Cubic Hermite Interpolation
Shape a cubic with two endpoint values and slopes and inspect how its four Hermite basis functions combine.
Free theory articleShape a cubic with two endpoint values and slopes and inspect how its four Hermite basis functions combine.
Concept & interpretation
Cubic Hermite interpolation is a method to construct a continuous curve given its values and derivatives (slopes) at its endpoints. Instead of fitting a generic polynomial to data points, it ensures both position and tangent direction match specific constraints. We construct this unique cubic function on the normalized unit interval [0, 1] using four basis functions.
Interactive Experiment
You can test the same values in the interactive module using these steps:
- Open the Cubic Hermite Interpolation module.
- Set the Left value y0 to 0.
- Set the Right value y1 to 1.
- Set the Left slope m0 to 1.
- Set the Right slope m1 to 1.
- Set the Probe x to 0.25.
- Observe that the value is exactly 0.25, and the derivative is exactly 1. Note the individual basis contributions matching our calculations.