Right now, I am having trouble skewing a radial gradient that is based on sqrt(x^2+y^2). What I would like is a smooth skewing much in the same way that Illustrator have, but for pixel image processing related to distortion.
My attempt to apply a skewed radial gradient for distortion can be seen below:
Description of filter - Use Spiral gradient for finding the x-location of image, and radial gradient for finding y-location.
Then use the values that are found in order to distort the image.
Scripting Language - G'MIC-QT
x is x-location of pixel within for loop
y is y-location of pixel within for loop
w is width
h is height
foo:
r2dx 200%,3#Resize Image using linear interpolation. Used for subpixel processing#
f "begin(
sd=max(w,h)/min(w,h); #Divide the biggest side by the smallest size.#
sx=w>h?sd:1; #Find x-scale to scale x-coordinate#
sy=w>h?1:sd; #Find y-scale to scale y-coordinate#
ang=pi*(0/180); #Convert angle to radian. 0 next to /180 is the function angle.#
slx=2; #Scale of x-coordinate#
sly=2; #Scale of y-coordinate#
skew_x=.15; #Offset x-skewing#
skew_y=.15; #Offset y-skewing#
skew_ang=atan2(skew_y,skew_x)+pi/2; #Find skew angle#
skew_fact=sqrt(skew_x^2+skew_y^2); #Find multiplier for skewing#
srot_x(a,b)=a*cos(skew_ang)-b*sin(skew_ang); #Function for rotating the skewing function#
srot_y(a,b)=a*sin(skew_ang)+b*cos(skew_ang); #Function for rotating the skewing function#
rot_x(a,b)=a*cos(ang)-b*sin(ang); #Distortion Angle Function#
rot_y(a,b)=a*sin(ang)+b*cos(ang); #Distortion Angle Function#
);
XX=(x/w-.5)*2*sx*slx; #Convert x into -1,1 range if image is a square#
YY=(y/h-.5)*2*sy*sly; #Convert y into -1,1 range if image is a square#
SXX=(x/w-.5)*2*sx*slx; #Convert x into -1,1 range if image is a square. Used for skewing!#
SYY=(y/h-.5)*2*sy*sly; #Convert y into -1,1 range if image is a square. Used for skewing!#
xx=rot_x(XX,YY); #Rotation of function#
yy=rot_y(XX,YY); #Rotation of function#
sxx=srot_x(SXX,SYY)*sx*slx; #Rotation of skewing function#
syy=srot_y(SXX,SYY)*sy*sly; #Rotation of skewing function#
skew_atan=atan2(abs(sxx),syy)*skew_fact*sqrt(sxx^2+syy^2);#Generate Skewing Function#
radial=sqrt(xx^2+yy^2)*1+skew_atan; #Combine radial gradient with skewing Function#
if(1,sur_atan=1-(atan2(xx,yy)+pi)/(2*pi);,sur_atan=(atan2(xx,yy)+pi)/(2*pi););#Determine direction of spiral#
es=(sur_atan+radial*1)*1; #Part 1 of Spiral Gradient#
es=es-floor(es); #Part 2 of Spiral#
if(0,es=(es>.5?1-es:es)*2;); #If true, then spiral is continuous, else spiral is non-continuous#
i((es^1)*w,radial*h,z,c,2,3);#i(x-location,y-location,z-location,channel_numbers,interpolation,boundary); The i means image.#
"
r2dx 50%,3 #Resize Image using linear interpolation. Used for subpixel processing#
Target Image
The result using this code
If anything isn't clear, let me know.
I have finally found my solution to the problem. What I did is to make functions to rotate x-coordinate,y-coordinate,boundary box size, and use x-coordinate and y-coordinate to influence the skew factor.
Here's the current G'MIC-QT code for reference. It's hard to explain what I did though.
r2dx 200%,3
f "begin(
sd=max(w,h)/min(w,h);
sx=w>h?sd:1;
sy=w>h?1:sd;
ang=pi*(0/180);
slx=10;
sly=10;
skew_x=.5;
skew_y=.5;
nw=abs(w*sin(ang))+abs(h*cos(ang));
nh=abs(w*cos(ang))+abs(h*sin(ang));
rot_x(a,b)=a*cos(ang)-b*sin(ang);
rot_y(a,b)=a*sin(ang)+b*cos(ang);
);
xx=(x/w-.5)*sx;
yy=(y/h-.5)*sy;
mx=((rot_x(xx,yy)/sx)+.5)*w;
my=((rot_y(xx,yy)/sy)+.5)*h;
nx=mx-abs(skew_x)*rot_x(xx,yy)*(skew_x>0?nw-mx:mx);
ny=my-abs(skew_y)*rot_y(xx,yy)*(skew_y>0?nh-my:my);
xx=(nx/w-.5)*2*slx;
yy=(ny/h-.5)*2*sly;
radial=sqrt(xx^2+yy^2);
if(1,sur_atan=1-(atan2(xx,yy)+pi)/(2*pi);,sur_atan=(atan2(xx,yy)+pi)/(2*pi););
es=(sur_atan+radial*1)*1;
es=es-floor(es);
if(0,es=(es>.5?1-es:es)*2;);
i((es^1)*w,radial*h,z,c,2,3);
"
r2dx 50%,3
Here's the result: