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The example blob function at the end of the isosurface tutorial behaves
differently at different scales, as can be seen in the example below. This is
not a problem with the built-in blob object. I was wondering if anyone could
provide a better formula for when using isosurfaces? Thanks!
// Begin
#version 3.6;
#include "colors.inc"
#include "functions.inc"
#include "math.inc"
#include "Axes_macro.inc"
#declare Scene_scale = frame_number;
global_settings
{
assumed_gamma 1.0
max_trace_level 5
}
// ----------------------------------------
#declare screen_scale = 1;
camera
{
#local CameraDistance = 10;
#local ScreenArea = 6;
#local AspectRatio = image_width/image_height;
orthographic
location -z*CameraDistance
direction z*CameraDistance
right x*ScreenArea*AspectRatio
up y*ScreenArea
rotate x*asind(tand(30))
// rotate x*90
rotate y*45
scale Scene_scale
}
background { color rgb <0.6,0.7,1.0> }
light_source
{
<0, 0, 0> // light's position (translated below)
color rgb <1, 1, 1> // light's color
translate <-30, 30, -30>
shadowless
scale Scene_scale
}
light_source
{
<0, 0, 0> // light's position (translated below)
color rgb <1, 1, 1> // light's color
translate <-30, 30, -30>
rotate y * 90
shadowless
scale Scene_scale
}
plane { y,0 pigment {color rgbt 1/2}}
// ----------------------------------------
#declare Blob_threshold = 0.5;
#declare Blob_start = 1;
#declare fn_A = function { pow(x+Scene_scale/2,2) + pow(y+Scene_scale/2,2) +
pow(z+Scene_scale/2,2) - pow(Scene_scale,2) };
#declare fn_B = function { pow(x-Scene_scale/2,2) + pow(y-Scene_scale/2,2) +
pow(z-Scene_scale/2,2) - pow(Scene_scale,2) };
#declare fn_C = function { Blob_start + Blob_threshold }
difference
{
isosurface
{
function
{
fn_C(x,y,z)
- pow(Blob_threshold, fn_A(x,y,z))
- pow(Blob_threshold, fn_B(x,y,z))
}
threshold 0
accuracy 0.001*Scene_scale
max_gradient 4
contained_by { sphere { 0, 2 * Scene_scale } }
}
pigment {color rgb x}
}
// End
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SharkD wrote:
> #declare Blob_threshold = 0.5;
> #declare Blob_start = 1;
> #declare fn_A = function { pow(x+Scene_scale/2,2) + pow(y+Scene_scale/2,2) +
> pow(z+Scene_scale/2,2) - pow(Scene_scale,2) };
> #declare fn_B = function { pow(x-Scene_scale/2,2) + pow(y-Scene_scale/2,2) +
> pow(z-Scene_scale/2,2) - pow(Scene_scale,2) };
> #declare fn_C = function { Blob_start + Blob_threshold }
Shouldn't this be something like:
#declare fn_A =
function {
pow(x/Scene_scale+1/2,2) +
pow(y/Scene_scale+1/2,2) +
pow(z/Scene_scale+1/2,2) -
1 };
etc?
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Dan Connelly <djc### [at] yahoo com> wrote:
> SharkD wrote:
>
> > #declare Blob_threshold = 0.5;
> > #declare Blob_start = 1;
> > #declare fn_A = function { pow(x+Scene_scale/2,2) + pow(y+Scene_scale/2,2) +
> > pow(z+Scene_scale/2,2) - pow(Scene_scale,2) };
> > #declare fn_B = function { pow(x-Scene_scale/2,2) + pow(y-Scene_scale/2,2) +
> > pow(z-Scene_scale/2,2) - pow(Scene_scale,2) };
> > #declare fn_C = function { Blob_start + Blob_threshold }
>
>
> Shouldn't this be something like:
>
> #declare fn_A =
> function {
> pow(x/Scene_scale+1/2,2) +
> pow(y/Scene_scale+1/2,2) +
> pow(z/Scene_scale+1/2,2) -
> 1 };
>
> etc?
Could you please explain why?
-Mike
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S
>> #declare fn_A =
>> function {
>> pow(x/Scene_scale+1/2,2) +
>> pow(y/Scene_scale+1/2,2) +
>> pow(z/Scene_scale+1/2,2) -
>> 1 };
>>
>> etc?
>
> Could you please explain why?
>
> -Mike
>
So the function "spreads out" as the multiplication factor changes, but that the value
at a given scaled value of (x,y,z) doesn't change.
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S
>> #declare fn_A =
>> function {
>> pow(x/Scene_scale+1/2,2) +
>> pow(y/Scene_scale+1/2,2) +
>> pow(z/Scene_scale+1/2,2) -
>> 1 };
>>
>> etc?
>
> Could you please explain why?
>
> -Mike
>
So the function "spreads out" as the multiplication factor changes, but that the value
at a given scaled value of (x,y,z) doesn't change.
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"SharkD" <nomail@nomail> wrote:
> The example blob function at the end of the isosurface tutorial behaves
> differently at different scales, as can be seen in the example below. This is
> not a problem with the built-in blob object. I was wondering if anyone could
> provide a better formula for when using isosurfaces? Thanks!
I found to equations that fit the bill. However, I don't know which one to
choose. Both are said to model the behavior of electric fields. One is from
Wikipedia, the other is from a GameDev.net article.
Here is the first:
#declare Blob_threshold = pow(2,frame_number-3);
#declare fn_A = function { 1.5*Scene_scale / sqrt(pow(x+1*Scene_scale,2) +
pow(y,2) + pow(z,2)) };
#declare fn_B = function { 1.5*Scene_scale / sqrt(pow(x-1*Scene_scale,2) +
pow(y,2) + pow(z,2)) };
#declare fn_C = function { Blob_threshold };
#declare fn_D = function { fn_A(x,y,z) + fn_B(x,y,z) - fn_C(x,y,z) };
#declare fn_E = function { max(0,min(1,fn_D(x,y,z))) };
Here is the second:
#declare Blob_threshold = clock;
#declare fn_A = function { 1.5*Scene_scale / (pow(x+1*Scene_scale,2) + pow(y,2)
+ pow(z,2)) };
#declare fn_B = function { 1.5*Scene_scale / (pow(x-1*Scene_scale,2) + pow(y,2)
+ pow(z,2)) };
#declare fn_C = function { Blob_threshold };
#declare fn_D = function { fn_A(x,y,z) + fn_B(x,y,z) - fn_C(x,y,z) };
#declare fn_E = function { max(0,min(1,fn_D(x,y,z))) };
Which of the two is correct in terms of modeling nature?
-Mike
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Dan Connelly <djc### [at] yahoocom> wrote:
> S
> >> #declare fn_A =
> >> function {
> >> pow(x/Scene_scale+1/2,2) +
> >> pow(y/Scene_scale+1/2,2) +
> >> pow(z/Scene_scale+1/2,2) -
> >> 1 };
> >>
> >> etc?
> >
> > Could you please explain why?
> >
> > -Mike
> >
>
> So the function "spreads out" as the multiplication factor changes, but that the
value at a given scaled value of (x,
y,z) doesn't change.
I can't argue as to its merits. It is simply the function I copied from the
isosurface tutorial.
-Mike
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"SharkD" <nomail@nomail> wrote:
> The example blob function at the end of the isosurface tutorial behaves
> differently at different scales, as can be seen in the example below. This is
> not a problem with the built-in blob object. I was wondering if anyone could
> provide a better formula for when using isosurfaces? Thanks!
Success!
I managed through trial and error to eliminate the variables that caused the
function to be affected by scale.
#declare Blob_threshold = clock;
#declare Blob_start = 1;
#declare fn_A = function { (pow(x+1*Scene_scale,2) + pow(y,2) + pow(z,2) -
pow(1.5*Scene_scale,2)) / pow(Scene_scale,2) };
#declare fn_B = function { (pow(x-1*Scene_scale,2) + pow(y,2) + pow(z,2) -
pow(1.5*Scene_scale,2)) / pow(Scene_scale,2) };
#declare fn_C = function { (Blob_threshold + Blob_start) }
#declare fn_D = function { pow(Blob_threshold, fn_A(x,y,z)) +
pow(Blob_threshold, fn_B(x,y,z)) - fn_C(x,y,z) };
#declare fn_E = function { max(0,min(1,fn_D(x,y,z))) };
The next step is to duplicate the results of the internal "blob" object.
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"SharkD" <nomail@nomail> wrote:
> Success!
>
> I managed through trial and error to eliminate the variables that caused the
> function to be affected by scale.
>
> ...
>
> The next step is to duplicate the results of the internal "blob" object.
I've compiled what I've learned about blobs, here:
http://www.geogebra.org/en/upload/files/english/Michael_Horvath/Metaballs/geogebra_metaballs.htm
I'd appreciate any insights you might have regarding this class of shapes.
-Mike
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