Find all the points inside a triangulation

Question

Karthik Uthaman 2011-10-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/18459-find-all-the-points-inside-a-triangulation

I am currently working on problem in which I am using delanauy triangles to warp and morph two images.

Say i have

%These are the points marked on two different images that are to be morphed....
im2_pts = [y2(:) x2(:)];
im1_pts = [y1(:) x1(:)];
%calculating the average shape...
avg_pts=[x_avg(:) y_avg(:)];
%Triangulation...
tri = delaunay(x_avg,y_avg);
%For each triangle in tri i will perform the action below...
%First Triangle's co-ordinates
t1_x = [ 2736 1882 2736];
t1_y = [ 2736 1060 1];
%Second Triangle's co-ordinates
t2_x = [ 2736 1933 2736 ];
t2_y = [ 2736  991 2736 ];
tri1 = [t1_x(:) t1_y(:)];
tri2 = [t2_x(:) t2_y(:)];
%calculating the affine transformation...
t_affine = cp2tform(tri1,tri2,'affine');

now to apply the transformation, i need to find out all points in the triangle tri1. I know i need to use tsearch for the same. But i am not sure how to use it.

Please do let me know how do i perform this action. Thanks !!!! :D

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Answer 1

Florin Neacsu 2011-10-17

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/18459-find-all-the-points-inside-a-triangulation#answer_24866

Hi,

Given any triangle, defined by the coordinates of its vertices you can "easily" find the interior points. Have a look at barycentric coordinates. Define a barycentric coordinate system with the triangle's vertices. Then any point will have 3 coordinates say a,b,c. If they all are positive then the point is inside the triangle. If not, the point is outside.

Hope this helps. Regards, Florin