gforge(1) gforge(1)
May 18 1996 ver 1.3
NAME
gforge - fractal forgery of landscapes and textures
SYNOPSIS
gforge [-mesh size] [-dimension dim [-adim dim scale]] [-power factor]
[-limit low high] [-peak xpos ypos] [-craters [density
height]] [-seed seed] [-name filename] [-type
TGA|PGM|PG8|OCT|MAT|PNG] [-bpfilter cent_freq Q] [-brfilter
cent_freq Q] [-lpfilter cut_freq Order] [-hpfilter cut_freq
Order] [-version]
DESCRIPTION
gforge generates a landscape texture by "random fractal forgery," the
term coined by Richard F. Voss of the IBM Thomas J. Watson Research
Center for seemingly realistic pictures of natural objects generated
by simple algorithms embodying randomness and fractal self-similarity.
The techniques used by gforge are essentially those given by Voss[1],
particularly the technique of spectral synthesis explained in more de-
tail by Dietmar Saupe[2]. The source code (and this man page) was
mostly taken from the "ppmforge" module[3] in the PBMPLUS package of
graphics utilities. The gforge "crater" option was contributed by
Heiko Eissfeldt <heiko@colossus.escape.de>.
The generation of a landscape begins with the preparation of an array
of random data in the frequency domain. The size of this array, the
"mesh size," can be set with the -mesh option; the larger the mesh the
more realistic the pictures but the calculation time and memory re-
quirement increases as the square of the mesh size. The degree of
roughness, which you can specify with the -dimension option, deter-
mines whether the resulting terrain is rolling hills or jagged moun-
tins. As the dimension value is increased, more high frequency com-
ponents are added into the random mesh. (Note that this number does
NOT directly correspond to a conventional 'fractal' dimension, eg. a
Hausdorff- Besicovich dimension. All gforge surfaces have a 'fractal
dimension' near 2.0.)
You may apply a band-pass and/or band-reject filter to the frequency
data, specifying the normalized [0..1] center frequency and Q (sharp-
ness) of each filter. Lowpass and highpass filters are also available.
Then an inverse Fourier transform is performed upon it, which converts
the original random frequency domain data into spatial amplitudes. We
scale the real components that result from the Fourier transform into
numbers from 0 to 1 associated with each point on the mesh. You can
further modify this number by applying a "power law scale" to it with
the -power option. Unity scale leaves the numbers unmodified; a power
scale of 0.5 takes the square root of the numbers in the mesh, while a
power scale of 3 replaces the numbers in the mesh with their cubes.
Powers less than 1 yield landscapes with vertical scarps that look
like glacially-carved valleys (with -limit -1.0 1.0); powers greater
than one make fairy-castle spires (which require large mesh sizes for
best results). Craters, if that option is selected, are added at this
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gforge(1) gforge(1)
May 18 1996 ver 1.3
point. After these calculations, we have an array of the specified
size containing numbers that range from 0 to 1. Six output formats are
available as described below.
Invoking the program with no options writes a 128x128 TGA file called
"output.tga" which looks like a somewhat bumpy hillside (in POV any-
way... being a special format, it will look like green speckled noise
in a standard viewer). "gforge -help" tells you briefly what options
are available. You can abbreviate keywords also. Try
gforge -t pg8 -pow 1 -dim 4 -n sand.pgm
for an image of sand, or
gforge -type tga -pow 1.8 -dim 2.4 -m 400 -n mountain.tga
for a mountain range to render with POV. Getting your landscape to
look just right will require playing around with the -dimension and
-power specs.
OPTIONS
-mesh meshsize
The size of the (n x n) IFFT (inverse fast-fourier transform) ma-
trix. To prevent the IFFT from becoming a _slow_ fourier
transform, it is suggested that the mesh size be a power of two,
but you can choose any number you want. If it happens to have a
large prime factor, or be itself a prime number, the IFFT calcu-
lation will be considerably slowed. The default meshsize is 128.
Note that a mesh size of 1024 will require just over 8 megabytes
of memory.
-dimension dim
Sets the dimension to the specified dim, which may be any float-
ing point value between 0 and 3. Higher dimensions create more
``chaotic'' images, which require higher resolution output and a
larger FFT mesh size to look good. If no dimension is specified,
2.15 is used. To be precise, the initial mesh is filled with
gaussian noise of amplitude (1/f)^(4 - dim). Accordingly, dim=4
would give you pure white noise.
-adim ad ascale
Adds an additional component of noise in the frequency domain
with the dimension ad and amplitude (scaled relative to the first
specified dimension) of ascale. You can add up to nine addition-
al dimensions, although one or two is almost certainly enough.
Often you don't need any at all. An example might be to have
large rolling hills of dim 1.7, with a touch of higher frequen-
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gforge(1) gforge(1)
May 18 1996 ver 1.3
cies for a rougher texture:
gforge -dim 1.7 -adim 2.0 0.1 -pow 1.8
-bpfilter center-freq Q
-brfilter center-freq Q
Apply a band-pass (bpfilter) and/or band-reject (brfilter) to the
frequency data before the inverse FFT. Center-frequency should be
between 0.0 and 1.0. A band-pass filter at f=0 is just a low-pass
filter, and at f=1.0 it is a high-pass filter. Q ("quality fac-
tor") = 0.5 is a broad filter, Q=20 is narrow. Try these options
to see their effects.
-lpfilter cut-freq Order
-hpfilter cut-freq Order
Apply a low-pass or high-pass filter to the frequency data.
Cutoff-frequency, between 0 and 1, is the frequency at which the
response drops by half. Order may be any positive value; 1 is a
soft filter, 1000 is a brick-wall filter.
-power exponent
Raise the elevation powers to the specified exponent, giving a
nonlinear scaling effect, useful for some purposes.
-limit min max
Only relevant if a -power exponent other than 1.0 is selected.
Scales terrain to the range [ min- max ] prior to raising to a
power. Default is [0.0 - 1.0]. See the sample script/batch file
for example usages.
-crater density height
Add craters to the landscape. The optional density parameter con-
trols how many there are. The default 1.0 gives you moderate
cratering, but you can specify any positive value. Crater height
defaults to 1.0, for what I felt were reasonable looking craters.
This is the vertical crater height relative to the underlying
landscape scale, and will need to be changed depending on how you
scale the vertical axis of your heightfield when you render it.
As height goes to zero, the craters dwindle in height and disap-
pear. Crater radius follows a power law distribution.
-wrapoff
Turn off the default wraparound of craters. The underlying
landscape is always tilable, but with this option it will become
farther and farther from being tilable as more craters are added.
I'm not sure if this is actually useful. Note: cannot be used
with the "peak" option.
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gforge(1) gforge(1)
May 18 1996 ver 1.3
-peak xpos ypos
You can specify the location of the largest value (highest peak)
in the image as a fraction of the image height and width. For ex-
ample,
gforge -dim 1.5 -pow 3 -peak 0.5 0.5 -name mtn.tga
puts the highest peak in the center of the image. This is most
useful for lower values of dim where there is only one or a few
broad maxima; at -dim 2 or above it tends to make less differ-
ence. If you don't specify it, it's somewhere random.
-seed seed
You can give it a random number seed, otherwise it chooses one
based on the current time from the system clock. If you use the
same seed, you get the same image every time.
-name filename
If you don't specify it, it's "output.tga" (or "output.xxx", the
extension depending on which file type is being written). Exist-
ing files with that name are overwritten without warning.
-type TGA|PGM|PG8|OCT|MAT|PNG
Six options, default is TGA. TGA and PGM are 16-bit formats, and
PG8 is just PGM 8-bit binary format. PG8 , will produce a stan-
dard PGM file suitable for viewing in a standard graphic viewer
to check out what the options are doing to your landscape. OCT
produces an ascii file compatible with Octave v1.1.1, a matrix-
math package similar in function to Matlab. MAT produces a 32-
bit floating-point file in the Matlab binary format. PNG gen-
erates 16-bit PNG (portable network graphics) greyscale, which at
the time of this writing is a very new format, but gaining in
support.
Flags may be abbreviated.
BUGS
tiling 'feature'
Because the FFT operates on periodic functions, the opposite
edges of the image will always match up. If it turns out you want
to cover a large area by tiling these textures together, this is
just what you want (ie, it's a FEATURE... in fact one way to gen-
erate useful tilable textures is by taking the FFT of any in-
teresting picture, filtering a bit, and doing the inverse
transform.) If you don't want periodicity, just generate a larger
image than you need and use some smaller fraction of it. The "-
wrapoff" option applies only to craters crossing the page edge.
The "-peak" and "-wrapoff" options cannot be used simultaneously.
fixed output sizes
The output is always a square grid. If you want a different as-
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gforge(1) gforge(1)
May 18 1996 ver 1.3
pect ratio, you should use another image processing package to
crop or rescale as appropriate. Unfortunately most of them don't
support 16 bits of precision. John Cristy's ImageMagick 3.6.5 can
be compiled to support 16-bit PNG, and Andreas Dilger's patch to
POV-Ray 2.2 supports PNG input, output, imagemaps, and height-
fields. POV-Ray 3.0 supports PNG.
http://www.wizards.dupont.com/cristy/ImageMagick.html
http://www-mddsp.enel.ucalgary.ca/People/adilger/povray
SEE ALSO
ppmforge(1), ppm(5), povray(1)
[1] Voss, Richard F., ``Random Fractal Forgeries,'' in Earnshaw et.
al., Fundamental Algorithms for Computer Graphics, Berlin:
Springer-Verlag, 1985.
[2] Peitgen, H.-O., and Saupe, D. eds., The Science Of Fractal Im-
ages, New York: Springer Verlag, 1988.
[3] Walker, John, "ppmforge.c" in Jef Poskanzer's PBMPLUS raster
toolkit, 1991. <kelvin@fourmilab.ch> <http://www.fourmilab.ch/>
AUTHORS
John Beale Heiko Eissfeldt
1745 Webster St. <heiko@colossus.escape.de>
Palo Alto, CA 94301
-----------------------------------------------------------------
beale@best.com http://jump.stanford.edu:8080/~beale
http://www.best.com/~beale http://chomsky.stanford.edu/~beale
The gforge program is copyright (c) 1995 by John P. Beale, and the
crater code is copyright (c) 1995 Heiko Eissfeldt. This program comes
with ABSOLUTELY NO WARRANTY. Permission is granted to redistribute the
full source code under the terms of the GNU General Public License,
version 2. For more details, see the GPL.
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