Multi-Viewpoint Assessment of Urban Waterfront Skylines: Fractal and Spatial Hierarchy Analysis in Shanghai

Abstract

With the global trend of waterfront urban expansion, nonlinear urban growth has generated skyline patterns marked by multidimensional spatial heterogeneity. Traditional single-viewpoint methods often fall short in capturing the layered spatial relationships among buildings and the complexity of multi-axis urban forms. This study focuses on the Lujiazui waterfront in Shanghai and proposes a multi-viewpoint assessment framework to evaluate urban waterfront skylines based on fractal and spatial hierarchy analysis. The framework consists of: (1) selecting eight representative viewpoints along the Huangpu River using visual cognition theory and GIS tools; (2) calculating skyline contour complexity using fractal dimension models; (3) establishing spatial hierarchy coefficients to measure depth gradients of building clusters; and (4) validating the results through visual field analysis and local skyline planning guidelines. This method integrates multi-viewpoint observation with quantitative morphological analysis, enabling a comprehensive evaluation from 2D skyline contours to 3D spatial structures. The key findings reveal that the fractal dimensions of the Lujiazui skyline demonstrate clear spatial differentiation, with viewpoints such as Financial Plaza and Chenyi Plaza reaching benchmarks typical of international metropolises. Spatial hierarchy coefficients exhibit a gradient attenuation trend, meeting the planning expectations in central zones but revealing stratification discontinuities in peripheral areas. Comparative analysis shows that over 50% of the observation points present imbalanced height ratios and excessive interface continuity, indicating potential risks associated with uncoordinated morphological control. This research confirms that multi-viewpoint assessment effectively captures spatial heterogeneity in nonlinear urban skyline development. A dual-variable evaluation model—fractal dimension and spatial hierarchy—is proposed, forming a quantitative mapping mechanism between visual characteristics and planning regulations. The findings contribute to the development of standardized 3D morphological evaluation methods for complex urban waterfront environments.

1. Introduction

1.1. Uniqueness of Nonlinear Expansion in Urban Waterfront Areas

Many globally renowned urban building clusters are located along waterfronts due to three key characteristics. First, waterfront areas serve as transitional zones between land and water, enabling the extension of land-based architectural landscapes into aquatic environments. This spatial overlap enhances the rhythmic quality of skyline contours through multidimensional expansion [1]. Second, water bodies function similarly to open spaces—such as parks or plazas—by minimizing visual obstructions and allowing for unobstructed views of urban skylines. Third, and most importantly, water naturally increases the viewing distance between observers and buildings. This greater distance helps to establish an optimal height-to-distance ratio, enhancing the complete visual perception of building clusters within the human field of view [2]. As a medium for visual communication, the skyline becomes a recognizable image that facilitates the spread of urban identity and strengthens public memory.

In the early stages of urban development, waterfront cities often expand linearly, with buildings arranged parallel to the shoreline. As urban cores densify and space becomes limited, expansion shifts inward, producing more compact and layered urban forms. This spatial transition fundamentally alters the morphology of the urban skyline. The resulting nonlinear expansion introduces greater spatial diversity and visual richness, enhancing the symbolic and perceptual significance of skylines as key elements of urban form.

1.2. Necessity of the Research on Nonlinear Urban Expansion in Waterfront Areas

The research on nonlinearly expanding urban waterfront areas focuses primarily on analyzing and evaluating skyline morphology. As a subfield of urban morphology, skyline studies investigate the formation, evolution, and perceptual influence of skylines on urban identity. Applying scientific methods to analyze skyline contours allows for the quantitative evaluation of spatial configurations and supports more precise and systematic urban planning [3]. According to environmental psychology, two key visual variables influence public perception of skylines. The first is the skyline contour, defined by the Oxford English Dictionary as “the outline formed by the intersection of building tops with the sky, or the silhouette of buildings” [4]. This contour shapes both daytime cityscapes and nighttime silhouettes.

With the advancement of technology, skylines—understood as the marginal forms of three-dimensional urban space—can now be analyzed using more rigorous and interdisciplinary methods. Studies of skylines in nonlinearly expanding waterfront areas generally exhibit four defining characteristics: (1) Integration of visual perception theory and aesthetic evaluation, often through viewshed analysis, which examines spatial hierarchy and visual permeability by combining the physical form, visual experience, and behavioral patterns [5]; (2) Application of fractal dimension models to quantitatively assess skyline contour complexity; (3) Use of remote sensing, 3D modeling, and virtual reality for the immersive visualization of skyline form; and (4) Development of regulatory strategies through control indicators, such as building gap ratios (to ensure visual permeability along waterfront interfaces) and skyline profile ratios (to regulate height transitions across different zones) [6].

Despite these advances, the current skyline research methods face three major limitations. First, conventional fractal analyses are typically based on static, single-viewpoint images. These approaches can capture local contour fluctuations, but fail to reflect spatial heterogeneity across multiple urban axes. Second, many studies treat skyline contour complexity and spatial hierarchy as isolated variables, lacking a quantitative framework to link fractal dimension and depth structure. Third, the existing planning guidelines—such as those regulating building height ratios and continuous interfaces—often operate without closed-loop validation mechanisms based on dynamic, multi-viewpoint observations.

Shanghai’s Lujiazui Financial District exemplifies these challenges. Its skyline extends along both sides of the Huangpu River while forming a polycentric spatial structure. Iconic high-rise clusters, historical neighborhoods, and public spaces interweave to create dispersed visual focal points and complex hierarchical layering. This spatial heterogeneity exposes the limitations of traditional single-viewpoint analysis. For instance, the classic view from Chenyi Plaza on the Bund captures the skyline contours of landmarks like the Oriental Pearl Tower and Shanghai Tower, but neglects spatial occlusions and shifts observable from alternative angles.

To address these limitations, this study introduces three innovations: the construction of an eight-viewpoint observation matrix based on GIS and visual cognition theory; a dual-variable analytical framework combining fractal dimension and spatial hierarchy coefficients; and the incorporation of multi-viewpoint diagnostics into planning regulation, shifting from static control metrics to dynamic, responsive standards.

This planning framework draws from China’s first regional skyline regulation—Tianjin Key Urban Area Skyline Planning Guidelines—as a benchmark. Both Lujiazui and Tianjin waterfronts exhibit nonlinear, multi-axis spatial expansion patterns and similar regulatory logic. These guidelines emphasize vertical gradient principles, encouraging stepped height increases from the foreground to background, along with rhythmically articulated skyline variations to enhance the overall coherence.

Table 1. Methods for skyline morphology research.

Methods	Content	Characteristics
Viewshed Analysis	This method analyzes viewpoints and visual corridors within cities. Its objectives are to protect and enhance urban visual corridors, ensuring public appreciation of significant natural and built landscapes.	This method integrates GIS technology with quantitative analysis to optimize view corridor planning. It further regulates building heights within sightlines to achieve controlled height parameters [7].
Fractal Dimension	Fractals are geometric forms with self-similar properties. The researchers calculate skyline fractal dimensions using methods, like the box-counting dimension, to quantitatively analyze morphological features.	This metric measures the complexity of two-dimensional shapes. When combined with human visual perception, it models the visual information perceived by observers in spatial contexts.
Eye-Tracking	This method, combined with virtual reality (VR) and other virtual technologies, analyzes the visual impact of spatial elements on participants.	Based on the new perspective of landscape perception quantification and its connection with public visual preference perception [8], the analysis results represent the unification of subjectivity and objectivity.
Power–Law Distribution	Power–law distribution is a type of probability distribution that describes phenomena where a few events have very large scales while most events are relatively small [9].	By analyzing the power–law characteristics of urban skylines, it is possible to identify which buildings contribute significantly to the skyline.
Subjective Perspectives	This approach examines the visual perception of urban form from different subjective perspectives, such as those from transportation vehicles and pedestrians, focusing on differences in viewpoint height and visual domain size.	It provides diverse observational angles and, when combined with modern technologies for visual simulation, offers a more comprehensive assessment of urban skylines.
Spatial Hierarchy	Based on the visual analysis theory, this method categorizes building clusters into multiple layers according to their visual clarity, calculating the visible area ratios of each layer for morphological analysis.	Starting from a three-dimensional perspective and combining it with the vertical outline, this approach provides a more comprehensive analysis of the morphological characteristics of building clusters.
Oblique Photography	Oblique photography captures images from different distances and angles, both vertical and tilted, within a coordinate system to create an oblique photographic system [10].	This technique provides richer side-texture information compared to traditional orthophotography, resulting in more accurate three-dimensional building models that better reflect the three-dimensional form and skyline characteristics of a city.
Subjective Evaluation	This study investigates respondents’ immediate experiences of building forms through on-site interviews, questionnaire surveys, and other methods, combined with a preference assessment method. The existing research has incorporated social needs, fairness, respect, cultural experience, etc., into the subjective evaluation system [11,12,13].	This approach is limited by the number of respondents and is highly subjective, making it difficult to generate precise quantitative data.

summarizes common analytical methods for studying skyline morphology. Among these, fractal dimension analysis, viewshed analysis, spatial hierarchy evaluation, and subjective perception studies are particularly suitable for skylines in nonlinearly expanding urban contexts.

As previously discussed, skyline morphology typically consists of two key variables. The first is contour complexity. In waterfront zones, irregular building heights generate pronounced skyline undulations, resulting in intricate and dynamic contour patterns. Fractal dimension analysis effectively captures both the self-similarity and variability of these skylines, providing a quantifiable indicator of urban contour complexity. However, this method has notable limitations: it struggles to detect sudden morphological shifts—such as the abrupt rise of landmark buildings—and lacks sufficient sensitivity to vertical gradient variations. These shortcomings weaken its ability to assess the dynamic rhythm inherent in building height distributions. To address these gaps, this study complements fractal analysis with qualitative assessments of vertical fluctuations in the skyline.

The second variable is spatial hierarchy. Nonlinearly expanding cities often feature polycentric structures, where visual focal points are distributed across multiple zones rather than centralized in a single area. This spatial configuration reflects the evolving, heterogeneous nature of urban growth. From a planning perspective, buildings within clusters may obscure one another at specific viewpoints, forming layered visual interfaces based on their distance from the observer. Spatial hierarchy analysis helps reveal these depth-wise morphological patterns, offering a critical insight into the skyline structures of cities undergoing nonlinear expansion.

Based on a systematic review of the existing skyline evaluation methods, this study adopts fractal theory and spatial hierarchy analysis as its primary methodological framework.

1.3. Relationship Between Fractal Theory and Spatial Hierarchy

Fractal dimension and spatial hierarchy form dual theoretical pillars for skyline perception, rooted in 2D geometric and 3D topological perspectives.

Fractal dimension (D) quantifies the geometric irregularity of skyline contours, indicating visual information density and rhythm. Higher D values indicate better rhythmic quality in skyline contours; lower D values correspond to monotonous linear outlines prone to visual fatigue.

The spatial hierarchy coefficient (C) characterizes gradient distribution order of building clusters along depth axes, determining the structural organization of visual information. Lower C values reflect progressive layering (low–near, high–far) enhancing spatial legibility; higher C values indicate stratification fractures disrupting visual coherence.

High contour complexity (D↑) paired with clear hierarchy (C↓) organizes fractal richness into “complex yet ordered” aesthetics, maximizing visual pleasure. High complexity with poor hierarchy (D↑ + C↑) or low complexity with hierarchy fractures (D↓ + C↑) creates dual negative effects: visual overload/monotony from contour uniformity (Figure 1).

1.4. Relationship Between Nonlinearly Expanded Cities and Multi-Viewpoint Observation

The distinctive spatial attributes of urban waterfront areas result in varying visual perceptions of building clusters when viewed from different locations—differences shaped by variations in building height, density, and spatial arrangement. As such, the selection of observation viewpoints critically influences the accuracy and depth of research on waterfront spatial structures and skyline morphology.

Single-viewpoint observation, which analyzes the urban skyline from a fixed location, has been widely utilized in early studies and urban planning practices. While effective in capturing basic contour information, it provides a limited visual scope and lacks the capacity to represent complex depth structures and spatial hierarchies. For instance, observing Lujiazui from the Bund enables the identification of prominent landmarks, such as the Oriental Pearl Tower and Jin Mao Tower, yet it fails to reveal the layered composition of structures behind the primary skyline, or the interactions between the waterfront and the urban hinterland. These limitations significantly reduce the method’s suitability for analyzing the multidimensional features of nonlinearly expanding cities.

Multi-viewpoint observation, by contrast, incorporates multiple spatially distributed vantage points to systematically examine waterfront skylines. This method captures directional variations in building outlines and uncovers the depth-oriented spatial hierarchies that characterize polycentric urban formations. Its comprehensive and integrative nature makes it particularly well-suited for the analysis of skylines in cities undergoing nonlinear spatial expansion.

2. Research Methods

2.1. Methodology

Building on the previous research in skyline morphology, this study introduces a multi-viewpoint observation framework composed of two primary phases.

In the first phase, eight observation points were strategically selected within Shanghai’s Lujiazui area, guided by principles from visual cognition theory and site-specific contextual factors. Field investigations were conducted to capture two-dimensional skyline contours from each viewpoint, providing the empirical basis for subsequent quantitative analysis.

In the second phase, fractal theory and spatial hierarchy analysis were employed. Specifically, the box-counting dimension method was used to calculate the contour complexity of skylines at each viewpoint, while spatial hierarchy metrics were applied to quantify depth-wise spatial gradients.

Subsequently, in alignment with the regulatory benchmarks set by the Skyline Planning Guidelines, values derived from the eight viewpoints were compared across two key dimensions. For the skyline contour evaluation, the analysis considered fractal dimension values, building height ratios, and overall contour morphology. For the spatial hierarchy assessment, indicators included visible area ratios, hierarchy coefficients, vertical density distribution, and continuous interface coverage across hierarchical layers. This comparative analysis identified both high-performing viewpoints and those with suboptimal skyline features.

The evaluation outcomes informed a series of targeted design optimizations. Viewpoints with low contour complexity were addressed through vertical adjustments to building heights, enhancing rhythmic variation. Areas with weak spatial hierarchy were improved by modifying building layouts and recalibrating hierarchical interface areas to reinforce depth perception.

In conclusion, this multi-viewpoint methodology, which integrates assessments of skyline contour complexity and spatial hierarchy, provides a robust framework for the comprehensive, quantitative evaluation of urban waterfront skylines across multiple dimensions, as illustrated in Figure 2.

2.2. Comparison with Other Methods

(1) Complexity-Driven Evaluation—This method quantifies skyline morphology using indicators such as silhouette complexity or contour complexity [14]. While it performs well in single-viewpoint analyses, its applicability in multi-viewpoint contexts is limited due to high sensitivity to viewpoint position, observation angle, and viewing distance.

(2) Subjective Preference Assessment—Through questionnaires or interviews, this approach captures observers’ intuitive perceptions of skylines [15]. However, it lacks objectivity and consistency, as aesthetic preferences vary significantly between individuals. Moreover, the absence of quantitative metrics hinders the conversion of perceptual outcomes into standardized data.

(3) Surface Visibility Analysis—Utilizing Grasshopper (Version 1.0.0007 for Rhinoceros 6; McNeel, 2018), this method evaluates skyline visibility by analyzing building cluster overlaps using simplified shapes (rectangular, circular, or linear) [16]. Greater visibility is associated with lower levels of overlap in specific viewing directions [17]. Nevertheless, the method focuses solely on two-dimensional visibility from single viewpoints, ignoring three-dimensional depth structures. As a result, it falls short in addressing the requirements of multi-viewpoint analysis.

3. Method Verification

3.1. Sample Selection

Shanghai’s Lujiazui Financial and Trade Zone represents a hallmark of China’s contemporary urbanization, serving as the nation’s largest economic hub and a vanguard of reform and opening-up. Its iconic waterfront skyline, marked by clustered skyscrapers such as the Oriental Pearl Tower (468 m), Jin Mao Tower (420 m), and Shanghai Tower (632 m), defines Shanghai’s global image. The stark height variations—from mid-rise structures like World Plaza (199 m) to soaring landmarks—create a visually intricate skyline characterized by dramatic contrasts.

Unlike linearly expanding waterfront cities, such as Qingdao or Lanzhou—where strip-like skylines necessitate fixed panoramic viewpoints—Lujiazui features a multidimensional spatial structure. Its skyline unfolds bidirectionally along the Huangpu Riverbanks and extends inward with pronounced depth. Multi-viewpoint observation enables a more comprehensive capture of this spatial complexity.

3.2. Selection of Observation Viewpoints

In The Formation of Cities, Kostof identifies three key categories of meaningful urban skyline viewpoints: roadway viewpoints at city entrances, waterfront viewpoints along rivers or coastlines, and elevated viewpoints within urban landscapes. Building upon this framework and adapting it to Lujiazui’s specific spatial conditions, eight observation points were selected based on the following criteria:

Prioritizing unobstructed views, high pedestrian flow, and static spaces where crowds naturally pause and observe [18];

Ensuring adequate spatial separation between points to generate sequential visual experiences while avoiding redundant information;

Selecting locations free from traffic obstructions or external disturbances to ensure observational consistency and data reliability.

The final eight observation points included: Bund Tourism Pier (A1), Bund Pier District 1 (A2), Meteorological Square (A3), Financial Plaza (A4), Chen Yi Square (A5), Monument to the People’s Heroes (A6), International Passenger Center (A7), and Marine Plaza (A8) (see Figure 3).

This study employed GIS-based visibility analysis to support the selection of observation points, integrating high-resolution digital elevation models (DEMs) and building vector data with height attributes to accurately reflect terrain variations and three-dimensional building morphology. The observer’s sightline height was set at 1.7 m—simulating the average human eye level—to compute the visible area from each candidate viewpoint. The analysis results are visualized as raster maps, where green areas indicate visible zones and red areas denote non-visible zones (see

Table 2. Viewpoint visibility analysis. (Green areas indicate visible zones, red areas denote non-visible zones).

A1	A2	A3	A4
A5	A6	A7	A8

). The data confirm that all eight selected viewpoints achieve visibility ratios of 40% or higher relative to the defined study area (north of Dongchang Road and west of Pudong South Road), thereby meeting the established visibility criteria and validating their suitability for further skyline analysis.

This study implemented strict controls on viewpoint positioning and atmospheric conditions to minimize their influence on fractal and spatial hierarchy analyses. Given the fractal dimension’s high sensitivity to local geometric variations, even minor horizontal or vertical shifts in viewpoints can disrupt contour self-similarity, potentially exaggerating or diminishing localized fluctuations. Similarly, slight changes in viewpoint height can alter the visible area ratios across foreground, midground, and background layers. To eliminate such positional biases, all photographs were captured from a fixed eye level of 1.7 m and at a standardized distance from the riverbank.

Atmospheric conditions, particularly haze, also affect skyline interpretation. Reduced visibility blurs contour edges, which may artificially inflate fractal dimension values by introducing false complexity through edge diffusion. In parallel, haze obscures distant buildings, skewing spatial hierarchy assessments by underrepresenting deeper visual layers. To ensure atmospheric consistency, all field photography was conducted on a single clear day. Additionally, visibility data were derived from 3D models rather than image-based interpretations to further reduce weather-related data distortions.

3.3. Complexity Evaluation

Mathematician Benoit Mandelbrot established the fractal theory in 1975, defining its core concepts and mathematical foundations [19]. Fractal dimension quantifies spatial occupation scale and morphological complexity, serving as a key metric for characterizing irregularity in natural and artificial forms [20]. In architectural studies, this metric assesses design complexity through geometric fractal dimension calculations, directly correlating with visual perception outcomes.

This methodology integrates the fractal dimension with human visual perception distances, introducing two key concepts: visual complexity and fractal dimension trend analysis [21]. These innovations enhance the fractal theory’s applicability in architectural morphology studies.

The original input image had a resolution of 1920 × 1080 pixels. First, the BGR color space image was converted to grayscale using the OpenCV’s cv2.cvtColor function with the parameter cv2.COLOR_BGR2GRAY, serving as the input for Canny edge detection. The Canny algorithm, renowned for its noise resistance and edge continuity advantages [22], was implemented with dual-threshold filtering (low threshold = 50, high threshold = 150) via the code cv2.Canny(gray_image, 50, 150), generating a binary-edge image edges, where edge pixels were marked white (255) against a black background (0). For vertical edge extraction, the program iterated column-wise across the image width, scanning pixels from top to bottom in each column to record the first detected edge pixel (first occurrence value: 255). This process was implemented through nested loops, with the core code shown in Figure 4:

Generate logarithmically spaced box sizes using np.logspace, with the core code shown in Figure 5.

Iterate through each box size (scale), partition the image grid with a step size equal to scale, and count boxes containing skyline contours, as shown in Figure 6.

Determine the fractal dimension by fitting the slope of log(counts) versus log(1/scales) through linear regression. The complete procedure is visually summarized in Figure 7.

The calculation results of the fractal dimensions for each viewpoint are now statistically presented, as shown in

Table 3. Fractal dimensions at each viewpoint.

Viewpoint	A1	A2	A3	A4	A5	A6	A7	A8
Picture
Fractal Dimension	1.128	1.126	1.114	1.182	1.191	1.136	1.140	1.121

.

Fractal dimension values for skylines typically range between 1.100 and 1.200. Major global cities, like New York and Tokyo, exhibit values concentrated between 1.180 and 1.200 [23]. Higher values indicate greater contour curvature and superior overall skyline morphology. Contour curvature is quantified as the ratio between the total length of upper horizontal skyline elements and the skyline’s total horizontal span [24]. Additionally, Nasar’s experimental studies demonstrate public preference for building facades featuring single-curve profiles (convex, concave, or flat) over complex multi-curve designs [25].

3.4. Spatial Hierarchy Evaluation

Spatial hierarchy describes urban spatial structures by quantifying variations in visible building areas across different viewing distances. The Urban Skyline Planning Guidelines for Key Areas emphasize two core principles. First, skylines should exhibit a riparian gradient, with building heights increasing progressively from the waterfront to the inland, thereby establishing distinct foreground, middleground, and background layers. Second, continuous visual walls must be avoided—no more than three consecutive buildings over 54 m, or five under 54 m, may align horizontally. These principles promote a spatial organization strategy of “low–near, high–far; sparse–near, dense–far”.

The spatial hierarchy coefficient (SHC) measures the dominance of visible areas in lower layers (sum of the first and second layers) relative to upper layers. A higher SHC indicates strong horizontal visual presence near the pedestrian level, emphasizing layered transparency and visual accessibility. Conversely, a lower SHC reflects vertical dominance by tall buildings, often associated with minimalist aesthetics. As a financial core, Lujiazui favors bold, modern vertical forms. Therefore, adopting lower SHC values aligns with its urban identity by balancing vertical expression with selective spatial permeability.

(a)

Spatial Hierarchy Division

Skyline spatial hierarchy depends primarily on two elements: the number of hierarchical layers and the proportional visible area within each layer [26]. A well-structured cityscape allows observers to perceive not only skyline contours but also dynamic spatial relationships between building groups, enriching visual layering and façade complexity [27].

Empirical analysis under ideal conditions—natural daylight, acceptable air quality (PM2.5 ≤ 150 μg/m³), and standard visual acuity (≥1.0)—reveals distance-based thresholds of visual perception. At distances under 30 m, architectural details, such as materials, colors, and fenestration patterns, are clearly visible. Around 300 m, building contours and fenestration outlines remain discernible. At 600 m, while fine details blur, silhouettes and grouped window patterns are still distinguishable. Beyond this, visual perception is largely limited to skyline contours.

The 600–800 m range represents a critical perceptual boundary where architectural detail dissolves and the skyline contour becomes the dominant visual feature. Integrating these thresholds with the Huangpu River’s width and Lujiazui’s building density, this study delineates three spatial hierarchy zones:

• First hierarchy: within 800 m, where architectural details (e.g., windows, doors) are still perceptible.
• Second hierarchy: between 800 and 1000 m, where only building outlines remain visible.
• Third hierarchy: beyond 1000 m, where perception is limited to overall skyline form.

Chen Yi Square (Viewpoint A5) exemplifies this layered classification, as illustrated in Figure 8.

(b)

Spatial Hierarchy Coefficient

Visibility analysis identifies the three-dimensional visual range of specific points and evaluates mutual visibility among observation locations [28]. This method is particularly suitable for analyzing large-scale spatial configurations, offering detailed insights into visual corridors, occlusion patterns, and barriers within dense urban environments. By visualizing these spatial relationships, visibility analysis intuitively reveals the hierarchical layering of urban space—foreground, middleground, and background.

The process began with exporting the building footprint data from the OpenStreetMap platform. These 2D outlines, enriched with height attributes, were converted into 3D models using SketchUp. To optimize computational efficiency, non-essential elements, such as vegetation and roads, were removed, while primary building geometries were preserved to maintain spatial integrity. The eight preselected viewpoints (A1 to A8) were then defined with accurate spatial coordinates, sightline directions, and field-of-view angles, which were recorded using the scene-saving function.

For visibility analysis, the section tool was employed to cut the model along each viewpoint’s sightline, generating profile diagrams that clearly depicted occlusion relationships among foreground, middleground, and background buildings. Within each profile diagram, buildings with unobstructed visibility were manually labeled and organized into separate layers via SketchUp’s layer management system. The FredoTools plugin was then used to isolate and batch-calculate the visible surface areas of buildings within these designated layers.

Based on the spatial hierarchy zoning map (Figure 5) and the visibility analysis workflow, spatial hierarchy diagrams for the eight observation viewpoints were generated. The results are presented in

Table 4. Spatial hierarchy diagrams at each viewpoint.

Bund Tourism Pier (A1)	Bund Pier District 1 (A2)	Meteorological Square (A3)	Financial Plaza (A4)
Chen Yi Square (A5)	Monument to the People’s Heroes (A6)	International Passenger Center (A7)	Marine Plaza (A8)

.

The visible area was divided into three non-overlapping layers: foreground (S1), middleground (S2), and background (S3). The spatial hierarchy coefficient for each viewpoint was calculated using the skyline spatial hierarchy coefficient formula.

$$\mathrm{C} (Spatial Hierarchy Data)={\displaystyle \frac{\mathrm{S}1+\mathrm{S}2}{\mathrm{S}3}}$$

The ratios of visible areas for the three layers (S1, S2, S3) and the spatial hierarchy coefficients are listed in

Table 5. Spatial hierarchy data at each viewpoint.

	A1	A2	A3	A4	A5	A6	A7	A8
S1/m2	131,697	166,275	179,771	126,531	46,409	57,169	47,167	144,091
S2/m2	86,241	55,935	88,453	130,120	53,562	12,738	31,756	35,579
S3/m2	35,387	39,826	65,605	132,929	82,050	65,793	34,572	34,043
C	6.158	5.579	4.088	1.994	1.218	1.062	2.282	5.277

, providing quantitative data for the subsequent visual evaluation.

4. Research Results

4.1. Research Findings on Skyline Contour

The data from all viewpoints were compared against the established criteria. Among them, viewpoints A4 and A5 fully complied with all three standards. Viewpoints A3 and A6 met only the building height ratio requirement, while others failed to satisfy any criteria. These results are comprehensively summarized in

Table 6. Analysis of contour line results.

Viewpoint	Fractal Dimension Value (1.180–1.200)	Height Ratio (3:1.5:1)	Overall Contour Trend (Convex, Concave, Flat)
A1	×	×	×
A2	×	×	×
A3	×	√	√
A4	√	√	√
A5	√	√	√
A6	×	√	×
A7	×	×	×
A8	×	×	×

(“×” means failing to meet the criteria, and “√” means meeting the criteria.).

4.2. Research Findings on Spatial Hierarchy

Among the five evaluation criteria, Viewpoints A4 and A5 demonstrated full compliance across all metrics. Viewpoint A6 ranked next, meeting the standards for the spatial hierarchy coefficient, low–near/high–far gradient layering, and continuity of building interface areas. Viewpoint A7 satisfied the latter two criteria—gradient layering and interface continuity. In contrast, Viewpoints A1 and A3 met only the interface continuity requirement, while A2 and A8 failed to meet any of the specified standards, as shown in

Table 7. Analysis of spatial hierarchy results.

Viewpoint	Visible Area Ratio (S1 < S2 < S3)	Spatial Hierarchy Coefficient (C < 2)	Gradual Height Increase	Density Variation (Sparse Near, Dense Far)	Maximum Continuous Buildings < 5
A1					√
A2
A3					√
A4	√	√	√	√	√
A5	√	√	√	√	√
A6		√	√		√
A7			√		√
A8

(“×” means failing to meet the criteria, and “√” means meeting the criteria).

5. Discussion

5.1. Skyline Contour

Heath et al. explored the aesthetic role of high-rise buildings in urban skylines and landscapes, revealing a dual-component influence of complexity on aesthetic judgment: the architectural complexity of individual towers and the overall skyline complexity formed by their aggregation. Their study established a direct correlation between skyline contour complexity and visual preference, with higher fractal dimensions consistently correlating with stronger observer preference [29].

Among the fractal dimension analysis results for the eight viewpoints, only A4 and A5 exceeded a value of 1.180, indicating higher contour curvature and distinct rhythmic variations in their skylines, which enhance visual appeal. In terms of the building height ratios, viewpoints A3, A4, A5, and A6 displayed a consistent 3:1.5:1 distribution pattern. However, despite adhering to this ratio, A6’s skyline lacked a cohesive form due to excessively linear contours of generic high-rises, which failed to create progressive layering and ultimately diminished visual engagement. In contrast, viewpoints A1, A2, A7, and A8 demonstrated lower fractal dimensions and irregular height ratios, resulting in unrecognizable skyline profiles.

5.2. Spatial Hierarchy

At viewpoint A5, the first layer consists of low-rise, well-ordered buildings, such as the Shanghai International Convention Center and Grand Gateway Plaza. The second layer includes mid-rise structures, like the Zendai Building and Oriental Pearl Tower. The third layer features iconic skyscrapers, such as the Shanghai Tower and Shanghai World Financial Center, whose heights and visible area densities substantially exceed those of the lower layers. This configuration adheres to the “low–near, high–far; sparse–near, dense–far” principle.

For viewpoints A1, A2, and A3, the first layer is dominated by taller buildings with larger visible areas. At viewpoint A2, extensive contiguous buildings obstruct visual corridor permeability. Viewpoint A1, by contrast, exhibits minimal third-layer visible areas compared to the first two layers, resulting in weak hierarchical depth perception.

6. Conclusions

With the rapid acceleration of urbanization and the continuous expansion of urban spaces, modern cities are increasingly exhibiting complex and dynamic development patterns. Urban areas are progressively extending in depth, forming multi-layered and multidimensional three-dimensional structures. This nonlinear expansion has reshaped the physical morphology of cities. In this context, urban waterfront areas—serving as interfaces between the built and natural environments—have become critical windows reflecting urban developmental characteristics and spatial configurations through their skyline forms. Therefore, studying waterfront skyline morphology, particularly under conditions of nonlinear expansion, holds significant theoretical and practical value for understanding urban spatial evolution, optimizing landscape design, and enhancing residents’ spatial experiences.

As a relatively mature skyline example in China, Shanghai’s Lujiazui Financial and Trade Zone has been extensively studied by both domestic and international scholars. However, the existing research primarily focuses on skyline contours and high-rise buildings, often overlooking a comprehensive analysis of building group compositions and vertical spatial layouts. Furthermore, traditional studies relying on single-viewpoint static imagery fail to capture Shanghai’s multilayered, multidimensional skyline characteristics and urban spatial complexity. To address these gaps, this study adopts a multi-viewpoint observation method, analyzing the Lujiazui skyline from diverse angles and positions. By examining the complexity of the waterfront skyline and depth-wise spatial hierarchies, it uncovers trends in urban spatial development, providing a scientific foundation for urban planning and design.

For planning guidelines, integrating the fractal dimension (D-value) and spatial hierarchy coefficient (C-value) as core regulatory metrics is essential. Modern financial districts should aim for D-values near 1.20, enhancing contour complexity through rooftop setbacks and facade articulation. In contrast, historical districts must restrict D-values to maintain low-complexity silhouettes that align with traditional textures—an approach exemplified by the Najaf Old City Mosque, where low-rise structures define the distinctive skyline [30]. Spatial hierarchy management requires gradient zoning: core waterfront areas should enforce C < 2.0 (low–near/high–far), transitional zones may allow C ≤ 3.0, and peripheral developments should restrict C > 5.0, complemented by visual corridor optimization.

Architectural design practices should implement multi-viewpoint collaborative mechanisms. The early-phase integration of GIS-based visibility analysis and three-dimensional modeling can establish a network of 6–8 critical observation points covering waterfront interfaces, arterial roads, and public spaces, thereby preventing imbalanced skyline development.

Although this study provides a more comprehensive perspective on the skyline form characteristics of Shanghai’s Lujiazui Financial and Trade Zone from multiple viewpoints, the current research method still has limitations in terms of studying skyline visual continuity and dynamics. Future research is expected to further supplement and refine this area.