Computational Design Calculator

Computational Design Calculator

Calculator Overview

This skill provides 7 production-grade Python calculators purpose-built for computational design workflows in Architecture, Engineering, and Construction (AEC). Each calculator is a standalone command-line tool that accepts domain-specific parameters and returns precise, well-formatted results.

All calculators share common design principles:

• Human-readable output by default with clear section headers, formatted tables, and summary statistics.
• --json flag on every calculator for structured machine-readable output, enabling pipeline integration with parametric design tools, Grasshopper scripts, Dynamo graphs, or custom automation.
• Strict input validation with meaningful error messages that guide the user toward correct usage.
• SI units throughout (millimeters for geometry, kilonewtons for forces, degrees for angles) with Imperial equivalents noted where relevant.
• Deterministic calculations based on published engineering formulas (Eurocode, ASCE, ASHRAE) so results can be cross-checked and audited.

Calculator Index

| # | Calculator | Script | Primary Domain |

|---|-----------|--------|---------------|

| 1 | Geometry Calculator | geometry_calculator.py | Cross-section properties |

| 2 | Structural Checker | structural_checker.py | Member sizing & verification |

| 3 | Solar Calculator | solar_calculator.py | Solar position & radiation |

| 4 | Panel Optimizer | panel_optimizer.py | Facade rationalization |

| 5 | Mesh Analyzer | mesh_analyzer.py | Mesh quality & topology |

| 6 | Material Estimator | material_estimator.py | Quantity takeoff & carbon |

| 7 | Fabrication Calculator | fabrication_calculator.py | CNC / 3D print / laser costing |

Directory Structure

cd-calculator/
  SKILL.md                          # This file
  references/
    formulas.md                     # Complete formula reference
  scripts/
    geometry_calculator.py          # Cross-section geometry
    structural_checker.py           # Beam/column/deflection checks
    solar_calculator.py             # Solar position & radiation
    panel_optimizer.py              # Panel clustering & waste
    mesh_analyzer.py                # OBJ mesh quality analysis
    material_estimator.py           # Material quantity takeoff
    fabrication_calculator.py       # Fabrication time & cost

1. Geometry Calculator

Script: scripts/geometry_calculator.py

Computes cross-section properties for common AEC shapes used in structural analysis, fabrication planning, and parametric design. All inputs are in millimeters; all outputs are in mm-based units (mm^2, mm^4, etc.).

Supported Shapes

| Shape | Description | Key Parameters |

|-------|------------|----------------|

| rectangle | Solid rectangular section | width, height |

| circle | Solid circular section | radius |

| triangle | Solid triangular section | base, height |

| i-beam | Standard I/H section | width, height, flange thickness, web thickness |

| hollow-rect | Rectangular hollow section (RHS) | width, height, wall thickness |

| hollow-circle | Circular hollow section (CHS) | outer radius, inner radius |

| l-shape | L-angle section | width, height, thickness |

| t-shape | T-section | width, height, flange thickness, web thickness |

| polygon | Arbitrary polygon | vertex coordinates |

Parameters

| Parameter | Type | Unit | Description |

|-----------|------|------|-------------|

| --shape | string | -- | Shape type (required) |

| --width | float | mm | Overall width |

| --height | float | mm | Overall height |

| --radius | float | mm | Radius for circular sections |

| --outer-radius | float | mm | Outer radius for hollow circle |

| --inner-radius | float | mm | Inner radius for hollow circle |

| --base | float | mm | Base width for triangle |

| --flange-thickness | float | mm | Flange thickness for I-beam / T-shape |

| --web-thickness | float | mm | Web thickness for I-beam / T-shape |

| --wall-thickness | float | mm | Wall thickness for hollow sections |

| --thickness | float | mm | Leg thickness for L-shape |

| --vertices | string | mm | Comma-separated x,y pairs for polygon |

| --json | flag | -- | Output as JSON |

Example Usage

# Solid rectangle 300 x 500 mm
python geometry_calculator.py --shape rectangle --width 300 --height 500

# Circular section with 150 mm radius
python geometry_calculator.py --shape circle --radius 150

# Standard I-beam
python geometry_calculator.py --shape i-beam --width 200 --height 400 --flange-thickness 15 --web-thickness 10

# Hollow rectangular section
python geometry_calculator.py --shape hollow-rect --width 300 --height 300 --wall-thickness 12

# JSON output for pipeline integration
python geometry_calculator.py --shape rectangle --width 300 --height 500 --json

Sample Output

========================================
  GEOMETRY CALCULATOR - Rectangle
========================================

  Dimensions:
    Width  (b) :   300.00 mm
    Height (h) :   500.00 mm

  Section Properties:
    Area             :   150,000.00 mm²
    Perimeter        :     1,600.00 mm
    Centroid (x, y)  :   (150.00, 250.00) mm

  Second Moment of Area:
    Ix (about x-axis):   3,125,000,000.00 mm⁴
    Iy (about y-axis):   1,125,000,000.00 mm⁴

  Section Modulus:
    Sx               :    12,500,000.00 mm³
    Sy               :     7,500,000.00 mm³

  Radius of Gyration:
    rx               :       144.34 mm
    ry               :        86.60 mm
========================================

2. Structural Checker

Script: scripts/structural_checker.py

Performs quick structural sizing and verification checks for steel members based on simplified Eurocode 3 and ASCE 7 formulas. Designed for early-stage feasibility assessments, not detailed design.

Check Types

| Check | Description | Key Inputs |

|-------|------------|------------|

| beam | Bending capacity and section sizing | span, UDL, steel grade |

| column | Axial capacity and buckling check | axial load, height, steel grade |

| deflection | Serviceability deflection check | span, UDL, section properties |

Parameters

| Parameter | Type | Unit | Description |

|-----------|------|------|-------------|

| --check | string | -- | Check type: beam, column, deflection |

| --span | float | mm | Beam span or effective length |

| --load | float | kN/m or kN | UDL for beams, axial for columns |

| --steel-grade | string | -- | S235, S275, S355 |

| --height | float | mm | Column height |

| --buckling-length-factor | float | -- | Effective length factor (default 1.0) |

| --moment-of-inertia | float | mm^4 | Section Ix for deflection check |

| --section | string | -- | Named section (e.g., IPE300) |

| --deflection-limit | string | -- | L/250, L/360, or custom (default L/250) |

| --json | flag | -- | Output as JSON |

Example Usage

# Size a beam: 6m span, 15 kN/m UDL, S355 steel
python structural_checker.py --check beam --span 6000 --load 15 --steel-grade S355

# Check a column: 2000 kN axial, 4m height, S355
python structural_checker.py --check column --load 2000 --height 4000 --steel-grade S355

# Deflection check with named section
python structural_checker.py --check deflection --span 8000 --load 10 --section IPE300

Sample Output

========================================
  STRUCTURAL CHECKER - Beam Sizing
========================================

  Input:
    Span             :  6,000 mm (6.00 m)
    UDL              :  15.00 kN/m
    Steel Grade      :  S355 (fy = 355 MPa)

  Bending Analysis:
    Max Moment (M)   :  67.50 kN·m
    Required Sx      :  190,141 mm³
    Suggested Section:  IPE 270 (Sx = 429,000 mm³)

  Shear Analysis:
    Max Shear (V)    :  45.00 kN
    Shear Utilization:  0.12  [OK]

  Deflection:
    Max Deflection   :  10.82 mm
    Limit (L/250)    :  24.00 mm
    Utilization      :  0.45  [OK]

  Overall Status:    PASS
========================================

3. Solar Calculator

Script: scripts/solar_calculator.py

Computes solar geometry, shadow projections, and photovoltaic parameters for any location on Earth at any date and time. Essential for daylighting analysis, shadow studies, and PV system sizing in early-stage design.

Parameters

| Parameter | Type | Unit | Description |

|-----------|------|------|-------------|

| --latitude | float | deg | Site latitude (-90 to 90) |

| --longitude | float | deg | Site longitude (-180 to 180) |

| --date | string | -- | Date in YYYY-MM-DD format |

| --time | string | -- | Solar time in HH:MM format |

| --annual-summary | flag | -- | Monthly solar data summary |

| --shadow-analysis | flag | -- | Shadow length computation |

| --object-height | float | m | Object height for shadow analysis |

| --pv-tilt | flag | -- | Optimal PV tilt calculation |

| --json | flag | -- | Output as JSON |

Example Usage

# Solar position for London at noon on summer solstice
python solar_calculator.py --latitude 51.5 --longitude -0.12 --date 2025-06-21 --time 12:00

# Annual summary for Dubai
python solar_calculator.py --latitude 25.2 --longitude 55.3 --annual-summary

# Shadow analysis for a 30m building in New York
python solar_calculator.py --latitude 40.7 --longitude -74.0 --shadow-analysis --object-height 30

# Optimal PV tilt for Berlin
python solar_calculator.py --latitude 52.5 --longitude 13.4 --pv-tilt

Sample Output

========================================
  SOLAR CALCULATOR - Position
========================================

  Location:
    Latitude         :   51.500° N
    Longitude        :   -0.120° W
    Date             :   2025-06-21

  Solar Position at 12:00:
    Altitude         :   62.07°
    Azimuth          :  180.00° (South)

  Day Information:
    Sunrise          :   03:43 solar time
    Sunset           :   20:21 solar time
    Day Length       :   16h 38m

  Shadow (per 1m object):
    Shadow Length    :    0.53 m
    Shadow Direction :    0.00° (North)
========================================

4. Panel Optimizer

Script: scripts/panel_optimizer.py

Rationalizes facade panel inventories by clustering similar panel dimensions within a configurable tolerance, then estimates material waste and cost impacts. Critical for design-for-manufacture workflows in curtain wall and cladding systems.

Parameters

| Parameter | Type | Unit | Description |

|-----------|------|------|-------------|

| --panels | string | mm | Comma-separated WxH panel dimensions |

| --tolerance | float | mm | Grouping tolerance (default 10) |

| --sheet-width | float | mm | Raw sheet/stock width |

| --sheet-height | float | mm | Raw sheet/stock height |

| --cost-per-unique | float | $ | Cost premium per unique type (default 500) |

| --json | flag | -- | Output as JSON |

Example Usage

# Basic panel clustering
python panel_optimizer.py --panels "1200x800,1200x810,1205x800,1200x800,1190x795,1200x800,2400x800,2400x810"

# With sheet size for waste estimation
python panel_optimizer.py --panels "1200x800,1200x810,1205x800" --tolerance 15 --sheet-width 3000 --sheet-height 2000

# Cost-focused analysis
python panel_optimizer.py --panels "1200x800,1200x810,1205x800,1500x900,1510x895" --cost-per-unique 750

Sample Output

========================================
  PANEL OPTIMIZER - Clustering
========================================

  Input Summary:
    Total Panels     :   8
    Raw Unique Sizes :   5
    Tolerance        :  10 mm

  Panel Families:
    Family 1 (1200 x 800 mm):
      Members: 1200x800, 1200x810, 1205x800, 1190x795, 1200x800, 1200x800
      Count: 6
    Family 2 (2400 x 800 mm):
      Members: 2400x800, 2400x810
      Count: 2

  Rationalization:
    Unique types (before) :   5
    Unique types (after)  :   2
    Reduction             :  60.0%

  Cost Impact:
    Uniqueness premium    :  $1,000.00
    Savings vs. raw       :  $1,500.00
========================================

5. Mesh Analyzer

Script: scripts/mesh_analyzer.py

Evaluates mesh quality and topological properties for architectural meshes. Reads standard OBJ files or accepts inline vertex/face data. Essential for assessing mesh suitability for FEA, fabrication unfolding, and rendering.

Parameters

| Parameter | Type | Unit | Description |

|-----------|------|------|-------------|

| --file | string | -- | Path to OBJ file |

| --vertices | string | -- | Inline vertices: "x,y,z;x,y,z;..." |

| --faces | string | -- | Inline faces: "i,j,k;i,j,k;..." |

| --json | flag | -- | Output as JSON |

Example Usage

# Analyze an OBJ file
python mesh_analyzer.py --file model.obj

# Analyze inline mesh data (a simple quad split into two triangles)
python mesh_analyzer.py --vertices "0,0,0;1,0,0;1,1,0;0,1,0" --faces "0,1,2;0,2,3"

# JSON output
python mesh_analyzer.py --file facade_mesh.obj --json

Sample Output

========================================
  MESH ANALYZER
========================================

  Topology:
    Vertices         :       4
    Faces            :       2
    Edges            :       5
    Euler Char. (V-E+F):    1
    Genus            :       0
    Is Manifold      :     Yes
    Boundary Edges   :       4

  Face Area Statistics:
    Min Area         :   0.500 units²
    Max Area         :   0.500 units²
    Mean Area        :   0.500 units²
    Std Dev          :   0.000 units²
    Total Area       :   1.000 units²

  Aspect Ratio Statistics:
    Min              :   1.000
    Max              :   1.414
    Mean             :   1.207
    Faces > 3.0      :       0  (0.0%)

  Normal Consistency  :   PASS (all normals consistent)

  Bounding Box:
    X range          :   0.000 to 1.000 (1.000)
    Y range          :   0.000 to 1.000 (1.000)
    Z range          :   0.000 to 0.000 (0.000)
========================================

6. Material Estimator

Script: scripts/material_estimator.py

Estimates material quantities, weights, and embodied carbon for buildings at the early design stage. Operates in two modes: parametric (from building type and GFA) or direct (from explicit material quantities).

Parameters

| Parameter | Type | Unit | Description |

|-----------|------|------|-------------|

| --building-type | string | -- | residential, office, industrial, retail |

| --gfa | float | m^2 | Gross floor area |

| --floors | int | -- | Number of floors |

| --concrete-volume | float | m^3 | Direct concrete volume |

| --steel-ratio | float | kg/m^3 | Reinforcement ratio |

| --glass-area | float | m^2 | Direct glass area |

| --timber-volume | float | m^3 | Direct timber volume |

| --waste-factor | float | -- | Override waste factor (e.g. 1.10) |

| --include-embodied-carbon | flag | -- | Calculate embodied carbon |

| --json | flag | -- | Output as JSON |

Example Usage

# Parametric estimate for a residential building
python material_estimator.py --building-type residential --gfa 5000 --floors 8

# Direct material quantities with embodied carbon
python material_estimator.py --concrete-volume 450 --steel-ratio 120 --glass-area 2000 --include-embodied-carbon

# Office building with custom waste factor
python material_estimator.py --building-type office --gfa 12000 --floors 20 --waste-factor 1.12 --include-embodied-carbon

Sample Output

========================================
  MATERIAL ESTIMATOR - Parametric
========================================

  Building Parameters:
    Type             :  Residential
    Gross Floor Area :  5,000.00 m²
    Floors           :       8
    Floor Area/Floor :    625.00 m²

  Material Quantities (incl. waste):
    Concrete         :    750.00 m³  (1,800.00 tonnes)
    Rebar Steel      :     67.50 tonnes
    Structural Steel :     50.00 tonnes
    Glass            :    500.00 m²  (6.25 tonnes)
    Timber           :     75.00 m³  (33.75 tonnes)

  Total Weight       :  1,957.50 tonnes

  Embodied Carbon:
    Concrete         :  187,500 kgCO2e
    Rebar Steel      :  101,250 kgCO2e
    Structural Steel :   75,000 kgCO2e
    Glass            :    6,875 kgCO2e
    Timber           :  -10,125 kgCO2e (carbon stored)
    ─────────────────────────────────
    Total            :  360,500 kgCO2e
    Per m² GFA       :    72.10 kgCO2e/m²
========================================

7. Fabrication Calculator

Script: scripts/fabrication_calculator.py

Estimates fabrication time and cost for three digital fabrication processes: CNC milling, FDM 3D printing, and laser cutting. Uses industry-standard feed rates, material costs, and process parameters.

Parameters

| Parameter | Type | Unit | Description |

|-----------|------|------|-------------|

| --process | string | -- | cnc-milling, 3d-print, laser-cut |

| --path-length | float | mm | CNC tool path length |

| --tool-changes | int | -- | Number of CNC tool changes |

| --material | string | -- | Material type (varies by process) |

| --feed-rate | float | mm/min | Override default feed rate |

| --volume | float | cm^3 | 3D print volume |

| --height | float | mm | 3D print height |

| --layer-height | float | mm | 3D print layer height |

| --infill | float | % | 3D print infill (default 20) |

| --cut-length | float | mm | Laser cut total path length |

| --thickness | float | mm | Material thickness for laser |

| --hourly-rate | float | $/hr | Machine/labor rate (default 75) |

| --json | flag | -- | Output as JSON |

Example Usage

# CNC milling job in wood
python fabrication_calculator.py --process cnc-milling --path-length 5000 --tool-changes 3 --material wood

# 3D print estimate
python fabrication_calculator.py --process 3d-print --volume 500 --height 200 --layer-height 0.2

# Laser cutting acrylic
python fabrication_calculator.py --process laser-cut --cut-length 8000 --material acrylic --thickness 6

# Custom hourly rate
python fabrication_calculator.py --process cnc-milling --path-length 12000 --tool-changes 5 --material aluminum --hourly-rate 120

Sample Output

========================================
  FABRICATION CALCULATOR - CNC Milling
========================================

  Process Parameters:
    Material         :  Wood (Hardwood)
    Path Length       :  5,000.00 mm
    Feed Rate        :  3,000 mm/min
    Tool Changes     :       3
    Change Time      :    2.00 min each

  Time Estimate:
    Cutting Time     :    1.67 min
    Tool Change Time :    6.00 min
    Setup Time       :   15.00 min
    Total Time       :   22.67 min (0.38 hr)

  Cost Estimate:
    Machine Time     :   $28.33
    Material (est.)  :   $15.00
    ─────────────────────────────
    Total            :   $43.33

========================================

Usage Notes

Integration with Parametric Tools

All calculators support --json output for integration with parametric design pipelines:

import subprocess, json

result = subprocess.run(
    ["python", "geometry_calculator.py", "--shape", "rectangle",
     "--width", "300", "--height", "500", "--json"],
    capture_output=True, text=True
)
data = json.loads(result.stdout)
area = data["area"]

Chaining Calculators

Calculators can be chained for multi-step workflows. For example, compute section properties, then verify structural adequacy:

# Step 1: Get section properties
python geometry_calculator.py --shape i-beam --width 200 --height 400 \
  --flange-thickness 15 --web-thickness 10 --json > section.json

# Step 2: Check deflection with computed Ix
python structural_checker.py --check deflection --span 8000 --load 10 \
  --moment-of-inertia 198540000

Error Handling

All calculators validate inputs and return meaningful error messages:

ERROR: --radius must be a positive number.
ERROR: --shape 'hexagon' is not supported. Choose from: rectangle, circle, triangle,
       i-beam, hollow-rect, hollow-circle, l-shape, t-shape, polygon.
ERROR: --inner-radius (160 mm) must be less than --outer-radius (150 mm).

Exit codes: 0 for success, 1 for input errors, 2 for computation errors.

Units Convention

| Quantity | Unit | Notes |

|----------|------|-------|

| Length / dimensions | mm | All geometry inputs |

| Area | mm^2 | Cross-section areas |

| Volume (geometry) | mm^3 | Section volumes per unit length |

| Moment of inertia | mm^4 | Second moment of area |

| Section modulus | mm^3 | Elastic section modulus |

| Force | kN | Structural loads |

| Stress | MPa (N/mm^2) | Steel yield, concrete fck |

| Moment | kN*m | Bending moments |

| Angle | degrees | Solar angles, bearings |

| Building area | m^2 | GFA, floor areas |

| Material volume | m^3 | Concrete, timber |

| Mass | tonnes (1000 kg) | Material weights |

| Carbon | kgCO2e | Embodied carbon |

| Fabrication length | mm | Tool paths, cut lengths |

| Cost | $ (currency units) | Fabrication costs |

| Time | minutes | Fabrication time |

Formula Reference

For the complete mathematical formulas behind every calculation, see references/formulas.md. This includes derivations, source standards, and unit conversion tables.

Version History

| Version | Date | Changes |

|---------|------|---------|

| 1.0.0 | 2026-03-23 | Initial release with 7 calculators |