Description
Return both adjacent spacings and nextSpacing / previousSpacing.
Interpolation knots divide a coordinate range into intervals. Repeated nodes, unequal spacing, and exact boundary selection can change how a piecewise interpolant is interpreted.
Return both adjacent spacings and nextSpacing / previousSpacing.
When to use this tool
Use Knot Spacing Geometric Ratio when you need one knot-interval or multiplicity diagnostic.
How to use the tool and how it works
- Enter previousKnot, currentKnot, nextKnot. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read previousSpacing, nextSpacing, ratio. Use the output convention below.
Require previousKnot < currentKnot < nextKnot. Return both adjacent spacings and nextSpacing / previousSpacing.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| previousKnot | Previous Knot | Required. Finite number. |
| currentKnot | Current Knot | Required. Finite number. |
| nextKnot | Next Knot | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| previousSpacing | Previous Spacing | Required. Finite number. |
| nextSpacing | Next Spacing | Required. Finite number. |
| ratio | Ratio using the numerator and denominator conventions stated above. | Required. Finite number. |
json
{
"input": {
"previousKnot": 0,
"currentKnot": 2,
"nextKnot": 6
},
"output": {
"previousSpacing": 2,
"nextSpacing": 4,
"ratio": 2
}
}Limitations and assumptions
- The ratio compares local spacing only; it does not generate a geometric grid or establish spline quality.
- 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
Validate the complete knot sequence and interpolation method, including tolerance and extrapolation policies.
References
Similar or alternative tools
- Knot Coalescence Distance
Compute abs(secondKnot - firstKnot).
- Spline Knot Interval Zero Span Flag
Return next knot minus current knot and zero for an exact repeated pair.