Can I ask what sort of improvements you made?
I tried to render power 2 Mandelbulb using your formula but fractals look very strange. I converted your DE to Daniel's (Tweenbe) formula and now it is possible to render z^2+c fractal. I tested lots of estimators on 2D slices and I this was the most accurate (but still not perfect). Most of estimators work only very well for high powers (>4). During rendering z^2+c fractal for z=0 there is no problem but for higher values of z these estimators generates lots of artefacts.
There is my version of DE below
p = 6.0; //mandelbulb power
x = a;
y = b;
z = c;
dzx = 1;
dzy = 0;
dzz = 0;
r_dz = 1;
ph_dz = 0;
th_dz = 0;
r = sqrt(x * x + y * y + z * z);
for (L = 0; L < N; L++)
{
r1 = pow(r, p - 1);
r2 = r1 * r;
th = atan2(y, x);
ph = -atan2(z, sqrt(x * x + y * y));
p_r1_rdz = p * r1 * r_dz;
ph_phdz = (p - 1.0) * ph + ph_dz;
th_thdz = (p - 1.0) * th + th_dz;
dzx = p_r1_rdz * cos(ph_phdz) * cos(th_thdz) + 1.0;
dzy = p_r1_rdz * cos(ph_phdz) * sin(th_thdz);
dzz = p_r1_rdz * sin(ph_phdz);
r_dz = sqrt(dzx * dzx + dzy * dzy + dzz * dzz);
th_dz = atan2(dzy, dzx);
ph_dz = -atan2(dzz, sqrt(dzx * dzx + dzy * dzy));
x = r2 * cos(p * ph) * cos(p * th) + a;
y = r2 * cos(p * ph) * sin(p * th) + b;
z = r2 * sin(p * ph) + c;
r = sqrt(x * x + y * y + z * z);
if (r > 1e15)
{
dist1 = r;
dist2 = r_dz;
distance = r * log(r) / r_dz;
break;
}
}
Maybe there is somebody who knows proper distance estimator for z^2+c
First off the distance estimate should be:
distance = 0.5*r * log(r) / r_dz;
secondly the distance you actually step should normally be less than this for accuracy, e.g. multiply by 0.5 again - better still allow a user "accuracy" parameter.
Also I found that to get the DE correct I had to multiply the DE by sqrt(p-1) where p is the power:
distance = 0.5*sqrt(p-1)*r * log(r) / r_dz;
The sqrt(p-1) was arrived at by experimentation and works well for me
November 22, 2009, 08:49:18 PM
Dilber MC Theme by HarzeM