Calculates the numerical integral of data collected on a 2D triangle mesh using first order trapezoidal quadrature.
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Syntax |
Description |
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out = quadtri(tri,vtx,u,n); |
Calculates the integral of data collected on triangle mesh. A scalar is returned if the input data corresponds to a scalar quantity and a vector with three components is returned if the input data corresponds to a vector quantity. |
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Parameter |
Default value |
Type |
Description |
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tri |
required |
matrix |
[Mx3] connectivity matrix for the M triangle elements on the mesh. |
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vtx |
required |
matrix |
[Nx2] or [Nx3] matrix containing the (x,y,z) coordinates of the N vertices of the mesh. If the matrix has only two columns, the z coordinate is assumed to be zero. |
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u |
required |
matrix |
[Nx1] or [Nx3] matrix containing the data to be integrated at the location of each vertex. If the matrix is of size [Nx1], the data is assumed to be a scalar quantity. If the matrix is of size [Nx3], the data is assumed to be a vector quantity. |
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n |
optional |
empty |
matrix |
[Mx3] matrix with the surface normal vectors for each of the M triangles on the mesh. The columns correspond to the (x,y,z) components of each vector. This input is required only if the data to be integrated is a vector quantity. |
Example
The following example finds the approximate integral of u on a finite element mesh.
# define 4 vertices in the shape of a rectangle, #point[#1;#2;#3;#4] vtx = [0,0; 4,0; 4,3; 0,3]; # make two triangles (#1,#2,#4) and (#2,#3,#4) with area = 6 tri = [1,2,4; 2,3,4]; # Define result values at each vertex point, #point #1, #2, #3, #4 u=[4,3,2,0]; # the result of this integral should be # ((4+3+0)/3 + (3+2+0)/3)*6 = 24 ?I = quadtri(tri,vtx,u); result: 24
See Also