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I'll put this here for now.
Can't use sci-hub from where I'm currently at.
Likely going to want more journal articles in the future, so I'll just start a
thread.
Stress Analysis of Heated Complex Shapes
Richard H. Gallagher
Joseph Padlog
P. P. Bijlaard
30 April 1962
journal article
Published by American Institute of Aeronautics and Astronautics (AIAA) in ARS
Journal
Vol. 32 (5) , 700-707
https://doi.org/10.2514/8.6128
- BE
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Related request:
What is the earliest version of POV-Ray that has the "Pyramid Vector",
located (presently) in povray/source/core/material/normal.cpp?
/*****************************************************************************
* Local constants
******************************************************************************/
static const Vector3d Pyramid_Vect [4]= { Vector3d( 0.942809041,-0.333333333,
0.0),
Vector3d(-0.471404521,-0.333333333,
0.816496581),
Vector3d(-0.471404521,-0.333333333,-0.816496581),
Vector3d( 0.0 , 1.0 ,
0.0) };
/*****************************************************************************
Thanks,
- BE
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hi,
"Bald Eagle" <cre### [at] netscape net> wrote:
> Related request:
>
> What is the earliest version of POV-Ray that has ...
if it helps, the early sources up to v3.62 are available via FTP:
<ftp.povray.org/pub/povray/Old-Versions>
regards, jr.
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"jr" <cre### [at] gmailcom> wrote:
> if it helps, the early sources up to v3.62 are available via FTP:
> <ftp.povray.org/pub/povray/Old-Versions>
It did.
In version 3.1d, 1998, in file NORMAL.C, created 6/3/1998 at 7:05 pm,
static CONST
VECTOR Pyramid_Vect [4]= {{ 0.942809041,-0.333333333, 0.0},
{-0.471404521,-0.333333333, 0.816496581},
{-0.471404521,-0.333333333,-0.816496581},
{ 0.0 , 1.0 , 0.0}};
first appears, with no author cited except for "The POV Team".
No citation, no author, no comments, just magic numbers.
It is then implemented in the function
void Perturb_Normal(VECTOR Layer_Normal, TNORMAL *Tnormal, VECTOR EPoint)
with the following comment:
/* Note, even though DELTA and Pyramid_Vect are constants, we may later
make DELTA a user-defined parameter. Good optimising compilers
should merge the constants anyway. */
I was able to dig back in the literature to an article by Gallagher et al from
1962 concerning Finite Element Analysis (FEM) which is the earliest that I was
able to find documenting this method of calculating a gradient with sample
points arranged in a tetrahedron.
The method used in our source has a vector pointing in the cardinal y-direction,
which could possibly introduce bias that might not be present when using all
off-axis vectors.
- BE
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