Room b hp(d) hp(d) hp(b) hp(b) 12/ 6/ 2005 ENPM 643 – System Validation & Verification 20
Verifying the presence of a region S.No hp(a) hp(b) hp(c) hp(d) R 1 False False False False True 2 False False False True True 3 False False True False True 4 False False True True True 5 False True False False True 6 False True False True True 7 False True True False False 8 False True True True False 9 True False False False False 10 True False False True False 11 True False True False False 12 True False True True False 13 True True False False True 14 True True False True True 15 True True True False False 16 True True True True False
Verifying the presence of the region Room Region S.No. R Restroom R1 13 True Bedroom R2 14 True Living room R3 3 True Kitchen R4 4 True Passageway R5 6 True 12/ 6/ 2005 ENPM 643 – System Validation & Verification 22
Border adjacency � Given a minimal description of a region R expressed by hp(x 1 ) hp(x 2 ) . . . hp(x n ), a region R adj is border adjacent to R iff it differs in only one hp(xi), such as hp(xi) in R is hp(xi) in R adj . 12/ 6/ 2005 ENPM 643 – System Validation & Verification 23
Border adjacency for R1 and R2 ∧ � Restroom hp ( a ) hp ( d ) ∧ ¬ hp ( b ) hp ( d ) � Bedroom → � From the constraints hp(b) hp(a) � Thus, restroom is region adjacent to the bedroom as it differs in only in one hp(xi) i.e. [hp(d)] 12/ 6/ 2005 ENPM 643 – System Validation & Verification 24
Relative position Half plane Begin end Denotation Abbreviation a 1-3 Left L b 1-3 Centre C c 1-3 Right R d 4-2 Above A U 1 2 4 3 12/ 6/ 2005 ENPM 643 – System Validation & Verification 25
Relative position R1 and R2 ∧ hp ( a ) hp ( d ) � Restroom ∧ ¬ hp ( b ) hp ( d ) � Bedroom � The difference is restroom hp(d) and bedroom hp(d) therefore topographically restroom is above bedroom 12/ 6/ 2005 ENPM 643 – System Validation & Verification 26
Adding portals hp(f) & hp(g) hp(g) hp(f) f g a b c hp(i) i hp(i) d hp(e) e hp(e) hp(h) hp(h) h 12/ 6/ 2005 ENPM 643 – System Validation & Verification 27
Representing the bedroom door ∧ ¬ ∧ ∧ hp ( d ) hp ( d ) hp ( b ) hp ( e ) U hp(b) a b hp(b) d R2 e hp(e) hp(e) 12/ 6/ 2005 ENPM 643 – System Validation & Verification 28
Visibility through the portals Visible Portal hp(xi)(1,0) Region U L hp(d) R2 hp(b) 12/ 6/ 2005 ENPM 643 – System Validation & Verification 29
Software Packages Used � MS Visio � MS Office 12/ 6/ 2005 ENPM 643 – System Validation & Verification 30
Recommend
More recommend
