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THE FEUTEX TOOLKIT

Cubic Hermite Endpoint Interpolation

Interpolate between endpoint values while preserving specified endpoint slopes.

Math workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaValue = (2*t**3-3*t**2+1)*y0+(t**3-2*t**2+t)*(x1-x0)*m0+(-2*t**3+3*t**2)*y1+(t**3-t**2)*(x1-x0)*m1; X = x0+t*(x1-x0)
Sources and model references

Made for real tasks

  • Interpolate between endpoint values while preserving specified endpoint slopes.
Explore step-by-step workflows →

Worked example

Inputs

Left x
0 number
Right x
1 number
Left value
0 number
Right value
1 number
Left slope
0 number
Right slope
3 number
Interval fraction
0.5 fraction

Expected results

Value
0.125 number
X
0.5 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter left x, right x, left value, right value, left slope, right slope, interval fraction.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "x0": 0,
  "x1": 1,
  "y0": 0,
  "y1": 1,
  "m0": 0,
  "m1": 3,
  "t": 0.5
}

Accuracy and scope

Uses finite-precision arithmetic. Results describe the stated mathematical model, not measurement accuracy.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.