template<typename T>
| T hermiteInterpolate | ( | T | t, | |
| T | value0, | |||
| T | value1, | |||
| T | derivative0, | |||
| T | derivative1 | |||
| ) |
Hermite interpolation.
- Parameters:
-
t The function argument. value0 f(0) value1 f(1) derivative0 f'(0) derivative1 f'(1)
This function implements the algorithm presented in "Geometric Tools for Computer Graphics" by Philip Schneider and David Eberly. The cubic Hermite polynomials are given below.
![\[ a_0(t) = 2 t^3 - 3 t^2 + 1 \]](form_7.png)
![\[ a_1(t) = -2 t^3 + 3 t^2 \]](form_8.png)
![\[ b_0(t) = t^3 - 2 t^2 + t \]](form_9.png)
![\[ b_1(t) = t^3 - t^2 \]](form_10.png)
The cubic interpolant is
![\[ c(t) = f(0) a_0(t) + f(1) a_1(t) + f'(0) b_0(t) + f'(1) b_1(t). \]](form_11.png)
This function simply evaluates the interpolant.
- Returns:
- The interpolated value of the function.
- Note:
- Using this function is not efficient when one is evaluating a fixed interpolant for multiple arguments. For this usage scenario, use a divided differences algorithm instead.
