Description
Return signed rectangle axis gaps: positive separation, zero contact, negative overlap depth on each axis; no Euclidean distance inferred.
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.
Return signed rectangle axis gaps: positive separation, zero contact, negative overlap depth on each axis; no Euclidean distance inferred.
When to use this tool
Use this tool to return signed rectangle axis gaps: positive separation, zero contact, negative overlap depth on each axis; no Euclidean distance inferred.
How to use the tool and how it works
- Enter left, right using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.gaps. Interpret signs, units, ordering and null values using the rules below.
For x return max(right.minX−left.maxX,left.minX−right.maxX); repeat for y. Positive values mean separation, zero means contact and negative values mean overlap of the axis intervals.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left rectangle [minX,minY,maxX,maxY] with ordered bounds. | Dense list of at most 128 finite numbers, subject to the stated integer/shape rules. |
| right | Right rectangle [minX,minY,maxX,maxY] with ordered bounds. | Dense list of at most 128 finite numbers, subject to the stated integer/shape rules. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.gaps | Signed [xGap,yGap] axis endpoint gaps in coordinate units. |
{
"input": {
"left": [
0,
0,
2,
2
],
"right": [
1,
3,
4,
4
]
},
"output": {
"result": {
"gaps": [
-1,
1
]
}
}
}Limitations and assumptions
- For nested intervals the negative value is the smaller translation to an endpoint contact, which can exceed intersection width; it is not a Euclidean distance.
- 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 Signed Area Centroid
Compute algebraic signed polygon area and shoelace centroid, returning null for zero algebraic area; caller supplies a simple ordered polygon, no topology validation.