void Normal_Calc_HCompl(VECTOR Result, int N_Max, const Fractal *, DBL **IterStack)
{
DBL n1, n2, n3, n4;
int i;
DBL x, y, z, w;
DBL xx, yy, zz, ww;
DBL Pow;
/*
* Algebraic properties of hypercomplexes allows simplifications in
* computations...
*/
x = IterStack[X][0];
y = IterStack[Y][0];
z = IterStack[Z][0];
w = IterStack[W][0];
Pow = 2.0;
for (i = 1; i < N_Max; ++i)
{
/*
* For a map z->f(z), f depending on c, one must perform here :
*
* (x,y,z,w) * df/dz(IterStack[X][i],IterStack[Y][i],IterStack[Z][i],IterStack[W][i]) -> (x,y,z,w) ,
*
* up to a constant.
*/
/******************* Case z->z^2+c *****************/
/* the df/dz part needs no work */
HMult(xx, yy, zz, ww, IterStack[X][i], IterStack[Y][i], IterStack[Z][i], IterStack[W][i], x, y, z, w);
w = ww;
z = zz;
y = yy;
x = xx;
Pow *= 2.0;
}
n1 = IterStack[X][N_Max] * Pow;
n2 = IterStack[Y][N_Max] * Pow;
n3 = IterStack[Z][N_Max] * Pow;
n4 = IterStack[W][N_Max] * Pow;
Result[X] = x * n1 + y * n2 + z * n3 + w * n4;
Result[Y] = -y * n1 + x * n2 - w * n3 + z * n4;
Result[Z] = -z * n1 - w * n2 + x * n3 + y * n4;
}
void Normal_Calc_HCompl_Reciprocal(VECTOR Result, int N_Max, const Fractal *, DBL **IterStack)
{
DBL n1, n2, n3, n4;
int i;
DBL x, y, z, w;
DBL xx, yy, zz, ww;
DBL xxx, yyy, zzz, www;
/*
* Algebraic properties of hypercomplexes allows simplifications in
* computations...
*/
x = IterStack[X][0];
y = IterStack[Y][0];
z = IterStack[Z][0];
w = IterStack[W][0];
for (i = 1; i < N_Max; ++i)
{
/******************* Case: z->1/z+c *****************/
HReciprocal(&xx, &yy, &zz, &ww, IterStack[X][i], IterStack[Y][i], IterStack[Z][i], IterStack[W][i]);
HSqr(xxx, yyy, zzz, www, xx, yy, zz, ww);
HMult(xx, yy, zz, ww, x, y, z, w, -xxx, -yyy, -zzz, -www);
x = xx;
y = yy;
z = zz;
w = ww;
}
n1 = IterStack[X][N_Max];
n2 = IterStack[Y][N_Max];
n3 = IterStack[Z][N_Max];
n4 = IterStack[W][N_Max];
Result[X] = x * n1 + y * n2 + z * n3 + w * n4;
Result[Y] = -y * n1 + x * n2 - w * n3 + z * n4;
Result[Z] = -z * n1 - w * n2 + x * n3 + y * n4;
}
void HypercomplexFunctionFractalRules::CalcNormal(Vector3d& Result, int N_Max, const Fractal *fractal, DBL **IterStack) const
{
DBL n1, n2, n3, n4;
int i;
DBL x, y, z, w;
DBL xx, yy, zz, ww;
DBL xxx, yyy, zzz, www;
/*
* Algebraic properties of hypercomplexes allows simplifications in
* computations...
*/
x = IterStack[X][0];
y = IterStack[Y][0];
z = IterStack[Z][0];
w = IterStack[W][0];
for (i = 1; i < N_Max; ++i)
{
/**************** Case: z-> f(z)+c ************************/
HFunc(&xx, &yy, &zz, &ww, IterStack[X][i], IterStack[Y][i], IterStack[Z][i], IterStack[W][i], fractal);
HMult(xxx, yyy, zzz, www, xx, yy, zz, ww, x, y, z, w);
x = xxx;
y = yyy;
z = zzz;
w = www;
}
n1 = IterStack[X][N_Max];
n2 = IterStack[Y][N_Max];
n3 = IterStack[Z][N_Max];
n4 = IterStack[W][N_Max];
Result[X] = x * n1 + y * n2 + z * n3 + w * n4;
Result[Y] = -y * n1 + x * n2 - w * n3 + z * n4;
Result[Z] = -z * n1 - w * n2 + x * n3 + y * n4;
}
