APPROXIMATION DU SIN, COS, TAN, ACOS... , Source N°11086

Information sur la source

Catégorie :Maths & Algorithmes Niveau : Débutant Date de création : 09/07/2003 Date de mise à jour : 09/07/2003 17:05:54 Vu : 1 587

Auteur : psy4meuh

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Description

Cliquez pour voir la capture en taille normale

Voilà,

c'est des méthodes de ma classe Math, qui calculent les fonctions trigo de facon approximative... mais pas tant que ca, celà suffit dans bien des cas.... en plus très rapide comparé aux fonctions standar...

Source

//----------------------------------------------------------------------
Real Math::FastSin0 (Real fAngle)
{
Real fASqr = fAngle*fAngle;
Real fResult = 7.61e-03f;
fResult *= fASqr;
fResult -= 1.6605e-01f;
fResult *= fASqr;
fResult += 1.0f;
fResult *= fAngle;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastSin1 (Real fAngle)
{
Real fASqr = fAngle*fAngle;
Real fResult = -2.39e-08f;
fResult *= fASqr;
fResult += 2.7526e-06f;
fResult *= fASqr;
fResult -= 1.98409e-04f;
fResult *= fASqr;
fResult += 8.3333315e-03f;
fResult *= fASqr;
fResult -= 1.666666664e-01f;
fResult *= fASqr;
fResult += 1.0f;
fResult *= fAngle;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastCos0 (Real fAngle)
{
Real fASqr = fAngle*fAngle;
Real fResult = 3.705e-02f;
fResult *= fASqr;
fResult -= 4.967e-01f;
fResult *= fASqr;
fResult += 1.0f;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastCos1 (Real fAngle)
{
Real fASqr = fAngle*fAngle;
Real fResult = -2.605e-07f;
fResult *= fASqr;
fResult += 2.47609e-05f;
fResult *= fASqr;
fResult -= 1.3888397e-03f;
fResult *= fASqr;
fResult += 4.16666418e-02f;
fResult *= fASqr;
fResult -= 4.999999963e-01f;
fResult *= fASqr;
fResult += 1.0f;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastTan0 (Real fAngle)
{
Real fASqr = fAngle*fAngle;
Real fResult = 2.033e-01f;
fResult *= fASqr;
fResult += 3.1755e-01f;
fResult *= fASqr;
fResult += 1.0f;
fResult *= fAngle;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastTan1 (Real fAngle)
{
Real fASqr = fAngle*fAngle;
Real fResult = 9.5168091e-03f;
fResult *= fASqr;
fResult += 2.900525e-03f;
fResult *= fASqr;
fResult += 2.45650893e-02f;
fResult *= fASqr;
fResult += 5.33740603e-02f;
fResult *= fASqr;
fResult += 1.333923995e-01f;
fResult *= fASqr;
fResult += 3.333314036e-01f;
fResult *= fASqr;
fResult += 1.0f;
fResult *= fAngle;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastInvSin (Real fValue)
{
Real fRoot = Math::Sqrt(1.0f-fValue);
Real fResult = -0.0187293f;
fResult *= fValue;
fResult += 0.0742610f;
fResult *= fValue;
fResult -= 0.2121144f;
fResult *= fValue;
fResult += 1.5707288f;
fResult = HALF_PI - fRoot*fResult;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastInvCos (Real fValue)
{
Real fRoot = Math::Sqrt(1.0f-fValue);
Real fResult = -0.0187293f;
fResult *= fValue;
fResult += 0.0742610f;
fResult *= fValue;
fResult -= 0.2121144f;
fResult *= fValue;
fResult += 1.5707288f;
fResult *= fRoot;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastInvTan0 (Real fValue)
{
Real fVSqr = fValue*fValue;
Real fResult = 0.0208351f;
fResult *= fVSqr;
fResult -= 0.085133f;
fResult *= fVSqr;
fResult += 0.180141f;
fResult *= fVSqr;
fResult -= 0.3302995f;
fResult *= fVSqr;
fResult += 0.999866f;
fResult *= fValue;
return fResult;
}
//----------------------------------------------------------------------
Real Math::FastInvTan1 (Real fValue)
{
Real fVSqr = fValue*fValue;
Real fResult = 0.0028662257f;
fResult *= fVSqr;
fResult -= 0.0161657367f;
fResult *= fVSqr;
fResult += 0.0429096138f;
fResult *= fVSqr;
fResult -= 0.0752896400f;
fResult *= fVSqr;
fResult += 0.1065626393f;
fResult *= fVSqr;
fResult -= 0.1420889944f;
fResult *= fVSqr;
fResult += 0.1999355085f;
fResult *= fVSqr;
fResult -= 0.3333314528f;
fResult *= fVSqr;
fResult += 1.0f;
fResult *= fValue;
return fResult;
}
//----------------------------------------------------------------------

//----------------------------------------------------------------------
Real Math::FastSin0 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = 7.61e-03f;
    fResult *= fASqr;
    fResult -= 1.6605e-01f;
    fResult *= fASqr;
    fResult += 1.0f;
    fResult *= fAngle;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastSin1 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = -2.39e-08f;
    fResult *= fASqr;
    fResult += 2.7526e-06f;
    fResult *= fASqr;
    fResult -= 1.98409e-04f;
    fResult *= fASqr;
    fResult += 8.3333315e-03f;
    fResult *= fASqr;
    fResult -= 1.666666664e-01f;
    fResult *= fASqr;
    fResult += 1.0f;
    fResult *= fAngle;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastCos0 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = 3.705e-02f;
    fResult *= fASqr;
    fResult -= 4.967e-01f;
    fResult *= fASqr;
    fResult += 1.0f;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastCos1 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = -2.605e-07f;
    fResult *= fASqr;
    fResult += 2.47609e-05f;
    fResult *= fASqr;
    fResult -= 1.3888397e-03f;
    fResult *= fASqr;
    fResult += 4.16666418e-02f;
    fResult *= fASqr;
    fResult -= 4.999999963e-01f;
    fResult *= fASqr;
    fResult += 1.0f;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastTan0 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = 2.033e-01f;
    fResult *= fASqr;
    fResult += 3.1755e-01f;
    fResult *= fASqr;
    fResult += 1.0f;
    fResult *= fAngle;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastTan1 (Real fAngle)
{
    Real fASqr = fAngle*fAngle;
    Real fResult = 9.5168091e-03f;
    fResult *= fASqr;
    fResult += 2.900525e-03f;
    fResult *= fASqr;
    fResult += 2.45650893e-02f;
    fResult *= fASqr;
    fResult += 5.33740603e-02f;
    fResult *= fASqr;
    fResult += 1.333923995e-01f;
    fResult *= fASqr;
    fResult += 3.333314036e-01f;
    fResult *= fASqr;
    fResult += 1.0f;
    fResult *= fAngle;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastInvSin (Real fValue)
{
    Real fRoot = Math::Sqrt(1.0f-fValue);
    Real fResult = -0.0187293f;
    fResult *= fValue;
    fResult += 0.0742610f;
    fResult *= fValue;
    fResult -= 0.2121144f;
    fResult *= fValue;
    fResult += 1.5707288f;
    fResult = HALF_PI - fRoot*fResult;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastInvCos (Real fValue)
{
    Real fRoot = Math::Sqrt(1.0f-fValue);
    Real fResult = -0.0187293f;
    fResult *= fValue;
    fResult += 0.0742610f;
    fResult *= fValue;
    fResult -= 0.2121144f;
    fResult *= fValue;
    fResult += 1.5707288f;
    fResult *= fRoot;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastInvTan0 (Real fValue)
{
    Real fVSqr = fValue*fValue;
    Real fResult = 0.0208351f;
    fResult *= fVSqr;
    fResult -= 0.085133f;
    fResult *= fVSqr;
    fResult += 0.180141f;
    fResult *= fVSqr;
    fResult -= 0.3302995f;
    fResult *= fVSqr;
    fResult += 0.999866f;
    fResult *= fValue;
    return fResult;
}
//----------------------------------------------------------------------
Real Math::FastInvTan1 (Real fValue)
{
    Real fVSqr = fValue*fValue;
    Real fResult = 0.0028662257f;
    fResult *= fVSqr;
    fResult -= 0.0161657367f;
    fResult *= fVSqr;
    fResult += 0.0429096138f;
    fResult *= fVSqr;
    fResult -= 0.0752896400f;
    fResult *= fVSqr;
    fResult += 0.1065626393f;
    fResult *= fVSqr;
    fResult -= 0.1420889944f;
    fResult *= fVSqr;
    fResult += 0.1999355085f;
    fResult *= fVSqr;
    fResult -= 0.3333314528f;
    fResult *= fVSqr;
    fResult += 1.0f;
    fResult *= fValue;
    return fResult;
}
//----------------------------------------------------------------------

Conclusion

Merci à Wild-Magic ;-)

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Commentaires

Commentaire de Maegis le 14/07/2003 14:04:45

2 - 3 commentaires seraient les bienvenus
Commentaire de psy4meuh le 15/07/2003 07:17:28

en fait Wild Magic a dévelopé un prog d'analyse de courbe, et à partir des courbes de fonctions Cos, Sin, etc... on a des formules du genre :
x²+1589/255*x²+65887/155124*1-x²+258744/899... c'est de l'aproximation, (pas tres au point fô dire , mais une fois un peupris, on a des formules qui tiennent la route.
On retranscri ca en code C assez rapide et on obtient des fonction plus rapides que les standard, et qui donnent un resultat largement sufisent dans la plupart des cas...
Mais le code est compréhensible non?
Commentaire de Maegis le 16/07/2003 11:52:46

Il aurait pu quand même expliquer le fonctionement parce que la il balance les chiffres comme ça. J'avais pas pigé que c'était une aproximation à partir des courbes
Commentaire de drpark le 18/12/2004 17:52:03

hello, j'ai fait un test de rapidité,
et c kifkif avec les fonctions standarts...