function [ w, xyz ] = pyra_unit_o06 ( ) %*****************************************************************************80 % %% PYRA_UNIT_O06 returns a 6 point quadrature rule for the unit pyramid. % % Discussion: % % The integration region is defined as: % % - ( 1 - Z ) <= X <= 1 - Z % - ( 1 - Z ) <= Y <= 1 - Z % 0 <= Z <= 1. % % When Z is zero, the integration region is a square lying in the (X,Y) % plane, centered at (0,0,0) with "radius" 1. As Z increases to 1, the % radius of the square diminishes, and when Z reaches 1, the square has % contracted to the single point (0,0,1). % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 13 April 2009 % % Author: % % John Burkardt % % Reference: % % Carlos Felippa, % A compendium of FEM integration formulas for symbolic work, % Engineering Computation, % Volume 21, Number 8, 2004, pages 867-890. % % Parameters: % % Output, real W(6), the weights. % % Output, real XYZ(3,6), the abscissas. % w(1:6) = [ ... 0.21000000000000000000, ... 0.21000000000000000000, ... 0.21000000000000000000, ... 0.21000000000000000000, ... 0.06000000000000000000, ... 0.10000000000000000000 ]; xyz(1:3,1:6) = [ ... -0.48795003647426658968, -0.48795003647426658968, 0.16666666666666666667; ... 0.48795003647426658968, -0.48795003647426658968, 0.16666666666666666667; ... 0.48795003647426658968, 0.48795003647426658968, 0.16666666666666666667; ... -0.48795003647426658968, 0.48795003647426658968, 0.16666666666666666667; ... 0.00000000000000000000, 0.00000000000000000000, 0.58333333333333333333; ... 0.00000000000000000000, 0.00000000000000000000, 0.75000000000000000000 ]'; return end