function [h,g] = crosshatch_poly(x, y, lineangle, linegap, varargin)
% Fill a convex polygon with regular diagonal lines (hatching, or cross-hatching)
%
% file: crosshatch_poly.m, (c) Matthew Roughan, Mon Jul 20 2009
% created: Mon Jul 20 2009
% author: Matthew Roughan
% email: matthew.roughan@adelaide.edu.au
%
%
% crosshatch_poly(x, y, angle, gap) fills the 2-D polygon defined by vectors x and y
% with slanted lines at the specified lineangle and linegap.
%
% The one major limitation at present is that the polygon must be convex -- if it is not, the
% function will fill the convex hull of the supplied vertices. Non-convex polygons must be
% broken into convex chunks, which is a big limitation at present.
%
% Cross-hatching can be easily achieved by calling the function twice.
%
% Speckling can be roughly achieved using linestyle ':'
%
%
% INPUTS:
% (x,y) gives a series of points that defines a convex polygon.
% lineangle the angle of the lines used to fill the polygon
% specified in degrees with respect to vertical
% default = 45 degrees
% linegap the gap between the lines used to fill the polygon
% default = 1
% options can be specified in standard Matlab (name, value) pairs
% 'edgecolor' color of the boundary line of the polygon
% 'edgewidth' width of the boundary line of the polygon
% 0 means no line
% 'edgestyle' style of the boundary line of the polygon
% 'linecolor' color of the fill lines
% 'linewidth' width of fill lines
% 'linestyle' style of fill lines
% 'backgroundcolor' background colour to fill the polygon with
% if not specified, no fill will be done
% 'hold_n' hold_n=1 means keep previous plot
% hold_n=0 (default) means clear previous figure
%
% OUTPUTS:
% h = a vector of handles to the edges of the polygon
% g = a vector of handles to the lines
%
% Works by finding intersection points of the fill lines with the boundary lines, and then
% drawing a line between intersection points that lie on the boundary of the polygon.
%
% version 0.1, Jul 20th 2009, Matthew Roughan
% version 0.2, Jul 22nd 2009, fixed typo, Matthew Roughan
%
%
% There are a number of similar functions, that I'll point to, but they are a little
% different as well.
% linpat.m by Stefan Bilig does essentially the same thing, but only in rectangular regions
% applyhatch_pluscolor.m by Brandon Levey (from Brian Katz and Ben Hilig) maps colors in
% an image to patterns, which is cool, but I just want hatching to be easy, and
% direct, so I can do things like plot two regions and cross hatch both
% hatching.m by ijtihadi ijtihadi does hatching between two (arbitrary) functions, which
% could include many shapes, but isn't easy to use directly for polygons or other
% shapes. Note that often smooth curves can be well approximated by polygons so
% this function can be used for these cases as well.
%
%
% TODO: speckles and other more interesting patterns
% cross-hatching as a built in
% avoid dependence on optimization toolbox
%
% read the input options and set defaults
if (nargin < 4)
linegap = 1;
end
if (nargin < 3)
lineangle = 45;
end
edgecolor = 'k';
edgewidth = 1;
edgestyle = '-';
linecolor = 'k';
linewidth = 1;
linestyle = '-';
hold_n = 0;
if (length(varargin) > 0)
% process variable arguments
for k = 1:2:length(varargin)
if (ischar(varargin{k}))
argument = char(varargin{k});
value = varargin{k+1};
switch argument
case {'linecolor','lc'}
linecolor = value;
case {'backgroundcolor','bgc'}
backgroundcolor = value;
case {'linewidth','lw'}
linewidth = value;
case {'linestyle','ls'}
linestyle = value;
case {'edgecolor','ec'}
edgecolor = value;
case {'edgewidth','ew'}
edgewidth = value;
case {'edgestyle','ew'}
edgestyle = value;
case {'hold'}
hold_n = value;
otherwise
error('incorrect input parameters');
end
end
end
end
% reset plot of needed
if (hold_n==0)
hold off
plot(x(1), y(2));
end
hold on
% get the convex hull of the supplied vertices, partly to ensure convexity, but also to sort
% them into a sensible order
[k] = convhull(x,y);
x = x(k(1:end-1));
y = y(k(1:end-1));
N = length(k)-1;
% make everything row vectors
if (size(x,1) > 1)
x = x';
end
if (size(y,1) > 1)
y = y';
end
% if the background is set, then fill, and set the edge correctly
if (exist('backgroundcolor', 'var'))
h = fill(x,y,backgroundcolor);
if (edgewidth > 0)
set(h, 'LineWidth', edgewidth, 'EdgeColor', edgecolor, 'LineStyle', edgestyle);
else
set(h, 'EdgeColor', backgroundcolor);
end
end
% plot edges if needed
for i=1:N
if (edgewidth > 0 & ~exist('backgroundcolor', 'var'))
% only need to draw edges if width is > 0 and haven't already done so with fill
j = mod(i, N)+1;
h(i) = plot([x(i) x(j)], [y(i) y(j)], ...
'color', edgecolor, 'linestyle', edgestyle, 'linewidth', edgewidth);
end
end
% now find the range for the lines to plot
c = [cosd(lineangle), sind(lineangle)]; % normal to the lines
v = [sind(lineangle), -cosd(lineangle)]; % direction of lines
obj = c * [x; y];
[mx, kmx] = max(obj, [], 2);
[mn, kmn] = min(obj, [], 2);
% plot(x(kmx), y(kmx), 'r*');
% plot(x(kmn), y(kmn), 'ro');
distance = sqrt( (x(kmx)-x(kmn)).^2 + (y(kmx)-y(kmn)).^2 );
% find a line describing each edge
for i=1:N
j = mod(i, N)+1;
if (abs(x(j) - x(i)) > 1.0e-12)
% find the slope and intersept
slope(i) = (y(j) - y(i)) / (x(j) - x(i));
y_int(i) = y(i) - slope(i)*x(i);
else
% the line is vertical
slope(i) = Inf;
y_int(i) = NaN;
end
end
% now draw lines clipping them at points that are on the edge of the polygon
g = [];
% find a slightly larger polygon
centroid_x = mean(x);
centroid_y = mean(y);
epsilon = 0.001;
x_dash = (1+epsilon) * (x - centroid_x) + centroid_x;
y_dash = (1+epsilon) * (y - centroid_y) + centroid_y;
% fill(x_dash, y_dash, 'g');
for m=0:linegap:distance
counter = ceil(m/linegap)+1;
sigma = [x(kmn), y(kmn)] + m*c;
% plot(sigma(1), sigma(2), '+', 'color', linecolor);
% for each line, look where it intersepts the edge of polygon (if it does)
for i=1:N
% find the intercept with this line, and the relevant edge
if (isinf(slope(i)))
if (abs(v(1)) > 1.0e-12)
t = (x(i) - sigma(1)) / v(1);
x_i(i) = x(i);
y_i(i) = sigma(2) + t * v(2);
else
x_i(i) = NaN;
y_i(i) = NaN;
end
else
if (abs(v(2) - slope(i)*v(1)) > 1.0e-12)
t = (slope(i) * sigma(1) - sigma(2) + y_int(i)) / ( v(2) - slope(i)*v(1));
x_i(i) = sigma(1) + t * v(1);
y_i(i) = sigma(2) + t * v(2);
else
x_i(i) = NaN;
y_i(i) = NaN;
end
end
end
k = find(inpolygon(x_i, y_i, x_dash, y_dash));
if (length(k) == 2)
g(counter) = plot(x_i(k), y_i(k), ...
'color', linecolor, 'linestyle', linestyle, 'linewidth', linewidth);
elseif (length(k) < 2)
% don't plot because we have no clear line
elseif (length(k) > 2)
% find two unique points
d = [x_i(k)', y_i(k)'];
d = round(100*d)/100;
d = unique(d, 'rows');
g(counter) = plot(d(:,1), d(:,2), ...
'color', linecolor, 'linestyle', linestyle, 'linewidth', linewidth);
end
end
