/cd-calculator

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

# 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 m