Description
Subtract the left segment's secant slope from the right segment's slope for slopeJump.
Interpolation knots divide a coordinate range into intervals. Repeated nodes, unequal spacing, and exact boundary selection can change how a piecewise interpolant is interpreted.
Subtract the left segment's secant slope from the right segment's slope for slopeJump.
When to use this tool
Use Piecewise Linear One Knot Curvature when you need one knot-interval or multiplicity diagnostic.
How to use the tool and how it works
- Enter leftX, knotX, rightX, leftY, knotY, rightY. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read slopeJump. Use the output convention below.
Require leftX < knotX < rightX. Subtract the left segment's secant slope from the right segment's slope for slopeJump.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftX | Left X | Required. Finite number. |
| knotX | Knot X | Required. Finite number. |
| rightX | Right X | Required. Finite number. |
| leftY | Left Y | Required. Finite number. |
| knotY | Knot Y | Required. Finite number. |
| rightY | Right Y | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slopeJump | Slope Jump | Required. Finite number. |
{
"input": {
"leftX": 0,
"knotX": 1,
"rightX": 3,
"leftY": 0,
"knotY": 2,
"rightY": 4
},
"output": {
"slopeJump": -1
}
}Limitations and assumptions
- This is a derivative jump of a piecewise linear curve, not an ordinary finite second derivative at the knot.
- 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
- Monotone Linear Segment Direction
Require leftX < rightX and return sign(rightY - leftY) as direction plus an exact flat flag.
- Hermite Endpoint Data Continuity Gap
Return rightValue - leftValue and rightSlope - leftSlope as valueGap and slopeGap.