# Knowledge Base

Calculates the numerical integral of data collected on a 2D triangle mesh using first order trapezoidal quadrature.

 Supported Product: FDTD, MODE, DEVICE, INTERCONNECT

 Syntax Description 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.

 Parameter Default value Type Description tri required matrix [Mx3] connectivity matrix for the M triangle elements on the mesh. 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. 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. 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