## -*- mode: tcl ; fill-column: 90 -*-
# # ## ### ##### ######## ############# #####################
## Generators -- Virtual Image - Origin map of a wobble/ripple effect
operator warp::wobble {
section generator virtual warp
example {width 11 height 11 | -matrix}
note Returns the origin map for a wobble effect around the \
specified __center__, with base __amplitude__, __frequency__, \
__chirp__, and __attenuation__ powers.
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 the \
"<!xref: aktive op warp bicubic>" operation 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
import wobble-config.tcl
body {
if {[llength $center]} {
lassign $center dx dy
} else {
set dx [expr {$width /2.}]
set dy [expr {$height/2.}]
}
# identity as displacement base
set index [aktive image indexed width $width height $height]
# shift origin to desired wobble center
set cdelta [aktive image from band width $width height $height values $dx $dy]
set center [aktive op math sub $index $cdelta]
# switch to distance/angle representation in prep for the distance modulation
set polar [aktive op cmath topolar $center]
set dist [aktive op cmath real $polar]
set angle [aktive op cmath imaginary $polar]
# modulate the distance according to the formula
# attenuator -- (1+d)^attenuation
set attenuate [aktive op math1 shift $dist offset 1]
if {$attenuation != 1} {
set attenuate [aktive op math1 pow $attenuate exponent $attenuation]
}
# envelope -- amplitude / attenuate -- amplitude / (1+d)^attenuation
set envelope [aktive op math1 reciproc-scale $attenuate factor $amplitude]
# chirp factor -- dist^chirp
if {$chirp != 1} {
set dist [aktive op math1 pow $dist exponent $chirp]
}
# wave -- sin (frequency * dist^chirp)
set wave [aktive op math1 sin [aktive op math1 scale $dist factor $frequency]]
# assemble the pieces -- wave * envelope
# -- sin (frequency * dist^chirp) * amplitude / (1+d)^attenuation
set dist [aktive op math mul $wave $envelope]
# switch back to cartesian representation for proper displacement
set polar [aktive op cmath cons $dist $angle]
set deltas [aktive op cmath tocartesian $polar]
# and generate the origin map from the displacements
aktive op math add $index $deltas
}
}
##
# # ## ### ##### ######## ############# #####################
::return