Taking a slice of a two dimensional array

[jing2178]

The source of this question is an unanswered question at stackoverflow but I believe is more mathematical than computational.

My question arising from this is.

You have a two dimensional array of numbers, each element of the array is represented by a square box. The boxes arranged into a rectangle with element (i,j) represented by the box in position (i,j). A 1-dimensional slice of the array is formed by drawing a line across the boxes, choosing boxes based on the position of the line crossing them and a vector formed on the basis of the chosen boxes.

This pdf file shows an issue arising following one attempt to do this.

Are there already recognised ways of doing this?
Are there better ways of doing this than the way I have tried?
Can the question be stated in a more succinct way?

Any help please.

 

[mfb]

All 3 methods are possible - and you could take alternating lower/upper pixel as well if "combined pixel" is not practical for some reason.
To make things even more complicated: The cell right of 2 is not hit in the center - you could try to take that into account as well.

Which method is best for you depends on the application.

 

[NemoReally]

http://en.wikipedia.org/wiki/Bresenham's_line_algorithm for example ...

 

[jing2178]

http://en.wikipedia.org/wiki/Bresenham's_line_algorithm for example ...

Thank you that is useful. As it is still a 2D representation of the line I think I will need to look at the projection of the line (and hence pixels) on boundary lines parallel to the axes.

 

[CellCoree]

I would approach this question by first clarifying the specific goal or purpose of taking a slice of a two-dimensional array. Is it to extract specific data points for further analysis? Is it for visualization purposes? Answering these questions can help determine the most appropriate method for taking the slice.

Next, I would explore existing literature and research on this topic to see if there are already established methods or algorithms for taking slices of two-dimensional arrays. It is possible that there are recognized ways of doing this that have been extensively studied and tested.

If there are no established methods or if the existing methods do not suit the specific needs of the question, then I would suggest experimenting with different approaches and comparing their effectiveness. This could involve varying the position and direction of the slicing line or using different criteria for choosing which boxes to include in the slice.

In terms of stating the question more succinctly, it may be helpful to clearly define the specific parameters and goals of the slice, such as the dimensions of the array, the position of the slicing line, and the desired output. This can help focus the research and provide a more concise question to be answered.

Overall, I would recommend further research and experimentation to find the most effective and efficient way to take a slice of a two-dimensional array for the specific purpose in question.