Research on the intelligent generation of the spatial form of the island city historic district Based on parameterization: taking Macau Taipa Village as an example

ABSTRACT

In this paper, Macau Taipa Village, a historical district in an island-type city, is the research focus, and a parametric design-based method for designing historical districts is proposed. First, the shape and distribution of roads in historical districts is studied through on-the-spot investigation and measurement and data are collected on the width, depth, and area of street blocks, average street length and width, street orientation, building width, depth, acreage, and height, and building orientation. Second, the acquired data are transmitted to the Grasshopper parameterization platform, and an intelligently generated program produces calculations. Through multiple iterations and evaluations of genetic algorithms based on the needs of modern urban design and planning constraints, the building density is further reduced, and more landscape areas are added. The parametric model is optimized to gradually generate the urban spatial design that meets contemporary requirements. The research reveals that (1) the grasshopper algorithm’s generated block design inherits the characteristics of the conventional historical block. (2) The historical block where the data were collected on site and the block where Grasshopper is applied should maintain the consistency of the regional context. (3) This method can be applied to the design of new urban areas, and the scope of application can be further adjusted through collaboration and the needs of the owners at a later stage.

KEYWORDS:

• Island city
• historic district
• design method
• genetic algorithm
• Macau

1. Introduction

1.1. Research background

China has a vast territory and a long history. Even today, there are numerous historical structures, historical districts, ancient towns, and villages in both urban and rural areas. According to the data of the third national cultural relics census, a total of 766,722 immovable cultural relics have been registered nationwide (Central Government Portal 2023). However, many are not in good preservation conditions and urgently need to be rescued and protected. However, in many places, the project to protect and repair real cultural relics has turned into the vigorous construction of “fake antiques”, and the inheritance of culture has become the target of tourism development and cultural real estate development for the purpose of achieving political points. In 2023, China will organize the fourth national cultural relics census. It is expected to require 3 to 4 years to fully grasp the quantity, distribution, characteristics, preservation status, and environmental conditions of immovable cultural relics (People’s Daily 2023). In the late 1990s, the Water Town of Zhouzhuang (an ancient town south of the Yangtze River), the Old Town of Lijiang (an ancient town in Yunnan), and other historical towns achieved great success in style protection and tourism development, triggering a nationwide “ancient town craze”. In this process, there are those who actively protect cultural heritage and rationally develop and utilize ancient town resources. However, there are also blind imitators, overexploiters, and builders of duplicates. There are also those areas that have poor conditions for historical resources and consequently develop a large number of “fake antiques” and manmade landscapes for the sake of seizing short-term benefits (urbanization website 2023). In the process of urban development, development is inevitable. How will the characteristics of excellent historical districts and cultural landscapes be “inherited” into the design of new cities?

Historic districts are the long-term manifestation of historical culture and a spiritual symbol of the people who live there, keeping a place’s spirit alive. These districts not only personalize the urban texture but also record the historical evolution of the city as a special carrier that is a comprehensive expression of culture and history. At the same time, the historic district is not a space that is made up of different things that stand independently. Instead, it is a part of the overall urban space. Its spatial form and road texture are the focus of planning and design, as are the elements that will inherit its characteristics in modern urban design. On the other hand, one of the most important things to consider when planning and building new urban areas is how to keep the traditional urban texture. Macau is an important city in China, and it is no exception to these considerations of historical preservation.In the “Consultation Text of New Urban Master Planning,” released in 2015 by the Land and Urban Construction Bureau of the Macau Special Administrative Region, the continuity of the urban texture is particularly emphasized. The consultation text mentions the following goal: “Continuing the unique urban texture of the old city, such as the Largo, the Pátio, and the Beco, to form a small-scale characteristic street space” (Consultation Text of New Urban Master Planning 2023). Therefore, this study determines urban characteristics through the study of the spatial form and roads of the historical district and then captures them through a parametric method. The past serves the present, combining traditional and excellent design concepts in an advanced and modern way. Finally, these characteristics can be adapted to the current new city design.

1.2. Literature review

1.2.1. Research on the spatial form of historic districts

A “historic district” is a district with many cultural relics and historic sites. It can also be a district that shows the traditional style and local traits of a certain time in history. The Athens Charter, adopted by the Congrès International d’Architecture Moderne (CIAM) in August 1933, stated that “buildings and districts with historical value should be properly preserved and not destroyed” (International Museum of Modern Architecture, 2023). China first proposed the concept of historic districts in 1985 (Li 2010; Yao and Jiang 2020). Therefore, in the last 100 years, scholars have performed much research from the point of view of spatial form to maintain the historic district’s texture and protect its culture in the best way possible. In the past, the traditional district design was made by architects during the field survey, and the development design needed to be completed in combination with social needs or the subjective awareness of the owner (proprietor) of the land rights. At present, there are several common methods used to explore the spatial form of historic districts: the space syntax model and subjective analysis (Ali, Al-Hashimi, and Al-Samman 2018; Mansouri and Ujang 2017; Önder and Gigi 2010; Xu et al. 2020; Yu, TSOU, and Long 2009), architectural typology analysis (AlSadaty 2022; Arghavan et al. 2022; Borsi, Porter, and Nottingham 2016; Chen and Romice 2009; Weng, Wu, and Bao 2020), the SD method and the eye-tracking experimental method (Ding et al. 2023; Li et al. 2021), the GIS spatial analysis method (Kongphunphin and Srivanit 2022), and the improved spatial syntax model (sDNA model) (Guo and Cao 2021). Regardless of which method is used, their starting point is to better understand the historical district to facilitate subsequent protection and updated design.

1.2.2. The historical context extends to the new urban design

How can the historical context of the old city be extended to the new urban design? Scholars have carried out practical explorations of urban design, for example, by analysing Budapest’s compact and diverse blocks to unify urban planning (Benkõ 2011), by using the concept of “super blocks” to develop new cities, and by complementing the texture of Tirana’s historic districts (Naselli 2021). Designers have also used shape grammar and block morphological analysis to generate neighbourhoods with Nanjing characteristics (Weng, Wu, and Bao 2020), and combined deep reinforcement learning (DRL) and computer vision for the urban design of Shenyang’s industrial zone (Han, Yan, and Liu 2021). Some scholars have begun to examine how computer technology or artificial intelligence can help with the design of city blocks. Therefore, this is also a very promising field of exploration at present.

1.2.3. Parametric and urban design

Parametric design is a method of intelligent design that uses parameters to delimit design variables to achieve repeatability and adjustability (Liu et al. 2019; Ramnath et al. 2021). Even though changing the parameters in parametric design is not technically designing, the solution is defined as a controlled design application through parameter scripts and algorithms. This gives parametric design the flexibility and stability of general design. In recent years, with the popularization of parameterization, research has also been carried out in the field of urban design. For example, for an urban design to be oriented to a certain factor of the physical environment, the corresponding variables can be controlled through parameterization to obtain the optimal solution (De Luca 2019; Ding, Lam, and Wong 2016; Kim, Choi, and Kim 2022; Salem et al. 2016; Schnabel, Zhang, and Aydin 2017; von Richthofen et al. 2018; Yuan and Ng 2012). The main goals of these urban design practices are to make outdoor temperatures more comfortable, reduce the direct sun exposure, and maintain a good breezeway. Historic districts belong to the traditional area of urban design, but they are often not formed in an instant but are the result of the historical evolution of the city. In the past, electronic records were not as advanced as they are now, however, now all design elements can be completely preserved with digital tools. There are no specific design parameters for modern architects to reference in these old districts, which also brings certain difficulties to the sustainable design of the historical district. Therefore, the parametric design method can not only improve design efficiency for architects but also extend the characteristics of historical districts to the texture of new urban design.

1.3. Problem statement and objectives

In general, learning the old ways of doing things in historic districts and determining how to use these elements in new urban design is a very complicated research topic. However, scholars have started to perform quantitative research, and the evaluation indicators and updated design models that have come from these projects have also led to new results. Districts with historical features are currently not suitable for blind imitation. However, the split between the skyscrapers designed for the new city and the old city is also a current phenomenon. There is a promising field of exploration in answering how to extend the spatial form and road texture of the old city (historic district) to the design of the new city, combined with artificial intelligence and parametric generative design methods. In this paper, the researchers explored the following questions:

1. In an island-type city, what are the characteristics of the spatial form and road organization of the historic district?

2. What are the morphological criteria of the historic urban fabric? How can the collected data of spatial form, road organization, street width, orientation, and the height, depth, and width of buildings be combined into the algorithm?

3. How does the genetic algorithm assist in the intelligent design of historic districts? What characteristics of historical districts did this algorithm “inherit” during its implementation?

4. What are the developed workflow’s applications? How can it be applied to urban design?

2. Materials and methods

2.1. Study area: Taipa Village

Taipa Village is situated in Taipa’s oldest and best-preserved region (Authentic Macau 2023). With its traditional shophouses (Figure 2a) and charming cobbled streets, Taipa Village, which was formerly home to local fishermen, offers an antidote to the glitz of the nearby Cotai Strip. This place was originally part of the seaside, and in the past, houses and streets were built according to coastal cities or island-type coastal blocks. Taipa Village is a culturally diverse landmark destination that is richly endowed with a blend of Portuguese and Chinese architecture and unmistakable Mediterranean touches (Figure 2b,c). Due to the land reclamation in Macau, Taipa, which used to be an outlying island, is now the oldest old town and has become the centre (Figure 1). It is now surrounded by modern high-rise buildings built on later reclaimed land. At the same time, many historical buildings are preserved in Taipa Village: Vila da Taipa, Tin Hau Temple (Figure 2d), Museum of Taipa and Coloane History, Pak Tai Temple, Carmo Hall, Our Lady of Carmo Church, Sam Po Temple, I Leng Temple, Kun Lam Temple, Feira do Carmo, and a large number of traditional streets and traditional houses (Figure 2e).

Figure 1. Study area: Taipa Village.

Figure 2. Traditional streets and houses in Taipa Village.

This area mainly consists of 25 streets: Rua do Meio, Rua dos Mercadores, Travessa da Glória, Rua dos Clérigos, Rua dos Bem Casados, Rua de Horta e Sousa, Largo Sanches Miranda, Rua de S. João, Rua do Retiro, Largo Maia de Magalhães, Travessa das Canastras, Rua dos Negociantes, Rua das Virtudes, Rua das Gaivotas, Rua do Cunha, Travessa das Bruxas, Beco das Flores, Rua de Montenegro, Travessa Nova, Rua do Sol, Travessa dos Mercadores, Travessa da Felicidade, Travessa de Santa Gertrudes, Travessa da Esperança, and Rua Ho Lin Vong.

2.2. Analysis of the spatial form and street characteristics of Taipa Village

In Taipa Village, the unique urban texture and spatial form are mainly described as Largo, Pátio, and Beco. In Macau, Largo is the product of the fusion of Chinese and Western cultures. It was introduced by Portuguese colonists as an open space for religious activities in front of churches (Tong 2007; Tong and Sheng 2005). In Portuguese, it is called “Largo, Praca, Praceta”. After the introduction of “Largo” to Macau, to meet the integration needs of the Chinese and Portuguese people and provide a living environment, the nature of Largos gradually changed from a religious place to a more general place for daily activities (Grzybek et al. 2014). Today, many churches in Macau retain Largos in front of them, which are still used for religious activities but can also be used for other public events. From the perspective of history and architectural typology, the traditional “Pátio” and “Beco” in Macau are urbanized, high-density, and relatively closed residential forms derived from the traditional rural residential model. A Pátio is an outdoor space with no roof in a Portuguese house. This small space is combined with the parvis or yard from the Guangdong architectural idiom to form a garden space with Macao characteristics (Ferreira, M., Lima, J., Freire, Ferreira et al. 2017). Portuguese “Beco” refers to alleys as types of secondary streets. Unlike in Portugal, this narrow street in Macau is defined as a “connecting place” between neighbourhoods and is used as a narrow walkway between city houses and residences (Xie, Ursini, and Samo 2023). Some of the Pátio and Beco are open and connected to the city roads, creating minimal street space. Therefore, it can be understood that in the past, Pátio and Beco were not only an important part of the neighbourhoods scattered around the current Macau World Heritage Historic City but also were part of the unique texture of Macau’s urban development (Zou 2020). At the same time, these are also residential spaces that have the traditional settlement and community organization of Macau and reflect the social lifestyle, living culture, and value of the Chinese in Macau in the early days.

2.2.1. Spatial features of Taipa Village

Before the 20th century, Taipa was mainly an island fishing village. After the 1950s, the urban development plan was implemented, and the island’s infrastructure was built, including roads, green spaces, and public spaces. With the rise of industry and commerce, the space in the district has gradually developed from the original residential design to a complex space mixed with commercial and residential buildings. Taipa has a unique style of streets and alleys, forming a neighbourhood with European characteristics and Chinese-Portuguese fusion. Most of the streets, alleys, and buildings in the existing districts retain the spatial form of the early stage of urban development, including original residences, commerce buildings, commercial residences, largos, and public spaces (Figures 3 and 4). It is worth mentioning that although this historic district is called “Taipa Village”, it does not currently have any villages, and it is difficult to find the original trace of the village. For historical reasons, the name has carried over to the present.

Figure 3. Distribution of residential, commercial, public, temple, largo, and land spaces, and surrounding building areas in Taipa Village.

Figure 4. Distribution of building types in Taipa Village.

Today, the most preserved spaces are residential, most of which were built before 1980. Residential buildings over 30 years old are mostly located in the middle of the historic district (Taipa Village), such as Travessa da Esperança, Travessa das Bruxas, and Travessa de Santa Gertrudes. Residential buildings under 30 years old are mainly located at the boundaries of neighbourhoods, such as Rua do Regedor and Rua Correia da Silva. However, due to the long history of the village, the title registration system of half a century ago was not perfect, and the property titles of many buildings still cannot be checked. The buildings with a clear registration status are shown in Table 1 below. It can be seen from the layout of the residential space that the older residential space is relatively small, and the volume varies. The buildings are usually grouped around a small public activity space, and the street names are dominated by Travessa. The residences that are closer to the present day have larger spaces and regular volumes, and the street names are dominated by Rua. This reflects the relationship between the size of the Taipa Village space and the age of construction. Most of the core areas are small-scale “Travessa” spaces, and the surrounding new residences are dominated by large-scale “Rua”.

Table 1. Statistics on building utilization in Taipa Village.

Building name	Year of issue of licence	Building age	Property Rights	Architectural composition	Number of independent units	Location	Cultural heritage assessment
Chong Tai Garden	1998	25	Private property	There is a basement and three floors above the ground floor.	10	Rua do Meio N°S 27–33	belongs to “buffer zone”
Estudio verde	2007	16	Government long-term leasehold land	Commercial use	9	Rua dos Mercadores N° 118	/
Edifício Tong lei	1997	26	Government long-term leasehold land	Residential use	4	Rua dos Mercadores N° 64	belongs to “buffer zone”
Edifício Soi Cheong	1998	25	Government long-term leasehold land	Residential use	25	Rua dos Mercadores N°S 46–A–60-A	belongs to “buffer zone”
Unnamed building	1993	30	Private property	There is a basement and three floors above the ground floor.	4	Rua dos Clérigos N°S 89–95	/
Unnamed building	2019	4	Private property	Three-storey residence.	2	Rua dos Clérigos N° 81	/
Edifício Iat iao koi	2012	11	Government long-term leasehold land	Three-storey residence.	2	Rua dos Clérigos N° 67	/
Unnamed building	2016	7	Private property	Four-storey building consisting of basement, ground floor, first floor and second floor for commercial use.	4	Rua dos Clérigos N° 47	/
Centro Comercial Fortuneup	2016	7	Government long-term leasehold land	The building is three storeys high, including the ground floor, the first floor and the second floor, and is used for commercial purposes.	3	Rua dos Clérigos N° 30-AA	/
Edificio Pon Lei	1994	29	Government long-term leasehold land	There is a basement and three floors above the ground floor.	8	Rua dos Bem Casados N°S 50–54	/
Unnamed building	2019	4	Government long-term leasehold land	A three-storey building consisting of ground floor, first floor and second floor for commercial use.	3	Rua dos Bem Casados N° 38	/
Edificio Pak Hung	1996	27	Private property	There is a basement and three floors above the ground floor.	18	Rua de Horta e Sousa N°S 3–9	/
Unnamed building	1989	34	Private property	There are three floors, the ground floor is used for commercial purposes and the other floors are used for residential purposes.	4	Rua de Horta e Sousa N° 4	/
Edifício Man lei	1990	33	Government long-term leasehold land	There is a basement and three floors above the ground floor.	16	Rua de S. João N°S 23–25	belongs to “buffer zone”
Edifício Yau Fu	1990	33	Private property	Residential use	8	Rua de S. João N°S 16–18	belongs to “buffer zone”
Tsui Lam Garden	1990	33	Private property	There is a basement and three floors above the ground floor.	16	Rua de S. João N°S 15–15-D	/
Son Keng Hin	2005	18	Private property	Residential use	3	Rua de S. João N°S 2–AA–12-AA	belongs to “building complex”
Edificio On Lok	1981	42	Private property	There is a basement and four floors above the ground floor.	10	Rua do Retiro N°S 14–16	/
Unnamed building	2019	4	Government long-term leasehold land	The building is three storeys high, including the ground floor, first floor and second floor, for commercial use.	3	Largo Maia de Magalhães N° 91	/
Edificio Meng zhu	1991	32	Private property	There is a basement and two floors above the ground floor.	3	Largo Maia de Magalhães N° 63	/
Edifício Keng Fong Yuen	2007	16	Private property	There is a basement and three floors above the ground floor.	2	Largo Maia de Magalhães N°S 21–25	/
Hei Kan Sio Hok	2014	9	Government long-term leasehold land	There are two floors: the attic and the ground floor.	3	Largo Maia de Magalhães N°S 13–13-A	/
Unnamed building	2017	6	Government long-term leasehold land	A five-storey building consisting of basement, ground floor, and first floor to third floor for commercial use.	5	Travessa da Glória N°S 64–72	/
Unnamed building	2014	9	Private property	Composed of ground floor, first floor and second floor, it is a building for commercial use.	3	Travessa da Glória N°S 2–A–12-A	/
Unnamed building	2009	14	Government long-term leasehold land	The ground floor and attic are for commercial use.	1	Rua dos Negociantes N° 19	belongs to “building complex”
Unnamed building	2016	7	Government long-term leasehold land	Four-storey building consisting of basement, ground floor, first floor and second floor for commercial use.	4	Rua dos Negociantes N°S 41–43	belongs to “building complex”
Unnamed building	2013	10	Government long-term leasehold land	Composed of the ground floor and the first floor, it is used for commercial purposes.	1	Rua dosNegociantess N° 31	belongs to “building complex”
Edifício Ieng Tak	1989	34	Private property	There is a basement and three floors above the ground floor.	4	Rua dos Negociantes N°S 9–9-A	belongs to “building complex”
Edifício San Fong Tan	2008	15	Government long-term leasehold land	Residential use	3	Rua das Virtudes N°S 7–15	/
Centro Comercial Hei Loi Tang Plaza	1995	28	Private property	There are three floors above the ground floor, including upper floors for commercial use.	16	Rua das Virtudes N°S 4–4	/
Edifício Wo heng	1999	24	Private property	There is a basement and two floors above the ground floor.	3	Rua do Cunha N° 104	/
Unnamed building	2012	11	Private property	There is a basement and three floors above the ground floor.	4	Rua do Cunha N°S 89–9	/
Unnamed building	2014	9	Private property	A single-ownership building consisting of four floors from the ground floor to the third floor for commercial use.	4	Rua do Cunha N° 86	/
Unnamed building	1990	33	Private property	Residential use	/	Rua do Cunha N° 33	/
Unnamed building	2003	20	Private property	Four storeys high, for commercial use.	4	Rua do Cunha N° 21	/
Edifício Fei Choi	1990	33	Private property	There is a basement and two floors above the ground floor.	3	Rua do Cunha N° 19	/
Edifício Comandante M.D. Pina	2009	14	Government long-term leasehold land	It consists of the ground floor, the first floor, the second floor, the attic and the rooftop.	2	Rua do Sol N°S 13–29	/
Edificio Lun Vo	1989	34	Private property	There is a basement and three floors above the ground floor.	17	Rua do Sol N°S 8–18	/
Casa de Penhores Pou Sun	1940s	80	Government long-term leasehold land	An old-style pawnshop with three floors.	1	Travessa da Felicidade N° 1	belongs to “buildings of architectural interest”

The commercial space in Taipa Village is transformed from residential space and retains the morphological characteristics of residential space. Commercial spaces are most typical on Rua do Cunha and Rua dos Clérigos. Taipa’s public spaces include the library, museum buildings, and five largos (squares). The public buildings are located on the outer street corners, and the building volume is relatively large. The largo space is located in a relatively dense residential area. As a place for residents to engage in fitness opportunities in their daily lives, the space is mainly enclosed. Among them, Largo do Carmo is located at one end of Rua do Cunha, and at the same time, it has a characteristic pavilion structure combining Chinese and Western styles, providing a place for the crowd to rest and gather. Its east side is a public toilet, and the rectangular square is surrounded by buildings on all sides, which have a high degree of aggregation (Figure 5).

Figure 5. Group distribution of residential buildings, commercial buildings, public buildings, Largos and landscapes.

2.2.2. Road organization

In Taipa Village, the overall road organization generally presents a regular “network structure”. The historic districts are divided into grid-like street blocks by the east‒west and north‒south main streets. The length of the north‒south road is between 43 and 120 metres, and the length of the east‒west street is between 87 and 142 metres. The width of the main street is relatively large, between 3 and 7 metres, and the streets inside the blocks carved by these main streets are relatively small, between 1 and 3 metres. These main road networks have been completely preserved in the process of urban development without major changes. The average road width is 3.76 metres, a very walkable size (Figure 6).

Figure 6. Analysis of the overall road network structure of Taipa Village.

Although the main street network is relatively regular, the roads inside the blocks are more complicated. As the residential function is gradually transformed into a commercial function, increasingly complex functional areas are divided inside the blocks, forming a rich network of internal streets and alley spaces. Figure 7 shows several typical street space types inside the block (Figure 7).

1. Commercial streets and alleys. The commercially oriented walkway has a wider street scale, with commercial shops on both sides, and the architectural layout is relatively regular and continuous. (Typical representative example: Rua do Cunha, Rua dos Clérigos, Rua dos Bem Casados, Travessa da Felicidade).

2. Residential streets and alleys. These are mainly used by pedestrians; with residential buildings on both sides or one side, the building layout is not regular, some spaces are broken, and the volume of single units is uneven. (Typical representative example: Travessa da Esperança, Travessa das Bruxas, Largo Sanches Miranda, Rua das Virtudes).

3. Commercial and residential mixed streets and alleys. People and nonmotor vehicles are mixed, and residents can enter by motorcycle. The building area is small, the space is scattered and blocky, the space is relatively fragmented, and the volume varies greatly. (Typical representative example: Travessa das Canastras, Rua dos Mercadores, Travessa da Glória, Rua de S. João)

Figure 7. Several typical street space types in Taipa Village.

2.2.3. Taipa spatial data statistics

According to the spatial characteristics of Taipa Village described above, the quantitative statistics of the block space are calculated from the scale of the Taipa Village street, street direction and building orientation, street width and depth, area of the street block, and street-to-lane ratio. A total of 25 streets, 93 street blocks, and 314 buildings were counted (see Appendix B for detailed statistics). The statistical results will be incorporated into the parameterized intelligent generation of the design, thus forming a new space with the characteristics of a historic district (Taipa Village).

First, the study calculated the statistics of the area by the azimuth. The direction of the streets and the orientation of the buildings present obvious orientation characteristics. The direction of the streets is mainly north by east; 55.41% of the streets are arranged in the direction of 56°, north by east, and 44.59% of the roads are arranged in the direction of 326°, north by west. The streets with a north-to-east direction of 56° accounted for the highest proportion, accounting for 26.12%. The orientation of the building is also very obvious, showing consistency according to the direction of the street. The orientation of buildings is mainly northwest, with 55.41% of the buildings facing northwest at 326° and 44.59% of the buildings facing northeast at 56°. The majority of all buildings face 326°, from north to west, accounting for 14.65% of the total buildings (Figure 8).

Figure 8. street direction and building orientation analysis in Taipa Village.

Second, the spatial scale of streets was quantified. Taipa Village’s street space includes streets, largos (squares), and landscape spaces, accounting for 25.05% of the total village area. Streets and alleys accounted for 17.49%, and squares and landscape spaces accounted for 7.56%. The street width is between 1 and 7 metres, and the street length varies greatly, ranging from 18.86 to 142 metres. Most of the roads named Rua are longer in length, and the street aspect ratios vary widely. The ones named Travessa are shorter and have a stable street aspect ratio (Figure 9).

Figure 9. Analysis of street block face width and depth.

Street blocks are architectural groups formed by dividing the site by streets. There are 93 street block spaces in Taipa village. Street block-scale data affect the generation of historic district space and serve as an important basis for the generation of historic district group space. After counting the length and width of each street block, the acreage of the street blocks is obtained. The street block length ranges from 4.39 to 69.59 metres, and the street block width ranges from 4.40 to 69.59 metres. The values of the length and width of the street blocks are very close, which further proves that the street network in Taipa Village presents a square network structure. The smallest street block has an acreage of only 127.64 square metres, and the largest is 1712.07 square metres. The street blocks with small acreage are dominated by streets named Travessa, and the street blocks with large acreage are dominated by streets named Rua, with large differences in scale. This shows that the volume of buildings inside the square street network varies greatly, and the spatial scale of streets and lanes varies greatly (Figure 10).

Figure 10. Analysis of street block acreage and depth.

Finally, the architectural scale is quantified. The building scale is related to the shape and feeling of the microspace of the historic district and has an important influence on the parametric generation of subsequent buildings. There are 314 buildings in Taipa Village, accounting for 74.95% of the land acreage. After the scale statistics of all buildings are obtained, it is found that the building width ranges from 2.66 to 41.76 metres (7.6 metres on average), the building depth ranges from 2.90 to 40.01 metres (10.81 metres on average), and the building height ranges from 5.2 to 27.80 metres (11.28 metres on average). The gross floor area ranges from 12.08 to 1043.12 square metres (84.49 square metres on average). The street and alley spaces have a large difference between the building’s face width and depth, showing a tendency for a large face width and small depth. Most other street-facing width scales are approximately 7.6 metres on average. In addition, the gross floor area and building height are also counted. Except for large public buildings, the gross floor areas of commercial and residential buildings are not much different, all of which are 84.49 square metres. There is no uniform rule for comparing the gross floor area and height, which shows that the building scale changes in Taipa Village are very rich (Figures 11 Figure 12)

Figure 11. Building face width and depth analysis.

Figure 12. Gross floor area and height analysis.

In summary, through the statistical analysis of Taipa Village by the spatial azimuth, street space scale, and building volume, this study obtained the data characteristics and range values of the spatial changes experienced by the historic district (Taipa Village). These azimuths, length and width scales, heights, areas, and other range data will be included in the parameterized generation of a historic district later in the article as an important basis for influencing the generation of new districts.

2.3. Construction of the parameterized program

This research aims to realize the intelligent generation of the spatial form of the island city’s historic districts and provide scientific and innovative references for urban planning and design. To achieve this goal, this paper proposes a comprehensive approach based on four steps: feature extraction, parametric translation, algorithm optimization, and application (Figure 13).

Figure 13. Research methods and process.

This method aims to use the technology of Grasshopper parametric programming and genetic algorithms to extract key features from existing historic districts, transform them into operable parametric forms, and then generate the best urban spatial form through algorithm optimization (see Appendix A for the operating system conditions for Grasshopper programming of parameterized operations). Through this intelligent generation method, urban design can fully consider the requirements of historical and cultural protection and sustainable development and provide effective solutions for the planning and design of island city historic blocks. The specific content of each step will be described in detail below:

1. Feature extraction. In the feature extraction stage, this study extracts key spatial features from Taipa Village in Macau. The spatial elements of Taipa Village are composed of three parts: streets, street blocks, and buildings, and detailed data statistics are calculated separately (Appendix B). The street calculations need to include the length and width of different streets to provide guidance for the derivation and generation of subsequent arterial roads and lanes. The street block calculations contain length, width, and area data that are critical for planning the scale and layout of a district. The building calculations include the statistical information of length, width, height, and floor area, and these data have important guiding significance for generating the shape and spatial layout of the buildings. Through the extraction of these key spatial elements, this study was able to obtain accurate data and provide a basis for the intelligent generation process.

2. Parametric translation. In the parametric translation step, the data obtained from feature extraction will be converted into an actionable parametric form. This translation process includes three key steps: main road generation, alleyway generation, and building footprint generation.

   1. Main road generation. In this step, it is necessary to select the applied plots and carry out basic division according to their contours, areas, and previously counted street block lengths and widths to generate the number and vector directions of arterial roads. Then, according to the statistical street length and orientation data, the curvature of the main road is adjusted to ensure that the generated main road conforms to the actual situation.

   2. Alleyway generation. In the alleyway generation stage, according to the previously divided street blocks, street blocks with inappropriate areas are excluded. Then, according to the statistical street and street block data, alleyway nodes are randomly generated and connected to form an alleyway network. The connection between these nodes is regarded as the generation of lanes; the street blocks are further divided according to the statistical street width, and the street blocks with a suitable area are screened out to prepare for the next step of building footprint generation.

   3. Building footprint generation. At this stage, the main building footprints are divided using the previously generated street blocks and the statistical data of building length, width, area, and orientation. Subsequently, building footprints that meet the range of statistical data are further screened. Depending on the ratio of building to landscape, the amount of area dedicated to a building footprint can be appropriately increased or decreased. Finally, areas for the building footprint and landscape footprint are demarcated. According to the statistical building height and the variance of the height value, district models were generated for these plots to complete the generation work on the entire model.

3. Algorithm optimization. In the algorithm optimization stage, this study uses a genetic algorithm to generate the best urban spatial form. Considering the high building density in Taipa Village, modern urban design usually needs to reduce building density and increase landscape area to meet planning restrictions and residents’ quality-of-life needs. Therefore, this research will apply a genetic algorithm to improve and optimize the model obtained through parametric translation to gradually generate urban spatial forms that meet the requirements. The genetic algorithm explores and improves the generated urban spatial morphology through multiple iterations and evaluations. In the genetic algorithm, the main control parameters include the length and width of the street block, the length and width of the building footprint, and the minimum area allowed to generate the building. The target parameters relate to the total building base area and landscape area of the plot. Through the genetic algorithm, tens of thousands of control parameter combinations can be calculated, and continuous iteration and optimization are carried out to gradually approach the optimal target parameter combination. For example, one could look for combinations that maximize the total building footprint, maximize the total landscape area, or strike a balance between the two. Through the optimization of a genetic algorithm, this research aims to generate an urban spatial design that not only meets modern planning requirements but also improves the quality of life for residents. The use of genetic algorithms makes the optimization process more intelligent and efficient, thereby obtaining better urban design solutions.

4. Application. In the application stage, this research will apply the compiled parametric model to the actual planning and design project of Zone A of the New District of Macau (Zona A dos Novos Aterros Urbanos), specifically involving the three plots D1, D2(a), and D2(b). The applicability of this research method to different types of plots is verified by practical experimentation, and the robustness of the model is tested. In the application process, the role of the model needs to be clarified. The parametric model in this study can only provide a reference plan for urban design and cannot completely replace all the work of designers. Therefore, in actual urban design work, the model needs to be improved and deepened according to the actual needs and site conditions. The use of mock-ups should be used as a useful aid in the design process in conjunction with the designer’s creative thinking. At the same time, the importance of cooperation and discussion with relevant stakeholders needs to be emphasized. Through close cooperation with relevant stakeholders, an optimized urban spatial design can be integrated with sustainable development principles to ensure the feasibility and practicality of the results. In practical applications, social, economic, and environmental factors need to be considered comprehensively, fully discussed, and balanced to finally achieve the goal of sustainable development.

5. Validation Criteria and Robustness: This study uses the results of the degree of conformity to the actual design proposal, collaboration, and discussions with relevant stakeholders. In addition, standards such as the degree of integration with the principles of sustainable development are used to verify the applicability and robustness of the model. Specific indicators include road area ratio, landscape area ratio, and building area ratio. For high-density historic districts, the building-to-land area ratio and road-to-land area ratio often reach 75% and 25%, respectively. For low-density historic districts, the building area ratio and road area ratio will be as low as 40% and 25%, respectively, and the landscape area ratio will be 35%. The design standard is determined according to the needs of the land. Therefore, it is necessary to combine the optimized urban spatial form with the principles of sustainable development through close cooperation with relevant stakeholders to ensure the feasibility and practicality of the generated results.

By applying the parametric model of this study to actual projects, combined with the opinions and suggestions of relevant stakeholders, the actual effect and feasibility of the model can be evaluated, and strong support can be provided for urban planning and design. From the organic combination of the above four steps, this research method can realize the intelligent generation of the spatial design of the historic district of the island city. The comprehensive application of this method can provide scientific and innovative references for urban planning and design while taking into account the requirements of historical and cultural protection and sustainable development.

3. Results

3.1. Grasshopper programming result

Parametric design is a design method based on parameters and rules. By transforming each element and relationship in the design process into the value, range, and relationship of adjustable parameters, a variety of design solutions can be quickly generated to meet design requirements under different needs and conditions. This research uses Grasshopper in Rhino as a parametric design tool. Grasshopper uses modular components and can complete programming operations in a visual way. The designed program is shown in Figure 14, which is mainly composed of numerical value setting, direction setting, and six-step functions.

Figure 14. Modules and ideas of parametric design.

1. Numerical setting: In this step, the outline of the target plot must be inputted and some basic numerical parameters are set. For example, specific values and ranges such as the length, width, and area of streets, plots, and buildings can also be manually selected by deriving a combination of various values through the genetic algorithm in step 5.

2. Direction setting: This step aims to meet the needs of different plot shapes and building orientations.

3. Step 1: In this step, first the edge of the input plot outline is extracted and then divided according to the previously counted street parameters. After the division is completed, the line segment is drawn as the arterial road. Nonquadrilateral plot outlines will be simplified to quadrilaterals to improve computational efficiency and reduce errors.

4. Step 2: Since the roads in historic districts are often not straight, there will be twists and turns on the main roads. Therefore, in this step, the straight line of the main road is converted into a curve, and the curvature is adjusted according to the previous statistical data.

5. Step 3: According to the generated district area, several road nodes are randomly generated in this step. The positions of these nodes are determined according to the width of the street block. If the width of the street block meets the requirements of the previously counted street block width range, a node is generated. Finally, these nodes are connected to form the line segments of the alleyway.

6. Step 4: In this step, values are assigned to the widths of arterial roads and alleyways and the area occupied by these roads is excluded. The remaining street blocks are used as locations for building generation. At the same time, the area of these street blocks is analysed, and the plots that meet the requirements (for example, plots larger than 100 square metres) are reserved for the division of building footprints. The direction of the footprint is parallel to the direction of the road. The remaining plots that cannot be used for building are used for landscaping.

7. Step 5: In this step, the genetic algorithm is used to derive different schemes. The genetic algorithm uses the Octopus component, connects various values in the value setting to the G port, and inputs the total building base area and landscape area to the O port. Through the derivation of the genetic algorithm, different numerical combinations can be obtained. These numerical combinations will eventually be reflected in the model, as well as in the total building area and landscape area. According to the requirements of different areas, several different schemes can be derived.

8. Step 6: In this step, a model is built according to the previously derived scheme. The main purpose is to raise the design plane and set the height according to the previously calculated building heights. At the same time, the variance is used to ensure that the building heights are scattered to be consistent with the original conditions in Taipa Village.

In summary, the parametric design provides a flexible, adjustable, and changeable method for the generation of the spatial form of the historic district of the island city. By translating design goals and constraints into specific parameters and rules, designers can explore diverse design options to meet the requirements of historical preservation, residents’ needs, and sustainable development. The application of parametric design ideas makes the design process more flexible and efficient, bringing new possibilities and innovations to the field of urban planning and design.

3.2. Generated process and results

The intelligence-generation process is multistep. It aims to achieve the goal of parametric design by selecting and dividing plots, setting road curvature, generating main roads, setting alleyway parameters, generating alleyways, filtering building plots, dividing building footprints, generating landscape areas, and finally generating models (Figure 15). In this process, the design goals and constraints are transformed into specific operation steps and rules through intelligent algorithms and optimization techniques. Each step in the generation process plays an important role, coordinating and influencing each other to finally generate the expected urban spatial form.

Figure 15. The process of the intelligent generation of the district space.

In the process of intelligent generation, first, according to the preset parameters and constraints, an area suitable for urban planning and design is selected from the available plots. Then, through the analysis of the plot outline and street parameters, the plot is divided into regular street blocks. On this basis, by setting the curvature of the road, the main road has the characteristic of a zigzag to adapt to the complex shape and curve characteristics of the city’s historical district. The next step in the generation process is to connect the divided street blocks to form the main transportation network of the city. At the same time, according to the setting of alleyway parameters, alleyways are generated to increase traffic flow and connectivity. The remaining available plots are screened and used for building generation, and the building area is generated according to the design requirements and the division direction of the building footprint. The plots that cannot be used for buildings are used as landscape areas to increase the greening and aesthetics of the city. In the final stage of the intelligent generation process, intelligent algorithms and genetic algorithms are used to adjust and optimize the generated parameters and rules to achieve design goals and constraints. This process is one of continuous iteration and optimization. Through quantitative and qualitative evaluation, the generated design results can be displayed, and their effect and feasibility can be verified (Figure 16).

Figure 16. Multiple designs generated using genetic algorithms.

Iterative optimization, result display, and evaluation in the generation process are indispensable links. Iterative optimization is the process of gradually improving and optimizing the generated urban spatial form through multiple iterations and optimizations. In each iteration, the design parameters are finetuned and optimized using an optimization algorithm to bring the resulting design closer to the desired goal. In addition, the generated design results are presented and evaluated through quantitative and qualitative evaluation methods. The building density of historic districts is different from the building density requirements in current urban design. Therefore, the evaluation results in this study are judged based on the land occupation proportions of buildings, landscapes, and roads (Figure 16) to ensure that the generated design scheme meets the expected goals and constraints.

In summary, the intelligent generation process converts design goals and constraints into specific parameters and rules through a series of operations and optimizations and generates urban spatial forms that meet expectations. It makes full use of the advantages of intelligent algorithms and optimization techniques to provide an efficient, flexible, and feasible method for the field of urban planning and design.

4. Conclusions

This study extracts key features from existing historical blocks and transforms them into operable parametric forms by using the technology of Grasshopper parametric programming and genetic algorithms and then generates the best urban spatial design through algorithm optimization. The intelligent generation of the spatial design of the historic district of the island city has been realized, which provides a scientific and innovative reference for urban planning and design, and the following conclusions have been drawn.

1. Based on the parametric platform that uses Grasshopper, the districts of a new urban design area can effectively be programmed and designed and at the same time the relevant spatial morphological characteristics are reflected through data input.

2. After completing the programming of the Grasshopper parametric platform, the genetic algorithm can be used to improve and optimize the model obtained through parametric translation to gradually generate urban spatial forms that meet the needs of modern urban design, thereby further enriching the landscape area.

3. Since Taipa Village is a component of the island-type city, the grasshopper-applied urban design area is also a significant waterfront space for the island-type city. Therefore, the extraction of historical district features and generative application should be consistent to achieve the best results. For example, if a model is compiled based on the characteristics of the historic districts of an island city and applied to the historic districts of an inland city, there may be mismatches or unsatisfactory results. However, Grasshopper has powerful programming and design assistance capabilities, and the design standards are determined according to the needs of the site. Therefore, it is also important to combine the best urban spatial design with the principles of sustainable development by working closely with the right people to ensure that the results are both possible and useful.

4. In this study, the feature extraction of the spatial design of the island city’s historic districts includes a very large amount of data, such as the width, depth and area of street blocks, street length and average width, street orientation, and building face width, depth, acreage, height, and orientation. It also relies heavily on long-term fieldwork by researchers. Conversely, if not enough data are collected, the compilation of the Grasshopper program will produce inaccurate results.

The method proposed in this study can basically realize the intelligent generation of the spatial design of the island city’s historic district. This comprehensive application can provide scientific and innovative references for urban planning and design while taking into account the requirements of historical and cultural protection and sustainable development. With the rise of big data and artificial intelligence, work efficiency has improved, and the fatigue caused by repetitive and boring work has been alleviated. However, it is difficult for computer technology to replace human subjective thinking, and it is difficult for it to capture the wisdom and local memories of emotions in traditional historical culture. Historic districts are the remnants of the continuation of the regional historical context and the home of cultural heritage to which modern society attaches great importance to protecting.

Modern architects or urban planners can think more about sustainable design and the application of artificial intelligence to continue the historical context. Historic districts are also part of the public space of modern cities and will still have broader opportunities for promotion and application in the future. For example, the research directions that can be considered in the future are as follows: (1) Not limited to the historical blocks of island cities, historical blocks in other regional cultural backgrounds can also continue to consider their street systems and architectural data. In this way, the programming of Grasshopper is redeveloped, expanded, and validated for greater universality. (2) Not limited to the historical blocks in the city, there are also core areas of architectural heritage in traditional villages, which can also be considered in combination with research and design in the future. (3) In addition to Grasshopper, there are many methods of artificial intelligence or intelligent design, such as semantic segmentation in machine learning and CGAN for generative design, which can be incorporated into future research in combination with Grasshopper.

Author contributions

Conceptualization, Y.C.; methodology, L.Z. and L.Y.; software, L.Z. and L.Y.; validation, L.Z. and L.Y.; formal analysis, Y.C. and L.Z.; investigation, Y.C. and L.Z.; resources, Y.C.; data curation, Y.C.; writ-ing – original draft preparation, Y.C. and L.Z.; writing – review and editing, Y.C. and L.Z.; visual-ization, L.Z.; supervision, Y.C. and L.Z.; project administration, Y.C. and L.Z.; funding acquisition, Y.C. and L.Z. All authors have read and agreed to the published version of the manuscript.

Informed consent statement

Not applicable for studies not involving humans.

Institutional review board statement

Not applicable for studies not involving humans or animals.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Additional information

Funding

This research was funded by CITT(Guangzhou) Enterprise Key Funding Project “Information System Engineering and Construction Engineering Testing”[grant number GZWX-23-007].

Notes on contributors

Yile Chen

Yile Chen is a PhD candidate in architecture at the Faculty of Humanities and Arts, Macau University of Science and Technology. Her research interests are urban design and renewal.

Liang Zheng

Liang Zheng is a PhD candidate in architecture at the Faculty of Humanities and Arts, Macau University of Science and Technology. His research interests include sustainable architectural design.

Lina Yan

Lina Yan is a PhD candidate in architecture at the Faculty of Humanities and Arts, Macau University of Science and Technology. Her research interests are urban design and renewal.

Appendix A:

Grasshopper environment configuration

Grasshopper environment configuration: The operating system is Windows 11 (X64), the Grasshopper version is Friday, 07 May 2021 19:00 Build 1.0.0007, the Rhinoceros version is 7 SR6 (7.6.21127.19001,2021-05-07), and the processor is AMD Ryzen 9 5900HX (3.30 GHz).

Appendix B:

Investigation and statistics of the data of 25 streets in Taipa Village

The researchers collected the data for 25 streets in Taipa Village through on-the-spot investigation.

Table

			Street						Building
No.	Name	Morphological layout	Face width of street blocks (M)	Depth of street blocks (M)	Area of street blocks (sq.)	Street length(M)	Average Street Width (M)	Street orientation	Building No.	Face width (M)	Depth (M)	Acreage (sq.)	Height (M)	Orientation (°)
1	Rua do Meio		39.037909	24.984223	975.3318239	43.682306	2	↖	1–1	15.392285	22.41906	345.080561	14.8	66.342672
									1–2	8.530962	22.603142	192.8265455	14.8	65.347727
									1–3	8.334105	16.847294	140.4071172	14.8	65.785435
									1–4	8.370108	24.984223	209.1206448	8.3	66.077794
			12.155069	30.516147	370.9258724				1–5	8.452465	6.454752	54.55856536	8.6	244.078529
									1–6	6.946991	8.992417	62.47023997	8.6	244.170127
									1–7	7.653275	5.637727	43.14707511	8.6	245.770829
			29.421559	35.729237	1051.209854				1–8	12.155069	30.516147	370.9258724	13.4	245.022126
2	Rua dos Mercadores		35.729237	29.421559	1051.209854	142.421819	3	↙	2–1	5.650583	7.653275	43.24546561	8.6	156.080839
									2–2	6.648861	8.017449	53.30690398	8.6	155.600342
									2–3	3.878247	10.350174	40.14053126	8.6	153.878095
									2–4	3.878247	10.350174	40.14053126	9.0	153.878095
									2–5	5.045305	6.917464	34.90071571	9.0	157.654105
									2–6	12.514305	4.739756	59.31475221	9.0	134.837593
			14.226464	43.581818	620.0151648				2–7	12.486105	4.306145	53.76697862	9.6	138.695221
			33.62675	44.883258	1509.278096				2–8	4.4088	9.04896	39.89505485	8.3	139.248301
									2–9	4.355868	15.051508	65.56238205	8.3	139.821089
									2–10	3.689743	20.399653	75.26947686	8.3	140.973724
									2–11	4.404149	20.399653	89.84311136	8.3	141.254655
									2–12	4.067635	21.942308	89.2533	9.7	140.581252
			4.389349	46.300495	203.2290314				2–13	4.389349	11.100368	48.72338918	9.7	130.8941
			35.621132	41.717526	1486.0255				2–14	3.345322	12.607997	42.17780974	11.7	131.83883
									2–15	4.623055	12.225631	56.51976452	11.7	130.868804
									2–16	4.204734	12.225631	51.40552634	11.7	130.7379
									2–17	5.569917	5.351851	29.80936587	11.7	131.488717
									2–18	3.609677	11.718342	42.2994296	11.7	141.336374
									2–19	3.679403	11.416919	42.00744602	11.7	148.813331
									2–20	7.306048	5.185401	37.88478861	11.7	149.458824
			32.708786	14.049224	459.5330613				2–21	4.143968	13.530852	56.0714177	13.7	320.481778
									2–22	3.562982	14.79669	52.72034013	13.7	319.485531
									2–23	3.372863	14.139677	47.69119339	13.7	318.795037
									2–24	3.931365	14.049224	55.23262751	13.7	319.24875
									2–25	4.320609	10.759001	46.48543655	13.7	319.130689
									2–26	9.204977	10.734237	98.8084047	8.9	319.631039
									2–27	5.173367	11.155342	57.71067818	8.9	315.249111
			14.676459	8.696623	127.6356309				2–28	3.302665	8.878103	29.32140004	11.2	316.848493
									2–29	2.931287	8.696623	25.49229794	11.2	316.439664
									2–30	7.827673	3.093915	24.21815491	11.20	324.923021
			17.265608	23.116672	399.123397				2–31	4.802452	10.606687	24.21815491	11.0	322.207531
									2–32	4.217928	11.783138	50.9381052	11.0	323.09908
									2–33	3.883193	11.524416	49.7004277	9.5	323.034646
									2–34	4.259097	10.854803	44.75153154	9.5	323.175496
			17.302425	20.52048	355.0540662				2–35	3.07568	21.461179	46.23165889	8.8	322.175359
									2–36	17.302425	20.52048	66.00771903	11.7	322.239378
			41.655778	12.155069	506.3288558				2–37	4.09387	15.494523	355.0540662	8.9	318.854427
									2–38	7.707202	14.285452	63.43256287	10.6	319.138557
									2–39	28.373528	12.155069	110.1008642	13.4	334.786332
3	Travessa da Glória		25.364804	23.445612	594.693353	114.915313	4	↖	3–1	16.146014	6.63823	107.1809545	14.8	221.366179
									3–2	7.040928	14.257912	100.3889318	13.3	223.5194
			41.717526	19.692439	821.519836				3–3	9.388459	19.692439	184.8816562	16.1	223.880731
									3–4	14.296992	13.079866	187.0027396	8.3	222.353837
									3–5	4.161222	9.66223	40.20668405	8.3	223.238641
									3–6	12.28318	4.204734	51.64750457	11.7	220.711753
									3–7	12.102719	4.60305	55.70942069	11.7	220.868804
									3–8	12.284166	3.345322	41.09449077	11.7	225.012111
			11.155342	32.708786	364.8776942				3–9	7.806533	5.173367	40.38606021	8.9	227.169791
									3–10	5.41607	5.41607	29.33381424	8.9	226.435499
			12.823696	48.58929	623.0942838				3–11	12.117005	4.279316	51.85249337	8.9	232.197592
			6.737706	69.594575	468.9077855				3–12	6.737706	9.792499	65.97897927	16.5	237.100247
			16.186312	17.619837	285.2001791				3–13	4.388925	16.186312	71.04050939	10.1	55.292462
			8.878103	14.676459	130.2991147				3–14	3.302665	8.878103	29.32140004	11.2	46.533575
			46.300495	4.408431	204.1125375				3–15	4.408431	11.099723	48.93236296	9.7	45.710738
									3–16	4.408431	11.478719	50.60314068	9.7	43.383318
									3–17	4.563793	7.364316	33.60921381	9.7	43.383318
									3–18	4.238133	8.306702	35.20490787	9.7	44.149182
			24.977014	55.244776	1379.849544				3–19	24.977014	10.139031	253.2427192	16.9	41.08705
4	Rua dos Clérigos		14.676459	8.696623	127.6356309	102.841205	4	↙	4–1	8.971482	10.139031	90.96213411	11.2	144.552019
									4–2	2.885661	8.792837	25.37314681	11.2	136.439664
									4–3	3.227485	8.878103	28.65394426	11.2	136.848493
			32.708786	15.579393	509.5830316				4–4	5.41607	3.348872	18.13772517	8.9	134.83063
									4–5	8.302728	10.734268	89.12370748	8.9	139.631039
									4–6	4.440278	10.759001	47.77295544	8.9	139.130689
									4–7	3.355765	14.049224	47.14589418	13.7	139.24875
									4–8	3.435507	14.049224	48.2662074	13.7	138.795037
									4–9	3.39732	14.879499	50.55041954	13.7	139.485531
									4–10	3.863541	13.530852	52.27700147	13.7	140.481778
			29.28220	47.767986	1398.751815				4–11	4.195717	9.122959	38.27735417	9.1	144.388884
									4–12	7.787968	11.47852	89.39434645	14.9	168.323947
									4–13	4.295561	12.42082	53.35438998	13.8	168.468704
									4–14	4.110016	14.181067	58.28441227	9.0	168.072201
			22.950062	22.224016	510.0425451				4–15	4.514886	14.026468	63.327904	7.6	168.543466
									4–16	2.661224	10.872334	28.93371618	7.6	168.931956
									4–17	3.836912	13.735783	52.70299062	7.6	155.842661
									4–18	4.50166	14.181067	63.83834207	7.6	156.158939
									4–19	4.50166	13.93271	62.7203233	13.9	155.182351
									4–20	3.058141	6.026402	18.42958704	13.9	150.691447
			26.618278	15.170192	403.804388				4–21	4.22279	15.26932	64.4791318	11.9	330.00286
									4–22	7.027488	15.255666	107.2090097	11.9	330.739809
									4–23	9.856081	14.279516	140.7400663	13.5	331.473216
									4–24	4.161325	15.261909	63.50976347	13.5	340.215111
			48.58929	15.579393	756.9916445				4–25	3.120196	16.517311	51.53724771	9.8	322.465459
									4–26	4.210669	16.517311	69.54892939	9.8	320.9973
									4–27	4.955981	13.549362	67.15038063	9.8	319.957825
									4–28	4.283222	13.549362	58.0349254	9.8	319.906108
									4–29	3.900409	12.117005	47.26127536	9.8	322.197592
			17.619837	15.431629	271.9027876				4–30	3.838248	16.186312	62.12707966	10.1	324.944182
									4–31	4.668158	15.431629	72.03728237	10.1	325.046305
									4–32	4.444097	15.431629	68.57965614	12.5	325.046305
									4–33	4.59864	16.565815	76.18021949	12.5	325.051935
5	Rua dos Bem Casados		48.58929	15.579393	756.9916445	75.583209	3	↙	5–1	4.279316	12.117005	51.85249337	9.8	142.197592
									5–2	4.332538	12.823696	55.55915022	9.8	139.906108
									5–3	5.09287	13.549362	69.00513925	9.8	139.957825
									5–4	4.406403	15.579393	68.64908405	9.8	140.9973
									5–5	2.764757	16.517311	45.66635121	9.8	142.465459
									5–6	3.630171	7.563682	27.45745905	9.8	140.794805
									5–7	4.230729	4.129022	17.46877312	9.8	162.596308
			26.618278	15.170192	403.804388				5–8	4.532539	15.261909	69.17519776	13.5	160.215111
									5–9	14.910705	15.170192	226.1982577	13.5	151.473216
									5–10	4.111705	15.255666	62.72679817	11.9	150.739809
									5–11	4.419198	15.26932	67.47814841	11.9	150.00286
			69.594575	7.016247	488.2927281				5–12	3.918266	7.352062	28.80733456	10.7	329.657735
									5–13	4.779361	7.453477	35.62285729	10.7	328.675019
									5–14	7.032111	7.464411	52.4905667	27.8	330.240838
									5–15	3.303746	7.277887	24.04429006	27.8	329.260307
									5–16	11.684689	7.277887	85.03984617	27.8	328.478628
									5–17	5.308732	7.026729	37.3030211	8.5	328.542604
									5–18	4.576512	7.016247	32.10993859	8.5	329.509613
									5–19	4.657068	6.891621	32.09474763	9.7	329.166566
									5–20	4.597108	6.891621	31.68152603	9.7	329.590945
									5–21	3.394157	6.695164	22.72443776	9.7	329.9759
									5–22	3.397818	6.695164	22.74894875	9.7	329.9759
									5–23	9.792499	6.737706	65.97897927	16.5	326.854338
6	Rua de Horta e Sousa		37.754992	19.831649	748.7437493	73.267219	5	↙	6–1	10.87312	19.831649	215.6318994	13.7	150.531766
									6–2	4.188767	9.875556	41.36640308	16.0	150.57967
									6–3	3.512541	9.996129	35.11181295	9.0	149.920974
									6–4	3.597456	9.996129	35.96063425	9.0	150.304204
									6–5	3.683806	9.996129	36.82379999	13.0	150.21642
									6–6	4.30826	9.930638	42.78377047	13.0	151.22055
			30.049784	40.008953	1202.260396				6–7	3.975412	40.008953	159.0520719	16.5	328.28076
									6–8	12.52394	33.089473	414.4105745	10.3	328.093363
			37.71299	22.9191	864.3477891				6–9	11.171682	26.726874	298.5841372	14.6	329.541996
									6–10	4.430109	17.154128	75.99465684	6.6	331.253592
									6–11	16.625455	11.447291	190.3164214	6.6	331.010053
7	Largo Sanches Miranda		46.652252	36.698621	1712.073315	53.362563	4	↙	7–1	28.423842	36.698621	1043.115805	13.6	151.439625
									7–2	3.983464	6.735232	26.8295542	7.3	61.517178
									7–3	3.799184	7.044264	26.76245508	7.3	62.423674
									7–4	10.888346	4.504302	49.04439866	7.3	150.646404
			47.647067	21.597604	1029.062485				7–5	4.447441	7.615266	33.86844623	14.8	242.502873
									7–6	8.342067	7.902659	65.92451086	11.3	242.598384
									7–7	4.365548	8.62216	37.64045334	8.8	242.449402
									7–8	4.393453	9.240901	40.59946422	8.8	241.812626
									7–9	12.52362	9.995309	125.1774517	12.9	332.953511
									7–10	8.606234	9.203335	79.20605459	15.9	333.134259
									7–11	10.196064	4.926275	50.22861518	5.2	64.652164
									7–12	4.521698	10.196064	46.1035222	5.2	334.915641
									7–13	4.434287	10.143546	44.97939416	5.2	335.053967
									7–14	5.730604	9.540296	54.67165842	5.2	332.954183
									7–15	8.625804	5.68457	49.03398664	8.2	154.605717
									7–16	9.275602	15.6363	145.0360956	5.2	334.562826
8	Rua de S. João		55.244776	24.977014	1379.849544	87.329508	7	↙	8–1	4.541764	10.921993	49.60511462	9.0	133.15239
									8–2	4.458073	10.840202	48.32641185	9.0	133.800205
									8–3	32.729007	21.774695	712.6641451	15.1	132.226607
									8–4	4.11705	22.853336	94.08832698	15.3	132.430362
									8–5	3.88981	6.973843	27.12692424	8.2	135.055198
									8–6	4.171656	2.895549	12.07923436	8.2	134.872876
									8–7	10.030357	24.977014	250.5283672	16.9	132.278781
			23.445612	25.364804	594.693353				8–8	14.257912	7.040928	100.3889318	13.3	131.614617
			19.692439	41.717526	821.519836				8–9	19.692439	9.388459	184.8816562	16.1	312.975692
			4.536482	46.300495	210.0413622				8–10	4.238158	16.616535	70.42350074	9.7	313.823455
			33.62675	44.883258	1509.278096				8–11	7.559682	19.376226	146.4781069	7.7	319.128968
									8–12	7.118193	4.430158	31.53471966	5.7	318.990489
			14.226464	43.581818	620.0151648				8–13	14.226464	11.285317	160.550156	9.1	319.794648
9	Rua do Retiro		37.588517	21.343956	802.287653	42.790545	3	↙	9–1	11.023893	4.449958	49.05586085	9.3	150.814084
									9–2	4.12117	10.802447	44.5187205	19.0	150.934062
									9–3	3.658341	10.775859	39.42176679	19.0	151.311036
									9–4	3.759011	10.840657	40.75014891	19.0	152.944655
									9–5	15.128078	10.755912	162.7162757	19.0	152.325299
			37.754992	19.831649	748.7437493				9–6	4.37294	9.935907	43.44912516	11.6	330.643503
									9–7	3.686542	9.879132	36.41983504	11.6	331.294653
									9–8	3.686542	9.900582	36.49891137	11.6	332.596603
									9–9	3.586885	9.865725	35.38722102	11.6	331.291743
									9–10	3.633614	9.986221	36.28607243	11.6	330.621272
									9–11	3.628165	9.990744	36.2480677	8.8	330.95152
									9–12	15.196765	19.831649	301.3769094	13.7	330.531766
10	Largo Maia de Magalhães		47.647067	21.597604	1029.062485	54.277388	4	↙	10–1	8.625804	5.68457	49.03398664	8.2	154.605717
									10–2	5.730604	9.540296	54.67165842	8.2	152.954183
									10–3	8.576632	9.203335	78.93361747	15.9	153.134259
									10–4	9.995309	12.554754	125.4886456	12.9	152.953511
									10–5	9.240901	4.393453	40.59946422	8.8	150.716128
			21.555276	18.003563	388.0717694				10–6	4.52947	10.795	48.89562865	15.9	241.927513
									10–7	4.437139	13.67264	60.66740418	15.9	242.700693
									10–8	4.46607	14.984135	66.9201958	15.9	242.21902
									10–9	17.746944	9.140587	162.2174856	15.8	242.089486
			11.74905	14.176439	166.5596906				10–10	11.74905	7.933933	93.21617551	7.5	349.146113
			30.764358	14.582605	448.6244808				10–11	8.001284	9.077348	72.63043931	7.5	343.960967
									10–12	6.683125	25.147096	168.061186	8.8	330.146034
									10–13	8.605311	4.124441	35.49209751	7.8	62.819891
									10–14	8.605311	4.168572	35.87185849	7.8	62.187046
11	Travessa das Canastras		44.883258	33.62675	1509.278096	49.38721	4	↖	11–1	4.430158	7.118193	31.53471966	5.7	224.351139
									11–2	4.229597	6.950361	29.39722603	5.7	229.270843
									11–3	4.317459	6.675733	28.82220352	5.7	229.246034
									11–4	10.71002	8.148247	87.26788833	7.7	230.970997
									11–5	4.710875	11.242112	52.96018437	10.2	308.397682
									11–6	11.96337	4.270673	51.09164125	11.6	228.06564
									11–7	9.04896	4.4088	39.89505485	8.3	229.245007
			49.38721	13.301632	656.9304929				11–8	11.285317	12.486105	140.909653	9.6	49.137401
									11–9	4.193127	12.512811	52.46780565	9.6	48.703438
									11–10	4.047708	12.520648	50.67992707	8.4	48.576543
									11–11	4.181412	12.607716	52.71805497	16.4	49.1377
									11–12	4.443151	13.401483	59.54481259	16.4	49.203725
									11–13	8.397149	13.301632	111.6957858	8.8	49.628571
									11–14	3.642277	13.652121	49.72480632	11.2	49.3924
									11–15	4.304719	14.226464	61.24092988	9.1	41.857292
12	Rua dos Negociantes		43.581818	14.226464	620.0151648	66.23272	6	↖	12–1	4.739756	14.226464	67.4299681	8.1	221.857292
									12–2	15.494523	13.652121	211.5331028	11.2	229.3924
									12–3	9.59325	13.301632	127.6058812	8.8	229.628571
									12–4	4.601691	13.401483	61.66948371	16.4	229.203725
									12–5	7.203992	12.607716	90.8258852	16.4	229.1377
									12–6	4.633532	12.520648	58.01482317	8.49.6	228.576543
									12–7	4.120156	12.512811	51.55473332	9.6	228.703438
									12–8	4.168634	12.486105	52.05000183	11.7	229.137401
			20.52048	20.022636	410.8741016				12–9	4.166692	17.302425	72.09387583	8.9	227.447648
			15.49452	41.655778	645.4362853				12–10	4.209752	4.09387	17.23417742	10.0	49.07081
			29.421559	35.729237	1051.209854				12–11	15.404825	9.87314	152.0939939	10.0	43.867366
									12–12	4.55308	10.368725	47.20963442	9.2	43.867366
									12–13	6.733862	5.350498	36.02951516	9.2	47.029734
									12–14	4.107036	6.125671	25.15835132	8.4	49.413837
									12–15	4.264663	6.44091	27.46831056	8.4	49.230819
									12–16	4.994137	6.569568	32.80932262	8.4	49.184916
13	Rua das Virtudes		41.75694	24.073022	1005.215735	82.582651	6	V	13–1	14.296992	24.073022	344.1718029	15.9	218.506665
			28.118701	17.711154	498.0146437				13–2	33.14425	6.661113	220.7775946	13.2	149.347942
									13–3	13.146458	7.485306	98.40526095	13.2	138.325142
									13–4	5.09422	9.459563	48.18909503	10.1	148.99743
			41.717526	19.692439	821.519836				13–5	14.356193	13.079866	187.7770807	8.3	42.353837
									13–6	19.692439	8.912275	175.5044318	16.1	318.375003
			25.364804	23.445612	594.693353				13–7	14.257912	7.110711	101.3838917	13.3	135.205115
									13–8	4.493955	10.025489	45.05409642	13.3	315.820097
									13–9	4.198098	10.980402	46.09680368	13.3	133.94469
									13–10	4.558428	10.888912	49.63632135	13.3	134.270726
14	Rua das Gaivotas		36.176462	36.698621	1327.626268	52.759279	5	↖	14–1	21.115883	36.176462	763.8979389	10.6	243.692772
			21.597604	47.647067	1029.062485				14–2	11.597615	9.275602	107.5748609	5.2	244.542763
									14–3	9.725275	8.625804	83.888316	8.2	244.72428
			41.75694	24.073022	1005.215735				14–4	41.75694	24.073022	1005.215735	15.9	61.963392
15	Rua do Cunha		39.113276	37.290486	1458.553071	120.901245	5	↖	15–1	8.014109	11.083798	88.82676531	14.5	242.161046
									15–2	4.076116	11.0851	45.18415347	14.5	242.170444
			21.612197	37.48574	810.1491976				15–3	4.321575	11.173865	48.28869564	15.4	241.772175
									15–4	4.277136	11.151748	47.69754283	15.4	241.378059
									15–5	4.396413	11.202257	49.2497483	15.4	241.815291
									15–6	4.178501	10.999138	45.95990913	14.0	241.193314
									15–7	4.386527	10.946082	48.01528424	14.0	241.416694
			21.343956	37.588517	802.287653				15–8	4.332324	10.941533	47.40226601	16.1	241.689781
									15–9	4.288377	11.028452	47.2941599	16.1	241.879768
									15–10	4.264942	11.074486	47.23204047	16.1	241.773488
									15–11	4.181887	11.047883	46.2009983	9.3	242.847249
									15–12	4.449958	11.135878	49.55418939	9.3	241.662714
			19.831649	37.754992	748.7437493				15–13	19.831649	15.196765	301.3769094	13.7	241.91221
			7.352062	69.594575	511.6636303				15–14	7.352062	3.918266	28.80733456	10.7	60.373011
			15.26932	15.26932	233.1521333				15–15	15.26932	4.419198	67.47814841	11.9	60.900455
			22.224016	22.224016	493.9068872				15–16	12.243085	8.820184	107.9862624	13.9	61.851472
									15–17	3.958577	10.817205	42.82073892	8.7	62.158077
			21.555276	18.003563	388.0717694				15–18	4.460198	9.101508	40.59452778	8.8	62.022695
									15–19	4.209538	8.74613	36.81716659	15.8	62.21902
									15–20	4.292892	14.984135	64.32527327	15.9	62.21902
									15–21	4.288778	13.67264	58.63891763	15.9	62.212964
									15–22	4.484385	12.388834	55.55630136	15.9	62.700693
			21.597604	47.647067	1029.062485				15–23	4.393453	9.240901	40.59946422	8.8	61.812626
									15–24	4.365548	8.905027	38.87532281	8.8	61.785963
									15–25	8.342067	8.62216	71.9266364	11.3	62.449402
									15–26	4.447441	7.902659	35.14660965	14.8	62.598384
			36.698621	46.652252	1712.073315				15–27	4.504302	10.888346	49.04439866	7.3	61.556686
									15–28	3.799184	7.044264	26.76245508	7.3	62.423674
									15–29	3.983464	6.735232	26.8295542	7.3	61.517178
16	Travessa das Bruxas		11.749	14.176439	166.5589818	29.458881	2	V	16–1	7.715334	11.749	90.64745917	7.5	256.242888
									16–2	11.933263	5.756334	68.69184754	7.5	257.309863
									16–3	4.241099	12.439585	52.7575115	9.0	348.072201
									16–4	4.119295	11.370506	46.83846851	13.8	348.468704
									16–5	7.874447	11.263063	88.69039265	14.9	348.050559
									16–6	3.693312	6.512018	24.05091422	8.6	71.429588
									16–7	4.375443	7.398824	32.37313268	8.8	70.053943
									16–8	9.077348	8.001284	72.63043931	8.8	73.682795
17	Beco das Flores		15.261909	26.618278	406.2457366	18.857364	1	↖	17–1	4.129022	5.830694	24.0750638	13.5	250.215111
			16.517311	16.517311	272.8215627				17–2	15.261909	4.230729	64.569001	13.5	73.861139
18	Rua de Montenegro		21.555276	18.003563	388.0717694	31.092297	2	↖	18–1	9.140587	4.723431	43.17493199	15.8	242.089486
			22.224016	22.950062	510.0425451				18–2	14.026468	4.024545	56.45015166	7.3	243.097507
			15.67668	23.498703	368.3816473				18–3	12.42082	4.241099	52.67792728	9.0	79.058345
			23.498703	11.74905	276.0874365				18–4	5.616353	11.933263	67.02141745	7.5	78.514698
									18–5	7.933933	11.749	93.21577882	7.5	77.309863
19	Travessa Nova		18.003563	21.555276	388.0717694	21.225916	3	↙	19–1	4.723431	8.749847	41.32929857	15.8	152.089486
									19–2	3.922372	8.693819	34.10039222	18.8	151.509988
									19–3	9.101508	4.460198	40.59452778	8.8	150.475002
			22.950062	22.224016	510.0425451				19–4	10.718589	3.958577	42.43035989	8.7	330.371811
20	Rua do Sol		37.290486	39.113276	1458.553071	41.846107	3	↙	20–1	11.112302	4.042426	44.92065852	14.6	150.720999
									20–2	26.127506	16.986892	443.8251227	13.3	151.321166
			37.48574	21.612197	810.1491976				20–3	26.57554	10.683119	283.9096563	16	330.651595
									20–4	11.173865	4.244225	47.42439718	15.4	330.173071
21	Travessa dos Mercadores		46.300495	4.536482	210.0413622	49.626747	7	↖	21–1	16.235164	4.563793	74.09392782	9.7	225.426115
									21–2	7.523252	4.536482	34.12909728	9.7	223.383318
									21–3	11.305019	4.408431	49.83739622	9.7	225.69847
									21–4	11.100368	4.389349	48.72338918	9.7	225.710738
			44.883258	33.62675	1509.278096				21–5	21.942308	4.067635	89.2533	9.7	51.969355
22	Travessa da Felicidade		21.461179	20.022636	429.7093752	25.405483	3	↖	22–1	10.897913	4.259097	46.41526856	9.5	234.305939
									22–2	11.910285	4.29636	51.17087206	11.8	232.052499
									22–3	21.461179	3.07568	66.00771903	8.8	47.925554
23	Travessa de Santa Gertrudes		8.696623	14.676459	127.6356309	30.297553	2	↖	23–1	3.093915	8.287107	25.63960465	11.2	226.447247
									23–2	4.529595	8.971482	40.63718001	11.2	232.536153
			15.431629	17.619837	271.9027876				23–3	16.565815	4.59864	76.18021949	12.5	234.460874
			23.116672	17.265608	399.123397				23–4	8.520143	4.707643	40.10979155	9.0	52.343844
									23–5	10.606687	4.802452	50.9381052	11.0	54.52955
24	Travessa da Esperança		47.767986	29.282202	1398.751815	49.869521	2	↖	24–1	8.680089	4.124441	35.80051496	7.8	242.819891
									24–2	8.605311	4.168572	35.87185849	7.8	62.187046
									24–3	25.147096	6.683125	168.061186	8.8	242.798483
									24–4	8.624613	6.671514	57.53922637	9.1	234.880634
			14.139677	32.708786	462.4916691				24–5	13.530852	4.143968	56.0714177	13.7	53.893337
			41.717526	35.621132	1486.0255				24–6	4.401162	7.306048	32.15510083	11.3	60.09073
									24–7	5.274612	7.391797	38.98886116	11.3	57.238693
									24–8	3.984755	11.50069	45.82743198	11.3	59.575375
									24–9	3.678132	4.425469	16.27745914	11.3	60.351327
									24–10	6.318606	5.09422	32.18836906	13.2	63.324291
25	Rua Ho Lin Vong		37.48574	21.612197	810.1491976	42.169525	4	↙	25–1	11.072331	4.386527	48.56907888	14.0	151.337418
									25–2	4.15975	10.908828	45.37799727	11.6	151.796261
									25–3	3.740088	10.922806	40.85225565	11.6	150.684536
									25–4	3.713897	10.860104	40.33330767	11.6	150.637936
			37.588517	21.343956	802.287653				25–5	14.277142	10.750284	153.4833312	12.9	330.461372
									25–6	10.941533	4.332324	47.40226601	16.1	331.713576