Chebyshev Interval Uncertainty Gap Tool

Description

Return minimum Chebyshev gap between axis-aligned boxes.

Distances between intervals and bounds on metric distances describe geometric separation under declared assumptions. Touching intervals have zero gap; triangle bounds require distances that share a common endpoint in an actual metric.

Return minimum Chebyshev gap between axis-aligned boxes.

When to use this tool

Use Chebyshev Interval Uncertainty Gap when checking a supplied interval gap or metric distance bound.

How to use the tool and how it works

Enter firstLower, firstUpper, secondLower, secondUpper. Keep parallel arrays aligned. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read distance. Use the output convention below.

Return minimum Chebyshev gap between axis-aligned boxes. Require equally long nonempty endpoint arrays and ordered intervals; compute each axis interval gap and take the maximum.^[1]

Input field	Meaning and units	Accepted input
firstLower	First Lower	Required. Array of finite number; maximum items 256.
firstUpper	First Upper	Required. Array of finite number; maximum items 256.
secondLower	Second Lower	Required. Array of finite number; maximum items 256.
secondUpper	Second Upper	Required. Array of finite number; maximum items 256.

Output field	Interpretation	Returned shape
distance	Distance	Required. Finite number.

json

{
  "input": {
    "firstLower": [
      0,
      0
    ],
    "firstUpper": [
      2,
      2
    ],
    "secondLower": [
      3,
      1
    ],
    "secondUpper": [
      4,
      3
    ]
  },
  "output": {
    "distance": 1
  }
}

Limitations and assumptions

Axes must use compatible scales; no rotations or full uncertainty dependence is modeled.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use the full point or set geometry and a suitable metric when you need an actual distance rather than a bound or local term.

References

Calculation and input contract: distance/chebyshev-interval-uncertainty-gap — tool.io

Similar or alternative tools

Distance Interval Absolute Value Envelope
Map a real interval through absolute value.
Distance: Point To Open Interval Distance
Return distance infimum to an open interval and whether it is attained.