zoukankan      html  css  js  c++  java
  • How to determine which grid cells a line segment passes through?

    https://cn.mathworks.com/matlabcentral/answers/230155-how-to-determine-which-grid-cells-a-line-segment-passes-through

    How to determine which grid cells a line segment passes through?

    Similar to my previous question, lets say you have a grid with cells in the x-direction from [1:5] and in the y-direction from [1:5] (5 x 5 grid). Now lets say you have two points on the grid: (0.35, 2.65) and (4.2,4.73).

    Is there a simple way to determine which grid cells the line connecting those two points passes through (and the distances of each line segment)?

    It is very easily visually to see which cells the line passes through (see figure below). Clearly the line segment passes through cells B1, C1, C2, D2, D3, E3 and E4.

    Determining the distances of each line segment through each cell would be more difficult by hand.

    I have currently solved the problem by finding the slope and intercept of the line, then determining the intercepts of the line with the grid cell lines. Using this, I can determine the distance of each line segment. Then, to find which cell the line segment falls in, I have to find the centre point of each grid cell and the midpoint of each line segment and do a for loop to determine the minimum distance between each line segment and each cell centre.

    Is there a more elegant way to solve this problem? Obviously when dealing with multiple lines and/or a large grid, this will become much more time intensive.

    This brings back memories of How do I store the Coordinates of Lines Intersecting a Grid? I refer you to it for the description and documentation.

    I later updated the code for it but didn’t post it. The updated code is:

    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 = -5;                             % Slope (or slope array)
    b = 15;                             % 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
    
    hvix = [hrz; vrt];                 % Concatanated ‘hrz’ and ‘vrt’ arrays
    exbd = find( (hvix(:,2) < 0) | (hvix(:,2) > 25) );
    hvix(exbd,:) = [];
    srtd = unique(hvix,'rows');        % Remove repeats and sort ascending by ‘x’
    
    exL1 = find((L1 < 0) | (L1 > 25)); % Find ‘y’ values for ‘L1’ off grid
    xp = x;                            % Create plotting x-vector for L1
    xp(exL1) = [];                     % Eliminate out-of-bounds ‘y’ values from ‘x’
    L1(exL1) = [];                     % Eliminate out-of-bounds ‘y’ values from ‘Li’
    
    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(xp, L1)                        % Plot more lines here (additional ‘plot’ statements)
    hold off
    axis equal
    

    It’s been over a year since I wrote it so I would have to study it to remember what I did, but I did my best at the time to document it exhaustively with comments, so that should help. The output (grid intersections) is in the srtd array.

  • 相关阅读:
    XML&nbsp; XmlDocument
    程序集报错
    程序打开网页
    写入文件txt
    读取文件txt
    MSM8953中Android系统添加启动脚本.rc文件
    SELinux基础知识
    嵌入式Linux设备查看USB相关信息
    Linux内核态文件读写相关函数API
    C语言中sscanf()函数相关用法
  • 原文地址:https://www.cnblogs.com/gisalameda/p/6526323.html
Copyright © 2011-2022 走看看