how to design Siemens star pattern like on the image?

how to create Siemens star pattern using meshgrid and cart2pol?

Answer 1

[Jack]

This way you get a sinusoidal as well as a binary Siemens star, don't need the image processing toolbox and it's more intuitive:

r = 256;                                    %px, radius of star
cycles = 36;                                %number of spokes

[X,Y] = meshgrid(-r:r);
phy = atan2(Y,X) * cycles;                  %phase at each pixel
int = cos(phy);                             %relative intensity

sinStar = uint8(int*127.5 + 127.5);         %sinusoidal Siemens star

binStar = uint8(zeros(r*2+1));
binStar(int>=0) = 255;                      %binary Siemens star

Answer 2

[Image Analyst]

It should be straightforward to adapt my colorwheel demo, attached. Let me know if you can't figure it out. Also let me know if you want a binary one or a sinusoid one.

[Toto]

Thank you very much! But unfortunately I couldn't figure it out how to draw it b/w. And even less how to draw a sinoidal star.

Could you help me again? :)

Answer 3

[Toto]

I'm also searching for an answer. My idea was to plot a 3D-plot in polar coordinates with:

r=0:0,01:1     %Radius in 100 steps
th = (0:3:360)*pi/180      %theta in 120 steps
z = 255 * (½ + ½ sin((P*th))     %1/2 so that it is only  in the positive area, 255 for the grayscale

My idea then is to "look from above" so I only see the r-th-plane and save this picture.

Can anybody help us?

[Toto]

I used another way. Maybe you could help me with this one as well:

if true
  % [r,t]=meshgrid(0:1/10:10, (0:.5:360)*pi/180)
P = 20      % AUFFORDERUNG ZUM EINTIPPEN der Anzahl der schw Balken (=Anzahl Perioden)  
Z = 255 .* (0.5 + 0.5 .*sin(P*t)+(pi/2));
[X,Y,Z] = pol2cart(t,r,Z)
colormap(gray)
grid off 
star3d = surf(X,Y,Z,'linestyle','none') 
view([0 -90])
set(gca,'XTickLabel',[],'YTickLabel',[]); 
axis off 
end

If i save Z into a Picture I only get stripes (because it isn't in polar coordinates, right?). How can I do it? Any hint?

[DGM]

The easy way to avoid this problem is simply to build Z such that the Z array is structured WRT the X,Y arrays. The simple way to do that is to start by defining your grids (or vectors) in rectangular coordinates, and then basing your polar operations off of that. See @Jack's answer for an example.

Answer 4

[Jack]

This works for a raw binary Siemens Star. It is raw in the sense that there is no anti-aliasing so the edges are truly binary. It uses image processing toolbox function poly2mask to fill triangles given cartesian coordinates of the three corners (x0,y0) (x1,y1) (x2,y2). The result is 'logical' and can be saved and/or converted to a format of choice.

r = 256;                                    %px, radius of star
cycles = 36;                                %number of spokes (triangles)

a = 2*pi/cycles/2;                          %angle subtended by 1 spoke
[x,y] = pol2cart(-a/2:a:2*pi-a,r);          %coordinates of outer corners

x = [ x(1:2:end); x(2:2:end); zeros(1,length(x)/2) ] + r+1;  %(x1;x2;x0)
y = [ y(1:2:end); y(2:2:end); zeros(1,length(y)/2) ] + r+1;  %(y1;y2;y0)

star = poly2mask(x(:),y(:),2*r+1,2*r+1);    %fills triangles (5x5 subsampling)