Abstract
JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING https://doi.org/10.1080/13467581.2023.2172337 ARCHITECTURAL HISTORY AND THEORY A parametric analysis of the “digitally-derived geometric design” of the façade of the Macau St. Dominic’s Church a,b a Jian Tang and Liyao Lan a b Key Laboratory of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou, MOE of China; Guangdong University of Finance & Economics, Guangzhou, P.R. China ABSTRACT ARTICLE HISTORY Received 19 April 2022 The Macau St. Dominic’s Church was built in 1588 and renovated in 1828. This ancient building Accepted 19 January 2023 in Macau’s historical town is listed in UNESCO’s World Heritage List. “Digitally-derived Geometric Design” is an important implicit logic of the correlation between numbers and KEYWORDS shapes in Western Classic Architecture, and the method of parametric analysis is highly The Macau St. Dominic’s effective in the interpretation of “Digitally-derived Geometric Design”. However, there are Church; parametric analysis; limited digital studies on Western Classic Buildings in the Far East and even less conducted stratification; successive from a parametric and detailed perspective. With the façade of the Macau St. Dominic’s Church decrease by equal difference; golden ratio as the research subject, this study applied the methods of historical document research, field measurement and digital analysis, especially parametric analysis with the assistance of the modeling software of Rhinoceros 6.0 and the software plug-in of Grasshopper, and analyzed the design features of the façade: its upward “successive decrease by equal difference” in stratification, modularization and golden ratio. The “digitally-derived” design pattern of the Macau St. Dominic’s Church is of significant historical value. 1. Introduction to analyze the implicit logic of the correlation between numbers and shapes without useful analytical method. Macau St. Dominic’s Church (also known as Ban Zhang Digital analysis and especially parametric analysis are Tang in Chinese) was built in 1588 (Lam 1982, 18) highly effective in the interpretation of “Digitally- (Domingos and Ka-tseung 1982a) (Figure 1) and reno- derived Geometric Design”. vated in 1828, laying the foundation for today’s church Professor (Suzuki 1998) had discussed the charac- (Valente 1993a) (Figure 2). Most of the existing teristics of buildings of Baroque Style. However, there Western-classical buildings in China were built after are limited digital studies on Western Classic Buildings the Opium War in 1840. The Macau St. Dominic’s in the Far East (Ge 2005) and even less conducted from Church is a rare Western Baroque style building built a parametric perspective (Tang 2018, 2021). before the Opium War (1840) in China. Included in the UNESCO’s World Heritage List, this building in Macau’s historic town is of significant conservation and 2. Research objectives and methods research value. Geometrical composition and rational order are beloved and common factors in Western Previous research has found that Macao’s Baroque Classic Architecture, while the rule of proportion is an style buildings (churches) are characterized by upward important one in “digitally-derived” design. “Digitally- successive decrease in stratification (Tang 2018). derived Geometric Design” is an important implicit However, there is no definite mathematical pattern logic of the correlation between numbers and shapes behind this successive decrease. With the façade of in Western Classic Buildings, and the origin of the the Macau St. Dominic’s Church as the research subject profound “grammar” and “rational composition” (Figures 2 and 3), this study applied the methods of behind western classic building. Christianity plays historical document research, field measurement and a significant role in Western civilization. In the con- digital analysis, especially parametric analysis, and ana- struction of Western classical architecture in Macao, lyzed the design patterns of the “digitally-derived geo- especially churches, people proficient in mathematics metric” of the modular, especially the feature of are always chosen to take charge of the planning and “Upward Successive Decrease by Equal Different” and design. The favor for geometry comes from the favor Golden section and its combination of Macau for “number” (Ambrosio 1628). However, in the study St. Dominic’s Church. of Western classical architecture, it’s almost impossible The research methods are listed as follows: CONTACT Jian Tang kentangjian@yahoo.co.jp; tangjian1117@aliyun.com Associate Professor, MOE of China (Jinan University), P.R.China. Tel: (+86)013802532560 Fax: (+86)020-85228275. (The publisher will insert here: received, accepted)JAABE vol.X No.X November 20XX © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 J. TANG AND L. LAN and Zhang 1992). Ban Zhang Tang is also known as St. Dominic’s Church (Igreja de São Domingos in Portuguese) and Our Lady of the Rosary Church. Father Jianjun Lin believed that it was built in 1588 (Lam 1982, 18) (Domingos and Ka-tseung 1982a). According to him, the church was built by Spanish Dominicans and it soon became the headquarter for Dominican missionaries in Fujian, China, after the com- pletion of its construction. The Dominican missionaries played an important role in Macao’s history, since Abelha da China, the first newspaper in Macao, was edited by the Dominican missionary (currently col- lected in the library in the Macao Municipal Building). Macau St. Dominic’s Church is now the only existing architectural heritage proof of Dominican missionaries’ campaign in Macao. However, Silva (1995, 24) (Beatriz Basto 1995) believed that it was built on 23 October 1587. In Bry’s City Map of Macao in the 1590s (1607) (Bry 2000), Macau St. Dominic’s Church Figure 1. Macau St. Dominic’s Church (Ban Zhang Tang) in the was composed of three two-storey buildings with city map of Macao in the 1590s (1607; Bry 2000). gable roof. In front of those buildings was an open square, the St. Dominic’s Square. There was a huge cross standing in the center of the square (Figure 1). Macau St. Dominic’s Church was rebuilt with bricks and a. A Cross-reference Research of Historical stones in 1721. The following renovation was con- Documents and Literature: this study collected and ducted in 1828 and was hosted by a Spanish priest conducted a cross-reference research on the related excel in architecture. This renovation laid the founda- historical documents, literature and pictures about tion for today’s church and the facade of 24 meters Macau St. Dominic’s Church and the remaining wes- high (Valente 1993a). On 9 May 1874, St. Dominic’s tern classic buildings in Macao, while verifying the Church was struck by lightning, which caused the fire results of digital analyses. that burned down the main altar. On 29 February 1884, b. Field Measurements and Parametric Analyses: this the Portuguese Royal approved the reopening of the study used aerial photography by unmanned aerial Macau St. Dominic’s Church for public use (Silva 1998, vehicles (DJI Mavic Pro) to generate three- 194/233) (da Silva 1998) (Figure 2). dimensional point cloud and manual measurement (accurate to the millimeter) to measure Macau St. Dominic’s Church and digitalized it with the assis- tance of the software AutoCAD while revising them 4. Obtaining the horizontal and vertical with reference to data acquired from related architec- controlling lines (axes) and hereby deducing tural drawings. This study further conducted the partition patterns in the overall dimension a parametric analysis of the design patterns of the of the façade Golden Ratio (nestings and combinations), modular, 4.1. Obtaining the main controlling line in the equal partition and successive decrease in the façade horizontal direction (Axis ①-⑪) and hereby with the assistance of the modeling software of deducing symmetry, three-segment in the Rhinoceros 6.0 and the software plug-in of horizontal direction and modular Grasshopper (using Rhinoceros 6.0 to place the façade and axes used in drawing analyses and using 1) The overall width of the facade: the overall width Grasshopper to write programs that composes data- of Axis ①-⑪ (Figure 3, Table 1) is 17,100 mm and it mapping diagram). is bilaterally symmetric along the Axis ⑥. The facade is also divided into three parts by Axis ④ and Axis ⑧: the left part, the middle part and the right part. If 3. Historical research the width of these three parts is respectively: a, b, a (a = 4,500 mm, b = 8,100 mm, a + b + a = 17,100 mm), According to A Brief History of Macao, written in 1751, their geometrical relationship would be (unit: mm, “the original Ban Zhang Tang was said to be low and small, the poor foreigners used planks to build it (Yin the same below): Bry, T. 2000. The City Map of Macao in 1607. Beijing: Sino-Cultural Press. The First Historical Archives of China, One Country Two Systems Research Institute Selected Historical Maps of Macao. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 3 Figure 2. Painted by George Smirnoff (Russia), the Macau St. Dominic’s Church, 1944–1945. 17,100 (the overall width) = 8,550 × 2 (bilateral Accordingly, all the vertical Axes in the horizontal symmetry) = 4,500 + 8,100 + 4,500 (a + b + a) direction (Axis ①-⑪) are obtained. The combination of 2) In the left part of the facade (Axis ①-④) and the the modular in the horizontal direction is: right part (Axis ⑧-⑪), the modular of the width of the (a + b + a) = (200 + c + 200 + d + 200) + double column (c = 1,050 mm) is equally divided by (e + 200 + f + 200 + e) + Axis ② and Axis ⑩. The modular of two side doors (200 + d + 200 + c + 200) = 4,500 + 8,100 + 4,500 (d = 2400 mm) is equally divided by Axis ③ and Axis (three-Segment in the horizontal direction) = 17,100 ⑨. Dividing the left and right parts of the facade by the (the overall width) modular in sequence of “200 + c + 200 + d + 200” from outside to inside brings about Axis ②, ③, ⑨ and ⑩. 3) In the middle of the facade (Axis ④-⑧), the 4.2. Obtaining the main controlling line in the modular of the double column (e = 2,150 mm) and vertical direction (Axis Ⓐ-Ⓝ) and hereby deducing the modular of the main door (f = 3,400 mm) are five-segment in the vertical direction and upward equally divided by Axis ⑥. Dividing the middle part “decrease by equal difference” in stratification of the facade by the modular in sequence of “e + 200 + f + 200 + e” brings about Axis ⑤, ⑥ and ⑦. 1) The Cross Storey (Axis Ⓛ-Ⓝ): George Smirnoff, 1944–1945, Macao Art Museum 4 J. TANG AND L. LAN Figure 3. A parametric analysis of the facade of the Macau St. Dominic’s Church. The peak of the cross is 22,350 mm high and drawing than the one in the second storey, which is 1,090 mm) brings about the separating line of the Second and Third a horizontal line through this point brings about Axis Ⓝ. Storey, Axis Ⓖ. The height h3 of the Third Storey is Shifting Axis Ⓝ downward by 1,350 mm brings about the 2,250 mm + 1,240 mm + 1,060 mm = 4,550 mm. Axis Ⓜ, which is the bottom edge of the cross. Shifting 4) The second Storey (Axis Ⓓ-Ⓖ): Axis Ⓜ downward by 800 mm is Axis Ⓛ, which is the Shifting Axis Ⓖ downward by 650 mm brings about peak of the triangle pediment. The height h5 of the Cross Axis Ⓕ, the horizontal line of the bottom edge of the Storey is 1,350 mm + 800 mm = 2,150 mm. eaves in the second storey. Shifting Axis Ⓕ downward 2) The Triangle Pediment Storey (Axis Ⓚ-Ⓛ): by 3,910 mm brings about Axis Ⓔ, the top edge of the Shifting Axis Ⓛ downward by 3,250 mm (the height column base in the second storey. Shifting Axis Ⓔ h4 of the Pediment Storey) brings about the bottom downward by 1,090 mm (the height of the column edge of the pediment, Axis Ⓚ. The triangle pediment is base in the second storey, less than the one in the bilaterally symmetric along the Axis ⑥. Connecting K3 first storey, which is 1,380 mm) brings about Axis Ⓓ, and L6 as well as K9 and L6 brings about the slopes of the separating line of the First and Second Storey. The the pediment rooftop. The slope gradient is 1.677, height h2 of the Second Storey is 650 mm + 3,910 mm close to the Golden Ratio (the height is 3,250 mm + 1,090 mm = 5,650 mm. and the bottom line is 5,450 mm × 2). 5) The First Storey (Axis Ⓐ-Ⓓ) 3) The third Storey (Axis Ⓖ-Ⓚ): Shifting Axis Ⓓ downward by 670 mm brings about Shifting Axis Ⓚ downward by 2,250 mm brings about Axis Ⓒ, the horizontal line of the bottom edge of the eaves the central line of the oval decoration, Axis Ⓙ, which in the first storey. Shifting Axis Ⓒ downward by 4,700 mm almost equally divided the third storey in the vertical brings about the Axis Ⓑ, the top edge of the column base direction. Shifting Axis Ⓙ downward by 1,240 mm brings in the first storey. Shifting Axis Ⓑ downward by 1,380 mm about the top edge of the column base in the third brings about Axis Ⓐ, the Ground. The height h1 of the First storey, Axis Ⓗ. Shifting Axis Ⓗ downward by 1,060 mm (the height of the column base in the third storey, less Storey is 670 mm + 4,700 mm + 1,380 mm = 6,750 mm. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 5 Table 1. The corresponding relationship between axes and positions. Axis The Highest Point of the Cross Axis The Horizontal Line of the Bottom Edge of the Cross Axis The Horizontal Line of the Peak of the Pediment The Right Axis The Horizontal Line of the Bottom Edge of the Pediment The Central Line of Side Axis The Horizontal Line of the Half Storey Height in the Third Storey The Central Line the Double Line of Axis The Horizontal Line of the Top Edge of the Column Base in the Third Storey The Right Side Line of of the Door Column in the Far the Axis The Separating Line between the Second and Third Storey The Left Side Line of the Right Double- and Window in Right Part of the Facade Axis The Horizontal Line of the Bottom Edge of Eaves in the Second Storey The Axis of the Right Double- column in the the Right Part Facade Axis The Horizontal Line of the Top Edge of Column Base in the Second Storey The Right Side Line of Symmetry column in the Middle Doorway Axis The Separating Line between the First and Second Storey The Left Side Line of the Left Double- of the Middle Doorway Hole Axis The Horizontal Line of the Bottom Edge of The Central Line the Left Double- column in the Facade Hole Eaves in the First Storey of the Door column in the Middle Doorway Axis The Horizontal Line The Central Line of and Window Middle Doorway Hole of the Top Edge the Double in the Left Part Hole of Column Bases Column in the Far Axis The Left Part of the Ground The Left Facade Side Axis of the Line of Facade the Facade Axis ① Axis ② Axis ③ Axis ④ Axis ⑤ Axis ⑥ Axis ⑦ Axis ⑧ Axis ⑨ Axis Axis 6 J. TANG AND L. LAN Thus, all the axes in the vertical direction, Axis Ⓐ-Ⓝ, and all the axes in the horizontal direction, Axis ①-⑪ are obtained (Table 1). 4.3. The partition patterns in the overall dimension of the facade In the horizontal direction, Axis ④ and ⑧ divide the facade into three parts: the left, middle and right part. The facade is bilaterally symmetric along Axis ⑥. The height and width of the middle doorways in each storey are bigger than those in the left and right one. The width Figure 4. The composition of golden section (the Fibonacci of the double-column in the middle (Modular e) is bigger sequence). than the ones in the right and left part (Modular c). The horizontal width of the facade narrows from Golden Section and Fibonacci Sequence (Figure 4): “a + b + a” in the Third Storey to “a” through the circular A Golden Rectangle could be divided into arcs on the two sides and continued to narrow in the a subordinate golden rectangle and a square in succes- Pediment Storey by the slope of the Golden Ratio until sion, that is to say “A main golden rectangle = a sub- the Cross Storey. More spectacularly, the facade is strati- ordinate golden rectangle + a square”. Such divisions fied into five parts in the vertical direction while the bring about a series of mutually perpendicular/ height of each part is upward successively decreased by mutually paralleled sidelines, diagonals and golden equal difference. The height is successively decreased by spirals. The mathematical expression of Golden Ratio pffiffi the equal difference of 1,100 mm in the First/Second/ 5þ1 2 pffiffi is ¼ � 1:618. The Fibonacci Sequence, also Third storey (the height h1 of the First Storey minus 5 1 known as the Golden Section Sequence, is: 1, 1, 2, 3, 5, 1,100 mm is equal to the height h2 of the Second 8, 13, 21, 34 . . . . . . Storey; the height h2 of the Second storey minus In actual construction, architects usually take round 1,100 mm is equal to the height h3 of the Third storey). number in measurement so the Golden Ratio applied The difference between the height h3 of the Third storey in actual construction is usually a range rather than an and the height h4 of the Pediment Story is 1,300 mm (the exact number like 1.618. In this study, the author takes height h3 of the Third Storey minus 1,300 mm is equal to the range between 3:2 (1.5) and 5:3 (1.67) in the the height h4 of the Pediment Storey). The difference Fibonacci Sequence as the range of the Golden Ratio between the Cross Story and the Pediment Story returns (Range Value: 0.17). to 1,100 mm (the height h4 of the Pediment Storey minus Root Rectangle Composition (Figure 5): 1,100 mm is equal to the height h5 of the Cross Story). Root Rectangle Section is one of the partition meth- After the analyses of the partitions of the facade in pffiffiffi pffiffiffi pffiffiffi pffiffiffi ods. They are mainly 2; 3; 4; 5 . . . rectangle the horizontal and vertical direction (Axes) (Table 1), composition. this study continues to conduct a parametric analysis In this study, the author imports the facade into the of the diagonal lines (gradient of slopes) and succes- Rhino 6.0 software and writes parametric programs sive partitions (spiral lines). with the assistance of the software plug-in of [The golden rectangle of none-partition is marked Grasshopper. Based on the analysis of the slope k of by one solid diagonal line; the golden rectangle of one- time partition is marked by two diagonal lines (dotted lines); the golden rectangle of two-time partition is marked by golden spiral lines (dotted lines)]. 5. Parametric analysis of the facade: the combination and successive partition of rectangles and spirals controlled by golden ratio 5.1. Assessment of “Golden Rectangles+Squares” or “Root Rectangles” in the composition of the facade There are mainly “Golden Rectangles + Squares” and “Root Rectangles” in the proportion partition in Western Classic Architecture. Figure 5. The composition of root rectangle. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 7 wiring of the axis intersection (diagonal of rectangle) [k Sub-rectangle1 (A1-A7-D7-D1): Line A1-A7 is pffiffiffi of 2 rectangles (Range: 1.32–1.49/Range Value: 0.17), 10,450 mm long and Line A1-D1 is 6,750 mm long. k of golden rectangles (Range: 1.5–1.67/Range Value: Their proportion is 1.55, approximate to the Golden 0.17), k of rectangles (Range: 1.68–1.85/Range Value: Ratio, that is to say that the proportion of the distance pffiffiffi 0.17), k of 4 rectangles (Range: 1.915–2.085/Range between the left side line of the facade and the left pffiffiffi Value: 0.17) and k of 5 rectangles (Range: 2.151– side line of the double column on the right side of the 2.321/Range Value: 0.17) with 0.01 as the partition middle doorway to the height h1 of the First Storey is value of the range of k], this study finds that the in accordance with the Golden Ratio, which brings nodes and sides of golden rectangles have the largest Sub-golden-rectangle 1. numbers and coverage area and are usually the main Square 1 (D1-D7-K7-K1): Line D1-D7 is 10,450 mm controlling lines of the division of the facade, and that long and Line D1-K1 is 10,200 mm long. Their propor- these golden rectangles bring about golden spirals tion is approximate to 1:1, the one of a square, that is to through successive partition. say that the proportion of the distance between the left Accordingly, this study concludes that Golden Ratio side line of the facade and the left line of the double is an important foundation of the partition of the column on the right side of the middle doorway to the facade of the Macau St. Dominic’s Church. combined height (h2+ h3) of the Second and Third Storey is in accordance with 1:1, which brings about Square 1. 5.2. A parametric analysis of the façade: the Sub-rectangle 1.1 (A5-A7-D7-D5): Line A5-A7 is complicated combination of rectangles and spirals 3,800 mm long and Line A5-D5 is 6,750 mm long. controlled by golden ratio Their proportion is 1.776, approximate to the Golden Ratio, that is to say that the proportion of the distance (1) Golden Rectangles and Spirals from the Two- (200+ the width f of the middle doorway+200) times Partition (Table 2) between the double columns on both sides of the 1) Main Rectangle 1 = Sub-rectangle 1 + Square 1; middle doorway to the height h1 of the First Storey is Sub-rectangle 1 = Sub-rectangle 1.1 + Square 1.1 in accordance with the Golden Ratio, which brings Main Rectangle 1 (A1-A7-K7-K1): Line A1-A7 is 10,450 mm long and Line A1-K1 is 16,950 mm long. about Sub-golden-rectangle. 1.1. Their proportion is 1.62, approximate to the Golden Square 1.1 (A1-A5-D5-D1): Line A1-A5 is Ratio, that is to say that the proportion of the distance 6,650 mm long and Line A1-D1 is 6,750 mm long. (a + e + 200 + f + 200) between the left side line of the Their proportion is approximate to 1:1, the one of facade and the left side line of the double column on a square, that is to say that the proportion of the the right side of the middle doorway to the combined distance (a + e) between the left side line of the height (h1+ h2+ h3, three times the height of the facade and the right side line of the double column Second Storey, 3× h2) of the First, Second and Third on the left side of the middle doorway to the Storey is in accordance with the Golden Ratio, which height h1 of the First Storey is in accordance with brings about Main Golden Rectangle 1. 1:1, which brings about Square 1.1. Table 2. Golden rectangles and spirals. Golden Rectangles and Spirals from the Two-times Partition Width Height Ratio Main Rect. A1-A7-K7-K1 10,450 16,950 1.62 1 Sub- A1-A7-D7-D1 10,450 6,750 1.55 Rect. Sub-Rect.1.1 A5-A7-D7-D5 3,800 6,750 1.776 1 Square 1.1 A1-A5-D5-D1 6,650 6,750 1.02 Square1 D1-D7-K7-K1 10,450 10,200 1.02 Golden Rectangle From the One-time Partition Width Height Ratio Main Rect. A1-A7-D7-D1 10,450 6,750 1.55 2 Sub-Rect. 2 A1-A4-D4-D1 4,500 6,750 1.50 Square 2 A4-A7-D7-D4 5,950 6,750 1.13 Main Rect. D1-D11-K11-K1 17,100 10,200 1.676/5:3 3 Sub-Rect. 3 D7-D11-K11-K7 6,650 10,200 1.53 Square 3 D1-D7-K7-K1 10,450 10,200 1.02 Main Rect. D6-D11-M11-M6 8,550 14,250 1.67/5:3 4 Sub-Rect. 4 D6-D11-G11-G6 8,550 5,650 1.51 Square 4 G6-G11-M11-M6 8,550 8,600 1.01 Main Rect. D4-D9-G9-G4 9500 5650 1.68 5 Sub-Rect. 5 D7-D9-G9-G7 3550 5650 1.59 Square 5 D4-D7-G7-G4 5950 5650 1.05 Please be noted that “Rectangle” is abbreviated as “Rect.” and the unit is mm in this table. 8 J. TANG AND L. LAN (2) Golden Rectangles from the One-time Partition 3) The Main Rectangle 4 = Sub-rectangle 4 + Square 4 (Table 2) Main Rectangle 4 (D6-D11-M11-M6): Line D6-D11 is 1) Main Rectangle 2 = Sub-rectangle 2 + Square 2 8,500 mm long and Line D6-M6 is 14,250 mm long. Their Main Rectangle 2 (A1-A7-D7-D1): Line A1-A7 is proportion is 1.67 (5:3), approximate to the Golden 10,450 mm long and Line A1-D1 is 6,750 mm long. Ratio, that is to say that the proportion of the half of Their proportion is 1.55, approximate to the Golden the overall width of the facade to the combined height Ratio, that is to say that the proportion of the distance of the Second, Third and Pediment Storey as well as the (a + e + 200 + f + 200) between the left side line of the base of the Cross is in accordance with the Golden Ratio, facade and the left side line of the double column on which brings about Main Golden Rectangle 4. the right side of the middle doorway to the height h1 Sub-rectangle 4 (D6-D11-G11-G6): Line D6-D11 is of the First Storey is in accordance with the Golden 8,550 mm long and Line D6-G6 is 5,650 mm long. Ratio, which brings about Main Golden Rectangle 2. Their proportion is 1.51, approximate to the Golden Sub-rectangle 2 (A1-A4-D4-D1): Line A1-A4 is Ratio, that is to say that the proportion of the half of 4,500 mm long and Line A1-D1 is 6,750 mm long. the overall width of the facade to the height h2 of the Their proportion is 1.50, approximate to the Golden Second Storey is in accordance with the Golden Ratio, Ratio, that is to say that the proportion of the width which brings about Sub-golden-rectangle 4. a of the left part of the facade (the distance between Square 4 (G6-G11-M11-M6): Line G6-G11 is the left side line of the facade and the left side line of 8,550 mm long and Line G6-M6 is 8,600 mm long. left double column of middle doorway) to the height Their proportion is approximate to 1:1, the one of h1 of the First Storey is in accordance with the Golden a square, that is to say that the proportion of the half Ratio, which brings about Sub-golden-rectangle 2. of the overall width of the facade to the combined Square 2 (A4-A7-D7-D4): Line A4-A7 is 5,950 mm height of the Third and Pediment Storey as well as long and Line A4-D4 is 6,750 mm long. Their propor- the base of the Cross is in accordance with 1:1, which tion is approximate to 1:1, that is to say that the brings about Square 4. proportion of the distance (e + 200 + f + 200) between 4) The Main Rectangle 5 = Sub-rectangle 5 + Square 5 the left side line of the double column on the left side Main Rectangle 5 (D4-D9-G9-G4): Line D4-D9 is of the middle doorway and the left side line of the 9,500 mm long and Line D9-G9 is 5,650 mm long. double column on the right side of the middle door- Their proportion is 1.68, approximate to the Golden way to the height h1 of the First Storey is in accordance Ratio, that is to say that the proportion of the distance with 1:1, which brings about Square 2. between the left side line of double column on the left 2) Main Rectangle 3 = Sub-rectangle 3 + Square 3 side of middle doorway and the center line of the right Main Rectangle 3 (D1-D11-K11-K1): Line D1-D11 is doorway to the height h2 of the Second Storey is in 17,100 mm long and Line D1-K1 is 10,200 mm long. accordance with the Golden Ratio, which brings about Their proportion is 1.676 (5:3), approximate to the Main Golden Rectangle 5. Golden Ratio, that is to say that the proportion of the Sub-rectangle 5 (D7-D9-G9-G7): Line D7-D9 is overall width (a + b + a) of the facade to the combined 3,550 mm long and Line D9-G9 is 5,650 mm long. height (h2+ h3) of the Second and Third Storey is in Their proportion is 1.59, approximate to the Golden accordance with the Golden Ratio, which brings about Ratio, that is to say that the proportion of the distance Main Golden Rectangle 3. between the left side line of the right column of the Sub-rectangle 3 (D7-D11-K11-K7): Line D7-D11 is middle doorway and the central line of the right door- 6,650 mm long and Line D7-K7 is 10,200 mm long. way to the height h2 of the Second Storey is in accor- Their proportion is 1.53, approximate to the Golden dance with the Golden Ratio, which brings about Sub- Ratio, that is to say that the proportion of the distance golden-rectangle 5. (e + a) between the left side line of the right double Square 5 (D4-D7-G7-G4): Line D4-D7 is 5,950 mm column of middle doorway and the right side line of the long and Line D4-G4 is 5,650 mm long. Their proportion facade to the combined height (h2+ h3) of the Second is approximate to 1:1, the one of a square, that is to say and Third Storey is in accordance with the Golden Ratio, that the proportion of the distance (e + 200 + f + 200) which brings about Sub-golden-rectangle 3. between the left side line of the double column on the Square 3 (D1-D7-K7-K1): Line D1-D7 is 10,450 mm left side of middle doorway and the left side line of the long and Line D1-K1 is 10,200 mm long. Their propor- double column on the right side of middle doorway to tion is approximate to 1:1, the one of a square, that is the height h2 of the Second Storey is in accordance with to say that the proportion of the distance 1:1, which brings about Square 5. (a + e + 200 + f + 200) between the left side line of The golden rectangles, spirals and their partitions are the facade and the left side line of the double column bilaterally symmetric along the Medial Axis with another on the right side of the middle doorway to the com- correspondent set of golden rectangles, spirals and par- bined height (h2+ h3) of the Second and Third Storey titions. Accordingly, it could be concluded that the is in accordance with 1:1, which brings about Square 3. Golden Ratio is one of the important underlying basis JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 9 of the design drawing and lines and number-rounding Funding adjustments of the controlling points. This work is funded by the National Social Science Fund of China [Grants No. 20BZJ026]. Gratitude should also be extended to Dufeng Yu; National Office of Philosophy and Social Science of China [The National Social Science Fund of 6. Conclusions China 20BZJ026]. According to previous studies, the characteristic of upward successive-subtraction in stratification also exists in other Baroque-style buildings such as the ORCID the same as Church of St. Paul in Macau (Tang, 2018) Jian Tang http://orcid.org/0000-0003-3925-6145 (Tang 2018). Moreover, the upward “Successive Decrease by Equal Difference” in Stratification in the facade of Macau St. Dominic’s Church has References embodied high-level mathematical design. The underlying aesthetics-mathematics pattern of “digi- Ambrosio, F. 1628. Spinora. Rome: Francesco Corberetti. tally-derived geometric design” is of unparalleled Quoted from Corcero 1997. Macau Cathedral of the Mother historical value: of Catholicism (Or St. Paul) (1601-1640), Culture Magazine, 1) Its designer applied three-section upward nar- 18–19. Vol. 30. Beatriz Basto, D. S. 1995. Cronologia da Hitoria de Macau, rowing in the horizontal directions and especially trans, 24. Macau Foundation: Xiao Yu. Macau. five-section stratification upward successive Bry, T. 2000. “The City Map of Macao in 1607. Beijing: decrease by equal difference in stratification in Sino-Cultural Press. The First Historical Archives of China, One Country Two Systems Research Institute Selected height in the overall dimension of the façade. The Historical Maps of Macao”. height of the First, Second, Third, Pediment and da Silva, B. B. 1998. Cronologia da Hitoria de Macau: Secula Cross Storey have successive decrease by equal dif- XIX, trans, 194. Macau Foundation: Yao Jingming. Macau. ference in stratification in sequence; the subtraction Domingos, D., and L. A. M. Ka-tseung. 1982a. “Aomen Sengtang Shilue. Macao: Macau Catholic Education only deviates between the Pediment and Third Office”, printed version, p.18 Storey. Ge, D. 2005. “Buildings of “Neo-classicism” in China and 2) Its designer applied modularization (modular) Western.” Huazhong Architecture 23 (5): 26–28. design and combination in details of the columns Suzuki, H. 1998. Chronological Handbook of Architecture and doorways. Pictures/ Styles of Western Architectures, 39–42. Tokyo: Shokokusha. 3) Parametric analyses with the assistance of the Tang, J. 2018. “A Digital Analysis of the “Digitally-derived modeling software of Rhinoceros 6.0 and the soft- Geometric Design” of the Front Wall of St.Paul’s Church ware plug-in of Grasshopper found that the (succes- in Macao.” Journal of Asian Architecture and Building sive) partition of the façade is closer to the “Golden Engineering 17 (2): 159–165. doi:10.3130/jaabe.17.159. Section” than “Root Rectangle Partition”, and further Tang, J. 2021. “A Parametric Analysis of the “Digitally-derived Geometric Design” of the Façade of the Macau Holy House analyses lead to Golden Rectangle (one-time divi- of Mercy.” Journal of Asian Architecture and Building sion) and Golden Spiral (successive division) in the Engineering 8: 1–14. façade. Valente, M. R. 1993a. “Igrejas de Macau. Macau: Instituto Cultural de Macau”, p.68. Valente, M. R. 1993b. Igrejas de Macau. Macau: Instituto Cultural de Macau, 68. Disclosure statement Yin, G., and Zhang. 1992. R. A Brief History of Macao, 50. Macao: No potential conflict of interest was reported by the author(s). Macao Instituto Cultural edition. Book Two. Macao Part.
Journal
Journal of Asian Architecture and Building Engineering
– Taylor & Francis
Published: Sep 3, 2023
Keywords: The Macau St. Dominic’s Church; parametric analysis; stratification; successive decrease by equal difference; golden ratio