# Hermite interpollation¶

• Author or source: various
• Created: 2002-04-09 16:55:35
notes
```These are all different ways to do the same thing : hermite interpollation. Try'm all and
benchmark.
```
code
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48``` ```// original inline float hermite1(float x, float y0, float y1, float y2, float y3) { // 4-point, 3rd-order Hermite (x-form) float c0 = y1; float c1 = 0.5f * (y2 - y0); float c2 = y0 - 2.5f * y1 + 2.f * y2 - 0.5f * y3; float c3 = 1.5f * (y1 - y2) + 0.5f * (y3 - y0); return ((c3 * x + c2) * x + c1) * x + c0; } // james mccartney inline float hermite2(float x, float y0, float y1, float y2, float y3) { // 4-point, 3rd-order Hermite (x-form) float c0 = y1; float c1 = 0.5f * (y2 - y0); float c3 = 1.5f * (y1 - y2) + 0.5f * (y3 - y0); float c2 = y0 - y1 + c1 - c3; return ((c3 * x + c2) * x + c1) * x + c0; } // james mccartney inline float hermite3(float x, float y0, float y1, float y2, float y3) { // 4-point, 3rd-order Hermite (x-form) float c0 = y1; float c1 = 0.5f * (y2 - y0); float y0my1 = y0 - y1; float c3 = (y1 - y2) + 0.5f * (y3 - y0my1 - y2); float c2 = y0my1 + c1 - c3; return ((c3 * x + c2) * x + c1) * x + c0; } // laurent de soras inline float hermite4(float frac_pos, float xm1, float x0, float x1, float x2) { const float c = (x1 - xm1) * 0.5f; const float v = x0 - x1; const float w = c + v; const float a = w + v + (x2 - x0) * 0.5f; const float b_neg = w + a; return ((((a * frac_pos) - b_neg) * frac_pos + c) * frac_pos + x0); } ```

• Date: 2002-05-25 13:37:32
• By: theguylle
```              great sources but what is Hermite ?
if you don't describe what is your code made for, you will made a great sources but I don't know why?

cheers Paul
```
```hermite is interpollation.
have a look around the archive, you'll see that the word 'hermite' is in more than one item ;-)

-bram
```
```Please, would like to know of hermite code it exists in delphi.

thankful

Ronaldo
Cascavel/Paraná/Brasil
```
```Please,
add, at least, the meaning of each parameter (I mean x, y0,  y1,y2,  y3)....
m.
```
• Date: 2003-11-28 10:48:17
• By: musicdsp@[remove this]dsparsons.co.uk
```Ronaldo, it doesn't take much to translate these to Delphi - for float, either use single or double to your preference!

Looking at the codes, it seems quite clear that the parameters follow a pattern of: Sample Position between middle two samples, then the sample before current, current sample, curernt sample +1, current sample +2.

HTH
DSP
```
```What are all these variables standing for? Not very clear :|
```
• Date: 2004-04-20 00:25:29
• By: George
```parameters are allright.

xm1 ---> x[n-1]
x0  ---> x[n]
x1  ---> x[n+1]
x2  ---> x[n+2]

fractional position stands for a fraction between 0 and 1 to interpolate
```
```Couldn't #2 be sped up a hair by commenting out

float c0 = y1;

and then replacing c0 with y1 in the return line?  Or do the compilers do that kind of thing automatically when they optimize?
```
```"Couldn't #2 be sped up a hair"
It gets optimized out.
```