In article <37EEAA92.6CB17750@peak.edu.ee> , Margus Ramst 
<mar### [at] peakeduee>  wrote:

> The manual gives a fairly complete overview of the blob object, complete with
> the falloff formula. Other than that, what mathemathics are you referring to?

Perhaps he is looking for how exactly blobs work. It is a bit technical but
maybe this (for the source code) helps:


/***************************************************************************
*
* FUNCTION
*
*   All_Blob_Intersections
*
* INPUT
*
*   Object      - Object
*   Ray         - Ray
*
* OUTPUT
*
*   Depth_Stack - Intersection stack
*
* RETURNS
*
*   int - true, if a intersection was found
*
* AUTHOR
*
*   Alexander Enzmann
*
* DESCRIPTION
*
*   Generate intervals of influence for each component. After these
*   are made, determine their aggregate effect on the ray. As the
*   individual intervals are checked, a quartic is generated
*   that represents the density at a particular point on the ray.
*
*   Explanation for spherical components:
*
*   After making the substitutions in MakeBlob, there is a formula
*   for each component that has the form:
*
*      c0 * r^4 + c1 * r^2 + c2.
*
*   In order to determine the influence on the ray of all of the
*   individual components, we start by determining the distance
*   from any point on the ray to the specified point.  This can
*   be found using the pythagorean theorem, using C as the center
*   of this component, P as the start of the ray, and D as the
*   direction of travel of the ray:
*
*      r^2 = (t * D + P - C) . (t * D + P - C)
*
*   we insert this equation for each appearance of r^2 in the
*   components' formula, giving:
*
*      r^2 = D.D t^2 + 2 t D . (P - C) + (P - C) . (P - C)
*
*   Since the direction vector has been normalized, D.D = 1.
*   Using the substitutions:
*
*      t0 = (P - C) . (P - C),
*      t1 = D . (P - C)
*
*   We can write the formula as:
*
*      r^2 = t0 + 2 t t1 + t^2
*
*   Taking r^2 and substituting into the formula for this component
*   of the Blob we get the formula:
*
*      density = c0 * (r^2)^2 + c1 * r^2 + c2,
*
*   or:
*
*      density = c0 * (t0 + 2 t t1 + t^2)^2 +
*                c1 * (t0 + 2 t t1 + t^2) +
*                c2
*
*   Expanding terms and collecting with respect to "t" gives:
*
*      t^4 * c0 +
*      t^3 * 4 c0 t1 +
*      t^2 * (c1 + 2 * c0 t0 + 4 c0 t1^2)
*      t   * 2 (c1 t1 + 2 c0 t0 t1) +
*            c2 + c1*t0 + c0*t0^2
*
*   This formula can now be solved for "t" by any of the quartic
*   root solvers that are available.
*
* CHANGES
*
*   Jul 1994 : Added code for cylindrical and ellipsoidical blobs. [DB]
*
*   Oct 1994 : Added code to convert polynomial into a bezier curve for
*              a quick test if an intersection exists in an interval. [DB]
*
*   Sep 1995 : Added code to avoid numerical problems with distant blobs.
[DB]
*
***************************************************************************/



____________________________________________________
Thorsten Froehlich, Duisburg, Germany
e-mail: tho### [at] trfde

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