## -*- mode: tcl ; fill-column: 90 -*-
# # ## ### ##### ######## ############# #####################
## Generators -- Virtual Image - Origin map of polar/cartesian transforms
operator warp::2polar {
section generator virtual warp
example {width 11 height 11 | -matrix}
note Returns the origin map for a transformation to polar around the image center.
note The inverse transformation is created by "<!xref: aktive warp 2cartesian>."
note Inspired by <http://libvips.blogspot.com/2015/11/fancy-transforms.html>
ref http://libvips.blogspot.com/2015/11/fancy-transforms.html
note The result is designed to be usable with \
"<!xref: aktive op warp bicubic>" \
and its relatives.
note At the technical level the result is a 2-band image \
where each pixel declares its origin position.
# image configuration
uint width Width of the returned image
uint height Height of the returned image
body {
# identity as displacement base
set index [aktive image indexed width $width height $height]
# shift origin to the center
set dx [expr {$width /2.}]
set dy [expr {$height/2.}]
set cdelta [aktive image from band width $width height $height values $dx $dy]
set index [aktive op math sub $index $cdelta]
# rescale to fit
set scale [expr {min ($width, $height) / double($width)}]
set index [aktive op math1 scale $index factor [expr {2./$scale}]]
# switch to distance/angle representation
set index [aktive op cmath topolar $index]
# shift angles from [-pi,pi] to [0,2pi] -- offset +pi = 4*atan(1)
set offset [expr {4*atan(1)}]
set offset [aktive image from band width $width height $height values 0 $offset]
set index [aktive op math add $index $offset]
# scale angles to [0,height-1] - 2pi = 2*4*atan(1)
set ascale [expr {($height-1) / (8*atan(1))}]
set ascale [aktive image from band width $width height $height values 1 $ascale]
set index [aktive op math mul $index $ascale]
# done
return $index
}
}
operator warp::2cartesian {
section generator virtual warp
example {width 11 height 11 | -matrix}
note Returns the origin map for a transformation to cartesian \
from a polar around the image center.
note The inverse transformation is created by "<!xref: aktive warp 2polar>."
note Inspired by <http://libvips.blogspot.com/2015/11/fancy-transforms.html>
ref http://libvips.blogspot.com/2015/11/fancy-transforms.html
note The result is designed to be usable with \
"<!xref: aktive op warp bicubic>" \
and its relatives.
note At the technical level the result is a 2-band image \
where each pixel declares its origin position.
# image configuration
uint width Width of the returned image
uint height Height of the returned image
body {
# identity as displacement base
set index [aktive image indexed width $width height $height]
# scale the angles (in [0,height-1]) to [0,2pi]
set ascale [expr {(8*atan(1)) / ($height-1)}]
set ascale [aktive image from band width $width height $height values 1 $ascale]
set index [aktive op math mul $index $ascale]
# shift angles from [0,2pi] to [-pi,pi] -- offset -pi = 4*atan(1)
set offset [expr {-4*atan(1)}]
set offset [aktive image from band width $width height $height values 0 $offset]
set index [aktive op math add $index $offset]
# switch to cartesian
set index [aktive op cmath tocartesian $index]
# scale from fit
set scale [expr {min ($width, $height) / double($width)}]
set index [aktive op math1 scale $index factor [expr {$scale / 2.}]]
# shift origin out of center
set dx [expr {$width /2.}]
set dy [expr {$height/2.}]
set cdelta [aktive image from band width $width height $height values $dx $dy]
set index [aktive op math add $index $cdelta]
# done
return $index
}
}
##
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::return