EquidistancePoint

This subroutine returns the equidistance points in the Hexahedron.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION EquidistancePoint_Hexahedron(order, xij) &
    & RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! number of rows = 3
    !! number of cols = 8
    REAL(DFP), ALLOCATABLE :: ans(:, :)
    !! returned coordinates in $x_{iJ}$ format
  END FUNCTION EquidistancePoint_Hexahedron
END INTERFACE

️܀ See example

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order
  real( dfp ), allocatable :: x(:,:)
  type(String) :: astr
  order=1
  x = EquidistancePoint_Hexahedron( order=order )
  astr = "| no | $x_1$ | $x_2$ | $x_3$ |" // char_lf
  astr = astr //  mdencode( arange(1.0_DFP, (order+1.0_DFP)**3) .colconcat. TRANSPOSE(x))
  call display( astr%chars(), "xij (order="//tostring(order)//")=" // char_lf // char_lf )
end program main

xij (order=1)=

no	$x_1$	$x_2$	$x_3$
1	-1	-1	-1
2	1	-1	-1
3	1	1	-1
4	-1	1	-1
5	-1	-1	1
6	1	-1	1
7	1	1	1
8	-1	1	1

↢

Interface 2

INTERFACE EquidistancePoint_Hexahedron
  MODULE PURE FUNCTION EquidistancePoint_Hexahedron2(p, q, r, xij) &
    & RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: p
    !! order in x direction
    INTEGER(I4B), INTENT(IN) :: q
    !! order in y direction
    INTEGER(I4B), INTENT(IN) :: r
    !! order in z direction
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! number of rows = 3
    !! number of cols = 8
    REAL(DFP), ALLOCATABLE :: ans(:, :)
    !! returned coordinates in $x_{iJ}$ format
  END FUNCTION EquidistancePoint_Hexahedron2
END INTERFACE EquidistancePoint_Hexahedron

p,q,r

order in x, y, and z direction.

xij

xij is the nodal coordinates of Hexahedron. The number of rows in xij are 3, and number of columns in xij is 8.

Results

Order 1

See results

no	$x_1$	$x_2$	$x_3$
1	-1	-1	-1
2	1	-1	-1
3	1	1	-1
4	-1	1	-1
5	-1	-1	1
6	1	-1	1
7	1	1	1
8	-1	1	1

Order 2

See results

no	$x_1$	$x_2$	$x_3$
1	-1	-1	-1
2	1	-1	-1
3	1	1	-1
4	-1	1	-1
5	-1	-1	1
6	1	-1	1
7	1	1	1
8	-1	1	1
9	0	-1	-1
10	-1	0	-1
11	-1	-1	0
12	1	0	-1
13	1	-1	0
14	0	1	-1
15	1	1	0
16	-1	1	0
17	0	-1	1
18	-1	0	1
19	1	0	1
20	0	1	1
21	0	0	-1
22	0	0	1
23	-1	0	0
24	1	0	0
25	0	-1	0
26	0	1	0
27	0	0	0

Order 3

See results

no	$x_1$	$x_2$	$x_3$
1	-1	-1	-1
2	1	-1	-1
3	1	1	-1
4	-1	1	-1
5	-1	-1	1
6	1	-1	1
7	1	1	1
8	-1	1	1
9	-0.33333	-1	-1
10	0.33333	-1	-1
11	-1	-0.33333	-1
12	-1	0.33333	-1
13	-1	-1	-0.33333
14	-1	-1	0.33333
15	1	-0.33333	-1
16	1	0.33333	-1
17	1	-1	-0.33333
18	1	-1	0.33333
19	0.33333	1	-1
20	-0.33333	1	-1
21	1	1	-0.33333
22	1	1	0.33333
23	-1	1	-0.33333
24	-1	1	0.33333
25	-0.33333	-1	1
26	0.33333	-1	1
27	-1	-0.33333	1
28	-1	0.33333	1
29	1	-0.33333	1
30	1	0.33333	1
31	0.33333	1	1
32	-0.33333	1	1
33	-0.33333	-0.33333	-1
34	-0.33333	0.33333	-1
35	0.33333	0.33333	-1
36	0.33333	-0.33333	-1
37	-0.33333	-0.33333	1
38	0.33333	-0.33333	1
39	0.33333	0.33333	1
40	-0.33333	0.33333	1
41	-1	-0.33333	0.33333
42	-1	-0.33333	-0.33333
43	-1	0.33333	-0.33333
44	-1	0.33333	0.33333
45	1	-0.33333	0.33333
46	1	0.33333	0.33333
47	1	0.33333	-0.33333
48	1	-0.33333	-0.33333
49	0.33333	1	-0.33333
50	-0.33333	1	-0.33333
51	-0.33333	1	0.33333
52	0.33333	1	0.33333
53	-0.33333	-1	-0.33333
54	0.33333	-1	-0.33333
55	0.33333	-1	0.33333
56	-0.33333	-1	0.33333
57	-0.33333	-0.33333	-0.33333
58	0.33333	-0.33333	-0.33333
59	0.33333	0.33333	-0.33333
60	-0.33333	0.33333	-0.33333
61	-0.33333	-0.33333	0.33333
62	0.33333	-0.33333	0.33333
63	0.33333	0.33333	0.33333
64	-0.33333	0.33333	0.33333