How do you spherize an image?
To spherize an image, you must map it onto the surface of a sphere.
Like the wave effect, this requires a fair amount of calculations
First, it is necessary to agree on what 100 percent spherized means. One
hundred percent in our opinion means that the image is mapped onto exactly
half of a sphere, as if it were sliced down the middle. Fifty percent, by
this definition, would be the portion of the half-sphere cut at a height
half way between the base and the top. We will call the distance y.
Using fundamental trigonometry, we can derive the following equation for
the length of a central cross-section (a portion of a circle):
length = radius * pi * ( 180-2*arcsin( (100-percent)/100 ) ) / 180
The equation assumes that you are using degrees. Finding the length of the
circle segment is the hardest part, so you can breathe a sigh of relief :)
How does a circle help me?
It helps you to know how much longer the segment is than the height and width
of the square area that you are spherizing. Then, it is a matter of simply
stepping through each pixel index in the horizontal and vertical directions
of your original image. Find the distance from the center of the image using
the distance formula; distance = sqrt( (x1-xcenter)2 +
(y1-ycenter)2 ). If the pixel distance is more than the
radius, it is not affected. Otherwise, you can map it from its original
coordinates to an appropriate distance from the center and angle. The calculations
from this point on are comparatively simple.
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