Triangulation of n points in the plane
triEdges = mesh2d(x, y) [triEdges, bdy] = mesh2d(x, y) triEdges = mesh2d(x, y, bdy)
mesh2d computes a triangulation of
n points in the plane with coordinates given by vectors
returns a matrix
triEdges of size
triEdges(:,i) gives the vertices numbers of triangle
nbt is the number of triangles.
bdy is given as an input parameter this vector defines the
boundary and contains the indices of edges belonging to it, grouped by successive connected components. Each component is positively oriented, i.e. successive
bdy(i:i+1) segments have the interior of the domain to their left. Hence, for a simply connected domain, the boundary is given counterclockwise, and eventual holes are always given clockwise.
Each connected component must be closed and is represented by the vector
[i1,..,i_nc] such that
i1 == i_nc.
bdy is given as an output parameter the boundary is computed prior to the triangulation as the convex hull of input points
x,y and is returned in
bdy with the same convention as above, i.e. counterclockwise sucessive vertices numbers.
Possible error cases are the following:
The triangulation computed by
mesh2d is not guaranteed to be a Delaunay triangulation of points
function displayTri(X, Y, Tr) plot(0,0,rect=[-1 -1 2 2]) [m, n] = size(Tr); xpols = matrix(X(Tr), m, n); ypols = matrix(Y(Tr), m, n); xpolys(xpols, ypols, color("blue")*ones(n,1)); endfunction r1 = 1; n1 = 20; u = linspace(2*%pi, 0, n1); xc1 = r1*cos(u(1:$-1)); yc1 = r1*sin(u(1:$-1)); bdy1 = [1:n1-1, 1]; r2 = 2; n2 = 40; v = linspace(0, 2*%pi, n2); xc2 = r2*cos(v(1:$-1)); yc2 = r2*sin(v(1:$-1)); bdy2 = n1-1+[1:n2-1, 1]; xr = (rand(1, 100)-.5)*2*r2; yr = (rand(1, 100)-.5)*2*r2; r = sqrt(xr.^2+yr.^2); clf gcf().position(4)=300 // [t, bdy] = mesh2d(x, y) syntax subplot(1, 2, 1) k = find(r <= r2); [t, bdy] = mesh2d(xr(k), yr(k)); displayTri(xr(k), yr(k), t) plot(xr(k(bdy)), yr(k(bdy)),"r-o") xtitle("[triEdges, bdy] = mesh2d(x, y)") isoview // t = mesh2d(x, y, bdy) syntax subplot(1, 2, 2) k = find((r >= r1) & (r <= r2)); x = [xc1 xc2 xr(k)]; y = [yc1 yc2 yr(k)]; t = mesh2d(x, y, [bdy1 bdy2]); displayTri(x, y, t) plot(x(bdy1), y(bdy1),"r-o") plot(x(bdy2), y(bdy2),"r-o") xtitle("triEdges = mesh2d(x, y, bdy)") isoview
mesh2d was previously part of the
metanet ATOMS module.
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