Procedural Modelling of Cities implemented as a Blender Plug-In

Transcription

1 Procedural Modelling of Cities implemented as a Blender Plug-In Submitted in partial fulfilment of the requirements of the degree Bachelor of Arts (Honours) of Rhodes University Kevin Mullane November 5, 2007

2 Abstract The task of procedurally generating a three dimensional model of a city has been approached in a number of different ways. This literature review aims to review the approaches taken. Particular attention is paid to the methods used by Parish and Muller in [8] as it forms the underlying basis for this research project. Issues surrounding the type and style of virtual city generation and its relation to real world cities are discussed. The various methods of road network generation and building generation and texturing are discussed. Finally the conclusion is reached as to why the methodology provided by Parish and Muller is the one best suited to the requirements set forth by the Text-To-Scene system.

3 Acknowledgements I would like to acknowledge and thank my supervisors Shaun Bangay, Kevin Glass and Hannah Slay for all of their guidance and constructive criticism throughout the development of this research project. Thanks must also go to the Computer Sceince department of Rhodes University and their corporate sponsors Telkom SA; Business Connexion; Comverse SA; Verso Technologies; Stortech; Tellabs; Amatole; Mars Technologies; Bright Ideas Projects 39 and THRIP for providing the facilities and resources which made this research possible.

4 Contents 1 Introduction Problem Statement Background Purpose of Project Text-To-Scene Project Applications of Procedural City Modelling Research Goals To procedurally generate a virtual city To apply real world city layouts within the city generation process To combine multiple layouts within one city Related Work Real and Virtual Cities Simulation and Fabrication Real World Cities Virtual Cities City Generation Methodologies Road Network Generation Template based road generation Generation Methods Local Constraints Shape Modification Building Generation Division of Lots Geometry Procedural Texturing

5 CONTENTS Summary The City Generation Process City Generation Implementation Underlying Landscape Representation City Region Generation Midpoint Determination Far Point Determination Highway Network Generation Intersection Selection Ray Creation Legality Testing Road Layout Evaluation Endpoint Adjustment Road Intersections Dead-End Removal Suburb Extraction Region Extraction Exterior Region Detection and Removal Suburb Region Resizing Road Network Generation Triangle Combination Triangle and Quadrilateral Subdivision City Block Extraction Building Generation Road Layout Implementation Side Road Subdivision Layout City Region Conversion City Region Subdivision Checkered / Raster City Generation Branching City Generation Radial City Generation Composite City Generation Summary

6 CONTENTS 4 4 Implementationpre Free City Generation Restricted City Generation Checkered City Generation Branching City Generation Radial City Generation Composite City Generation Summary Results Parametrization Free City Generation Restricted City Generation Checkered / Raster City Generation Branching / Growth Based City Generation Radial City Generation Composite City Generation Summary Conclusion Procedural Generation of a Virtual City Generation of Various City Layouts Checkered Branching Radial Composite City Generation Blender Plug-In Text-To-Scene Further Extensions References 42

7 Chapter 1 Introduction 1.1 Problem Statement This project aims to explore procedural techniques for creating virtual cities of varying styles and appearances through the implementation of various road layout templates or patterns. The aim is to procedurally generate these cities using little or no user input and for the cities to appear visually consistent with real world layouts and patterns. In order to assist with the visual representation of the created cities this project will also aim to briefly explore some preliminary techniques for building generation and repesentation. 1.2 Background Purpose of Project This section will discuss the purpose for undertaking research into the field of procedural city generation. Specifically it will discuss the need for city generation techniques which require no user input Text-To-Scene Project This section will briefly discuss the text-to-scene project and the various constraints and limitations which it applies to this project. 1

8 CHAPTER 1. INTRODUCTION Applications of Procedural City Modelling This section will review some of the possible applications of the techniques developed in this project. Specifically it will discuss the implications for the field of virtual reality as a whole and how the application of the methodologies discussed in this project will extend and diversify virtual reality and computer graphics as a whole. 1.3 Research Goals To procedurally generate a virtual city To apply real world city layouts within the city generation process To combine multiple layouts within one city

9 Chapter 2 Related Work The effective generation of a complex virtual city requires the combination of a number of individual issues which must be sufficiently resolved to allow for the modeling of that city. These issues range from the generation of a full transportation network to the generation of individual building structures which are both detailed and non-uniform. This research project uses as its base the methodologies employed by Parish and Muller in [8]. It is also however influenced by the various other approaches used in both virtual and real life city design. The prevalent characteristics of a generated virtual city are to a large degree defined by the overall goals of the generated model. The requirements for virtual cities can range from large scale visually complex environments for use in the computer game or motion picture industries, to smaller scale but more realistically complex environments used for transport and population simulations. The aims of this research project dictate that its overall goal is to assist in the development of a larger overall project, namely the Text-To-Scene project which aims to generate complex three dimensional scenes based on descriptive input text such as novels. A greater focus is thus placed on the visually realistic characteristics of the generated virtual city as opposed to other characteristics such as population density or transport efficiency. With the specific end goals of this type of virtual city generation in mind this review will aim to discuss firstly the major differences and similarities between real and virtual worlds including those attributes which are best suited for a visually complex city. Following this the two major aspects of city generation are reviewed, specifically the generation of a complex transportation network and then the generation of the individual structures within the city. 3

10 CHAPTER 2. RELATED WORK Real and Virtual Cities The underlying similarities and differences between real and virtual cities need to be understood to allow for better prioritization of which aspects of real world cities need to be modeled. This will allow for the generation of a complex and visually realistic virtual city. This section will first examine the characteristics and influences upon real world city design as discussed by Rob Ingram [5] and Parish and Muller [8]. The relevance of these characteristics to virtual city generation and specifically the generation of a visually realistic city is then discussed. Finally the various approaches to virtual city generation are discussed including the methodologies of [3], [6] and [8] Simulation and Fabrication Two major approaches to the topic of virtual city generation have been explored, the first aims at city simulation and is based on data input which accurately reflects an existing real world city. The second is a more procedural approach which attempts to generate unique cities with little or no user input. The methods used for city simulation depend on large amounts of accurate data being input into the system in various forms which may include aerial photographs or detailed statistical models of the city such as population densities. These techniques however rely on large amounts of input data and thus are not well suited to the overall goal of the Text-To-Scene project. In [4] the process of city generation from aerial photography is discussed and the end uses of a virtual city which is sufficiently complex and realistic as to mimic its real world counterpart for the process of simulation is discussed in [2]. These techniques however are not directly relevant to the outcomes of this research project and thus are not discussed further. The process of city fabrication based on minimal input data however is discussed in [8], [6], [7] and [3]. The benefits of each of these approaches will be discussed further with specific reference to the requirements of the city generation system and the Text-To-Scene system. In order to successfully fabricate a virtual city however an understanding of the defining characteristics of a city as an entity are required as well as the relevance of each of those characteristics to the overall city structure.

11 CHAPTER 2. RELATED WORK Real World Cities Ingram [5] discusses the required similarities between real world and virtual cities as falling under three broad categories. Firstly large scale design or the general layout of the city including the size and location of various areas within the city such as industrial and residential areas. Secondly the small scale design, this includes characteristics which are more directly related to the visual design and architecture of the various buildings and roads which constitute the city. Finally the concepts of governance and management are discussed, these include such overall layout decision as the zoning of particular areas to particular styles of structure such as housing in residential areas. All three of these categories play a significant role in the generation of a virtual world as they form the basic parameters which the system must incorporate in order to generate a realistic environment. One of the advantages of a virtual city is that some of the restrictions which exist in terms of real world city design do not apply to the generation of a virtual world. These restrictions range from the existence of industrial pollution which prohibits the direct proximity of industrial areas with that of residential areas to the restriction that the city exist on a single plane which is governed by gravity. Theoretically a virtual city can have roads which run perpendicular to the landscape and allow for the generation of cities with structures based around various axis of orientation. As Ingram discusses however this will result in the loss of realism and a certain inability of the end user to be able to relate to the virtual city. Therefore any generation of a virtual city should follow some of the basic constraints which have governed the creation of real world cities. Parish and Muller [8] cite some of the influences on real world city generation as being historical, cultural, economic and social changes over time this results in the complex layouts and interactions which we experience in modern urban areas. This would suggest that the major contributing factor to a cities layout and design is in fact the various changes it experiences over a large period of time, older real world cities such as Paris which have existed from medieval times for examples are defined by the circular nature of their road network. This reflects the city s reliance on a circular wall for protection at some point in its history. Parish and Muller however do not suggest that a virtual world must take into account a huge range of variables over a set time period in order to generate a realistic city, they would suggest that rather the visual components of the city must be generated in such a manner as to accurately reflect the overall effects that these changes may have had. Specifically [8] discusses the use of road patterns a method of defining the overall nature and layout of the city. The raster

12 CHAPTER 2. RELATED WORK 6 or checker pattern they suggest most accurately reflects those newer cities which benefited from the intentional design of the layout of the road network. Cities such as New York which are characterized by evenly spaced rectangular city blocks use the raster pattern for road network generation. The radial or concentric pattern they suggest most accurately reflects such cities as Paris where the layout of the road network was based around the existence of a circular wall surrounding the city. A branching pattern may best reflect the natural progression of a smaller settlement or town where no concerted effort was made to plan the layout of the road network, these branches often reflect the shortest path between areas of higher population density or local environmental features such as rivers or valleys. By deciding on the overall pattern of the city layout during the generation process a visually realistic virtual city can be created without the need for complex influence simulations over time. Christopher Alexander in [1] reviews the layout of two kinds of cities, specifically what he terms as natural cities or cities which have developed over a long period of time taking into account the effects of changing variables over time, and artificial cities which are planned in advance and develop over a relatively short period of time. This differentiation again highlights the effects that outside variables such as economic status and history can play on the layout and design of a city. Alexander suggests that we should envision cities as various collections of objects which interact with each other to form a much larger set which is the city itself. He suggests that each object within a city is a part of some set of objects and has a direct effect on those objects, these sets in turn intersect with each other so as to directly affect the existence of other sets. It is the collection of all of these sets of objects which can be most effectively defined as the city. Alexander then goes on to suggest that the components of this city set should not be seen as a tree structure where various sets and objects can exist on different levels of the tree and thus making the overall city set a sum of its constituent parts, but rather this set must be seen as having a semi lattice structure which better reflects the various relationships of each set with its constituent components and with other sets and their components. The resulting conclusion from this type of structure would suggest that any accurate simulation of a city would require the simulation of each of its constituent object and the accurate description of the relationship between each object and any other objects which it may influence Virtual Cities The requirements of the city modeling system would suggest that some of the complexity raised by Alexander [1] may not be relevant to the type of virtual city which is being produced. Were the system to be aimed at the accurate simulation of population activities or traffic flow, then

13 CHAPTER 2. RELATED WORK 7 these more stringent requirements would have to be met. The three categories of city design as suggested by Ingram [5] are still relevant to the generation of visually accurate virtual cities. In the process of virtual city generation decisions must be made with regards to the overall layout and style of the city, road patterns such as those suggested by Parish and Muller[8] can be used to determine this. Small scale decision regarding the style of individual buildings and the type of roads used must also be made and must be in keeping with the large scale decisions. The realism of a virtual city would be degraded if these two categories were not similar in design, for example a city with large five lane highways but small wooden structures would not appear as realistic. The decision regarding governance and management however should act to ensure that the previous two categories are in keeping with each other, further restrictions on the cities layout can be enforced through its governance, restriction which would lead to the grouping of sky scrapers together in the commercial zones of the city and the grouping of small residential housing in the suburban outskirts. Whilst the stringent requirements of a real world city may be relaxed within the virtual realm, this ultimately results in a complete loss of realism, thus the more realistic that the various large scale, small scale and governance decisions are made, the more realistic and thus believable the resulting city will be. This level of complexity must however be sufficiently managed in order to create feasible virtual cities as reflected by Parish and Muller as opposed to the infeasible model suggested by Alexander City Generation Methodologies Various different methodologies can be employed in order to create a virtual city each of which has its own defining features. Most of these methodologies however seem to agree on a clear distinction of the process into two separate parts, specifically the generation of a road or transport network and then the generation of city blocks and their constituent buildings. The various methodologies however have differing requirements in terms of input data, area planning and overall city requirements. Three methodologies will be discussed in further detail, specifically the methodologies employed by Mole [6], Greuter et al. [3] and Parish and Muller[8]. The first of these methodologies is that employed by Alexander Mole as a part of his creation of a Blender plug-in for the generation of complex city environments. This system requires that an existing model be used as input where building layouts are represented as simple geometric blocks within the scene. The methodology employed then aims to add varying levels of detail to that scene, specifically by texturing the blocks to more accurately reflect buildings, creating roadways between these buildings and then by setting up other smaller objects within the scene to handle street lighting and other effects. The overall aim of this methodology is focused at gen-

14 CHAPTER 2. RELATED WORK 8 erating a smaller urban scene which consists of a fairly limited number of structures and a small regular road network. This is therefore not well suited to the requirements of the city generator and the Text-To-Scene system is likely to require cities of varying sizes and complexities. The techniques employed in [6] seem more focused on the process of procedural detailing than that of procedural modeling. A second methodology for the generation of virtual cities is that employed in [3] which aims to create Pseudo Infinite virtual cities. This is achieved by generating a large square grid upon which various building models are placed. This methodology does not take into account any form of city layout or road planning, but rather relies on the large range of building design to give the impression of a larger city. Each individual bailing is generated by continuously scaling and rotating a building footprint upwards to create a random overall building shape. This process is particularly well suited to the creation of taller sky scraper types of buildings. The overall methodology employed does not allow for the open ended requirements of the Text-To-Scene system. The implementation of a road system with this methodology is to generate a perfectly square grid of roads which is so large as to make it unlikely that the user would ever reach the edge of the city. This limits the usefulness of the generated city as it cannot be effectively incorporated into any existing scene and thus could not be used for the Text-To-Scene system. For the purposes of this research project, the methodologies employed by Parish and Muller are the most relevant and thus form the basis for the methods used. This methodology is the one that is most in keeping with the three major criteria discussed in [5], it relies on the input of image maps to determine any natural barriers to city development such as rivers or mountains. This input however can be easily replaced by information drawn directly from the scene into which the system will be generating the city. Once the legal and illegal areas for development have been determined on the map, the system uses an complex self-sensitive L-System to generate a road map over the landscape. This road map is then used as a a guide to divide the reaming spaces up into lots through a simple subdivision algorithm. These lots are then populated with simple buildings using another L-System which generates strings to represent the geometry and logical operations which will be used to represent each building. Finally that geometry is generated resulting in a full complex model of a virtual city. This methodology appears to represent the most versatile and flexible system for procedural city generation.

15 CHAPTER 2. RELATED WORK Road Network Generation The process of procedurally generating a virtual city that conforms to the requirements laid out above begins with the generation of a complex road network. This road network must conform as much as possible to a real world road network and thus is controlled to a large degree by outside factors such as the underlying terrain and the overall style of the city being generated. Various methods for road construction are suggested in the relevant literature include the simple square grid system of roads used in [3] and the process of defining roads after the creation of the structures as implemented in [6]. The most common method and the most relevant to methodology which this research projects aims to follow is that of template or pattern based generation of road networks and suggested in [8] and [9] Template based road generation In conforming to the criteria suggested in [5] which suggests that a generated city should have large scale design decisions and small scale design decisions, the process of template based road design as suggested in both [8] and [9] allows for the road network to be generated dependent on an overall city style. One of the main features of both of these methods is that they differentiate substantially between highways and side streets, both suggest that patterns or templates be used to generate a large network of highways and then the gaps between these highways be filled with a simple straightforward grid pattern of side streets. Parish and Muller discuss the use of population densities to determine the path of each segment of highway. This relies on the premise that highway roads will naturally evolve to connect neighboring areas of high population density. This process gives each successive highway segment a general direction and length, the actual placement of the highway however then relies on the conformation of that highway segment to some overarching road pattern which controls the layout of the road network. These patterns can be basic which suggests that there is no superimposed pattern and that the highway segments simply branch naturally from one point of population density to the other. The rectangular or raster pattern defines each successive segment with a specific angle and a maximum length, by setting the angle to be either 90 or 180 degrees, and by keeping the road length constant this pattern can be used to generate a perfectly square grid pattern. The radial pattern adjusts highway segments to follow circular paths around a central point which can be defined randomly or through population density. A final road pattern that is discussed in [8] is the San Francisco rule where each highway segment follows the path of least elevation and thus results in a road which simply follows the contour of the underlying terrain.

16 CHAPTER 2. RELATED WORK 10 These highway segments are then connected by smaller side streets which are short and follow the steepest possible path from each point to facilitate the connection of the highway segments. Sun, Baciu, Yu and Green in [9] suggest a system which is very similar to the one suggested by Parish and Muller. Their system is also based on an overarching city pattern which defines each segment of highway, they however only discuss three types of template from which to design a city, the first is a population based template which follows much the same rules and the basic branching pattern proposed by Parish and Muller, the second is a raster and radial based template which is again very similar to the Parish and Muller suggestions and finally they propose a mixed template which combines the effects of both the population based and raster templates to generate mode complex and realistic city scenes Generation Methods The process for initial road segment generation in both [8] and [9] uses the concept of beginning at a point, usually the end point of the previous road segment and then generating a spectrum of rays emanating out from that point. Each of the end points of these rays are then checked against the chosen road pattern and the natural limitations of the terrain in order to determine the best possible choice. Once the best possible ray has been chosen, it is converted into a road segment and the process is repeated. In Parish and Muller the possible rays are passed through an extended L-System or road generation grammar which determines which variables are most relevant to each road segment and what their possible ranges are. It may decide that the road cannot rise at a elevation about 20 degrees and thus will remove all possible rays where the end point results in a road segment with such an elevation. It depending on the chosen pattern may aim for the point which has the highest population density. The process implemented in [9] whilst not specifically called a construction grammar or an L-System appears to perform much the same form of calculations in order to determine the initial position of the next road segment Local Constraints The process suggested by Parish and Muller differs from that suggested by Sun et. al. in its application of local constraints. Once the L-System has determined the best possible road segment from the collection of rays generated, the road segment must be checked against a range of local constraints to determine if it is in fact a valid road segment. Local constraints include such checks as the intersection of a road segment with another road segment. If two roads intersect and the resulting road segment is too short or the angle between the roads is two small, the road

17 CHAPTER 2. RELATED WORK 11 fails the local constraints check. A further check is to determine if there exists any other road segments or intersections within a set proximity from the road ending. This is used to connect the ends of roads back into the road network and allow for a continuous flow of road segments. If a road segment fails to meet the requirements of the local constraints, then the system attempts to find a suitable location within the roads immediate vicinity, this helps to overcome the problem of roads continuing into illegal areas on the landscape, if a road segment passes over an illegal area, the system will shorten the road until it no longer crosses that boundary and thus becomes a legal road. If no legal road segment can be generated in the immediate facility then the road segment is simply ignored and the process of segment generation continues. The conclusion of this method is the generation of a complex highway network that follows not only the overall constraints of the road pattern, but also generates safe road segments which do not clash with any of the natural constraints associated with the landscape Shape Modification Road segments are rarely ever straight lines and thus some provision must be made within the generated road network for curved road segments. In [9] Sun, Baciu, Yu and Green suggest a method of shape modification which converts a straight segment of roadway into a curved and twisting segment dependent upon the underlying terrain. The process involves recursively breaking each road segment into two equal halves and then adjusting the midpoint according to the elevation and distance from the endpoints. The system attempts to minimize changes in elevation for each successive midpoint, this therefore results in the generation of road segments which curve naturally with the contour lines of the underlying terrain. The more times this process is applied to the road segment the more curved the road will become. This process of recursive shape modification can be used to alter the road segments according to any number of factors dependent on the road template used. 2.3 Building Generation Once the process of road generation is complete the internal regions formed by the various road segments can be converted into city blocks and populated with buildings. There are a wide range of methods for building generation ranging from simple rectangular blocks with procedural textures to complex shape generation grammars which produce various building shapes. A texture is then added to the surface of the buildings geometry to enhance the realism of the scene. For simple rectangular blocks complex procedural texture as are required which specifically map such

18 CHAPTER 2. RELATED WORK 12 objects as windows and doors onto the blocks in order to give the impression of many different types of buildings. The more complex the initial geometry the simpler the added texture can afford to be as the buildings are no longer relying solely on that texture for their unique nature Division of Lots The first task associated with procedurally modeling buildings is that of lot division. The regions between the road segments generated for the scene must be populated with buildings. In [8] city blocks are created by scaling downwards from the road edges and intersections. These blocks are then broken up into smaller rectangular shapes through the use of a simple subdivision algorithm. Any resulting rectangle that does not face directly onto a street is deleted to reduce the quantity of work which the system must perform and the remaining rectangles are populated with building structures Geometry A combination of complex geometry and complex textures can be used to generate a large variety of realistic building models for use in the virtual city. The basis for this is the underlying geometry of the buildings. Parish and Muller [8]use a combination of scale and rotation transformations upon a simple geometric object to derive complex building models. Specifically a shape is created which represents the footprint of the building, this shape is then extruded upward and becomes the base of the building. The shape is then copied and transformed upward on the building to rest upon the previous shape, a shape grammar is then applied to the shape, this adds a number of scale and rotation operations to the shape within a set of parameters defined by the grammar. The resultant shape is smaller than the previous shape and sits above it on the building. This process is repeated with different scale and rotation transformations being applied each time as the building begins to grow upwards. The result is a geometrically complex building shape upon which various textures can be applied. An extension to this method of building generation is provided in [3] where the same process of footprint extraction is followed, with this method however the shape is constructed in the opposite direction. The initial polygon used forms the top of the building shape and as further steps for transformation are applied to each successive shape, the original shape is extended downwards. Thus once the process of building generation is complete, the initial;l shape still exists at the top of the building, but it also extends down through the building to the floor. At each successive step a new simple polygon is generated which is in no way linked to the previ-

19 CHAPTER 2. RELATED WORK 13 ous shape. This polygon is then shifted slightly off-center and rotated. The new shape is then extruded downwards by a variable amount and the process repeats itself. This method of generating the building geometry from the top down with various unrelated polygon shapes allows for even more complex and unique building shapes. This method however applies mainly to taller buildings and does not appear suitable for house type structures. Another extension to this system is provided in [7] where the bottom up approach is used, but it is combined with the idea of multiple polygon shapes. Thus a complex building footprint is generated through the combination of various simple polygons and each polygon is extruded up to a unique height generating complex building geometries. [7] also adds to this method my providing for roof surfaces which are generated at the top of each polygon shape to give the buildings unique sloping roofs as opposed to the simple flat top of the extruded shape Procedural Texturing The true complexity of the individual buildings generated for the virtual city are derived from procedural texturing techniques. [8] and [10] both describe systems which use shape grammars to translate the co-ordinates of a large sample texture to the specific co-ordinates of the relevant face of the building shape. By successfully implementing these shape grammars, a large sample texture which includes specific regions to represent doors, windows and other unique areas, can be used to map the door region of the grammar to the from bottom face of the building geometry. The results of this is the ability to turn fairly non-descript shapes which represent the individual buildings into complex unique shapes each with their own combinations of windows and doors. Wonka et al. [10] implement a more complex shape grammar then Parish and Muller and are able to map specific areas of the texture to specific regions of the shape, not only dependent upon the building shape, but also dependent on the neighboring textures. This allows for such combinations as windows and separate window sills. This allows for a relatively few sample textures to be used whilst allowing for a huge number of unique building combinations. 2.4 Summary The task of generating a procedural model of a virtual city which conforms to the requirements of the Text-To-Scene system provides many challenges and complex constraints. If some of the broader characteristics of real world city design are successfully implemented as is suggested by the methodologies reflected in [8] then the challenges can be overcome. Specifically a city can be fabricated using the minimal input or even random choice of a road pattern and building style.

20 CHAPTER 2. RELATED WORK 14 From this a complex network of highways and side streets can be generated which conforms top both the constraints of the landscape and the constraints of the city itself and the regions between these roads can be converted into a wide array of unique and complex building structures. The results of this process will be the procedural generation of a complex and visually detailed city.

21 Chapter 3 The City Generation Process The process of city generation involves many complex steps ranging from the definition of the overall city region to the extraction of building objects from the final city layout. This chapter looks to discuss and explain the various techniques and methodologies implemented throughout the design phase of this research project. Initially the techniques that are implemented are similar in nature to the techniques discussed by Parish and Muller in [8], however as the implementation process continued it became necessary to alter some of these techniques and introduce some new techniques to resolve implementation difficulties. Initially this chapter will review the simple case of generating a virtual city without any specific restrictions or adjustments, this will serve to critically review the basic process of city generation and the methodologies that are implemented therein. The chapter will then move on to discuss the various changes and adjustments that were made to the system in order to allow for the generation of more customizable and complex cities which are governed by specific city layouts. The specific implementation concerns which each layout requires will be discussed as well as the ability of the system to apply some of the lower level methodologies at higher levels and vice-versa. 3.1 City Generation Implementation This section will review the city generation process step by step from the initial city region definition through the process of highway and side road generation and finally the process of building generation. This unrestricted generation process will serve as a simple base from which further techniques and adjustments will be developed in order to accommodate the more complex requirements of restricted city generation and road template implementation. 15

22 CHAPTER 3. THE CITY GENERATION PROCESS 16 Figure 3.1: A Simple Landscape Representation Underlying Landscape Representation The initial environment into which a city must be virtually generated is assumed to be some form of underlying landscape. This landscape to a large extent defines the possible size and layout of the generated city, initially this landscape is assumed to simply represent the height of the land at any given point within the generated scene however it may also contain further information such as the existence of uninhabitable regions or illegal areas which a city object cannot be generated over. The underlying landscape object may exist in a number of different representation formats and some common representation must be decided upon to allow the city generation system to effectively incorporate the information stored within the landscape object. This common representation is assumed to be a simple mesh type of object which is defined by a list of vertices and list of triangular face objects which contain index references into the vertices list as shown in Figure3.1. This representation effectively conveys all of the relevant landscape information to the city generation system whilst also easily allowing for further extensions whereby certain triangular faces or groups of faces can be recorded as illegal areas on top of which city generation cannot occur. For the purposes of this initial discussion on unrestricted city generation however the landscape object is assumed to only consist of legal triangular regions City Region Generation Within the landscape object, a region must be set aside into which the city object will be generated. This region is defined by a n number of points on a single Euclidean plane, thus the region representation is two-dimensional and simply defines the area on the landscape which the city object is to be generated within. This region representation proves to be quite useful however as it easily allows for the system to determine properties such as the area of the city as well as the midpoint and the furthest point away from the midpoint. These properties are used by the system

23 CHAPTER 3. THE CITY GENERATION PROCESS 17 Figure 3.2: A Sample City Region to determine such properties as the height of building objects and the number of suburb regions which can successfully be generated within the city limits. The city region object is generated from assumed initial data, it is created from a list of co-ordinated which either the user or the overarching system such as the Text-To-Scene system can pass directly to the city generation system. This allows for city objects to be created in specified locations within an existing scene. Once the region is generated the triangular faces which constitute the region are determined. This is done to assist in checking that all elements generated by the system fall within the cities overall region. In order to determine the faces of the region, any point is selected and its two neighboring points are joined thus using those three points as a face. One of the neighboring points is then selected and it remaining neighbor is used to form a new face, thus in figure 3.3 v0 is initially chosen and thus v1 and v6 are used to form the first face. V6 is then chosen as the new starting point and the hypothetical line between v6 and v1 is used as one side of the next face, this leaves v5 to be added to the face and thus creating the second face (v6,v5,v1). This process is repeated until all of the regions points are included in at least one face. Thus the region object has been triangulated which allows for far simpler area and point intersection calculations Midpoint Determination In order to determine the midpoint of a region object, all of the regions vertices are added together and then divided by the number of vertices. This results in a vertex whose x, y and z values correspond to the midpoint of the initial region object. This central point can then be used to

24 CHAPTER 3. THE CITY GENERATION PROCESS 18 Figure 3.3: A City Region Object determine the starting point for highway generation as well as to determine the distance of any object within the city from the city objects central point. This is specifically used to determine the heights of buildings where the central region of the city object is assumed to have taller buildings and be representative of a cities central business district. Thus the formula for midpoint determination is midp oint (x,y) = (v.x, v.y)/n where n is the number of vertices in the region object Far Point Determination Once the mid point of the city region has been calculated each vertex of the region object can be tested against the mid point in order to determine what the furthest point from the city center is that is still within the city region. This point and its corresponding difference are relevant in that they can be used to determine the maximum size of the city object and thus the level of detail to which the city generation system needs to create objects. The lengths of generated highway road segments are set to be some proportion of the maximum size of the city thus ensuring that the city object is generated to scale with the size of the landscape and region object. The distance between any given point and the cities midpoint is given by d = (farp oint midp oint).x 2 + (farp oint midp oint).y 2 this formula is then applied to all of the vertices in the region object in order to determine which point is furthest from the central point of the region.

25 CHAPTER 3. THE CITY GENERATION PROCESS 19 Figure 3.4: A Sample Highway Network Highway Network Generation Once the system has a landscape and a region object defining the overall limits of the city object it will attempt to generate a network of highway objects. This network consists of two types of object, highway segments and highway intersections. The process of highway network generation is based on the techniques discussed by Parish and Muller in [8]whereby each successive segment of highway is generated by creating multiple rays which extend outwards from the previous intersection object. These rays are then used with the length parameter of the highway generation system to determine a number of possible points to which the next segment of highway will link. Each of these point are tested according to a number of criteria and the next point is chosen. This point is than made into a highway intersection object and a highway segment is generated between the previous intersection and the newly created intersection. This new intersection is then added to a queue of intersection objects which are used for further segment generation. This process is continued whilst there remain intersection objects within the queue, thus the highway network will continue to grow until all possible highway segments have been generated and the highway network is complete Intersection Selection In order for the highway network generation process to begin an initial intersection must be created and used as the initial point for ray generation. This point is created within the city region object by the system and is dependent upon the city layout that is currently in use, however in the case of the simple unrestricted city which is currently being discussed, this point can be assumed

26 CHAPTER 3. THE CITY GENERATION PROCESS 20 Figure 3.5: Ray Creation and Endpoint Generation to be the midpoint of the city region. This point is then added to a queue data structure which is used to store references to all of the intersection objects from which road segments have not yet been generated. The process of highway generation can thus continue whilst this queue is not empty. For each iteration of the highway generation process, the intersection at the from of the queue is removed and used as the starting point for ray creation Ray Creation The processes of ray creation and endpoint generation are illustrated in figure 3.5. The length of each successive road segment is randomly selected from within a range defined by the layout style of the highway network, also determined by the layout style is the possible arc of new road segments. This arc is determined by a range of possible angles which are defined within the highway layout and the length of the road segment. Thus an arc can be visualized as in 3.5 which encompasses all of the possible angles of road generation at the specified road length. This arc is then divided into a number of rays dependent again on the road layout that is being used. Each of these rays represents a possible road segment which the system may create, these rays are also used to determine the possible endpoints of the new highway segment. These possible endpoints are then each tested against various criteria before a final road segment is generated Legality Testing Once a list of possible endpoints has been generated through the process of ray creation, those points can be tested for their legality. This testing process first determines whether or not the point is within the limits of the city, this is achieved by iterating through the triangular faces of the region and determining if the point lies within any of the triangles. If the point does not exist within the region, then it is discarded as it cannot be used to generate a highway segment.

27 CHAPTER 3. THE CITY GENERATION PROCESS 21 Figure 3.6: Endpoint Legality Testing A second test is then performed on the remaining points, this time comparing them to each of the triangular faces of the underlying landscape, if the point falls within a triangle which has been marked as illegal, the the point is discarded. Finally the angle created between the new point an the initial point is checked against any other roads which link to the initial point, if the angle between the prospective segment and some existing segment is too small then the prospective point is discarded, this prevents new roads from being generated too close to existing road segments as in figure 3.6. Once this process of legality testing has been completed each of the possible points which remain for consideration are legal and thus road segments can legally be generated from the initial intersection to each of them.in the case of figure 3.6 point a falls within an illegal triangle, points B and C fall outside of the city region and point D creates a road segment which is too close to the existing road segment. Thus no points would remain legal and no road segment would be generated from this point Road Layout Evaluation The list of viable points is then passed into an assessing function which rates each point based on a number of criteria. These criteria are determined by the road layout that is currently in use and this is where the major implementation of differing road layouts takes place. Each point is evaluated according to the criteria set out by the layout which will rank the points from most to least suitable for the layout in use. The point that is most suitable is then selected and and the new road segment can be created between the initial point and the newly selected point Endpoint Adjustment The new section of road is then evaluated within the context of all of the other roads and intersections which currently exist within the city. The distance between the new endpoint and each

28 CHAPTER 3. THE CITY GENERATION PROCESS 22 Figure 3.7: Endpoint Adjustment other intersection is calculated in order to determine if this points falls too close to any other intersection. If the intersection falls within a set radius of another intersection, then the system attempts to use that intersection as the endpoint for the new road segment. As shown in figure 3.7the new road segment is adjusted to snap to the existing intersection. A check is performed to ensure that the newly adjusted road still conforms to the overall road layout and that the angle created on the existing intersection is legal, if the newly adjusted road does not conform to these two checks, then the road is discarded and the second best point from the list is chosen Road Intersections One final check is performed on a newly generated road segment before the process of highway generation moves on to the next intersection within its build queue. This check compares the newly created road segment to all other road segments in order to determine if they intersect. Any intersections between road elements are then divided up into four new road segments with a new intersection object being created at the point where the two road objects crossed, this new intersection object is then processed through the endpoint adjustment phase in order to verify that it is in fact a valid intersection Dead-End Removal The process of highway generation results in a complex network of road segment object joined by intersection objects. The majority of highway segements will link together in order to create enclosed spaces which can be used to represent suburb regions. One final step is undertaken in the highway generation process, all road segments which only connect to the highway network through one intersection, specifically dead end segments of highway are removed. These road segments are removed by traversing the list of intersection objects associated with the road

29 CHAPTER 3. THE CITY GENERATION PROCESS 23 Figure 3.8: Road Intersections Figure 3.9: Dead-End Removal network, any intersections which have only one associated road segment, represent a dead end. These intersections and their associated road segments are removed from the network in order to allow for regular enclosed regions for the process of suburb extraction Suburb Extraction Suburb extraction or region extraction is applied to the completed highway network model in order to extract the enclosed suburb regions which are then divided up into smaller side roads and intersections. The process of region extraction requires that all completely enclosed spaces within the highway network are extracted and stored as separate region objects. The enclosed spaces are represented by a region object similar to the overall city region object. A region extraction algorithm was implemented which takes in the lists of intersections and road segments stored by the highway network object and returns a list of all of the regions contained within that network. These region objects are then used to create suburb objects, these suburb object are used to store information and parameters which apply only to the roads and structures within the suburb region. This allows for the creation of complex and varied virtual cities as each suburb

30 CHAPTER 3. THE CITY GENERATION PROCESS 24 Figure 3.10: Suburb Extraction from Highway Network can apply separate parameters to the side roads and city blocks within its region. The regions used to generate suburb objects are also scaled down in order to allow space within the model for the road objects to be represented. Each suburb object stores the side road network which is generated within the region of the suburb, as well as a list of all of the city blocks which are formed in the enclosed areas created by the side road network Region Extraction The central component to subor growthurb creation is the process of region extraction which aims to separate out each fully enclosed region created by the highway generation system. In order to allow for effective region extraction, each road segment object stored two additional properties, the number of regions which the segment forms a part of and a Boolean value which records which direction the segment has been traversed.the region extraction process begins with the selection of the first road segment which is associated with only one region, if all segments are associated with either no regions or with two, then any segment with no associated region is selected. Once a road segment is selected and the path traversal begins, at each intersection the angles of each of the other connected roads is determined and the smallest angle is chosen for the path as with the blue arrows in figure This ensures that the extraction algorithm traverses the region around its shortest path. As each segment is traversed the number of regions with which it is associated is incremented and the Boolean value is used to indicate whether the traversal was forwards or backwards. Each segment can only be traversed twice, once in each direction.the traversal continues until the intersection encountered is the same as the intersection

31 CHAPTER 3. THE CITY GENERATION PROCESS 25 Figure 3.11: (a) (b) Region Extraction - (a) Normal Extraction (b) Conflicting Traversal Problem which the region began with. At each step of the traversal, the intersection encountered is added to a region object, and once the first intersection is the same as the last a complete region has been extracted. The process of region extraction continues until each road segment has been traversed twice and thus is associated with two region objects. Each segment can only be traversed once in each direction in order to prevent the algorithm from creating region object which wholly contain other smaller regions, once a segment has been traversed in direction, then no other region can attempt to traverse that segment in the same direction. By selecting any road segment which has been associated with one region before any that have notwithin more restricted environments. the system ensures that neighboring regions are determined first and thus it avoids the possible problem of having two regions which share a commothe Results of Suburb Extractionn neighbor being traversed in opposing directions. This would lead to a situation where the common neighbor would not be traversal as two of its segments would have opposing directions as in figure 3.11(b). The system thus determines the first region and then works outwards from that region in order to determine the remaining regions. The process of region extraction thus returns a list of region objects representing all of the autonomous enclosed regions within a road network, as well as the region object which represents the external region around the outside of the road network. This exterior region however is unnecessary and creates complications for further steps of the city generation process and thus must be removed Exterior Region Detection and Removal The exterior region which the region extraction algorithm generates needs to be removed as it is treated by the system as region which perfectly covers all of the other suburb regions. This region is thus a combined duplicate of all of the other suburb region objects. In order to determine the exterior region, a sum total is kept of all of the angles used in the traversal of a path. This total is

32 CHAPTER 3. THE CITY GENERATION PROCESS 26 Figure 3.12: Sum of Interior Angles increases by Pi with each added side then compared to the number of sides or segments in the region and it can be easily determined which region was constructed from all of the exterior angles around a highway network. The sum of the interior angles of a triangle is Pi and as shown in figure 3.12, for each extra side added to a shape the sum of the interior angles increases by a further Pi. This is because each successive side that is added creates a further triangle within the shape. Thus in order to determine the sum of the interior angles of any polygon the following can be used, angles = (numsides 2)/P i. Thus each of the regions that the system generates can be tested to verify that the sum of their interior angles is correct, if the sum is greater than expected then the region was developed by traversing the outside of the shape and thus accumulating the exterior angles of each intersection. This region can thus be discarded and the remaining list of region objects converted into suburb objects and their parameters adjusted to produce the required city Suburb Region Resizing The region objects are generated from the center of each intersection object and thus they cover the enclosed areas completely without leaving any space for the visual representation of the road objects themselves. Thus the region objects have to be reduced slightly, this is achieved by determining the region s midpint as discussed in and adjusting each of the regions verticies towards the midpoint by a factor of the distance between the midpoint and the point itself. v (x,y) = v (x,y) (midpoint (x,y) v (x,y) )/p

33 CHAPTER 3. THE CITY GENERATION PROCESS 27 Figure 3.13: or growth Side Road Generation from Suburb Regions Road Network Generation A separate methodology was chosen to generate the side road network within each suburb region, instead of generating the roads outward from some central point according to various production rules, regions are subdivided down into more complex and regular mesh s which can be directly converted to road and intersection objects. This approach was adopted as it results in a more regular grid of side road objects which fill the entire suburb region. The side roads do not affect the overal layout of the city in the way the highway roads do and thus do not have to conform to the chosen road layout. As a result the approach used for road network generation is one based on a subdivision scheme. Due to the regular rectangular nature of city blocks and side roads, the aim of the subdivision mehtod was to fill the region with as many regular quadrilateral objects as possible whuch could then be used as city blocks for the representation of building objects. The process used is composed of two stages, firstly the region object is broken up into triangle faces as discussed in and then these faces are recombined in a pairwise fashion in order to create as many quadrilaterals as possible from the original region. The resulting shapes are then subdivide further and the pairwise matching of faces is reapplied in order to generate further quadrilateral obejcts. The edges between these faces are finally used to create side road objects and the vertices of the faces are used to create intersection objects Triangle Combination In order to create as many rectangular blocks as possible throughout the road generation process, an attempt is made to combine neighboring triangle objects in order to create quadrilaterals.

34 CHAPTER 3. THE CITY GENERATION PROCESS 28 Figure 3.14: (a) Triangle Combination (b) These quadrilaterals however need to be convex in nature to prevent the creation of illegal side roads which intersect with other road objects as shown in 3.14(a) once the resulting quadrilateral is subdivided further. Thus a check must be performed on all of the interior angles within the newly created quadrilateral to ensure that they are all below a maximum of Pi. This will ensure that the quadrilateral objects created are at a minimum convex in nature and thus can be succesfully subdivided. Further adjustment of this maximum angle can then be used to adjust the resulting side road network. Figure 3.14 (b) shows the resulting quadrilaterals when the angles are restircted to Pi Triangle and Quadrilateral Subdivision A simple midpoint subdivision method is used to further divide the triangular and quadrilateral objects. This method involved creating new endges that linked all of the midpoints of the previous edges. In the case of a triangle this results in the division of the triangle into four smaller triangle shapes as shown in 3.15(a), quadrilaterals have the midpoints of opposite sides joined in order to maintain the quadrilateral shape for the resulting faces as shown in 3.15(a). Figure 3.15(b) shows that by applying the triangle combination step to the triangles that result from subdivision can result in the combination of two of these triangles into a further quadrilateral which can then be further divided into more regular quadrilaterals. The repeated application of the subdivision step and triangle combination can be seen in figure City Block Extraction The process for city block extraction follows the same approach as that used for suburb extraction as discussed in where the region extraction algorithm from is applied to the side road network developed by subdividing the suburb region. The region extraction process will again

35 CHAPTER 3. THE CITY GENERATION PROCESS 29 Figure 3.15: (a) (b) Midpoint Subdivision And Triangle Combination Figure 3.16: Repeated Application of Midpoint Subdivision and Triangle Combination

36 CHAPTER 3. THE CITY GENERATION PROCESS 30 Figure 3.17: City Block Extraction from Side Road Network find the exterior region and thus it mus again be removed as discussed in These city block region also have to be resized as discussed in in order to allow for the representation of side streets. The final step applied to the city block objects is that the block is subdivided with the same method as and the resulting faces are used to generate building objects. Due to the nature of the triangular city block objects these are not sed for the process of building generation, but are rather left open as some form of open area within the city limits, thus all quadrilateral city blocks will contain four building objects whilst triangular objects will only contain one after its triangular faces have been recombined Building Generation For the purposes of the aims of this thesis fairly rudementary building objects were required that simply gave the impression of an urban city environment. The process of building generation is therefore simplstic and allows a large area for future work in this field. In order to represent building objects, the base region of each building as recived from its parent city block object is simply extruded upwards to a height which is randomly chosen with a range defined by a number of factors including the suburb parameters, the size of the overall city and the location of the suburb within the city and the block within the suburb. Due to the procedural nature of this system, the buildings height is decided as a factor of other paramters within the system that all ultimately rely on the overall size of the city object..

37 CHAPTER 3. THE CITY GENERATION PROCESS 31 Figure 3.18: Building Extrustion 3.2 Road Layout Implementation The defining attribute in the procedural generation of an urban city is the choice and application of a road layout to the city generation process. Road layouts primarily affect the highway generation process and thus set the look and feel for the overall city. A number of road layouts have been discussed and this section looks at the implementation considerations which are raised by the implementation of the various layouts. Initially the possibility of implementing no road layout, but rather implementing a futher step of the subdivision methods discussed in is discussed and then each of the three styles of road generation are discussed. Finally this section looks at the possibility of implementing a second level of highway generation prior to suburb extraction, this approach would allow for the creation of composite cities which incorporate various road layout styles Side Road Subdivision Layout In order to accomodate the implementation of a level of subdivision rather than the typical highway generation as discussed in the system would lose its ability to accomodate illegal areas within the city region as each road segment would not longer be checked for legality and it would lose much of its parameterization and variation as the subdivision step will result in the same road layout each time it is applied to a specific city region. In order to change the overall layout of the city, the inital city region would have to be altered. The implementation of this style of road layout however would be achieved in two separate steps, intially the region object itself would