I'm using knighty's formula with the following GPU optimizations (fR2 is fixed to one):
// precomputed somewhere
vec4 scalevec = vec4(SCALE, SCALE, SCALE, abs(SCALE)) / MR2;
float C1 = abs(SCALE-1.0), C2 = pow(abs(SCALE), float(1-iters));
// distance estimate
vec4 p = vec4(position.xyz, 1.0), p0 = vec4(position.xyz, 1.0); // p.w is knighty's DEfactor
for (int i=0; i<iters; i++) {
p.xyz = clamp(p.xyz, -1.0, 1.0) * 2.0 - p.xyz; // box fold: min3, max3, mad3
float r2 = dot(p.xyz, p.xyz); // dp3
p.xyzw *= clamp(max(MR2/r2, MR2), 0.0, 1.0); // sphere fold: div1, max1.sat, mul4
p.xyzw = p*scalevec + p0; // mad4
}
return (length(p.xyz) - C1) / p.w - C2;
This is fast because
min,
max and
mad(multiply-add) are fast no-branching operations and output saturation (clamping between 0 and 1) is free. Making
iters a constant unrolls the loop for another speedup.
I've found that the formula also works when
p0.xyz≠position (e.g. for julias or various transformations/foldings) as long as you keep
p0.w=1.
Alternative box folds (may be faster on some architectures):
p.xyz = clamp(p.xyz *0.5+0.5, 0.0, 1.0) *4.0-2.0 - p.xyz; // mad.sat, mad, add
p.xyz = abs(1.0+p.xyz) - p.xyz - abs(1.0-p.xyz); // add, add, abs.add, abs.add
August 27, 2011, 12:28:36 PM
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