Description
Clip an ordered polygon against the closed half-plane nx*x+ny*y<=maximum; no self-intersection validation or geographic geometry.
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.
Clip an ordered polygon against the closed half-plane nx*x+ny*y<=maximum; no self-intersection validation or geographic geometry.
When to use this tool
Use this tool to clip an ordered polygon against the closed half-plane nx*x+ny*y<=maximum; no self-intersection validation or geographic geometry.
How to use the tool and how it works
- Enter points, normalX, normalY, maximum using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.points. Interpret signs, units, ordering and null values using the rules below.
For each cyclic edge compute f = normalX×x+normalY×y−maximum. Keep endpoints with f≤0 and insert intersections where consecutive endpoint signs strictly differ. The normal must be nonzero.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. |
| normalX | x component of the half-plane normal; the pair of normal components must be nonzero. | Finite number satisfying the stated comparisons. |
| normalY | y component of the half-plane normal; components are bounded to ±1,000,000,000. | Finite number satisfying the stated comparisons. |
| maximum | Half-plane bound in normalX×x+normalY×y≤maximum; finite within ±1,000,000,000. | Finite number satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.points | Ordered resulting point coordinates under the stated clipping/intersection rule. |
{
"input": {
"points": [
[
0,
0
],
[
2,
0
],
[
2,
2
],
[
0,
2
]
],
"normalX": 1,
"normalY": 0,
"maximum": 1
},
"output": {
"result": {
"points": [
[
0,
0
],
[
1,
0
],
[
1,
2
],
[
0,
2
]
]
}
}
}Limitations and assumptions
- The closed half-plane includes its boundary. Near-boundary comparisons are exact floating arithmetic without a tolerance or topology repair.
- 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 Rectangle Clip
Clip an ordered planar polygon against four rectangle half-planes, preserving algorithm order; floating boundary arithmetic, no polygon topology repair.
- Polygon Edge Orientation Table
Report directed polygon edge displacements and radian orientations; zero edges have null direction, and the cycle is implicitly closed.