Description
Report directed polygon edge displacements and radian orientations; zero edges have null direction, and the cycle is implicitly closed.
Planar geometry operates on two-coordinate Cartesian points and explicit shape boundaries. A closed rectangle includes its edges, while a segment parameter locates a point along a supporting line. Signed cross products, areas and axis gaps preserve orientation or direction information that a magnitude alone would lose.
Report directed polygon edge displacements and radian orientations; zero edges have null direction, and the cycle is implicitly closed.
When to use this tool
Use this tool to report directed polygon edge displacements and radian orientations; zero edges have null direction, and the cycle is implicitly closed.
How to use the tool and how it works
- Enter points using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.edges. Interpret signs, units, ordering and null values using the rules below.
Close the point cycle implicitly and return dx, dy and atan2(dy,dx) for every directed edge. Return angle = null when both displacements are zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| points | Ordered planar [x,y] points. Polygon operations close the cycle implicitly; polyline operations use adjacent pairs only. | Dense list of at most 128 rows of at most 128 finite numbers; the operation’s shape constraints also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.edges | Cyclic edge records {index,dx,dy,angle}; angle is radians or null for zero displacement. |
{
"input": {
"points": [
[
0,
0
],
[
1,
0
],
[
0,
0
]
]
},
"output": {
"result": {
"edges": [
{
"index": 0,
"dx": 1,
"dy": 0,
"angle": 0
},
{
"index": 1,
"dx": -1,
"dy": 0,
"angle": 3.141592653589793
},
{
"index": 2,
"dx": 0,
"dy": 0,
"angle": null
}
]
}
}
}Limitations and assumptions
- Angles are radians under the caller’s coordinate-axis convention; no compass direction or screen-y interpretation is imposed.
- Point components and rectangle bounds are finite within ±1,000,000,000. Rectangles use [minX,minY,maxX,maxY] with ordered inclusive bounds. Floating arithmetic is used without an implicit robustness tolerance.
- Every declared top-level input is required and unknown fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and within the absolute safe-integer magnitude; exact larger integers use decimal text. Source positions are zero-based UTF-16 offsets and span ends are exclusive unless a different convention is explicitly stated.
Alternative or Complementary methods
Choose the boundary and coordinate convention explicitly. Use robust geometric predicates or a topology-aware library when near-coincidence, holes, invalid polygons or geographic coordinates matter.
References
Similar or alternative tools
- Polygon Zero Length Edge Audit
Identify exactly zero-length edges in an implicitly closed polygon coordinate cycle; explicit repeated closure creates a zero closing edge.
- Three Point Orientation
Orient three finite planar points by exact floating arithmetic cross-product sign; no adaptive numerical robustness, geographic coordinates or tolerance inference.