function [ w, xyz ] = pyra_unit_o48 ( ) %*****************************************************************************80 % %% PYRA_UNIT_O48 returns a 48 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(48), the weights. % % Output, real XYZ(3,48), the abscissas. % w(1:48) = [ ... 2.01241939442682455E-002, ... 2.01241939442682455E-002, ... 2.01241939442682455E-002, ... 2.01241939442682455E-002, ... 2.60351137043010779E-002, ... 2.60351137043010779E-002, ... 2.60351137043010779E-002, ... 2.60351137043010779E-002, ... 1.24557795239745531E-002, ... 1.24557795239745531E-002, ... 1.24557795239745531E-002, ... 1.24557795239745531E-002, ... 1.87873998794808156E-003, ... 1.87873998794808156E-003, ... 1.87873998794808156E-003, ... 1.87873998794808156E-003, ... 4.32957927807745280E-002, ... 4.32957927807745280E-002, ... 4.32957927807745280E-002, ... 4.32957927807745280E-002, ... 1.97463249834127288E-002, ... 1.97463249834127288E-002, ... 1.97463249834127288E-002, ... 1.97463249834127288E-002, ... 5.60127223523590526E-002, ... 5.60127223523590526E-002, ... 5.60127223523590526E-002, ... 5.60127223523590526E-002, ... 2.55462562927473852E-002, ... 2.55462562927473852E-002, ... 2.55462562927473852E-002, ... 2.55462562927473852E-002, ... 2.67977366291788643E-002, ... 2.67977366291788643E-002, ... 2.67977366291788643E-002, ... 2.67977366291788643E-002, ... 1.22218992265373354E-002, ... 1.22218992265373354E-002, ... 1.22218992265373354E-002, ... 1.22218992265373354E-002, ... 4.04197740453215038E-003, ... 4.04197740453215038E-003, ... 4.04197740453215038E-003, ... 4.04197740453215038E-003, ... 1.84346316995826843E-003, ... 1.84346316995826843E-003, ... 1.84346316995826843E-003, ... 1.84346316995826843E-003 ]; xyz(1:3,1:48) = [ ... 0.88091731624450909, 0.0000000000000000, 4.85005494469969989E-02; ... -0.88091731624450909, 0.0000000000000000, 4.85005494469969989E-02; ... 0.0000000000000000, 0.88091731624450909, 4.85005494469969989E-02; ... 0.0000000000000000, -0.88091731624450909, 4.85005494469969989E-02; ... 0.70491874112648223, 0.0000000000000000, 0.23860073755186201; ... -0.70491874112648223, 0.0000000000000000, 0.23860073755186201; ... 0.0000000000000000, 0.70491874112648223, 0.23860073755186201; ... 0.0000000000000000, -0.70491874112648223, 0.23860073755186201; ... 0.44712732143189760, 0.0000000000000000, 0.51704729510436798; ... -0.44712732143189760, 0.0000000000000000, 0.51704729510436798; ... 0.0000000000000000, 0.44712732143189760, 0.51704729510436798; ... 0.0000000000000000, -0.44712732143189760, 0.51704729510436798; ... 0.18900486065123448, 0.0000000000000000, 0.79585141789677305; ... -0.18900486065123448, 0.0000000000000000, 0.79585141789677305; ... 0.0000000000000000, 0.18900486065123448, 0.79585141789677305; ... 0.0000000000000000, -0.18900486065123448, 0.79585141789677305; ... 0.36209733410322176, 0.36209733410322176, 4.85005494469969989E-02; ... -0.36209733410322176, 0.36209733410322176, 4.85005494469969989E-02; ... -0.36209733410322176, -0.36209733410322176, 4.85005494469969989E-02; ... 0.36209733410322176, -0.36209733410322176, 4.85005494469969989E-02; ... 0.76688932060387538, 0.76688932060387538, 4.85005494469969989E-02; ... -0.76688932060387538, 0.76688932060387538, 4.85005494469969989E-02; ... -0.76688932060387538, -0.76688932060387538, 4.85005494469969989E-02; ... 0.76688932060387538, -0.76688932060387538, 4.85005494469969989E-02; ... 0.28975386476618070, 0.28975386476618070, 0.23860073755186201; ... -0.28975386476618070, 0.28975386476618070, 0.23860073755186201; ... -0.28975386476618070, -0.28975386476618070, 0.23860073755186201; ... 0.28975386476618070, -0.28975386476618070, 0.23860073755186201; ... 0.61367241226233160, 0.61367241226233160, 0.23860073755186201; ... -0.61367241226233160, 0.61367241226233160, 0.23860073755186201; ... -0.61367241226233160, -0.61367241226233160, 0.23860073755186201; ... 0.61367241226233160, -0.61367241226233160, 0.23860073755186201; ... 0.18378979287798017, 0.18378979287798017, 0.51704729510436798; ... -0.18378979287798017, 0.18378979287798017, 0.51704729510436798; ... -0.18378979287798017, -0.18378979287798017, 0.51704729510436798; ... 0.18378979287798017, -0.18378979287798017, 0.51704729510436798; ... 0.38925011625173161, 0.38925011625173161, 0.51704729510436798; ... -0.38925011625173161, 0.38925011625173161, 0.51704729510436798; ... -0.38925011625173161, -0.38925011625173161, 0.51704729510436798; ... 0.38925011625173161, -0.38925011625173161, 0.51704729510436798; ... 7.76896479525748113E-02, 7.76896479525748113E-02, 0.79585141789677305; ... -7.76896479525748113E-02, 7.76896479525748113E-02, 0.79585141789677305; ... -7.76896479525748113E-02, -7.76896479525748113E-02, 0.79585141789677305; ... 7.76896479525748113E-02, -7.76896479525748113E-02, 0.79585141789677305; ... 0.16453962988669860, 0.16453962988669860, 0.79585141789677305; ... -0.16453962988669860, 0.16453962988669860, 0.79585141789677305; ... -0.16453962988669860, -0.16453962988669860, 0.79585141789677305; ... 0.16453962988669860, -0.16453962988669860, 0.79585141789677305 ]'; return end