Create a box around points and use in inpolygon

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Dear all,
I used this code below in order to select the points that are placed in/on the polygon which is correct and gave me the right answer.
% lat and lon are the coordinates of my 96 points that I want to select between them
% and polygon1_x and polygon1_y are coordinates of the shape file
[in,on] = inpolygon(lat,lon,polygon1_x,polygon1_y); % Logical Matrix
inon = in | on; % Combine ‘in’ And ‘on’
idx = find(inon(:)); % Linear Indices Of ‘inon’ Points
latcoord = lat(idx); % X-Coordinates Of ‘inon’ Points
loncoord = lon(idx); % Y-Coordinates Of ‘inon’ Points
plot(lon, lat, '.') % Plot All Points
hold on
plot(polygon1_y, polygon1_x, '.') % Plot Polygon
plot(loncoord, latcoord, 'gp') % Overplot ‘inon’ Points
hold off
idx = idx.';
But I want to edit this code in order to consider each point as the center of 0.5 x 0.5 grid-box and then start checking. So if any part of this box placed in/on polygon I want to select (index) the former point (center).
I attached my data. I tried to edit this by myself but unfortunately it not accomplished well. So any suggestion is highly appreciated.
Thank you all.

Risposta accettata

KSSV il 4 Ago 2020
Modificato: KSSV il 4 Ago 2020
load("polygon1_x.mat") ;
load("polygon1_y.mat") ;
load("lon.mat") ;
load("lat.mat") ;
% remove Nan's from the data
xv = polygon1_y ; yv = polygon1_x ;
xv(isnan(xv)) = [] ;
yv(isnan(yv)) = [] ;
loncoord = zeros([],1) ;
latcoord = zeros([],1) ;
count = 0 ;
for i = 1:length(lon)
% make grid around (lon,lat)
x = lon(i)-0.5:0.5:lon(i)+0.5 ;
y = lat(i)-0.5:0.5:lat(i)+0.5 ;
[X,Y] = meshgrid(x,y) ;
[in,on] = inpolygon(X(:),Y(:),xv,yv); % Logical Matrix
inon = in | on; % Combine ‘in’ And ‘on’
idx = find(inon(:)); % Linear Indices Of ‘inon’ Points
if any(idx)
count = count+1 ;
loncoord(count) = lon(i); % Y-Coordinates Of ‘inon’ Point
latcoord(count) = lat(i) ;
hold on
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