How do I store the Coordinates of Lines Intersecting a Grid?

Hello,

I would like to first create a grid that is 5(x-direction) by 25 (y-direction), and each individual box in the grid is basically 1 X 1. Then I want to create lines over this grid, and store the coordinates of where the lines intersect the grid. So, for example, the intersections of where one line intersects the grid would be one matrix, and the next line would be another matrix. Is this even possible? Thank you.

Ashley

[Star Strider]

If the lines drawn on the grid are straight, it’s probably relatively easy.

[Ashley]

Hello, Yes, the lines are straight.

Ashley

Answer 1

[Star Strider]

This should get you started:

x = 0:5;                            % X-range
y = 0:25;                           % Y-range

lxmb = @(x,mb) mb(1).*x + mb(2);    % Line equation: y = m*x+b

m = 2;                              % Slope (or slope array)
b = 1;                              % Intercept (or intercept array)
mb = [m b];                         % Matrix of [slope intercept] values

L1 = lxmb(x,mb);                    % Calculate Line #1 = y(x,m,b)
hix = @(y,mb) [(y-mb(2))./mb(1);  y];   % Calculate horizontal intercepts
vix = @(x,mb) [x;  lxmb(x,mb)];     % Calculate vertical intercepts

hrz = hix(x(2:end),mb)'             % [X Y] Matrix of horizontal intercepts
vrt = vix(y(1:6),mb)'               % [X Y] Matrix of vertical intercepts

figure(1)                           % Draw grids & plot lines
plot(repmat(x,2,length(x)), [0 length(y)-1])    % Vertical gridlines
hold on
plot([0 length(x)-1], repmat(y,2,length(y)))    % Horizontal gridlines
plot(x, L1)                         % Plot more lines here (additional ‘plot’ statements)
hold off
axis equal

It creates the grid, plots the first line, and gives one matrix of [x y] coöridinates for the horizontal grid intercepts, and another one for the vertical grid intercepts. It is relatively simple to use a loop to generate more lines and grid intercept matrices with a matrix of [m b] values.

Have fun!

[Ashley]

Hello, Thank you so much for answering! Your code works great! I just have one additional problem. Is it possible to give the coordinates in the order that the line intersects, going left to right? So for example, the line might intersect a vertical grid line first, and then it might intersect a horizontal line second, and I would want to keep that order in a matrix. Is this possible? Thank you very much!

Ashley

[Star Strider]

My pleasure!

It’s an interesting problem, actually.

To get the combined arrays sorted in ascending order and without repeats, add these two lines just after the assignments for hrz and vrt:

hvix = [hrz; vrt];                 % Concatanated ‘hrz’ and ‘vrt’ arrays
srtd = unique(hvix,'rows');        % Remove repeats and sort ascending by ‘x’

The srtd array is the one you want.

[Albert]

Hi, Star Strider

There might be a small mistake in your code:

hrz = hix(x(2:end),mb)' % [X Y] Matrix of horizontal intercepts

vrt = vix(y(1:6),mb)' % [X Y] Matrix of vertical intercepts

should it be like:

hrz = hix(y(1:6),mb)'

vrt = vix(x(2:end),mb)'

Thank you