Îòïðàâëåíî Oval 13 èþëÿ 2005 ã. 20:49  îòâåò íà: §±§à§Õ§Ö§Ý§Ú§ä§Ö§ã§î §Ü§à§Õ§à§Þ Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) îòïðàâëåíî <font color=gray>pp2</font> 12 §Ú§ð§Ý§ñ 2005 §Ô. 19:06

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Hermite interpollation (click this to go back to the index)
References : Posted by various
Notes :
These are all different ways to do the same thing : hermite interpollation. Try'm all and benchmark.
Code :
// 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);

}
Comments
from : theguylle
comment : 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
from : bram@musicdsp.org
comment : hermite is interpollation.

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

-bram
from : ronaldowf@sanepar.com.br
comment : Please, would like to know of hermite code it exists in delphi.

thankful

Ronaldo

Cascavel/Paran¨¢/Brasil
from : m.magrini@NOSPAMbad-sector.com
comment : Please,

add, at least, the meaning of each parameter (I mean x, y0, y1,y2, y3)....

m.
from : musicdsp@[remove this]dsparsons.co.uk
comment : 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.