Examples
Examples
Try the starting example
- Samples: x,y, one pair per line
- 0,0 1,1 2,0
- Query x values within sample domain
- 0.5,1.5
- Boundary condition: natural or clamped
- natural
- Endpoint slopes for clamped mode
- 0,0
- Spline values in query order
- 0.6875, 0.6875
- Spline slopes at left and right endpoints
- 1.5, -1.5
- Largest absolute knot second derivative
- 3
- Selected boundary condition
- natural
Try another scenario
- Samples: x,y, one pair per line
- 0,0 1,1 2,0
- Query x values within sample domain
- 0.5,1.5
- Boundary condition: natural or clamped
- clamped
- Endpoint slopes for clamped mode
- 0,0
- Spline values in query order
- 0.5, 0.5
- Spline slopes at left and right endpoints
- 0, 0
- Largest absolute knot second derivative
- 6
- Selected boundary condition
- clamped
Calculation method
Calculation method
Spline values in query order
Solve the cubic-spline tridiagonal equations for knot second derivatives, then evaluate the appropriate interval polynomial.
Spline slopes at left and right endpoints
Calculate endpoint derivatives from the knot values and second derivatives.
Largest absolute knot second derivative
Maximum magnitude of solved knot second derivatives.
Selected boundary condition
Natural means zero endpoint second derivatives; clamped uses the entered two first derivatives.
Symbols and units
- a
- Samples: x,y, one pair per line
- b
- Query x values within sample domain
- c
- Boundary condition: natural or clamped
- d
- Endpoint slopes for clamped mode
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Sorts 2–100 distinct nodes by x and supports natural or clamped endpoint conditions. Queries outside the sampled domain are rejected; no extrapolation policy is guessed. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
SciPy: cubic spline boundary conditions ↗
Background reading; this does not imply endorsement or independent review of SumFizz.