4.4 Rectangular Coordinate Transformation
The first entries are rotation values around the X, Y, and Z axes. Think
of your starting image as a flat map: the X value tilts the bottom of
your monitor towards you by X degrees, the Y value pulls the left side
of the monitor towards you, and the Z value spins it counter-clockwise.
Note that these are NOT independent rotations: the image is rotated
first along the X-axis, then along the Y-axis, and finally along the Z-
axis. Those are YOUR axes, not those of your (by now hopelessly skewed)
monitor. All rotations actually occur through the center of the original
image. Rotation parameters are not used when a ray tracing option has
been selected.
Then there are three scaling factors in percent. Initially, leave the X
and Y axes alone and play with Z, now the vertical axis, which
translates into surface "roughness." High values of Z make spiky, on-
beyond-Alpine mountains and improbably deep valleys; low values make
gentle, rolling terrain. Negative roughness is legal: if you're doing an
M-set image and want Mandelbrot Lake to be below the ground, instead of
eerily floating above, try a roughness of about -30%.
Next we need a water level -- really a minimum-color value that performs
the function "if (color < waterlevel) color = waterlevel". So it plots
all colors "below" the one you choose at the level of that color, with
the effect of filling in "valleys" and converting them to "lakes."
Now we enter a perspective distance, which you can think of as the
"distance" from your eye to the image. A zero value (the default) means
no perspective calculations, which allows use of a faster algorithm.
Perspective distance is not available if you have selected a ray tracing
option.
For non-zero values, picture a box with the original X-Y plane of your
flat fractal on the bottom, and your 3D fractal inside. A perspective
value of 100% places your eye right at the edge of the box and yields
fairly severe distortion, like a close view through a wide-angle lens.
200% puts your eye as far from the front of the box as the back is
behind. 300% puts your eye twice as far from the front of the box as
the back is, etc. Try about 150% for reasonable results. Much larger
values put you far away for even less distortion, while values smaller
than 100% put you "inside" the box. Try larger values first, and work
your way in.
Next, you are prompted for two types of X and Y shifts (now back in the
plane of your screen) that let you move the final image around if you'd
like to re-center it. The first set, x and y shift with perspective,
move the image and the effect changes the perspective you see. The
second set, "x and y adjust without perspective", move the image but do
not change perspective. They are used just for positioning the final
image on the screen. Shifting of any type is not available if you have
selected a ray tracing option.