Parametric distance of a line in a grid (Line Integral Convolution)

[Avatrin]

Hi, the above image is from the Line Integral Convolution paper by Cabral and Leedom. However, I am having a hard time implementing it, and I am quite certain I am misreading it. It is supposed to give me the distances of the lines like in the example below, but I am not sure how it can. First of all, it looks like sbottom=stopsbottom=stop and sright=sleftsright=sleft. Also, it looks like the answer will always be zero since ⌊Pi⌋−Pi⌊Pi⌋−Pi will always be negative for an image. Any advice on how I can make progress?

My current implementation is:

def ds(x,y): Vxy = V(x,y) s_top=max((floor(y)-y)/Vxy[1],0) s_bottom=max((floor(y)-y)/Vxy[1],0) s_right= max((floor(x)-x)/Vxy[0],0) s_left =max((floor(x)-x)/Vxy[0],0) return(min([s_top,s_bottom,s_right,s_left]))

And, it always returns 0 (yes, I know I have ignored the instance in which V is parallel to e, but first I have to fix the issues I wrote about above).

 

[Future Bruno]

To solve the issues you mentioned, it is important to note that the s values refer to the distances along the vector field V, not the distances between pixels. Your implementation likely isn't working because you are computing the distances between pixels, not along the vector field. Also, it is important to remember that the s values should always be positive, not negative, so your implementation should use max instead of min. This ensures that all distances are positive, and therefore will always be greater than zero.Finally, it is important to note that the s values refer to the distances starting from the current pixel, so the equation should be (ceil(y)-y)/Vxy[1] rather than (floor(y)-y)/Vxy[1].Therefore, a properly implemented version of the line integral convolution should look something like this:def ds(x,y): Vxy = V(x,y) s_top=max((ceil(y)-y)/Vxy[1],0) s_bottom=max((floor(y)-y)/Vxy[1],0) s_right= max((ceil(x)-x)/Vxy[0],0) s_left =max((floor(x)-x)/Vxy[0],0) return(min([s_top,s_bottom,s_right,s_left]))