Interactive animation of cities over time

Paul C. DiLorenzo Victor B. Zordan

Riverside Graphics LabUniversity of California, Riversidepdiloren, vbz, dttran@cs.ucr.edu

http://www.cs.ucr.edu/rgl

Duong Tran

Abstract

We present an interactive approach for an-imating the evolution of a city, adding toprevious work in computer graphics related toautomating the process of creating realistic-looking cities. Specifically, we combine thevisual aspects of a graphical model with anoptimization-driven solver to aid entertainersand urban developers alike in synthesizing thecontrolled growth and decay of a city overtime. Our approach uses a hierarchical modelbased on primitive units of zoning and variousheuristics taken from sociological and empiricaldata about real-world cities. We break downthe city spatially into primitive units of zoningblocks, and the system performs optimizationat this level to satisfy given constraints forgrowth (or decay.) Through this simplifiedmodel, animation for an entire city over anumber of years can be performed quickly.To display the results, the system generatesa visual representation of the city with build-ings on the zoning blocks. To control theurban development of the generated city, theuser selects parameters to control changes inthe size of the population and land area used.

Keywords: Computer Graphics, Three-Dimensional Graphics and Realism - Anima-tion, Simulation and Modeling

1 Introduction

In this paper, we explore the animation of a cityover extended periods of time as it grows andevolves based on changes in population and landarea use. To this end, we propose an interac-tive approach that uses a sociologically basedmodel and a hierarchy of levels underlying itfocused on faithfully capturing the visual arti-facts as a city changes over time. By abstractingaway unimportant details, we are able to createan evolving urban system that mimics many ofthe aspects apparent in real modern cities at in-teractive rates.

To model a growable city, our system takesadvantage of two key features found in real ur-ban settings. Nearly all urban areas have one ormore city centers, steadfast business districts atthe economic heart of the city, both metaphori-cally and physically. These city centers are filledwith mostly commercial buildings and usuallyhave the tallest buildings in the city, thus drivingthe look of the city to a large degree. Also, manycities are broken down into block-size, or larger,areas assigned based on zoning. These zonesenable city planners to designate different areasfor different uses, residential, commercial, mu-nicipal and so on. By looking at the city struc-ture as being built up from these types of zoningunits around city centers, we offer a representa-tion that can easily be controlled by manipulat-ing these two well-understood features and their

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attributes, as they change over time. We canalso use these special ‘building blocks’ to de-scribe a large amount about how urban cities de-velop fairly easily. For example combining mul-tiple zones, we can create large parks or residen-tial communities and breaking such zoning unitsinto their smaller, constituent components yieldsbuildings, yards, streets, and more - matchingthe real world.

With this model of the city, we cast the anima-tion problem as a constrained, two-point bound-ary problem that must be solved in order to meetthe expected growth (or shrinkage) based on thechanges in population or land area use, as in-putted by the software user. To solve this prob-lem, we follow the approaches used to solve thethief’s Knapsack problem, well-known in com-puter science, based on its likeness to our evo-lution problem. To show the power of our ap-proach we reconstruct the development of thecentral basin in Los Angeles over an eighty-yearspan. With our system, we are able to capturethe growth of the downtown city center of LosAngeles and, at the same time, recreate the de-velopment of urban sprawl indicative of growthin Southern California.

We anticipate approaches like the one pre-sented will be useful in the area of urban devel-opment and sociology, since they can estimatethe population and size of a city over a long timeframe and include intuitive visual results. Socialscientists and students alike can play out what-ifscenarios with such a system and see how andwhat factors affect the growth and developmentof the synthesized city. Likewise, we hope thistool will find its utility in next-generation realis-tic environments for computer games and enter-tainment.

2 Background

The automatic creation of graphical city mod-els has received some attention in recent years.With the popularity of urban-set games like‘Sim-City’ and ‘Grand Theft Auto’ as well asthe creation of large synthetic environments forthe ‘Matrix,’ ‘Terminator III’, and ‘Spiderman’movies, there is no doubt that the need for auto-matically generated, believable cityscapes is onthe rise. The techniques proposed for the gener-ation of such realistic urban models have eithersought to rely on pure data recorded from thereal world as in the project described by Teller

et al. [1], through direct hand-crafted efforts likethose of Hamill and O’Sullivan [2], via procedu-ral approaches such as Parish and Muller [3] orsome combination there-in. One popular hybridapproach combines simple 3D models with realphotographs to create virtual architecture, as de-scribed by [4, 5, 6]. Also, the creation of InstantArchitecture [7] follows heuristic rules from ac-tual architectural design plus procedural gram-mars created to mimic the look of real worldbuildings. While our work most closely mod-els that of Parish and Muller in the generationof our initial, static city model, none of these ef-forts have addressed the evolution of a city as itchanges over time.

Urban development and planning as well asthe study of sociological aspects of city unitshave given way to both a plethora of models fordescribing the growth and decay of urban set-tings as well as the need for visualizing such en-vironments. We conclude from this work andthat of Palen [8], that the factors that drive theevolution of a city are both vast and difficultto separate into simple heuristics like ‘the pop-ulation of modern cities is directly correlatedwith its wealth’ for example or other unifyingrules. While Batty and Longley have shown thatthe gross changes of real urban environmentsover time share characteristics with models ofurban systems generated using fractals [9], theyshed little light on the practical visualization ofsuch models for use in computer graphics or forthe novice user interested in understanding thegrowth of a city. As such, in our work, weglean insights from the experts about urban de-velopment such as the Burgess zoning modeldescribed by Palen and combine them with agrounded approach focused on generating a re-alistic, graphical urban settings that are able toevolve over time based on user constraints.

2.1 Urban Geography

Consulting texts in the area of urban stud-ies [8, 10, 11], we found three basic mod-els for the use of land in urban settings: theBurgess’ concentric zone model; Hoyt’s sectoralmodel; and Harris and Ullman’s multiple-nucleimodel. According to Palen [8], one early modelrising from urban “spatial-organizational con-cerns” was the concentric-zone hypothesis pro-posed by Burgess in 1924 [12]. This hypothesisexplains the segregation of land into business,

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manufacturing, and residential usages, as seen inmodern industrial cities and purports that thesecities grow radially in a series of concentricregions surrounding a central business district(CBD), as seen in Figure 1. The sectoral modelsuggests that, instead of zonal rings, cities de-velop in wedge-like sectors moving radially out-ward from the CBD and it makes allowances forgrowth along main arterial routes like highwaysand railways. The third, multiple-nuclei modelsays that land usage depends on a number ofseparate centers of activity for industry, man-ufacturing, entertainment and more. Becauseof its simplicity and well-defined structure, wefound the Burgess model most appropriate forour animation purposes, although the sectoralmodel and multiple-nuclei models do contain in-teresting features and attractive avenues for fu-ture exploration.

3 Building a city

Following urban land-use theories, we modelthe city by explicitly placing different typesof zoning units in discrete regions that matchthose proposed by Burgess, surrounding oneCBD and potentially a number of other city cen-ters. For simplification, we consider only twodifferent zoning types, residential, which en-compasses low-income, middle and upper classhousing, and commercial/municipal, which in-cludes business, manufacturing, and govern-ment land usage. We define density for the twotypes based on population density for residen-tial and the number of employees per squarearea, analogous to the amount or ‘size’ of com-merce in the commercial zones. The individ-ual density of each zoning unit varies and themaximum-allowed density in each zone is basedon its distance to the nearby CBD, following anormal-distribution Gaussian curve. The ratioof residential-to-commercial zones within eachregion is created heuristically, based on the de-scribed regions found in the Burgess model.(See Figure 1)

3.1 Origination of a simple city

To create the starting model following theBurgess hypothesis, our system starts from auser-defined CBD and constrains the placementof zoning units based on the desired populationof the city, the average number of individuals

Figure 1: Burgess city model. Surrounding thecentral business district (CBD) are re-gions which move from highly com-mercial to commuter’s suburbia. Weapproximate the ratios of residential tocommercial land area for the regionsoutside of the CBD at 30, 50, 70,and90 percent, respectively.

per household, and the overall span and devel-oped area of the city. The model also relies ona number of fixed terms based on real cities re-lated to the amount of commerce needed to sus-tain a given population and its difference be-tween regions, the shape and size of the zon-ing units, and parameters associated with thepopulation density and average size of domi-ciles within regions. For the simplest case, hav-ing a single CBD with no geographical obstruc-tion, the system first creates empty (undevel-oped) zones moving outward from the CBD un-til the city’s span, area At, is met and then ‘de-velops’ zones randomly, weighted by their dis-tance from the CBD, until the desired amountof developed area, Ad, is met. The relationshipbetween Ad and At is controlled simply by thepercentage of developed land in the city. To keepthe development close to the CBD center, thedistance is weighted by an exponential when se-lecting zones at random. During this initializa-tion process, the system also randomly assignszoning usages based on the percentages associ-ated with the Burgess’ region and density basedon the fall-off curve:

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ρ(r) = ρmaxe−r

2

2σ2rt (1)

where the r is the distance from the zone to theCBD, rt is the circular radius surrounding At

and ρmax and σ are the height and standard devi-ation of the Gaussian. A secondary pass throughthe developed zones makes small, uniform posi-tive corrections in the densities of zones selectedat random until the desired population is met.To do this, we compute the current populationby summing up the number of people each resi-dential zone holds based on density and the areasize of the zone. This origination algorithm isoutlined here.

3.2 Additional features

For more complex cities, we incorporate a num-ber of additions to the simple city, to accountfor multiple centers and for geographic limita-tions by generating zones based on specific con-straints. Since a real city with multiple citycenters usually shows different size and growthrates among those centers, we allow the userto assign relative densities and rates of growthbetween different centers and the system usesthese when assigning zones for each. Also, thezones of each center are given a unique orienta-tion that may be assigned by the user or based onsome geographic features, for example directionof the coastline.

Geographic features are specified through acoded image map of the terrain, where regions,such as bodies of water, represent areas whereno urban zones may occupy and other, ‘gray-scale’ regions are used to specify changes in el-evation. The system calculates slopes to deter-mine the developable areas automatically basedon a given steepness threshold. Once the set ofassignable zones is determined for each centerbased on these various geographic constraints,

the origination of the city follows along themethod described above with the exception thatρi for a given zoning unit in centeri may be re-placed by the density from another centerj ifthe computed density of Equation 1 is larger forthat zone due to centerj . This adjustment avoidsunwanted jumps in the density profile for thewhole multi-centered urban region. The justifi-cation for this is straightforward when consider-ing the urban creep across borders seen in areassurrounding metropolitan centers, for examplethe edges of New Jersey state near New YorkCity.

To generate the appearance of the city fromthe zoning units described, we use heuristics to‘build’ different numbers and sizes of structuresappropriate according to the type of zone and itsdensity. We describe this in the rendering sec-tion following the next section on the evolutionof the city over time.

4 Animating growth and demise

To synthesize evolution, our system solves thetwo point-boundary problem between a city’scurrent state and the new, desired state usingthe origination algorithm to ‘establish’ the initialcity and an incremental optimizer which man-ages its construction and destruction over time.Once the desired city is ‘built’ as describedabove, the user makes specifications to controlthe evolution of the city over some period oftime. Specifically, the user may change the over-all population and the physical size (land area)of the city and dictates the number of years overwhich the changes should occur. Then, an op-timization routine manages the construction andre-development of the urban zones based on auniform ‘growth schedule’. This schedule issimply the equal distribution of the overall de-sired change(s) over the given number of one-year spans. Then, during each year, the in-cremental optimization problem is to meet thescheduled changes without any errors, although,if errors associated with unmet changes do arise,they are simply rolled-over and incorporatedinto the subsequent year’s growth.

To solve the incremental optimization prob-lem, as stated, we compare the desired goalto the classic “Knapsack” problem, which isdescribed in any algorithms text (for example,see [13]). Mapping this algorithm to our city-development problem, we introduce “Citysack”.

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4.1 Citysack

We define Citysack as equivalent to the classicproblem, KnapSack, which states “A thief rob-bing a store finds n items; the i-th item is worthvi dollars and weighs wi pounds. He wants totake as valuable a load as possible, but he cancarry at most W pounds in his knapsack. Whatitems should he take?” or

maxn∑

1

vi such thatn∑

1

wi ≤ W (2)

Citysack is stated as “A city needs to grow (orshrink) by modifying some subset of n zoningunits; the i-th zone has a current density valueof vi and potential wi (ρ(r) − vi). In orderto meet the growth demands and minimize thepeople displaced, the overall change in densityshould be minimized while the total change po-tential, W , meets the new population require-ments. What zones should be constructed or de-stroyed and redeveloped?” or

minn∑

1

vi such thatn∑

1

wi ≥ W (3)

By casting the development problem very simi-lar to the Knapsack problem, we can take advan-tage of its known solutions and characteristics.

In order to apply Citysack to meet our urban-development goals, we make a few simplifyingassumptions. We treat all zones based only onthe density, the most critical aspect with respectto changes in population and land usage, so thatit can be isolated and most directly managed bythe optimizer. We associate a non-trivial cost,equivalent to the density, for the destruction of aunit. This prevents the optimizer from destroy-ing more than is necessary. We also consideredadding the ability for Citysack to use zone-by-zone vs. partial destruction and re-constructionwithin a zone which stems from its likeness toKnapsack in which the thief is allowed to takewhole or partial items in his looting. However,in practice, the former, so-called ‘0-1’ problemresulted in solutions that were easier to manageand showed little visual difference.

4.2 Solving the Citysack problem

To solve the stated Citysack problem, we mimicthe origination algorithm by first generating newzones if the size of At has increased and againrandomly build until the new desired developed

amount, Ad, is met. At the end of this stage,if the population supported by the city is aslarge as or larger than the target population, theevolution algorithm halts. The assumption hereis that any excess developed space will be leftempty and abandoned but this will not neces-sarily prevent new development from occurring.(This step is analogous to the thief taking itemsthat have value but weight nothing) If there is adeficit in the supported population, the evolutionstep must include some destruction and redevel-opment.

The Knapsack problem can be solved in anumber of ways. In [13], they propose usingdynamic programming to find a globally opti-mal solution for the ‘0-1’ Knapsack problem.We decided to use locally optimal methods be-cause the computation constitutes several ordersof magnitude speed-up over dynamic program-ming (O(n log(n)) vs. O(nW)). We proposetwo algorithms and apply the best solution of thetwo. The first is a so-called greedy approachthat picks the zone with the greatest potentialimprovement and redevelops that zone to reachits maximum potential (density.) This cycle re-peats until the target population is met or all po-tential improvements are made. The second is aconservative approach where the zone with thesmallest density-to-potential ratio is improved toits maximum potential, again repeating until thetarget population is met or all potential improve-ments are zero. While the conservative approachusually resulted in a lower cost neither schemeworked best in all cases. Thus, after calculat-ing, the algorithm compares the solutions andapplies the one with the lower cost. The sched-ule advances along with any resulting deficitsor surpluses to the following year. The pseudo-code below outlines this incremental animationalgorithm.

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5 Rendering and Results

To generate the final look of the city, zonesare decomposed into individual buildings. Thedecomposition from zone to building is depen-dent on the assigned density of the zone and onthe equivalent building or set of buildings thatwould occupy such a density. To simplify theplacement of buildings, all structures in a par-ticular zoning unit are assigned the same heightvalue. Obviously, this is not in general true, al-though there is often a high correlation betweenthe heights of neighboring buildings. The heightof a building, which drives the size of its foot-print and subsequently the number of buildingsper zone, is derived from the assumption thata uniform number of people will occupy eachfloor of a given building and so, the proper num-ber of floors, therefore, may be computed basedon the specified density of the zone or the integernumber of floors is round(ρh) where factor h

is normalized based on the maximum densityρmax and the max number of floors allowed inthe city. Thus, for example, if a particular zoneis close to the maximum density, a single largeskyscraper would be assigned to the zone. But,a zoning unit with a much lower density will bedecomposed into several shorter buildings. Forthe high-resolution models shown in figure 3,we use the commercial libraries of Marlin Stu-dios [14] for real-looking urban and suburbanstructures.

To show the progression of a city’s evolutionover time, we use simple edits that ‘fill in’ empty‘lots’ with buildings or cross-dissolve betweenone building and its replacement. Again, this isa simplification, but it is not practical to animateactual brick-laying or demolition. At the rateof the animation, about a year every second orso, we assessed that the simplest animation gaveway to the least amount of distractions and themost pleasing results.

LA Basin. In Figure 2, we show the devel-opment of the Los Angeles basin over an 80year span. Urban sprawl, that is common inthe southern California area, begins to becomemore prevalent as time goes on. In Figure 3, weshow three close-up views of Central Los Ange-les. The top close-up image is from our interac-tive software, decomposed into buildings, show-ing the residential and commercial buildings inred and blue, respectively. The middle close-upimage is a rendered version of the model gener-

ated. The bottom image is a photograph of Cen-tral Los Angeles. In Figure 4, we show the SantaMonica area, the leftmost city center in Figure 2.Santa Monica is nestled between the ocean andthe mountains and therefore is constrained bythese geological obstacles, and forced to moveinland to build. We colored the zoning unitsin four different ways (Burgess model, density,type, age) to show the depth of the model.

6 Conclusions

Animating the development of any urban envi-ronment requires serious concessions - in onlymodeling select, pertinent processes and ignor-ing many details to keep the computations fast.By simplifying the animation of cities to theincremental adjustment of ‘zone’ density andcomparing the optimization of this to a well-known algorithm, we are able to find solutionsthat are easy to understand and implement butstill produce complex graphical results becauseof a visual model that is interpreted from the un-derlying zone structure. Of course, these resultsare constrained to expose the particular artifactsimportant to the problem we chose as the focusof this paper, i.e. animating population and areachanges over time.

We expect to improve this system and itsimplementation as our current system does getsluggish when animating the large city scenes,like the Los Angeles basin example, but shouldbe able to find speed-up by exploiting repeatedpatterns both in the program calculations and inthe city model itself. Even so, without speed-up,it runs at 2.5 years per second with full OpenGLgraphics on a 2.8 Gz Pentium 4 processor withNVidia TI 4600 for a single-center type city withno geographical obstructions (see the image un-der the title). By adding main transportationnetworks, such as large roads or highways, wecan use sociological models such as the sectoralmodel. Also, the addition of inner roads wouldincrease the visual appeal of the zoning units.We anticipate that trees and parks, as well aspeople and traffic, would add immensely to thevisual appeal of the final results. Although wedo currently account for ‘empty’ undevelopedland, the overall results arguably appear stark.Also, our city system currently ignores factorslike fire damage, demolition, and vandalism aswell as many other known and documented arti-facts that influence a city. With proper demo-

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graphics, we could likely make the final datalook more realistic and possibly convey more in-formation through its animation.

We see that such city development softwarecould be used in number of scenarios. In the areaof entertainment for computer animated moviesthat take place over time, in a city setting thesoftware could be used to create a consistent ur-ban world with a past, present, and future. Withproper validation, such software could also beused in sociology - understanding how a cityworks, armed with measured data, a sociolo-gist could play out careful scenarios to assesshow different factors affect real cities. The soft-ware could aid in city planning when govern-ment officials want to visualize (or show) howtheir choices change things and what their po-tential consequences may entail. Note, we arenot claiming this real-world problem-solving isvalidated in the models we present currently.But, by basing our system on a steadfast soci-ological theory like Burgess’ and adding otherknown/proven constraints, this type of city an-imation could become a valuable tool for pro-fessionals. Through easy-to-control, interactivevisualizations of city evolution, even simple an-imation models can allow novices to learn andunderstand the workings of a growing city in anatural and intuitive way.

Acknowledgements

The primary author’s funding was provided by aUCR COE’s Dean fellowship.

References

[1] Seth Teller. Mit city scanning project:Fully automated model acquisition in ur-ban areas. http://city.lcs.mit.edu//city.html.

[2] John Hamill and Carol O’Sullivan. Virtualdublin - a framework for real-time urbansimulation. Journal of WSCG, Vol.11, pp221-225.

[3] Yoav I. H. Parish and Pascal Muller. Pro-cedural modeling of cities. In Proceed-ings of ACM SIGGRAPH 2001, ComputerGraphics Proceedings, Annual ConferenceSeries, pages 301–308, August 2001.

[4] William Jepson, Robin Liggett, and ScottFriedman. An environment for real-timeurban simulation. In 1995 Symposium onInteractive 3D Graphics, pages 165–166,April 1995.

[5] Paul E. Debevec, Camillo J. Taylor, andJitendra Malik. Modeling and renderingarchitecture from photographs: A hybridgeometry- and image-based approach. InProceedings of SIGGRAPH 96, pages 11–20, August 1996.

[6] William Ribarsky, Tony Wasilewski, andNickolas Faust. From urban terrain modelsto visible cities. IEEE Computer Graph-ics and Applications, 22(4):231–238, July2002.

[7] Peter Wonka, Michael Wimmer,Francois X. Sillion, and William Ribarsky.Instant architecture. ACM Transactions onGraphics, 22(3):669–677, July 2003.

[8] J. J. Palen. The Urban World. TheMcGraw-Hill Co. Inc., 1997.

[9] M. Batty and P. Longley. Fractal Cities.Academic Press, 1994.

[10] R. Northam. Urban geography, 1975.ISBN 0-471-65135-4.

[11] E. B. Phillips and R. T. Legates. Citylights: Introduction to urban studies, 1981.ISBN 0-19-502797-3.

[12] E. W. Burgess. The growth of the city: Anintroduction to a research project. Publica-tions of the American Sociological Society,18:85–97, 1924.

[13] T. H. Cormen, C. E. Leiserman, and R. L.Rivest. Introduction to Algorithms. TheM.I.T. Press, 1994.

[14] T. Marlin. Marlin studios, premium 3dmodels. http://www.marlinstudios.com.

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Figure 2: Los Angeles basin over 80 years.

Figure 3: Top: Central Los Angeles Simulated.Middle: Central Los Angeles Ren-dered. Bottom: Central Los Angeles.

Figure 4: Close-up of Santa Monica area fromthe simulated growth of the LA basin.Top: Burgess model coloring as seenin Figure 1. Second: Density of zon-ing units, lighter colors are less dense.Third: Type of zoning unit, blue com-mercial and red residential. Bottom:Age of zoning unit, dark representsolder construction

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