1. Special effects
Jen-Chang Liu, Spring 2005

2. Polar coordinates 極座標 r θ x y
(x, y) y x
Origin:

3. MATLAB implementation
Cartesian coordinate -> polar coordinate
polar coordinate -> Cartesian coordinate
rows=256;
cols=256;
ox=ceil((rows+1)/2);
oy=ceil((cols+1)/2);
[y,x]=meshgrid([1:cols]-oy, [1:rows]-ox);
r=sqrt(x.^2+y.^2);
theta=atan2(y,x);
x2=round(r.*cos(theta))+ox;
y2=round(r.*sin(theta))+oy;

4. Pixelation effects 像素化
mod operation
Radial pixelation
% to Cartesian coordinate
xx=round(x2)+ox;
xx(find(xx>rows))=rows;
xx(find(xx<1))=1;
yy=round(y2)+oy;
yy(find(yy>cols))=cols;
yy(find(yy<1))=1;
for i=1:rows
for j=1:cols
f2(i,j)=fg(xx(i,j), yy(i,j));
end;
x=1:12
mod(x,4)
x-mod(x,4)
f=imread(‘flower.tif’);
fg=rgb2gray(f);
[rows cols]=size(fg);
% polar coordinate
r2=r-mod(r, 5);
theta2=theta-mod(theta, 0.087);
Ex.1: Try other mod parameters

5. Ripple effects Produce repeat patterns
Ripples in the Cartesian coordinate
x=1:12
x+mod(x,4)
[y,x]=meshgrid(1:cols,1:rows);
y2=y+mod(y,32);
y2(find(y2<1))=1;
y2(find(y2>cols))=cols;
for i=1:rows
for j=1:cols
ripples(i,j)=fg(x(i,j), y2(i,j));
end;
Ex.2: produce ripples
in the polar coordinate
(to r component)

6. Eyefish effects In the polar coordinate R=max(r(:)); r=r.^2/R;
Ex. 3: Produce the eyefish effect

7. Other effects Twirl Θ’(i,j) =θ(i,j)+r(i,j)/K
Ex. 4: Produce the Twirl effect with K=100