cd-calculator · v1.0.0 · 2026-03-26 · sha256 7361e868b7b75ba2
cd-calculator v1.0.0B
Immutable. This exact content never changes and is served at /api/v1/blob/7361e868b7b75ba2.
---
title: Computational Design Calculator
description: Python calculators for geometry analysis, structural checking, solar calculations, panel optimization, mesh analysis, material estimation, and fabrication cost estimation for AEC computational design
version: 1.0.0
tags: [calculator, computation, geometry, structural, solar, panels, mesh, materials, fabrication, Python]
auto_activate: true
user_invocable: true
invocation: /cd-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
```bash
# 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
```bash
# 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
```bash
# 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
```bash
# 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
```bash
# 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
```bash
# 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
```bash
# 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:
```python
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:
```bash
# 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 |