{"id":10438,"date":"2019-01-25T09:00:12","date_gmt":"2019-01-25T14:00:12","guid":{"rendered":"https:\/\/blogs.mathworks.com\/pick\/?p=10438"},"modified":"2019-01-21T18:17:33","modified_gmt":"2019-01-21T23:17:33","slug":"distance-from-points-to-polyline-or-polygon","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/pick\/2019\/01\/25\/distance-from-points-to-polyline-or-polygon\/","title":{"rendered":"Distance from Points to Polyline or Polygon"},"content":{"rendered":"
\n <\/p>\n

Sean<\/a>‘s pick this week is Distance from points to polyline or polygon<\/a> by Michael Yoshpe<\/a>.\n <\/p>\n

<\/introduction><\/p>\n

I recently had a problem where I was trying to identify which corners of a property lot were abutting a street.<\/p>\n

Below is an example; the polygons are stored in the relatively new polyshape<\/tt><\/a> class.\n <\/p>\n

load Polyshapes.mat<\/span>\r\n\r\np(1) = plot(lot, \"FaceColor\"<\/span>, \"b\"<\/span>);\r\nhold on<\/span>\r\np(2) = plot(street, \"FaceColor\"<\/span>, [0.5 0.5 0.5]);\r\nxticks([])\r\nyticks([])\r\nlegend([\"Lot\"<\/span> \"Street\"<\/span>])<\/pre>\n
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nidx = nearestvertex(street, lot.Vertices);\r\np(3) = plot(street.Vertices(nidx, 1), street.Vertices(nidx, 2), \"r*\"<\/span>, \"DisplayName\"<\/span>, \"Nearest Vertex on Street\"<\/span>);<\/pre>\n
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At first this looks good, but let’s zoom in:<\/p>\n
load zoomlimits.mat<\/span>\r\nxlim(xlimits)\r\nylim(ylimits)<\/pre>\n
 <\/p>\n
Nearest vertex is only looking at the vertices for a street.  There can be long distances between the vertices along a boundary so it could return ones that make absolutely no sense e.g. the far side of the street.  What I actually need is the distance from the lot vertices to the boundaries of the street.\n   <\/p>\n
Unfortunately, there was no obvious polyshape method in a computational geometry sense to do it.  I could use linspace to add thousands of points to each boundary to up the number of vertices so nearestvertex<\/tt> could get “close enough” but that seemed like a less than optimal means for solving this problem.\n   <\/p>\n
I searched MATLAB Answers<\/a> and came across this answer<\/a> from MathWorks’ Tech Support.  This provided a means for finding distance to a line.  One could loop over all of the boundaries of the street, calculate the shortest distance, and then keep the minimum at the end.  Instead, I searched the File Exchange and found Michael’s p_poly_dist<\/tt> function. It does exactly what I need (though requires looping over vertices instead of boundaries).\n   <\/p>\n
% Grab the boundary from the street.<\/span>\r\n[xbnd, ybnd] = boundary(street);\r\n\r\n% Loop over lot vertices, calculating shortest distance to street boundary.<\/span>\r\nfor<\/span> ii = size(lot.Vertices, 1):-1:1\r\n    dists(ii, 1) = p_poly_dist(lot.Vertices(ii, 1), lot.Vertices(ii, 2), xbnd, ybnd);\r\nend<\/span>\r\n\r\n% A vertex is on the border if it's within threshold or street interior.<\/span>\r\nthreshold = 2;\r\nonborder = (dists < threshold) | isinterior(street, lot.Vertices);\r\ndelete(p(3))\r\nplot(lot.Vertices(onborder, 1), lot.Vertices(onborder, 2), \"mp\"<\/span>, \"DisplayName\"<\/span>, \"On Street\"<\/span>)\r\nxlim auto<\/span>\r\nylim auto<\/span><\/pre>\n
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Comments<\/a><\/h3>\n
If you want this functionality in base MATLAB, please contact MathWorks Tech Support and add your vote by letting them know this answer was useful!\n   <\/p>\n
Give it a try and let us know what you think here<\/a> or leave a comment<\/a> for Michael.\n   <\/p>\n
I’d also like to give a shout out to Point To Line Distance<\/a> by Rik Wisselink<\/a> – who provided input checking to the tech support answer and extended it to work on multiple points.  I didn’t use it for this because I did not need 3d and looping over boundaries was many more iterations than looping over vertices.\n   <\/p>\n
I looked at the methods for polyshape<\/tt> and first thought nearestvertex<\/tt><\/a> would be the correct way to do it.  I.e. given the nearest vertex for each point, calculate the distance to it and apply a threshold.\n   <\/p>\n