# How to convert 2D triangulation to binary image?

조회 수: 1(최근 30일)
Geert 2013년 8월 21일
댓글: T. Dunker 2022년 7월 6일
Does anyone know of an easy way to convert a 2D triangulation to a binary image, which represents the inside?
Let my clarify my question with a picture: http://i41.tinypic.com/2gvvvnl.jpg The goal is to go from left to right...
My triangulation is given its Points and the ConnectivityList (i.e., it was created with the matlab function "triangulation").
It is important that no holes get filled and all features are preserved.
% Make some data
pts = rand(50,2);
DT = delaunayTriangulation(pts);
% Find a central triangle to remove
[~,holeTrias] = min(sum(abs(DT.incenter - 0.5),2));
holeTrias = [holeTrias DT.neighbors(holeTrias)];
% Define query points
X = 0:0.05:1;
Y = 0:0.05:1;
[xMat,yMat] = meshgrid(X,Y);
IN = false(size(xMat));
for t = 1:size(T,1)
vertsXY = T.Points(T.ConnectivityList(t,:),:);
IN = IN | inpolygon(xMat,yMat, vertsXY(:,1), vertsXY(:,2));
end
% Show the result
figure
patch('faces',T.ConnectivityList,'vertices',T.Points,'FaceColor','g')
hold on
plot(xMat(IN),yMat(IN),'b.',xMat(~IN),yMat(~IN),'r.')

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### 채택된 답변

Sven 2013년 8월 21일
편집: Sven 2013년 8월 21일
Hi Geert,
Here's something that does what you want. It's not optimised for speed as it simply iterates naively through triangles, but it's at least correct.
% Make some data
pts = rand(50,2);
DT = delaunayTriangulation(pts);
% Find a central triangle to remove
[~,holeTrias] = min(sum(abs(DT.incenter - 0.5),2));
holeTrias = [holeTrias DT.neighbors(holeTrias)];
% Define query points
X = 0:0.05:1;
Y = 0:0.05:1;
[xMat,yMat] = meshgrid(X,Y);
% Query each point
IN = false(size(xMat));
for i = 1:numel(IN)
for t = 1:size(T,1)
vertsXY = T.Points(T.ConnectivityList(t,:),:);
if inpolygon(xMat(i),yMat(i), vertsXY(:,1), vertsXY(:,2))
IN(i) = true;
break;
end
end
end
% Show the result
figure
patch('faces',T.ConnectivityList,'vertices',T.Points,'FaceColor','g')
hold on
plot(xMat(IN),yMat(IN),'b.',xMat(~IN),yMat(~IN),'r.')
How does that work for you?
##### 댓글 수: 5표시 이전 댓글 수: 4숨기기 이전 댓글 수: 4
T. Dunker 2022년 7월 6일
with R2018b and later this simplifies to
%% Make some data
pts = rand(50,2);
DT = delaunayTriangulation(pts);
% Find a central triangle to remove
[~,holeTrias] = min(sum(abs(DT.incenter - 0.5),2));
holeTrias = [holeTrias DT.neighbors(holeTrias)];
% Define query points
X = 0:0.02:1;
Y = 0:0.02:1;
%% use polyshape
tic
[xMat,yMat] = meshgrid(X,Y);
bp = boundaryshape(T);
IN = reshape(isinterior(bp, xMat(:), yMat(:)), size(xMat));
toc
Elapsed time is 0.178962 seconds.
%%
colormap(gray(2))
imagesc(X, Y, IN)
hold on;
patch('faces', T.ConnectivityList, 'vertices', T.Points, ...
'FaceColor', 'r', 'FaceAlpha', .2)
hold off;
axis equal;
axis tight;

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