# Polygon geometry workspace

- Human page: https://happytails.ai/en/calculators/polygon-geometry-workspace/
- Markdown: https://happytails.ai/en/calculators/polygon-geometry-workspace.md
- Structured JSON: https://happytails.ai/agents/en/calculators/polygon-geometry-workspace/index.json
- Visibility: public

## Tool capabilities

| Property | Value |
| --- | --- |
| Tool ID | `polygon-geometry-workspace` |
| Category | calculators |
| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |
| Browser execution | Use the visible action or interactive controls. |
| Browser processing | Browser; see tool notes for network behavior. |
| HTTP API | Not callable through HTTP. |
| Browser-agent interface | run_current_tool |

### Implementation notes

Enter ordered vertices in one coordinate system. The closing edge is added automatically. Up to 300 vertices; coordinates from -1,000,000,000 to 1,000,000,000. Calculations use floating-point arithmetic and scale-dependent tolerance. Self-crossing or overlapping edges are reported; their filled area and centroid are not assigned. Positive Y points up. Your input stays on your device.

### Inputs and settings

Text input: Ordered vertices.

Example or placeholder shown in the interface (not a validated fixture):

```text
0,0
4,0
4,3
0,3
```

Enter one X,Y pair per line, or paste a JSON array. Use a decimal point. The final edge closes automatically. Up to 200,000 characters. Review the settings before running.

No additional settings are declared for this tool.

### Browser-agent workflow

1. Open the human page in a browser that supports WebMCP.
2. Discover the interface exposed by that page; use its actual schema.
3. Select files on the page first when the tool requires files.
4. Call `run_current_tool` with valid input and settings.
5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.

Calls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.

### Planning specification

Enter 3 to 300 ordered vertices in one coordinate system. Each coordinate must be finite with magnitude no greater than 1,000,000,000. Use a decimal point, with one X,Y pair per line or a JSON array. The closing edge is added automatically; a repeated closing vertex is accepted. Adjacent duplicate vertices are rejected. Calculations are approximate and use scale-dependent tolerances. Area and centroid are not assigned to self-crossing or overlapping paths because their filled region depends on a fill rule. Zero-area paths have no centroid. Positive Y points up.

This describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.

### Complete machine-readable capability record

```json
{
  "id": "polygon-geometry-workspace",
  "category": "calculators",
  "built": true,
  "requirements": "Enter 3 to 300 ordered vertices in one coordinate system. Each coordinate must be finite with magnitude no greater than 1,000,000,000. Use a decimal point, with one X,Y pair per line or a JSON array. The closing edge is added automatically; a repeated closing vertex is accepted. Adjacent duplicate vertices are rejected. Calculations are approximate and use scale-dependent tolerances. Area and centroid are not assigned to self-crossing or overlapping paths because their filled region depends on a fill rule. Zero-area paths have no centroid. Positive Y points up.",
  "implementation": {
    "fields": [],
    "presentation": "metrics",
    "inputMaxLength": 200000,
    "placeholder": "0,0\n4,0\n4,3\n0,3",
    "note": "Enter ordered vertices in one coordinate system. The closing edge is added automatically. Up to 300 vertices; coordinates from -1,000,000,000 to 1,000,000,000. Calculations use floating-point arithmetic and scale-dependent tolerance. Self-crossing or overlapping edges are reported; their filled area and centroid are not assigned. Positive Y points up. Your input stays on your device.",
    "experience": {
      "automatic": false,
      "single": false,
      "inputMaxLength": 200000,
      "inputMode": "text",
      "label": "Ordered vertices",
      "placeholder": "0,0\n4,0\n4,3\n0,3",
      "help": "Enter one X,Y pair per line, or paste a JSON array. Use a decimal point. The final edge closes automatically. Up to 200,000 characters. Review the settings before running.",
      "action": null
    },
    "mode": "explicit",
    "interactive": false
  },
  "execution": "Browser interface",
  "api": null,
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}
```

## Page guide

Calculate polygon area, perimeter and centroid from ordered vertices. Find crossing or overlapping edges and download the drawing and coordinates.

How can we improve this tool?

Report a problem or share an idea.

Please leave out private information. Your message and the tool name go to our team via PostHog.

### How to use Polygon geometry workspace

1. Enter the polygon vertices in boundary order, one X,Y pair per line. You may include the first point again at the end.
2. Check the drawing and edge intersections. A simple polygon has an area and centroid; intersecting paths do not receive a fabricated filled area.
3. Download complete JSON, all vertices as CSV, or the SVG diagram.

## Useful next steps

- [Circle intersection calculator](https://happytails.ai/en/calculators/circle-intersection-calculator/) ([Markdown](https://happytails.ai/en/calculators/circle-intersection-calculator.md))

- [Graphing calculator](https://happytails.ai/en/calculators/graphing-calculator/) ([Markdown](https://happytails.ai/en/calculators/graphing-calculator.md))

- [Length](https://happytails.ai/en/unit-converters/length/) ([Markdown](https://happytails.ai/en/unit-converters/length.md))

## Vertex order defines the boundary

The calculator connects each point to the next, then closes the final edge. It does not sort points or invent a boundary for an unordered point cloud. A rectangle with points (0,0), (4,0), (4,3), (0,3) has area 12, perimeter 14 and centroid (2,1.5).

### Crossing paths need a different area definition

A self-crossing path can represent different regions depending on its fill rule. This tool reports crossing and overlapping edge pairs and draws them, but leaves area and centroid undefined. For a concave simple polygon, the centroid can lie outside its boundary.

### One unit, approximate arithmetic

Use the same coordinate unit throughout. Perimeter uses that unit; area uses its square. Raw downloads preserve computed numbers while displayed results follow your language’s number format. Very small features compared with the coordinate span may fall within the numerical tolerance.