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12/ 6/ 2005 ENPM 643 – System Validation & Verification 1

Validation and Verification Using Spatial Logic Framework for Building Layouts

By Abhinav Fatehpuria Vineet Gupta

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Agenda

Background

Project Description Floor Plan Goals System Requirements System Structure

Spatial Logic

Overview Application to Building Layouts

Conclusion Software Used References

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Background

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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

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Background - Floor Plan

Vent

B e d r o o m L iv in g R o o m K itc h e n P a s s a g e W a y R e s tR o o m

F lo o r P la n

Window Window Window Window Joint

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Background – Goals – Cont’d

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Background–System Requirements

• Architectural requirements of one bedroom apartment can be

broadly categorized as

• Apartment Level:

1.

Area of the apartment should be at least 10000 sq units.

2.

The apartment should have 1 bedroom, 1 living room, 1 kitchen, 1 restroom and one passageway.

3.

The apartment should have easy access to exit in case of fire.

• Room Level:

4.

Occupancy of the bedroom should be two.

5.

Bedroom should be adjacent to the restroom.

6.

Proximity strength between restroom and bedroom is 1.

7.

Bedroom should have air tight and sound proof doors.

8.

Orientation of the bedroom should be towards the west.

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Background–System Requirements

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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

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Background–System Structure

A rchitectu re 1 1

• Length
• B readth
• S hape

S p aces 1 *

• Length
• B readth
• H eight
• O ccupancy
• O rientation

R o o m s B ed ro o m R estro o m P assag e W ay K itch en Living ro o m P lu m b in g E lectricity D ivid ers

• Length
• B readth
• B ase D istance

P o rtals V en t Jo in ts D o o rs W in d o w s

• T hickness
• Inner/outer

W alls

• N um ber of W alls

A sso ciatio n _R o o m _W alls 1 *

• P roxim ity S trength
• A ccess V ent
• A ccess Light
• A ccess A dm it
• A ccess A udible

A sso ciatio n _R o om s * *

• Inner/O uter
• A ccess V ent
• A ccess Light
• A ccess A dm it
• A ccess A udible
• N o.of P ortals

A ssociatio n _W alls_P o rtals 1 *

G eneric C lass D iagram

F lo o r S tru ctu ral

V iew P oints

1 * «bind»

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Spatial Logic & Its Application

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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

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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

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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 A U B is U.

A B U

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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(a1) hp(a2) .. hp(an).

Since each halfplane can have truth value True or False, each region is an

interpretation of the Formula above.

• For our floor plan:

) ( ) ( ) ( ) ( δ γ β α hp hp hp hp U ∧ ∧ ∧ →

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Constraints

hp(b) hp(c) hp(c) hp(b) hp(b) hp(a)

• hp(b) hp(a)

→

→ ¬

¬

→ ¬ → ¬

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Defining Regions using Halfplanes -2

) ( ) ( ) ( a hp b hp hp → → γ

) ( ) ( b hp hp → γ

) ( ) ( c hp hp → α

) ( ) ( d hp hp → δ

α β δ γ R1 R2 R5 R3 R4 1 3 2 b c a 4 U

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Restroom R1

hp(a) a b hp(d) hp(a) hp(d) Rest Room

) ( ) ( ) ( ) ( c hp d hp b hp a hp ¬ ∧ ∧ ∧ ) ( ) ( d hp a hp ∧

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Bedroom R2

) ( ) ( ) ( ) ( c hp d hp b hp a hp ¬ ∧ ¬ ∧ ∧

hp(b) b hp(d) hp(b) hp(d) Bed Room

) ( ) ( d hp b hp ¬ ∧

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Living room R3

) ( ) ( ) ( d hp b hp a hp ¬ ∧ ¬ ∧ ¬ ) ( ) ( d hp b hp ¬ ∧ ¬

hp(b) b hp(d) hp(b) hp(d) Living Room

Verifying the presence of a region

False True True True True 16 False False True True True 15 True True False True True 14 True False False True True 13 False True True False True 12 False False True False True 11 False True False False True 10 False False False False True 9 False True True True False 8 False False True True False 7 True True False True False 6 True False False True False 5 True True True False False 4 True False True False False 3 True True False False False 2 True False False False False 1 R hp(d) hp(c) hp(b) hp(a) S.No

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Verifying the presence of the region

True 6 R5 Passageway True 4 R4 Kitchen True 3 R3 Living room True 14 R2 Bedroom True 13 R1 Restroom R S.No. Region Room

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Border adjacency

Given a minimal description of a region R expressed by hp(x1)

hp(x2) . . . hp(xn), a region Radj is border adjacent to R iff it differs in

• nly one hp(xi), such as hp(xi) in R is hp(xi) in Radj.

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Border adjacency for R1 and R2

Restroom 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)]

) ( ) ( d hp a hp ∧ ) ( ) ( d hp b hp ¬ ∧

→

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Relative position

A Above 4-2

d

R Right 1-3

c

C Centre 1-3

b

L Left 1-3

a Abbreviation Denotation Begin end Half plane 1 2 3 4

U

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Relative position R1 and R2

Restroom Bedroom The difference is restroom hp(d) and bedroom hp(d) therefore

topographically restroom is above bedroom

) ( ) ( d hp a hp ∧

) ( ) ( d hp b hp ¬ ∧

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Adding portals

a b c d f g e h i hp(g) hp(f) hp(i) hp(e) hp(e) hp(h) hp(f) & hp(g) hp(h) hp(i)

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Representing the bedroom door

) ( ) ( ) ( ) ( e hp b hp d hp d hp ∧ ∧ ¬ ∧

e a b d hp(b) hp(e) hp(e) hp(b)

U R2

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Visibility through the portals

L hp(d) hp(b)

Visible Region Portal U R2 hp(xi)(1,0)

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Software Packages Used

MS Visio MS Office

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References

Papers

A logic-based framework for shape representation by Jose C Damski and John

S Gero

A Referential Scheme for Modeling and Identifying Spatial Attributes of

Entities in Constructed Facilities by M. Kiumarse Zamanian & Steven J. Fenves

Implementing Topological Predicates for Complex Regions by Marcus

Schneider

A Spatial Logic based on Regions and Connection by David A. Randell, Zhan

Cui & Anthony G. Cohn

Class Notes

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Thank You!