Math problem, formula for finding circled points

ID:1067544
 
Nov 27 2012, 12:01 pm


I am trying to figure out the formula for finding where my grey lines intersect with the green box (circled in red). This would be for any grid or coordinate system. Orange represents a single point within a set of points and green represents the coordinate system minimum and maximum point range. The grey lines represent cardinal and diagonal direction. We are trying to find the formula that calculates at which point each direction would intersect maximum or minimum bounds based on a direction value from a single position within the bounds.
Nov 27 2012, 1:28 pm (Edited on Nov 27 2012, 1:52 pm)
I was about to write about Pythagoras but I believe there is a much simpler solution. Any diagonal that touches the boundary can be made into a right triangle with both "flat" sides equal, one of them being the border itself.

All you have to do is get the distance between you and the boundary, then subtract that from your coordinate in the other direction. So if you measure the distance to the boundary north, you would subtract that from your X

To figure out which side to use you could test the sum of your x and y coordinates for northwest/southeast diagonals, and for the other direction...wait I'm confused. I have to run to the store...

:P

EDIT: Okay I'm back and I figured it out. For northeast/southwest diagonals, just test if x > y or if x < y. Here's a quick diagram to show what I mean:

Nov 27 2012, 2:00 pm
It has to work for any point within the boundaries. So if you have 1,1 to 10,10 and you're at 7,7 the values will be different than if you were centered at point 4,6
Nov 27 2012, 5:19 pm
Alright well this is what I came up with:

mob
    var
        ne_x
        ne_y
        
        se_x
        se_y
        
        nw_x
        nw_y
        
        sw_x
        sw_y


proc
    Calculate_Intercepts(mob/source)
    
        if(source.y > source.x)             //For northeast and southwest diagonals, coordinates directly tell which side of the center
            source.ne_y = world.maxy        //diagonal we are on. When Y is greater than X, intercepts always hit the north and west 
            source.ne_x = source.x + (world.maxy - source.y)    //boundaries.
            
            source.sw_y = source.y - source.x + 1
            source.sw_x = 1
            
        else if(source.y < source.x)
            source.ne_y = source.y + (world.maxx - source.x)
            source.ne_x = world.maxx
            
            source.sw_y = 1
            source.sw_x = source.x - source.y + 1
        
        else    //x and y are equal
            source.ne_y = world.maxy
            source.ne_x = world.maxx
            
            source.sw_y = 1
            source.sw_x = 1
        
        //----------------------------------------------------------//
        
        var/sum = source.x + source.y - 1
        
        if(sum > world.maxx)    //For northwest and southeast diagonals, the coordinates have to be added together.
            source.nw_y = world.maxy
            source.nw_x = source.x - (world.maxy - source.y)
            
            source.se_y = source.y - (world.maxx - source.x)
            source.se_x = world.maxx
        
        else if(sum < world.maxx)
            source.nw_y = sum
            source.nw_x = 1
            
            source.se_y = 1
            source.se_x = sum
        
        else
            
            source.nw_y = world.maxy
            source.nw_x = 1
            
            source.se_y = 1
            source.se_x = world.maxx


I also made a little demo if you want to see it in action:

http://wikisend.com/download/166516/intercepts_src.zip