emily whiting john ochsendorf frédo durand massachusetts institute of technology, usa procedural...

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Emily Whiting John Ochsendorf Frédo DurandMassachusetts Institute Of Technology, USA

Procedural Modeling ofStructurally-Sound Masonry Buildings

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virtual environments

• models require visual realism• important to interact physically

with surroundings

state of the art• simple models• or react in scripted ways

architectural models

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structurally stable• will look more realistic• suitable for physical simulations

– react to external forces


our result

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structurally stable• will look more realistic• suitable for physical simulations

– react to external forces

earthquake simulation


our result

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Generate models that are structurally sound

• Inverse Statics

• Procedural modelingquickly generates complex architectural models

• Masonry material

goal

unstable input stable output

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Focus is on visual realism, mainly for detail in façades

our contribution: introduce physical constraints

related work procedural modeling

Parish et al. [2001] Wonka et al. [2003] Müller et al. [2006] Müller et al. [2007] Lipp et al. [2008]

[Muller et al. 2006]

8 [http://www.csiberkeley.com/]

related work structural analysis

Elastic Finite Element analysis

wrong physical model for masonrynot deformable

elastic material

stress profileoutput is visualizationsolves forward problem not inverse

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related work structural analysis

geometric configuration

rigid block assemblage [Heyman 1995]

linear constraint formulation[Livesley 1978, 1992; RING software]

elastic material

masonry

vs.

analyze material stress

wrong physical model for masonrynot deformable

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Non-Structural• Architectural free-form surfaces

[Pottmann et al. 2008]

• Variational surface modeling[Welch and Witkin 1992]

• Layout design [Harada et al. 1995]

Structural• Structure optimization

[Smith et al. 2002; Block et al. 2006]

• Tree modeling [Hart et al. 2003]

• Posing characters [Shi et al. 2007]

related work design by optimization

[Smith et al. 2002]

[Pottmannet al. 2008]

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procedural building generation

analysis method for masonry

inverse problem

overview

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procedural modeling

[Muller et al. 2006]

production ruleinput shape production type (parameters) {output shapes}

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procedural modeling

input shape production type (parameters) {output shapes}

library of primitives

production rule

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procedural modeling



production rule

production• subdivision, scale, translation, …

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procedural modeling



production rule

typical parameters• height• thickness of columns, walls, arches• window size• angle of flying buttresses

production• subdivision, scale, translation, …

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procedural modeling

A Repeat(“x”,0.2){B} B Subdiv(“y”){“wall”|C|”wall”}

C Subdiv(“y”){D|”arch”}

A

D Subdiv(“x”){E} E S(0.2,1,1){“wall”}

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• blocks: mass• interfaces: contact

surfaces between blocks

Output

procedural modeling

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inverse problem

overview

conditions for stability

• static equilibrium

• masonry compression-only

analysis overview

0

0

torques

forcesfor eachblock

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conditions for stability

• static equilibrium

• masonry compression-only

analysis overview

requires tension

feasible

0

0

torques

forcesfor eachblock

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linear system of equations

static equilibrium

weights,torques

geometrycoefficients

forces

each block0

0

torques

forces

Aeq· f + w = 0

weight, wj

f i

f i+1

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masonry

0inf

compression-onlypositive normal forces

inf

no “glue” holding blocks together

normal force

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linearized as pyramid

friction cone

in

it

it fff 21 ,

inf

itf 1

itf 2

normal forcefriction force

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summary model of feasibility

Stable solution existsUnstable no solution exists

unknownforces, f

Aeq· f + w = 0 static equilibrium

fni ≥ 0 compression

Afr· f ≤ 0 friction

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Stable solution existsUnstable no solution exists

unknownforces, f




Problembinary,solution f exists yes/no

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Problembinary,solution f exists yes/no

tension required to stand

how much “glue”

Our Solutionmeasure infeasibility





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tension required to stand

how much “glue”

Our Solutionmeasure infeasibility

measure of infeasibility




tension

relax constraint

minf

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fni = fn

i+ – fni- where fn

i+ ≥ 0 fni- ≥ 0

tension

split into positive, negative components

normal force variable transformation

compression

inf

e.g. for compression forces fni+ > 0

fni- = 0

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2)( inf

s.t.

minf

Aeq· f +w = 0 static equilibrium

fni+ ≥ 0, fn

i-≥ 0 allow tension


Quadratic program

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2)( inf


fni+ ≥ 0, fn



s.t.

minf

Quadratic program

scalar output y

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2)( inf


fni+ ≥ 0, fn



s.t.

minf

Quadratic program

y = 0 feasible

y > 0 measure of infeasibility

scalar output y

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inverse problem

overview

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ProceduralModel

feasible?

Analysis

parameters

optimization loop

Update Parameters

model fromoutput

parameters

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ProceduralModel

feasible?

parameters

nested optimizations

Update Parameters

model fromoutput

parameters

quadratic program

minimum tension at parameters

pi

pi+1


quadratic program


pi

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pi+1 update parameters

y(pi)

update parameters


quadratic program


pi

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pi+1

y(pi)

find parameters for feasible structure, want y(p*) = 0

update parameters

find parameters for feasible structure, want y(p*) = 0


quadratic program


pi

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pi+1

y(pi)

nonlinear programarg minp y(p)

MATLAB active-set algorithm, gradients with finite differencing

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p0

arch example

column widtharch thickness

columnwidth

archthickness

feasible regionzero tension

2)( tension

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Results

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typical parameters

• building height• thickness of columns,

walls, arches• window size• angle of flying buttresses

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results sainte chapelle

tension forcesunstable model frominput parameters

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results sainte chapelle 486 blocks, 17 sec/iter

4 parameter optimizationunstable model frominput parameters

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results sainte chapelle 486 blocks40 sec/iter


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results Bezier curves


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results tower

32 parameter optimization

96 blocks,12 sec/iter

unstable model frominput parameters

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results tower

with safety factorunstable model from

input parameters 32 parameter optimization

96 blocks,12 sec/iter

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• manually modify fixed parameters• re-optimize free parameters to retain stability

usage scenarios exploration

Exampleuser changes roof span

automatically update angle of flying buttress

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Load models into dynamic simulation

Bullet Physics Engine[http://www.bulletphysics.com/]

usage scenarios dynamics

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ground shake

Bullet Physics Engine [http://www.bulletphysics.com/]


51Bullet Physics Engine [http://www.bulletphysics.com/]


projectile

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blocksremoved



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• Inverse analysis method

• Procedural modeling to specify design parameters

• Measure of infeasibility

• Optimization scheme to generate stable models

summary stable buildings

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Singapore-MIT Gambit Game Lab

NSERC Canada

Phillippe SiclaitSylvain Paris

Yeuhi AbeJovan PopovicEugene Hsu

thanks...

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• Inverse analysis method

• Procedural modeling to specify design parameters

• Measure of infeasibility

• Optimization scheme to generate stable models

summary stable buildings

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extra slides

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ground shake

∆ ground velocity = 4 m/s

time step = 1/60 s

model width ~ 10 m

Bullet settings:

restitution (bounce) = 0.0

friction coefficient = 0.895



model #blocks #params #iters time/iter

Cluny 986

4579

10549

45.7 s57.3 s70.0 s

106.6 s

arch 10 2 6 0.1 s

SainteChapelle

486

357

10

4968

12.5 s26.5 s29.3 s40.1 s

tower 96 32 6 12.5 s

barrel vault 140 1 8 0.6 s

performance

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emily whiting john ochsendorf frédo durand massachusetts institute of technology, usa procedural...

Documents

inverse slide

deformable slide

procedural modeling

usa procedural modeling

production subdivision

output shapes

tree modeling hart

sound masonry buildings