An interactive computational methodology for urban mixed-use allocation according to density distribution, network analysis and geographic attractions P. Nourian1, S. Sariylidiz,2, S. Rezvani3 1
PhD researcher in Computational Urban Design, Department of Architectural Engineering + Technology, Chair of Design Informatics, Delft University of Technology, the Netherlands. Mail:
[email protected] 2 Professor, Chair of Design Informatics, Head of Computation and Performance Research Section Department of Architectural Engineering + Technology, Delft University of Technology, the Netherlands. Mail:
[email protected] 3 MSc student of architecture Politecnico di Milano/Guest Researcher in Computational Design, Delft University of Technology, the Netherlands, Faculty of Architecture, Chair of Design Informatics Mail:
[email protected]
Abstract Urban density distribution and mixed-use allocation patterns are considered to be affected primarily by the inherent spatial structure of urban neighborhoods and the geographic attractions of the district that affect people’s choices in movement and settlement. The space syntax theory (Hillier, Space is the Machine, 2007) clearly relates the configuration of urban grid to urban functioning in terms of its effect on the distribution of densities, allocation of land uses such as retail and residence: “Land uses and building density follow movement in the grid, both adapting to and multiplying its effects.” (Hillier, Space is the Machine, 2007, p. 127). It states that a spatially successful city is characterized by the “dense patterns of mixed use”, which are mainly settled as a consequence of movement, which is itself brought about by the grid configuration (Hillier, Space is the Machine, 2007, p. 4). Yet, space syntax theory is merely analytic per se and does not provide any means for ‘designing’ “spatially successful cities”; besides, it does not consider the geographic idiosyncrasies of places and their gravity-like ‘attraction’ effects in its models of movement patterns; and thus their effect on mixed-use allocation patterns. It is explicable that in vernacular settlements and in old harmonically grown cities we find a close correspondence between spatial configuration, geographic idiosyncrasies, density distribution, and mixed-use allocation patterns. However, it is important to know how to develop or change new settlements in such a balanced way. The inherent mathematical complicatedness of the abovementioned patterns, their interrelations, and their fundamental importance in the functioning of a city fully justifies the use of computation for supporting design and decision-making processes. This paper introduces a computational design methodology that relates the urban built-space density distribution and mixeduse land allocation patterns to network configuration and geographic attraction effects, guaranteeing that mixed-use allocation both complies with regional plan and local features. The proposed methodology embraces an inter-subjective understanding of place into the computational design process and combines it with the objective spatial measures such as centrality, integration, and walkability. The computational design approach presented in this paper is an effort for merging the split fields of urban planning, spatial analysis, and urban design. The computational methodology introduced in this paper is implemented within a tool-suite of computational methods for network analysis, built space density distributions, functional allocation techniques, weight/charge handlers, and equalization methods that guarantee the consistency of design alternatives with analysis results. Keywords: Computational Design, Mixed-Use Allocation, Density Distribution, Network Analysis, Geographic Attraction
Proceedings of the International Conference on “Changing Cities“: Spatial, morphological, formal & socio-economic dimensions ISBN: 978-960-6865-65-7, Skiathos island, Greece , June 18-21, 2013
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Introduction In urban planning and urban design processes, it may happen that a program of functional requirements is demanded from the regional authorities corresponding to their master plans that describe a scale of development plans, larger than those of local development do. A relevant question would be how to comply with such regional plans, in allocation of uses to the urban lots, while being able to decide on the land-uses at a local scale? It will be shown in this paper that the two regulatory demands can be essentially in conflict with each other as they are to make decisions about the same entities from two entirely different points of views, say local and regional. For instance, suppose that the regional authorities of a province have decided (rationally) that the total amount of residential built-space needs to be a certain amount of square meters at a district level, and that the total amount of industrial land-uses to be of some other quantity and so on for some other uses. On the other hand, in local planning we want to make sure we allocate the uses spatially in such a way that certain functions appear where they fit, say close to geographic attractions1. In this case, we need to designate certain portions of built-spaces for several functions and make sure that the total amount of land-uses of each kind equal to the amount demanded by the regional plans2. The reason for which we should be able to meet the regional plans is rather obvious: that the regional plans (ideally) are devised considering the regional potentials and features, a scale that is not observed when dealing with local issues. Besides, an appropriate mixed distribution of landuses at a local scale, matching with the geographic features of a district and its spatial configuration is a key to the well-functioning of urban districts; this is the state defined as the “dense patterns of mixed use” by Hillier in (Hillier, Space is the Machine, 2007). In fact, the problem of land-use allocation in this sense is a matter of rational transition between scales of planning and design. The theoretical underpinnings of the research presented in this paper are based on the theory of space syntax, particularly in that space syntax theory considers urban environments as spatial configurations. However, the network analysis methods referred to in this paper are different from those of space syntax and are independently developed based on graph theory. In this paper, we will present a computational methodology that allows for spatial distribution of district mixed-use programs such that users (planners) can interactively change the local pattern of allocation by interactively changing the weights (charges) of importance for spatial attractors. The present paper introduces the preceding part of a computational process of design and planning that begins with density distribution according to configurational structure of a street network and geographic attractions. The first two steps of this process are introduced by authors earlier in (Nourian, P, Sariyildiz, S, 2012). The idea of this computational process is to make sure we get a distribution of built space and uses according to the spatial structure of urban districts. Definitions, Notations and Formalism Suppose we are to allocate land-uses to a list of urban blocks within a district for which a functional program is demanded by a regional master plan, in terms of percentages of certain functions within that district, e.g. 70% Residential, 15% Retail, 5% Public Facilities, 5% Small Industries and Farms and 5% to be of flexible uses, given the built-areas available per urban blocks as gross floor area3 1
The term attractor is used in the literature to suggest a gravity-like effect. This is indeed just a metaphor here; nothing is really ‘attracted’ towards a place, nor there is a force as such; however, it is that some effects/phenomena are stronger where closer to certain places. This is referred to as the Tobler’s first law of geography: “Everything is related to everything else, but near things are more related than distant things”. There is a classical tradition of relating to the gravity law of Isaac Newton for explaining spatial interactions; a review of such models can be seen in (Kingsley E. Haynes, Fotheringham A. Stewart, 1984). In the process reported in this paper a different approach is proposed, but the term, attractor is chosen for its visual association. A similar approach to mixed-use allocation problem has been followed in (Beirão, J., Nourian, P. & Mashhoodi, B., 2011)). 2 In fact, the problem is the same for every two successive scales of planning. 3 This gross floor area is the total floor areas of buildings within a block. However, for the sake of utmost clarity of representations, all the images in this paper show a situation where the area of block outlines are considered as their
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GFA in the cells indexed with
, noted as
Ǥ
Within these blocks, a number of functional spaces (known as land-uses) are to be distributed and the sum of each functional built space is to be of a certain percentage of the available built space. For example in the mentioned case, the sum of each residential uses in all blocks should be equal to 70% of the regional plan program. On the other hand, there is supposed to be a spatial pattern of various ‘percentage mixture’ of land-uses for each urban block, such that certain functions emerge more where closer to certain urban entities. Conventionally this effect is referred to as distance decay effect; suggesting that the effect of presence of some object/entity is greater when closer to it. For example a block which is closer to the city center favors more residential uses than another block which is closer to city skirt. An ‘attraction effect model’ or ‘distance decay function’ can change the intensity of each function based on given weights to locations (attractions). The idea is that for each function we consider a particular field of attraction, considering how different locations favor the emergence of various land-uses. In any case, each urban block can ultimately accommodate functional spaces up to its own capacity, which is the built space available at that location. Main Question Is it possible to have various mixtures of land-uses in various locations (indexed by ) satisfying the above constraints? Following is a mathematical notation of the problem: It is assumed that each location has (can have) Total area available for all locations is noted as a portion of this area
the portion factor is noted as
. Such that:
(1) ; with the portion factor noted On the other hand, each function/land-use ( ) has a portion of as (either given as percentages or normalized as a list of percentages) (2)
A generic distribution function, with the matrix output
is desired such that: (3)
(4)
A mixture of land-uses at the location “i” is a column of the
matrix
as . Pictures below show the problem in terms of distribution of colours:
gross floor areas; as if they have 100% coverage and only one built level. Of course, working with actual GFA values makes no difference to the methods; since for each block, there needs to be one numeric attribute as its GFA.
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Figure 1 is the area of eight large rectangles and all ) functional areas (land-uses noted as
Figure 2 in this picture
values are the same. Colours represent five different
values are different but the sum of them is the same as the above picture.
Regarding these example pictures, we can reframe the question as below: How can we assign weight mixtures (portion mixtures to each location in such a way that the sum of area of each colour would be constant and equal to the demanded amount in the program? Problem Formulation We have formulated this problem as a matter of balancing the weights coming from and interactive attraction effect model in such a way that those weights become consistent with the abovementioned constraints. Meaning that the total area distributed per location should be equal to the available area of that location, and for each land-use, the total amount of areas distributed with its label should be equal to the demanded amount mentioned in the plan. We allow the user/planner to determine the way functions are to be distributed locally by assigning geometric attractors to each function and weighing them. This way the computational method interactively embraces the specific knowledge of the planner into the process of allocation. The planner can also determine how the distance decay function works by manipulating it graphically or numerically. By finding the distance4 of every single block towards different attractors and taking that as the argument of a distance decay function we find out how (in general) a location favors a certain function. We consider the output of this function as a set of preliminary weights. However, these weights must be equalized in a way to meet the constraints above. Of course, in the process of equalization and normalization, we have to adjust these weights and they will not be the same after the process; however, they should correspond to the initial definition of attractions by the planner. This is to say, if a matrix of provisional portions (weights) is defined by means of an attraction model, it should be normalized in its rows and columns so to satisfy the constraints mentioned as equations 3 and 4. This problem could be formulated as a linear programming5 problem. However, in that case for the matrix of local weights would be found by introducing an objective function that would describe the best distribution of functions around certain attractors. This means it could not be controlled by the planner directly. In this case, we wanted to allow the user to shape the distributions manually.
4
We use Euclidean distance metric in the abstract examples and a network distance metric based on the shortest path in the urban example case; because in urban street network, one cannot fly from an origin to a destination and the shortest path available through the street network counts as the distance. 5 An explanation of linear programming methodology is out of scope of this paper.
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Algorithmic Problem-Solving Considering the first step of the allocation as the distribution of first function over all locations (j=0) (according to the provisional weights), it is clear that the whole amount of area labelled as should be filled after the distribution. It is quite likely that the local weights are such that they result in excessive areas in certain locations. This is simply because the attraction model has no information of the program at the district level as it has only information about local objects and their tendency to configure land-uses of particular kinds around themselves. Thus, we should find out if a certain location could not contain the amount of area suggested by the combination of district program and its local weight for the first ( ) function. If so, that amount of excessive area should be redistributed over other locations in order to complete the distribution. When we adjust the local weights proportional to the area of locations, such necessary adjustments would be negligible. After each step of distribution the area of all location changes to a lesser amount, equal to the remainder of subtraction of newly distributed labelled area from its previous area. It is important to note that the last function’s distribution has to follow the rest of distributions as the last remainder of area values will be determined by setting the previous distributions. This is to say it is dependant to the previous distributions. Therefore, it is important that functions be introduced with their order of importance (preferably with their order of magnitude in terms of their areas) and the last one be considered as something like a flexible function left for future alterations. This algorithm is introduced in the following flowchart:
Figure 3 this flowchart shows how the matrix of area per function per location is formed to meet the constraints.
Results In order to present the performance of algorithm clearly, first we show a few abstract examples of spatial distributions. In these cases, as mentioned earlier, each colour corresponds to a land-use and the allocation problem is interpreted as assigning colours to parts of cells (pie charts) spread out spatially.
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Figure 4 the allocation algorithm implemented in VB.Net in action, in an abstract situation, within Rhinoceros® & Grasshopper® parametric modelling environments. The image a shows a situation where geometric attractors are the same and program is changing, note that the colours representing different functions appear nearby their attractors (lines representing streets for instance). The image b shows different situations in which the program is the same and attractors are differently positioned. In both cases, urban blocks are abstractly represented as circles, within which pie charts are drawn to depict the mixture of functions.
Figure 5 what happens if two functions are to be distributed in between 8 locations according to their distances towards two attractors?
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Figure 6 an example of functional distribution according to network analysis. The process is explained in (Nourian, P, Sariyildiz, S, 2012). The greener the color, the less accessible the location; the blacker the color the more dense the urban block (a) polycentric distribution of residential density, with the maximum weight of point #0; (b) with the maximum weight of point #1; (c) with the maximum weight of point #2; (d) polycentric distribution of residential density, with equal weights of importance
Figure 7: Mixed-use allocation of functions done by the algorithm implemented in VB.Net, within Rhinoceros® & Grasshopper© Parametric CAD modelling environment. It is the situation in which point 0 is considered as the attractor of Residential spaces, point 1 as the attractor of commercial spaces and point 2 as the attractor of public facilities. The whole neighbourhood is intentionally modelled as an imaginary neighbourhood in order to detach the method from peculiarities of places. In the next figure, a density distribution corresponding to the same attractors is shown.
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Figure 8 Residential density distribution according to the street-network configuration, attractor’s weights set to the weight of their associated functions.
Conclusions Interrelations of three aspects of the hidden structure of space have been dealt with in this research. Namely, these aspects are topological structure of street-networks, built-space density distribution and mixed-use allocation patterns. Specifically, we have connected land-use allocation problem to the density distribution and devised a method for shaping allocation patterns according to the inherent structure of place. From a technical point of view, a place has geographic idiosyncrasies and a space does not. This means, when we look at the spatial structure of a neighbourhood through studying its street network, in terms of a graph, we do not consider particular things such as the importance of a certain street just because of its particular history or geographic location. Whereas, in reality, a certain place can be considered as very important merely because of its particularities or its geographic situation. Obviously, when settlements develop gradually over time, like vernacular settlements or old towns, we find a close correspondence between geographic features, historical importance of places, the spatial structure of the settlement and density distribution over the settlement. However, it is not so in the case of modern developments necessarily. We find it very important to be able to design such patterns in correspondence to each other and that is the reason we have been developing tools to make it possible for planners and designers to do so. The best characteristic of computational methods is that they are transparent and can be judged explicitly. This is to say their defects will be so obvious. We think the whole process needs to be validated in actual urban design and planning to improve the formulation of the land-use allocation. Bibliography A. Ståhle, L. Marcus and A. Karlström. (2008). Place Syntax: Geographic Accessibility with Axial Lines in GIS. Proceedings in 5th Space Syntax Symposium. Delft. Beirão, J., Nourian, P. & Mashhoodi, B. (2011). Parametric urban design: An interactive sketching system for shaping neighborhoods. eCAADe 29 (pp. 279-288). Lublijana: eCAADe. Cross, N. (1999). Design Research a Disciplined Conversation. Design Issues, Vol.15(2), 5-10. Hillier, B. (2007). Space is the Machine. LONDON: Cambridge University Press. Hillier, B., & Hanson, J. (1984). The Social Logic of Space (1997 ed.). Cambridge: Cambridge University Press. Hillier, B., Penn, A., Hanson, J., Grajewski, T. & Xu, J. (1993). Natural movement: or, configuration and attraction in urban pedestrian movement. Environment and Planning B: Planning and Desig(20), 29-66. 1367
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