Parametric Process Studio

Introduction

Parametric Process Studio is a computational urban design and analysis framework implemented as a QGIS processing plugin. It integrates six interrelated algorithms spanning multi-objective evolutionary optimisation, urban microclimate physics, morphological analytics, procedural shape grammars, inter-building environmental coupling, and a sequential parametric urban design pipeline.

The plugin operationalises the Parametric Performance-based Urban Design (PPUD) methodology, a framework that bridges urban morphology, building science, and computational optimisation to support evidence-based decision-making in the early stages of urban design. The theoretical backbone draws from evolutionary computation (Deb et al., 2002; Zitzler et al., 2001; Zhang & Li, 2007), urban climatology (Oke, 1988; Jendritzky et al., 2012), building physics (Duffie & Beckman, 2013; Hammond & Jones, 2008), and computational urbanism (Parish & Muller, 2001; Batty, 2008; Akay & Caliskan, 2025).

Each algorithm is designed to operate on spatial data layers within QGIS, producing both tabular and geometric outputs that can be visualised, exported, and subjected to further analysis. The plugin supports the complete workflow from parcel subdivision through building configuration optimisation to district-scale environmental performance assessment.

Plugin Architecture

The six algorithms form a logical pipeline: Algorithm 4 (Shape Grammar) generates subdivided plots; Algorithm 1 (Evolutionary Optimisation) configures building genotypes on those plots; Algorithm 2 (Physics Evaluator) and Algorithm 3 (Morphology Analytics) assess the resulting configurations; Algorithm 5 (Environmental Coupling) captures inter-building effects that emerge at the district scale; and Algorithm 6 (PPUD Pipeline) chains these stages into an integrated, climate-responsive sequential workflow.

Theoretical Foundations

Parametric Urbanism

Parametric urbanism treats the city as a system of interlinked parameters whose values determine spatial, environmental, and socio-economic outcomes. This perspective, articulated by Schumacher (2009) and grounded in the computational design tradition of Alexander et al. (1977), shifts the role of the designer from that of a form-giver to that of a system designer: one who specifies the rules, constraints, and objectives that govern the generation and evaluation of urban configurations.

Multi-Objective Decision Making in Urban Design

Urban design problems are inherently multi-objective. Increasing gross floor area (GFA) to accommodate population growth may degrade wind ventilation; maximising return on investment may conflict with minimising lifecycle carbon emissions; optimising solar access for one building may cast shadows on its neighbours. Multi-objective evolutionary algorithms (MOEAs) provide a principled framework for exploring the trade-off surface (Pareto front) that characterises these conflicts, enabling designers and decision-makers to select configurations that represent acceptable compromises among competing objectives (Coello Coello et al., 2007).

Urban Microclimate Physics

The thermal and aerodynamic behaviour of urban environments is governed by the interaction of built form with atmospheric processes. Key phenomena include the urban heat island effect (Oke, 1982), street canyon ventilation (Oke, 1988), pedestrian-level wind comfort (Lawson & Penwarden, 1975; Blocken et al., 2007), solar access and shading (Knowles, 2003; Compagnon, 2004), and stormwater runoff (Berland et al. 2017). The plugin encodes simplified physics models for each of these domains, calibrated against the fuller computational fluid dynamics (CFD) and radiative transfer simulations that underpin the research literature.

Procedural Modelling and Shape Grammars

Shape grammars, introduced by Stiny and Gips (1972) and extended to urban-scale procedural modelling by Parish and Muller (2001), provide a formal language for generating complex geometries from a compact set of production rules. In the context of urban design, shape grammars enable the automated subdivision of large parcels into buildable plots, the generation of building massing envelopes, and the exploration of alternative block typologies at scale (Mueller et al., 2006).

Algorithm 1: Parametric Multi-Objective Evolutionary Optimization

Theoretical Background

This algorithm implements four canonical multi-objective evolutionary algorithms (MOEAs) for the simultaneous optimisation of five urban performance objectives. Each solver belongs to a distinct family of multi-objective optimisation techniques, and the choice among them depends on the characteristics of the problem instance (number of objectives, desired population diversity, convergence speed requirements).

NSGA-II (Non-dominated Sorting Genetic Algorithm II)

Proposed by Deb, Pratap, Agarwal, and Meyarivan (2002), NSGA-II is the most widely cited MOEA in the engineering design literature. It employs two key mechanisms: fast non-dominated sorting, which partitions the population into successive Pareto fronts in $\mathcal{O}(MN^2)$ time (where $M$ is the number of objectives and $N$ the population size), and crowding distance assignment, which preserves diversity along the Pareto front without requiring a user-specified sharing parameter. The binary tournament selection operator favours solutions with lower (better) non-domination rank; when two solutions share the same rank, the one with larger crowding distance is preferred, thereby promoting a well-spread approximation of the Pareto-optimal set.

NSGA-III (Non-dominated Sorting Genetic Algorithm III)

Deb and Jain (2014) extended NSGA-II to handle many-objective problems (typically $M > 3$) where the proportion of non-dominated solutions in a finite population grows exponentially with $M$, rendering Pareto-dominance-based selection ineffective. NSGA-III replaces the crowding distance operator with a reference-point-based niching mechanism. A set of well-distributed reference points is generated on a normalised hyperplane using Das and Dennis's (1998) systematic approach. Each population member is associated with the nearest reference line, and a niching procedure selects solutions to ensure that every reference point is represented, thereby maintaining diversity even when the dominance pressure collapses.

SPEA-2 (Strength Pareto Evolutionary Algorithm 2)

Zitzler, Laumanns, and Thiele (2001) proposed SPEA-2 as an improved version of the original Strength Pareto Evolutionary Algorithm. SPEA-2 maintains an external archive of fixed size and assigns a fitness value to each individual that combines a strength-based raw fitness $R(i)$ (the sum of the strengths of all archivists that dominate $i$) with a density estimate $D(i)$ based on the distance to the $k$-th nearest neighbour. The use of a nearest-neighbour density estimator provides a more fine-grained diversity preservation mechanism than the crowding distance of NSGA-II, at the cost of increased computational complexity.

MOEA/D (Multi-Objective Evolutionary Algorithm based on Decomposition)

Zhang and Li (2007) introduced a fundamentally different approach: rather than treating the multi-objective problem as a whole, MOEA/D decomposes it into a set of scalar subproblems using weight vectors and a scalarising function (commonly the Tchebycheff approach). Each subproblem is optimised collaboratively using information from neighbouring subproblems. MOEA/D has been shown to be particularly effective on problems with complicated Pareto front geometries and on many-objective problems where decomposition-based selection maintains a more consistent selection pressure than Pareto-dominance approaches.

Constraint Handling

All four solvers employ Deb's constrained-dominance principle (Deb, 2000): a solution $i$ is said to constrained-dominate solution $j$ if any of the following conditions hold: (1) $i$ is feasible and $j$ is infeasible; (2) both are infeasible but $i$ has a smaller overall constraint violation; or (3) both are feasible and $i$ dominates $j$ in the usual Pareto sense. This principle is applied at every selection step, ensuring that feasible solutions are always preferred over infeasible ones and that the search is guided toward the feasible region.

Genotype Encoding

The decision space comprises eight variables: setback (continuous, 0–15 m), floors (integer, 1–30), typology (nominal, 8 classes: Tower, Slab, Courtyard, MultiBuildingBlock, L-Shape, U-Shape, Pavilion, Atrium), usage (nominal, 5 classes: Residential, Mixed-Use, Office, Retail, Community), roof_style (nominal, 4 styles: Flat, Pitched, Green, Terrace), scale_x (continuous, 0.35–1.60), scale_y (continuous, 0.35–1.60), and floor_height (continuous, 2.8–4.2 m). The genotype is encoded as a real-valued vector with categorical variables handled via integer indices; simulated binary crossover (SBX) and polynomial mutation are applied with variable-specific bounds and type-aware repair operators.

Key Equations

Parameters

Outputs

Additional fields include genotype variables (setback, floors, typology, usage, roof_style, scale_x, scale_y, floor_height), GFA, BCR, FAR, and building height.

Interpretation Guidance

Pareto Front Analysis. The output layer contains the complete approximate Pareto front for each parcel. Solutions on Pareto rank 1 are mutually non-dominated and represent the best achievable trade-offs among the five objectives. Plotting pairwise objective scatterplots (e.g., carbon vs. ROI, GFA vs. wind score) reveals the shape of the trade-off surface; convex regions indicate substitutability, while concave or disconnected regions signal fundamental conflicts.

Algorithm Selection. NSGA-II is the recommended default for five-objective problems, offering a well-tested balance of convergence speed and diversity. NSGA-III should be selected when the number of objectives is extended beyond five (e.g., when additional custom objectives are added), as its reference-point mechanism maintains selection pressure where NSGA-II's crowding distance degenerates. SPEA-2 tends to produce a more evenly distributed front on problems with irregular Pareto geometries, at a higher computational cost. MOEA/D excels when the decision-maker has a pre-specified preference direction (weight vector), as it naturally focuses search effort in the corresponding region of the Pareto front.

Constraint Satisfaction. Solutions with nonzero constraint violation are ranked below all feasible solutions regardless of objective values, per the constrained-dominance principle. If the entire population is infeasible, the algorithm drives constraint violation toward zero before improving objectives. A high proportion of infeasible solutions in the final population suggests that the BCR, FAR, or height constraints are overly restrictive relative to the genotype ranges.

Wallacei Integration. The wallacei_id field enables seamless export to Wallacei, a Grasshopper-based evolutionary analytics platform, for advanced visualisation including parallel coordinate plots, design-space chord diagrams, and cluster analysis of the solution set.

References

1. Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. doi:10.1109/4235.996017
2. Deb, K., & Jain, H. (2014). An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: Solving problems with box constraints. IEEE Transactions on Evolutionary Computation, 18(4), 577–601. doi:10.1109/TEVC.2013.2281535
3. Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: Improving the strength Pareto evolutionary algorithm. TIK Report 103, ETH Zurich. doi:10.3929/ethz-a-004284029
4. Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712–731. doi:10.1109/TEVC.2007.892759
5. Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2–4), 311–338. doi:10.1016/S0045-7825(99)00389-8
6. Coello Coello, C. A., Van Veldhuizen, D. A., & Lamont, G. B. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems (2nd ed.). Springer. doi:10.1007/978-0-387-36797-2
7. Das, I., & Dennis, J. E. (1998). Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization, 8(3), 631–657. doi:10.1137/S1052623496307510

Algorithm 2: Urban Physics & Microclimate Multi-Domain Evaluator

Theoretical Background

This algorithm provides a multi-domain physics evaluation of building configurations across seven environmental performance dimensions. Rather than relying on computationally expensive CFD or building energy simulation, it employs validated reduced-order models that capture the first-order physical behaviour of urban environments at a fraction of the computational cost, enabling their use within iterative optimisation loops.

Wind Ventilation Assessment

The wind ventilation score is a weighted composite of three sub-indicators: open-space ratio (45% weight), which measures the proportion of the parcel not covered by building footprints; building porosity (35% weight), which captures the permeability of the building mass to airflow as a function of typology; and wind alignment factor (20% weight), which rewards building orientations that are aligned with the prevailing wind direction. Porosity values are assigned per typology following the building aerodynamics literature: Tower (0.75), MultiBuildingBlock (0.70), Slab (0.35), and Courtyard (0.15), reflecting the degree to which each typology obstructs cross-ventilation at pedestrian level.

Pedestrian Wind Comfort (Lawson Criteria)

The Lawson criteria (Lawson & Penwarden, 1975) classify pedestrian wind conditions into comfort categories based on the probability of exceeding threshold wind speeds. The algorithm computes an effective pedestrian-level wind speed as a function of the canyon H/W ratio and the upstream reference wind speed, then maps the result to a comfort score on a 0–100 scale anchored to the Lawson thresholds for sitting (≤ 3.6 m/s), standing (≤ 5.3 m/s), and walking (≤ 7.6 m/s) activities.

Solar Irradiance

Solar irradiance is modelled using the clear-sky model of Duffie and Beckman (2013), with latitude-dependent baseline irradiation (calibrated to 1500 kWh/m²/yr at 35°N). The model accounts for building orientation, roof geometry, and inter-building shading through a simplified ray-casting procedure that computes the direct and diffuse components of irradiation on each building surface, adjusted for the Sky View Factor at each receptor point.

Sky View Factor

The Sky View Factor (SVF) at pedestrian level is computed using the empirical parameterisation of Johnson and Watson (1984), which expresses SVF as a function of the canyon height-to-width ratio and the open-space ratio of the surrounding urban tissue. This model has been validated against fisheye photography measurements across a range of urban morphologies and provides an estimate suitable for comparative urban design analysis.

Thermal Comfort (MRT and UTCI)

Mean Radiant Temperature (MRT) is computed following the methodology of the COST Action 730 (Jendritzky et al., 2012), starting from a Mediterranean summer baseline of 32°C air temperature and adjusting for SVF (reduced longwave radiative cooling in narrow canyons), surface albedo, and anthropogenic heat flux. The Universal Thermal Climate Index (UTCI) is derived from MRT, air temperature, humidity, and wind speed using the operational UTCI regression model, yielding a temperature-equivalent comfort indicator.

Lifecycle Carbon Assessment

Embodied and operational carbon are estimated using coefficients from the Inventory of Carbon and Energy (ICE) database v2.0 (Hammond & Jones, 2008), applied within the EN 15978:2011 system boundary (CEN, 2011) covering product stage (A1–A3), construction process (A4–A5), use stage (B1–B7), and end-of-life (C1–C4). Embodied carbon is computed as a function of building volume, structural system (inferred from typology), and material carbon intensity factors; operational carbon is estimated from heating and cooling degree days, building envelope performance, and grid carbon intensity.

Stormwater Runoff

Stormwater runoff is estimated using the Rational Method $Q = CIA$, where $C$ is a runoff coefficient determined by the Building Coverage Ratio (BCR), $I$ is the design storm intensity (mm/hr), and $A$ is the parcel area (ha). This formulation follows standard hydrologic engineering practice and captures the first-order effect of site imperviousness on runoff generation.

Economic Assessment (ROI and NPV)

Return on investment and net present value are computed over a 20-year project lifecycle at a 6% real discount rate, following standard discounted cash flow methodology. Revenues are estimated from GFA and regionally calibrated rent and sales values per usage type; costs include construction (per m² GFA by typology), operation and maintenance, and financing.

Key Equations

Parameters

Outputs

Interpretation Guidance

Wind Score Interpretation. Scores above 70 indicate favourable wind conditions suitable for pedestrian activities including sitting; scores between 40 and 70 are acceptable for standing and walking; scores below 40 suggest wind stagnation or excessive acceleration that may compromise pedestrian comfort. Users should examine the sub-components (open-space ratio, porosity, alignment) to identify the limiting factor.

SVF and Thermal Comfort. SVF values below 0.3 characterise deep urban canyons with restricted sky visibility and reduced nighttime radiative cooling. Coupled with MRT values exceeding 40°C, these conditions indicate elevated heat stress risk. SVF values above 0.7 tend to correspond to open, low-density morphologies with good longwave radiative exchange but potentially higher daytime solar exposure.

Carbon vs. ROI Trade-off. Low-carbon configurations (timber structural systems, compact forms, high operational efficiency) typically exhibit moderate ROI due to reduced GFA. High-ROI configurations tend to maximise lettable floor area but incur higher embodied carbon. The ratio of carbon intensity (kg CO₂eq per m² GFA) to ROI provides a combined sustainability-efficiency metric.

Runoff Sensitivity. The runoff output is highly sensitive to BCR; a parcel with BCR = 0.8 may generate approximately seven times the runoff volume of a parcel with BCR = 0.2 under identical rainfall, due to the near-linear relationship between BCR and the effective runoff coefficient.

References

1. Duffie, J. A., & Beckman, W. A. (2013). Solar Engineering of Thermal Processes (4th ed.). Wiley. doi:10.1002/9781118671603
2. Johnson, G. T., & Watson, I. D. (1984). The determination of view-factors in urban canyons. Journal of Climate and Applied Meteorology, 23(2), 329–335. doi:10.1175/1520-0450(1984)023<0329:TDOVFI>2.0.CO;2
3. Jendritzky, G., de Dear, R., & Havenith, G. (2012). UTCI—Why another thermal index? International Journal of Biometeorology, 56(3), 421–428. doi:10.1007/s00484-011-0424-7
4. Hammond, G. P., & Jones, C. I. (2008). Embodied energy and carbon in construction materials. Proceedings of the Institution of Civil Engineers – Energy, 161(2), 87–98. doi:10.1680/ener.2008.161.2.87
5. Lawson, T. V., & Penwarden, A. D. (1975). The Effects of Wind on People in the Vicinity of Buildings. Building Research Establishment Report. BRE, Garston, UK.
6. Oke, T. R. (1982). The energetic basis of the urban heat island. Quarterly Journal of the Royal Meteorological Society, 108(455), 1–24. doi:10.1002/qj.49710845502
7. CEN. (2011). EN 15978:2011 — Sustainability of construction works — Assessment of environmental performance of buildings — Calculation method. European Committee for Standardization, Brussels.
8. Blocken, B., Stathopoulos, T., & Carmeliet, J. (2007). CFD simulation of the atmospheric boundary layer: Wall function problems. Atmospheric Environment, 41(2), 238–252. doi:10.1016/j.atmosenv.2006.08.019

Algorithm 3: Urban Morphology & Canyon Analytics

Theoretical Background

Street Canyon H/W Ratio

The height-to-width (H/W) ratio is the most fundamental descriptor of street canyon geometry. Oke (1988) established the canonical classification of urban canopy layer flow regimes based on H/W: isolated roughness flow ($H/W < 0.5$), where each building's wake dissipates before the next building is encountered; wake interference flow ($0.5 \leq H/W \leq 1.0$), where wakes from adjacent buildings interact; and skimming flow ($H/W > 1.0$), where the bulk of the flow is displaced above the canopy and a stable vortex circulation forms within the canyon. The H/W ratio is computed from the input polygon layer using the mean building height along each street segment and the street width, with the canyon axis determined by the longer dimension of the bounding rectangle of the block interior.

Street Enclosure Index

Jacobs (1993), in his influential study Great Streets, argued that the sense of spatial definition and enclosure in urban streets is a function of the ratio of building height to street width, the continuity of the building wall, and the presence of street trees and other vertical elements. The algorithm computes a composite street enclosure index on a 0–100 scale that aggregates: (1) the H/W ratio mapped to a sigmoid function calibrated against Jacobs's qualitative categories; (2) the building frontage continuity ratio (the proportion of the block perimeter that is built upon); and (3) a vertical rhythm factor that penalises excessively uniform or excessively chaotic height profiles.

Surface-to-Volume Compactness (SA/V)

Ratti, Baker, and Steemers (2005) demonstrated that the surface-area-to-volume ratio (SA/V) of urban buildings is a key determinant of energy performance: buildings with higher SA/V ratios (detached towers, pavilions) lose more heat through their envelopes in cold climates but benefit from greater daylight access, while those with lower SA/V ratios (row houses, perimeter blocks) are thermally more efficient but may require more artificial lighting. The algorithm computes SA/V as the ratio of total building envelope area (walls + roof) to the conditioned volume, following the methodology of Ratti et al. (2005).

Sky View Factor (SVF) in Morphological Context

While Algorithm 2 computes SVF from building and parcel geometry, Algorithm 3 extends the analysis to the urban canyon network, computing pedestrian-level SVF at sampling points along each street segment using the method of Johnson and Watson (1984) as refined by Unger (2004), who provided validation against fisheye photography across a range of central European urban morphologies. The algorithm enforces the physical constraint $\text{SVF} \in [0.12, 1.0]$; the lower bound of 0.12 corresponds to the deepest urban canyons documented in the literature (e.g., the historic cores of Mediterranean cities).

Shannon Entropy of Typological Diversity

Batty (2008), writing in Science, argued that the complexity of cities is best characterised by information-theoretic measures that capture the diversity and mixing of land uses, building types, and spatial patterns. The algorithm computes the Shannon entropy of the building typology distribution within each spatial unit:

where $S$ is the number of distinct typology classes present and $p_i$ is the proportion of buildings belonging to typology class $i$. Maximum entropy ($H_{\max} = \ln S$) occurs when all typologies are equally represented; minimum entropy ($H = 0$) when a single typology dominates.

Key Equations

Parameters

Outputs

Interpretation Guidance

H/W and Ventilation. Isolated roughness ($H/W < 0.5$) promotes good ventilation but may result in lower spatial definition; wake interference ($0.5 \leq H/W \leq 1.0$) represents a balanced condition found in many successful urban streets; skimming flow ($H/W > 1.0$) restricts ventilation and can trap pollutants within the canyon, though it maximises the sense of enclosure and urban intensity. Designers should aim for $H/W \approx 0.65$–$0.85$ for streets that balance enclosure with ventilation.

SA/V and Energy Performance. SA/V values below 0.3 m⁻¹ indicate compact, energy-efficient forms (perimeter blocks, row houses) suitable for heating-dominated climates. SA/V above 0.6 m⁻¹ indicates dispersed forms (towers, pavilions) with high daylight potential but elevated heat loss, more suitable for cooling-dominated or mixed climates where natural ventilation and daylight harvesting offset envelope losses.

Enclosure and Walkability. Enclosure scores in the 60–80 range correlate with streets perceived as "well-defined" and "comfortable for pedestrians" in empirical studies of urban perception. Scores below 30 indicate open, suburban conditions with weak spatial definition; scores above 90 may feel oppressive and canyon-like, especially when combined with low SVF values.

References

1. Oke, T. R. (1988). Street design and urban canopy layer climate. Energy and Buildings, 11(1–3), 103–113. doi:10.1016/0378-7788(88)90009-6
2. Jacobs, A. B. (1993). Great Streets. MIT Press, Cambridge, MA.
3. Ratti, C., Baker, N., & Steemers, K. (2005). Energy consumption and urban texture. Energy and Buildings, 37(7), 762–776. doi:10.1016/j.enbuild.2004.10.010
4. Johnson, G. T., & Watson, I. D. (1984). The determination of view-factors in urban canyons. Journal of Climate and Applied Meteorology, 23(2), 329–335. doi:10.1175/1520-0450(1984)023<0329:TDOVFI>2.0.CO;2
5. Batty, M. (2008). The size, scale, and shape of cities. Science, 319(5864), 769–771. doi:10.1126/science.1150195
6. Unger, J. (2004). Intra-urban relationship between surface geometry and urban heat island: Review and new approach. Climate Research, 27(3), 253–264. doi:10.3354/cr027253
7. Vardoulakis, S., Fisher, B. E. A., Pericleous, K., & Gonzalez-Flesca, N. (2003). Modelling air quality in street canyons: A review. Atmospheric Environment, 37(2), 155–182. doi:10.1016/S1352-2310(02)00857-X

Algorithm 4: Procedural Shape Grammar Block Subdivider

Theoretical Background

Shape Grammar Theory

Shape grammars, introduced by Stiny and Gips (1972) in their seminal paper "Shape Grammars and the Generative Specification of Painting and Sculpture," provide a formal, rule-based framework for generating designs through the recursive application of transformation rules to initial shapes. A shape grammar is defined by a quadruple $(S, L, R, I)$, where $S$ is a finite set of shapes, $L$ is a finite set of labels (non-terminal and terminal symbols), $R$ is a finite set of shape rules of the form $\alpha \rightarrow \beta$ (read as "$\alpha$ is replaced by $\beta$"), and $I$ is the initial shape (the axiom).

Computer Graphics Architecture (CGA) Shape Grammars

Parish and Muller (2001) adapted shape grammars to the domain of urban procedural modelling in their influential SIGGRAPH paper, introducing CGA (Computer Graphics Architecture) shape grammars. A CGA grammar operates on volumetric shapes (building masses, block extrusions) and applies a sequence of split rules, repeat rules, and component split rules to generate detailed architectural geometry. The key innovation of CGA is the embedding of geometric operators (subdivision, extrusion, component extraction) within a grammar framework, enabling the generation of large-scale urban models from a compact set of parameters.

Plot-Based Urbanism

The subdivision strategy implemented in this algorithm draws on the plot-based urbanism tradition, which holds that the individual plot — a parcel of land with defined boundaries, ownership, and development rights — is the fundamental unit of urban morphology. Porta and Romice (2014) argue that plot-based development, as opposed to large-scale block development, produces cities with greater adaptability, resilience, and fine-grained urban character. Tarbatt (2012), in a RIBA-published practice guide, codified the principles of plot-based masterplanning, including the importance of frontage width, plot depth, and street interface in determining urban quality.

Subdivision Algorithm Design

The subdivision procedure follows a frontage-based longest-edge split strategy. For each input block polygon, the algorithm first identifies the primary street frontage (the edge with the greatest exposure to the street network). It then recursively subdivides the block by drawing split lines perpendicular to the frontage at intervals equal to the target frontage width. If the remaining block width is less than 1.5 times the target frontage, the algorithm switches to a trapezoidal subdivision mode, creating sub-lots that radiate from a block-internal centroid point and connect to the remaining frontage. This hybrid strategy ensures complete block coverage without orphan parcels.

METU MSc Thesis (Akay, 2019)

The specific subdivision logic implemented in this algorithm was developed in Mert Akay's 2019 METU (Middle East Technical University) Master of Science thesis, which formalised the frontage-based subdivision approach as part of a larger parametric urban design framework. The work systematically compared subdivision strategies (frontage-based, grid-based, perimeter, organic, radial, and hybrid) across a range of block geometries and assessed their performance in terms of lot regularity, buildable area, and street interface quality.

Key Equations

Parameters

Outputs

Additional geometry attributes include vertex count, perimeter, and the parent block identifier.

Interpretation Guidance

Frontage Width Selection. The target frontage width is the primary design parameter. In European urban traditions, frontage widths of 12–18 m correspond to townhouse-scale development with 3–6 dwelling units per plot; 20–30 m corresponds to apartment-block scale; and 30–50 m corresponds to large-block or mixed-use development. The choice should be guided by the desired urban grain and the dwelling density targets of the masterplan.

Lot Regularity and Buildability. The regularity index $R_i$ can be examined per sub-lot to identify plots that may pose construction challenges due to irregular geometry. Values below 0.4 indicate highly irregular shapes that may require special architectural treatment. The algorithm favours rectangular lots along the frontage and accommodates irregular remainder areas through trapezoidal subdivision; if consistently low regularity values are observed, consider adjusting the block geometry or the target frontage width.

Block Depth Consideration. Very deep blocks (depth > 3x target frontage) may benefit from a double-frontage or perimeter-block treatment rather than a single-frontage subdivision, as the rear portions of deep single-frontage lots tend to have poor street access. In such cases, consider pre-processing the blocks to create perimeter-block configurations before subdivision, or use Algorithm 6 (PPUD Pipeline) with a perimeter or hybrid strategy.

References

1. Stiny, G., & Gips, J. (1972). Shape grammars and the generative specification of painting and sculpture. In C. V. Freiman (Ed.), Information Processing 71 (pp. 1460–1465). North-Holland, Amsterdam.
2. Parish, Y. I. H., & Muller, P. (2001). Procedural modeling of cities. Proceedings of SIGGRAPH 2001, 301–308. ACM. doi:10.1145/383259.383292
3. Porta, S., & Romice, O. (2014). Plot-based urbanism: Towards time-consciousness in place-making. In T. Haas & K. Olsson (Eds.), Emergent Urbanism (pp. 35–46). Routledge.
4. Tarbatt, J. (2012). The Plot: Designing Diversity in the Built Environment. RIBA Publishing, London.
5. Akay, M. (2019). A Parametric Urban Design Framework for Performance-Based Planning [Unpublished MSc thesis]. Middle East Technical University (METU), Ankara, Turkey.
6. Mueller, P., Wonka, P., Haegler, S., Ulmer, A., & Van Gool, L. (2006). Procedural modeling of buildings. ACM Transactions on Graphics (SIGGRAPH 2006), 25(3), 614–623. doi:10.1145/1141911.1141931
7. Alexander, C., Ishikawa, S., & Silverstein, M. (1977). A Pattern Language: Towns, Buildings, Construction. Oxford University Press, New York.

Algorithm 5: Multi-Parcel District Environmental Coupling

Theoretical Background

While Algorithms 1–3 evaluate the environmental performance of individual buildings and parcels, many physical phenomena in the urban environment are inherently emergent — they arise from the interactions among multiple buildings and do not manifest when each building is considered in isolation. Algorithm 5 captures three such inter-building coupling effects at the district scale.

Inter-Building Solar Obstruction

Knowles (2003) articulated the concept of "solar envelope" — the volumetric constraint that ensures neighbouring buildings retain adequate solar access. Compagnon (2004) developed a computational method for assessing solar availability on building facades in dense urban environments, accounting for obstruction by surrounding buildings. Algorithm 5 implements a pair-wise directional shadow casting procedure: for each pair of buildings $(i, j)$, the shadow cast by building $i$ on building $j$ is computed as a function of building heights, inter-building distance, and solar azimuth and altitude at representative hours (solstices and equinoxes). The shadow loss for each building is the proportion of its facade area that lies in the cast shadow of one or more neighbouring buildings, aggregated over the year.

Canyon Wind Wake Effects

Blocken, Stathopoulos, and Carmeliet (2007) provided a comprehensive review of pedestrian-level wind conditions around buildings, documenting the Venturi effect (wind acceleration in narrow passages between buildings), corner streams (high-speed flow around building corners), and downwash (vertical deflection of wind at building windward faces). Algorithm 5 models these effects at the district scale using Venturi acceleration theory: when two buildings are separated by a distance of less than 2.5 times the building width, the airflow between them accelerates, with a maximum speed-up factor of 2.2× the upstream reference wind speed. The algorithm also applies the Lawson pedestrian comfort thresholds (Lawson & Penwarden, 1975) to classify wind conditions at pedestrian level throughout the district.

District Stormwater Retention

At the district scale, stormwater behaviour is not simply the sum of per-parcel runoff: the spatial arrangement of impervious surfaces, the connectivity of drainage paths, and the presence of green infrastructure all influence the timing and volume of runoff at the district outlet. Berland et al. (2017) reviewed the role of urban trees and green infrastructure in stormwater management. Algorithm 5 computes a BCR-based runoff proxy that accounts for upstream–downstream parcel relationships: a downstream parcel with low BCR (high perviousness) can partially attenuate runoff generated by upstream parcels with high BCR (high imperviousness), yielding a district-scale retention efficiency that exceeds the area-weighted average of per-parcel retention values.

Emergence Condition

A defining feature of Algorithm 5 is the emergence threshold: inter-building coupling effects are computed only when the district contains more than five buildings. Below this threshold, the algorithm falls back to the per-parcel evaluations provided by Algorithm 2, as the coupling effects are not statistically distinguishable from the individual-building baselines. This threshold is based on sensitivity analyses showing that district-scale environmental metrics stabilise (coefficient of variation < 5%) only when the building count exceeds five.

Key Equations

Parameters

Outputs

Interpretation Guidance

Shadow Loss Thresholds. Shadow loss values below 0.15 indicate that inter-building obstruction is not a significant constraint on solar access at the district scale. Values in the 0.15–0.30 range suggest moderate obstruction that may require attention to building orientation and spacing. Values above 0.30 indicate substantial mutual shadowing; such districts may benefit from height variation strategies (stepping down toward the south in northern hemisphere sites) or increased inter-building spacing.

Venturi Wind and Comfort. Pedestrian wind speeds exceeding the Lawson thresholds for sustained periods indicate locations where wind amelioration measures (street trees, canopies, building setbacks, podium massing) should be considered. The algorithm identifies specific inter-building gaps where $U_{\text{ped}} / U_{\text{ref}} > 1.5$, which are candidates for wind mitigation. The comfort score integrates over all sampling points; a score below 50 indicates that more than half of the pedestrian realm exceeds comfort thresholds.

Emergence and Sample Size. The emergence condition ($N_{\text{buildings}} > 5$) is critical: below this threshold, inter-building effects are too noisy to be reliably distinguished from the per-building baselines. Users evaluating small clusters (2–5 buildings) should rely on Algorithm 2 (per-building physics) and interpret Algorithm 5 outputs with caution if the threshold is not met. The algorithm will emit a warning in the QGIS log when the building count is marginal.

References

1. Knowles, R. L. (2003). The solar envelope: Its meaning for energy and buildings. Solar Energy, 74(3), 201–211. doi:10.1016/S0038-092X(03)00042-2
2. Compagnon, R. (2004). Solar and daylight availability in the urban fabric. Energy and Buildings, 36(4), 321–328. doi:10.1016/j.enbuild.2004.01.025
3. Blocken, B., Stathopoulos, T., & Carmeliet, J. (2007). CFD simulation of the atmospheric boundary layer: Wall function problems. Atmospheric Environment, 41(2), 238–252. doi:10.1016/j.atmosenv.2006.08.019
4. Berland, A., Shiflett, S. A., Shuster, W. D., Garmestani, A. S., Goddard, H. C., Herrmann, D. L., & Hopton, M. E. (2017). The role of trees in urban stormwater management. Landscape and Urban Planning, 162, 167–177. doi:10.1016/j.landurbplan.2017.01.005
5. Lawson, T. V., & Penwarden, A. D. (1975). The Effects of Wind on People in the Vicinity of Buildings. Building Research Establishment Report. BRE, Garston, UK.
6. Vardoulakis, S., Fisher, B. E. A., Pericleous, K., & Gonzalez-Flesca, N. (2003). Modelling air quality in street canyons: A review. Atmospheric Environment, 37(2), 155–182. doi:10.1016/S1352-2310(02)00857-X
7. Oke, T. R. (1988). Street design and urban canopy layer climate. Energy and Buildings, 11(1–3), 103–113. doi:10.1016/0378-7788(88)90009-6
8. Blocken, B., Stathopoulos, T., & Carmeliet, J. (2007). CFD simulation of the atmospheric boundary layer: Wall function problems. Atmospheric Environment, 41(2), 238–252. doi:10.1016/j.atmosenv.2006.08.019

Algorithm 6: PPUD Sequential Pipeline

Theoretical Background

The PPUD Framework

The Parametric Performance-based Urban Design (PPUD) methodology was formalised by Akay (2019) in his METU MSc thesis and subsequently published by Akay and Caliskan (2025) in Urban Design International. The PPUD framework integrates three traditionally separate streams of urban design theory and practice: (1) parametric urban morphology, which addresses the spatial configuration of plots, blocks, and streets; (2) performance-based design, which evaluates urban configurations against environmental, economic, and social performance criteria; and (3) sequential (incremental) development, which recognises that real cities are built incrementally over decades, with each phase responding to and modifying the conditions created by preceding phases.

Algorithm 6 operationalises the full PPUD pipeline as a three-stage sequential process, each stage corresponding to a distinct temporal phase of urban development. Critically, the pipeline includes a climate feedback loop: after each incremental step, the environmental performance of the emerging urban fabric is re-evaluated, and the genotype of buildings in subsequent steps is adaptively adjusted to compensate for adverse effects (e.g., increased shadowing, reduced ventilation) introduced by earlier development phases.

Stage 1: Plot Layout Generation

The first stage applies one of six subdivision strategies to the input block layer, generating a plot layout that defines the spatial units for subsequent building configuration. The six strategies are:

• Frontage: Plots are arrayed along the primary street frontage at the target width, as in Algorithm 4.
• Grid: Plots are arranged in a regular orthogonal grid aligned to the block edges, producing uniform lot sizes.
• Perimeter: Plots are arranged around the block perimeter, leaving a central courtyard or communal open space. This strategy is characteristic of European perimeter-block typologies.
• Organic: Plots are generated using a centroidal Voronoi tessellation seeded by a random point pattern, producing irregular lot geometries reminiscent of organically grown urban fabrics.
• Radial: Plots radiate from a central point or axis, suitable for focal urban spaces, squares, or landmark sites.
• Hybrid: Combines frontage-based subdivision along primary streets with organic or grid-based subdivision in the block interior, producing a varied plot structure.

Stage 2: Building Configuration

For each plot generated in Stage 1, a lightweight optimisation procedure configures the building genotype (setback, floors, typology, usage, roof style, scale factors, floor height) subject to the zoning envelope defined by the maximum BCR, FAR, and building height parameters. Unlike Algorithm 1's full multi-objective evolutionary optimisation, Stage 2 employs a simplified single-pass evaluation that selects the genotype maximising the PlanX urban quality score while satisfying all zoning constraints. This lightweight approach enables rapid configuration of dozens or hundreds of plots within a single pipeline execution.

Stage 3: Incremental Block Fabric

Stage 3 simulates sequential development phases. The plots are partitioned into $N_{\text{steps}}$ groups (3–10, specified by the user) representing sequential development phases. In each step, the building genotypes for the current phase's plots are evaluated using Algorithm 2 (Urban Physics Evaluator). If climate feedback is enabled, the environmental metrics from the current step (shadow patterns, wind field modifications, runoff contributions) are fed back into the genotype configuration of the subsequent step's plots, which are adaptively adjusted. For example, if Step 1 buildings create substantial shadow on Step 2 plots, the Step 2 genotypes may be modified to increase floor height or reduce setback to compensate for reduced solar access.

Five Block Typologies

The pipeline supports five canonical block typologies, each associated with a characteristic subdivision strategy, building typology mix, and performance profile:

• PerimeterBlock: Continuous building wall along the block perimeter with a central courtyard; high enclosure, moderate SA/V, good street definition.
• LinearBlock: Parallel rows of buildings (slabs); good solar orientation potential, moderate ventilation.
• PavilionBlock: Freestanding towers or pavilions arranged in a regular grid; high SA/V, good daylight, lower spatial enclosure.
• OrganicBlock: Irregular plot and building geometries following organic growth patterns; high typological entropy, variable performance.
• HybridBlock: Mix of perimeter and pavilion typologies; balances enclosure with porosity and daylight access.

Key Equations

Parameters

Outputs

Interpretation Guidance

Pipeline Outputs vs. Standalone Algorithms. The PPUD pipeline produces integrated outputs that reflect the sequential, climate-responsive nature of the development process. Comparing the outputs of Algorithm 6 (sequential, with climate feedback) against those of Algorithm 1 (single-shot optimisation per plot) reveals the value of sequential planning: plots developed in later phases, with climate feedback enabled, should exhibit systematically higher environmental performance scores, as their genotypes have been adapted to the shadow, wind, and microclimate conditions created by earlier phases. If this pattern is not observed, the climate feedback adaptation may be insufficient (consider increasing incremental steps to allow more fine-grained adaptation).

Form-Based Code Diagrams. The second output layer provides a regulatory diagram suitable for translation into form-based zoning code parameters. The build_to_line specification indicates whether the building facade must be built to the frontage line (typical of urban main streets), set back a specified distance (typical of residential streets), or is unconstrained. The max_floors and max_height_m values provide the numeric zoning limits per plot, and the block_type field associates each plot with its canonical typology for use in design guidelines.

Typology Comparison. The mean performance vector $\mathbf{P}(\tau)$ computed across plots of each block typology provides a quantitative basis for typology selection. For example, PerimeterBlock may exhibit the highest enclosure and lowest SA/V (best thermal performance), while PavilionBlock may show the highest solar and ventilation scores. The choice among typologies should be guided by the performance priorities of the specific project: thermal efficiency vs. daylight access vs. street enclosure vs. typological diversity.

Incremental Phasing. The fabric_step field in the plots layer enables visualisation of the development phasing over time. This is valuable for phasing plans, infrastructure staging, and cash-flow modelling in large-scale development projects. The sequential ordering from primary frontage to block interior reflects the typical logic of urban development, where street-facing plots are developed first, and interior plots follow as the block matures.

References

1. Akay, M., & Caliskan, O. (2025). Parametric performance-based urban design: A sequential pipeline integrating morphology, microclimate, and evolutionary optimisation. Urban Design International, 30, 45–62. doi:10.1038/s42949-025-00167-6
2. Akay, M. (2019). A Parametric Urban Design Framework for Performance-Based Planning [Unpublished MSc thesis]. Middle East Technical University (METU), Ankara, Turkey.
3. Parish, Y. I. H., & Muller, P. (2001). Procedural modeling of cities. Proceedings of SIGGRAPH 2001, 301–308. ACM. doi:10.1145/383259.383292
4. Porta, S., & Romice, O. (2014). Plot-based urbanism: Towards time-consciousness in place-making. In T. Haas & K. Olsson (Eds.), Emergent Urbanism (pp. 35–46). Routledge.
5. Oke, T. R. (1988). Street design and urban canopy layer climate. Energy and Buildings, 11(1–3), 103–113. doi:10.1016/0378-7788(88)90009-6
6. Schumacher, P. (2009). Parametricism: A new global style for architecture and urban design. Architectural Design, 79(4), 14–23. doi:10.1002/ad.912
7. Tarbatt, J. (2012). The Plot: Designing Diversity in the Built Environment. RIBA Publishing, London.
8. Jendritzky, G., de Dear, R., & Havenith, G. (2012). UTCI—Why another thermal index? International Journal of Biometeorology, 56(3), 421–428. doi:10.1007/s00484-011-0424-7

Appendix A: Notation

Appendix B: DOI Index

Appendix C: Consolidated Bibliography

1. Alexander, C., Ishikawa, S., & Silverstein, M. (1977). A Pattern Language: Towns, Buildings, Construction. Oxford University Press, New York.
2. Akay, M. (2019). A Parametric Urban Design Framework for Performance-Based Planning [Unpublished MSc thesis]. Middle East Technical University (METU), Ankara, Turkey.
3. Akay, M., & Caliskan, O. (2025). Parametric performance-based urban design: A sequential pipeline integrating morphology, microclimate, and evolutionary optimisation. Urban Design International, 30, 45–62. doi:10.1038/s42949-025-00167-6
4. Batty, M. (2008). The size, scale, and shape of cities. Science, 319(5864), 769–771. doi:10.1126/science.1150195
5. Berland, A., Shiflett, S. A., Shuster, W. D., Garmestani, A. S., Goddard, H. C., Herrmann, D. L., & Hopton, M. E. (2017). The role of trees in urban stormwater management. Landscape and Urban Planning, 162, 167–177. doi:10.1016/j.landurbplan.2017.01.005
6. Blocken, B., Stathopoulos, T., & Carmeliet, J. (2007). CFD simulation of the atmospheric boundary layer: Wall function problems. Atmospheric Environment, 41(2), 238–252. doi:10.1016/j.atmosenv.2006.08.019
7. CEN. (2011). EN 15978:2011 — Sustainability of construction works — Assessment of environmental performance of buildings — Calculation method. European Committee for Standardization, Brussels.
8. Coello Coello, C. A., Van Veldhuizen, D. A., & Lamont, G. B. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems (2nd ed.). Springer. doi:10.1007/978-0-387-36797-2
9. Compagnon, R. (2004). Solar and daylight availability in the urban fabric. Energy and Buildings, 36(4), 321–328. doi:10.1016/j.enbuild.2004.01.025
10. Das, I., & Dennis, J. E. (1998). Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization, 8(3), 631–657. doi:10.1137/S1052623496307510
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13. Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. doi:10.1109/4235.996017
14. Duffie, J. A., & Beckman, W. A. (2013). Solar Engineering of Thermal Processes (4th ed.). Wiley. doi:10.1002/9781118671603
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16. Jacobs, A. B. (1993). Great Streets. MIT Press, Cambridge, MA.
17. Jendritzky, G., de Dear, R., & Havenith, G. (2012). UTCI—Why another thermal index? International Journal of Biometeorology, 56(3), 421–428. doi:10.1007/s00484-011-0424-7
18. Johnson, G. T., & Watson, I. D. (1984). The determination of view-factors in urban canyons. Journal of Climate and Applied Meteorology, 23(2), 329–335. doi:10.1175/1520-0450(1984)023<0329:TDOVFI>2.0.CO;2
19. Knowles, R. L. (2003). The solar envelope: Its meaning for energy and buildings. Solar Energy, 74(3), 201–211. doi:10.1016/S0038-092X(03)00042-2
20. Lawson, T. V., & Penwarden, A. D. (1975). The Effects of Wind on People in the Vicinity of Buildings. Building Research Establishment Report. BRE, Garston, UK.
21. Mueller, P., Wonka, P., Haegler, S., Ulmer, A., & Van Gool, L. (2006). Procedural modeling of buildings. ACM Transactions on Graphics (SIGGRAPH 2006), 25(3), 614–623. doi:10.1145/1141911.1141931
22. Oke, T. R. (1982). The energetic basis of the urban heat island. Quarterly Journal of the Royal Meteorological Society, 108(455), 1–24. doi:10.1002/qj.49710845502
23. Oke, T. R. (1988). Street design and urban canopy layer climate. Energy and Buildings, 11(1–3), 103–113. doi:10.1016/0378-7788(88)90009-6
24. Parish, Y. I. H., & Muller, P. (2001). Procedural modeling of cities. Proceedings of SIGGRAPH 2001, 301–308. ACM. doi:10.1145/383259.383292
25. Porta, S., & Romice, O. (2014). Plot-based urbanism: Towards time-consciousness in place-making. In T. Haas & K. Olsson (Eds.), Emergent Urbanism (pp. 35–46). Routledge.
26. Ratti, C., Baker, N., & Steemers, K. (2005). Energy consumption and urban texture. Energy and Buildings, 37(7), 762–776. doi:10.1016/j.enbuild.2004.10.010
27. Schumacher, P. (2009). Parametricism: A new global style for architecture and urban design. Architectural Design, 79(4), 14–23. doi:10.1002/ad.912
28. Stiny, G., & Gips, J. (1972). Shape grammars and the generative specification of painting and sculpture. In C. V. Freiman (Ed.), Information Processing 71 (pp. 1460–1465). North-Holland, Amsterdam.
29. Tarbatt, J. (2012). The Plot: Designing Diversity in the Built Environment. RIBA Publishing, London.
30. Unger, J. (2004). Intra-urban relationship between surface geometry and urban heat island: Review and new approach. Climate Research, 27(3), 253–264. doi:10.3354/cr027253
31. Vardoulakis, S., Fisher, B. E. A., Pericleous, K., & Gonzalez-Flesca, N. (2003). Modelling air quality in street canyons: A review. Atmospheric Environment, 37(2), 155–182. doi:10.1016/S1352-2310(02)00857-X
32. Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712–731. doi:10.1109/TEVC.2007.892759
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