# tri2grid

(Not recommended) Interpolate from PDE triangular mesh to rectangular grid

## Description

example

uxy = tri2grid(p,t,u,x,y) computes the interpolated function values uxy over the grid defined by the vectors x and y using the function values u on the triangular mesh defined by p and t.

tri2grid uses linear interpolation in the triangle containing the grid point.

example

[uxy,tn,a2,a3] = tri2grid(p,t,u,x,y) also returns the index tn of the triangle containing each grid point, and interpolation coefficients a2 and a3.

uxy = tri2grid(p,t,u,tn,a2,a3) uses the values tn, a2, and a3 returned by prior tri2grid call using the previous syntax to interpolate u to the same grid as in the prior call. This syntax is efficient for interpolating several functions to the same grid, such as interpolating hyperbolic or parabolic solutions at multiple times.

## Examples

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Generate a triangular mesh of the L-shaped membrane. The geometry of the L-shaped membrane is described in the file lshapeg.

[p,e,t] = initmesh('lshapeg');

Solve an elliptic PDE on the L-shaped geometry.

u = assempde('lshapeb',p,e,t,1,0,1);

Plot the solution and the mesh.

pdeplot(p,e,t,'XYData',u,'Mesh','on')

Interpolate the solution to the rectangular grid defined by the vectors x and y.

x = -1:0.1:1;
y = x;
uxy = tri2grid(p,t,u,x,y);

Plot the interpolated solution and the rectangular grid.

surface(x,y,uxy)

For comparison, plot the original solution and the rectangular grid.

[~,tn,a2,a3] = tri2grid(p,t,u,x,y);
pdeplot(p,e,t,'XYGrid','on','GridParam',[tn;a2;a3], ...
'XYData',u,'Mesh','on')

## Input Arguments

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Mesh points, specified as a 2-by-Np matrix of points (nodes), where Np is the number of nodes in the mesh. For details on mesh data representation, see initmesh.

Data Types: double

Mesh elements, specified as a 4-by-Nt matrix of triangles, where Nt is the number of triangles in the mesh. For details on mesh data representation, see initmesh.

Data Types: double

PDE solution, specified as a vector. For systems of equations, tri2grid interpolates only the first component. For solutions returned by hyperbolic or parabolic, pass u as a vector of values at one time, u(:,k).

x-coordinates for rectangular grid, specified as a vector of elements in ascending order.

Data Types: double

y-coordinates for rectangular grid, specified as a vector of elements in ascending order.

Data Types: double

## Output Arguments

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Interpolated values, returned as an ny-by-nx matrix, where nx and ny are the lengths of the vectors x and y, respectively.

tri2grid uses linear interpolation in the triangle containing the grid point. At grid points outside of the triangular mesh, interpolated values are NaN.

Indices of triangles containing each grid point, returned as an ny-by-nx matrix, where nx and ny are the lengths of the vectors x and y, respectively. At grid points outside of the triangular mesh, indices of triangles are NaN.

Interpolation coefficient, returned as an ny-by-nx matrix, where nx and ny are the lengths of the vectors x and y, respectively. At grid points outside of the triangular mesh, values of the interpolation coefficients are NaN.

Interpolation coefficient, returned as an ny-by-nx matrix, where nx and ny are the lengths of the vectors x and y, respectively. At grid points outside of the triangular mesh, values of the interpolation coefficients are NaN.

## Version History

Introduced before R2006a

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