EquidistanceInPoint_Line

This function returns the equidistance points strictly inside an edge.

• All points are inside the interval
• Points are in increasing order

Interface

܀ Interface

INTERFACE
  MODULE PURE FUNCTION EquidistanceInPoint_Line(order, xij) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order
    REAL(DFP), INTENT(IN) :: xij(2)
    !! coordinates of point 1 and point 2
    REAL(DFP), ALLOCATABLE :: ans(:)
  END FUNCTION EquidistanceInPoint_Line
END INTERFACE

xij

• xij(1) is 1D coordinate of point 1.
• xij(2) is 1D coordinate of point 2.

Interface 2

INTERFACE
  MODULE PURE FUNCTION EquidistanceInPoint_Line(order, xij) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
  !! order
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
  !! coordinates of point 1 and point 2 in $x_{iJ}$ format
  !! number of rows = nsd
  !! number of cols = 2
    REAL(DFP), ALLOCATABLE :: ans(:, :)
  !! returned coordinates in $x_{iJ}$ format
  END FUNCTION EquidistanceInPoint_Line
END INTERFACE

xij

• xij(:, 1) are coordinates of point 1.
• xij(:, 2) are coordinates of point 2.

ans

• If xij is present, then number of rows in ans is same as the number of rows in xij, otherwise it is 1.
• The rows in ans denote the spatial components.
• The points are arranged in increasing order.

️܀ See example

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order
  real( dfp ), allocatable :: x1( : ), x2( : ), x(:,:), ans(:,:)
  integer(i4b), allocatable :: degree(:,:)
  call reallocate(x, 1, 2)
  x(1,:)=[-1,1]
  x1 = EquidistanceInPoint_Line( order=1, xij=x(1,:) )
  call display( x1, "x1 = ", orient="row" )
  x1 = EquidistanceInPoint_Line( order=2, xij=x(1,:) )
  call display( x1, "x1 = ", orient="row" )
  x1 = EquidistanceInPoint_Line( order=3, xij=x(1,:) )
  call display( x1, "x1 = ", orient="row" )
  x1 = EquidistanceInPoint_Line( order=4, xij=x(1,:) )
  call display( x1, "x1 = ", orient="row" )

See results

results

x1 =
-----
x1 =
-------
0.00000
x1 =
--------------------
-0.333333   0.333333
x1 =
-------------------------------
-0.500000   0.000000   0.500000

  call reallocate(x, 3, 2)
  x(:,1)=[0.2,0.2,0.0]
  x(:,2)=[0.2,0.6,0.0]
  ans = EquidistanceInPoint_Line( order=1, xij=x )
  call display( ans, "ans = ")
  ans = EquidistanceInPoint_Line( order=2, xij=x )
  call display( ans, "ans = ")

See results

results

ans =
------
ans =
-------
0.20000
0.40000
0.00000

info

We can also call the routine without specifying the xij. In this case the reference domain is from -1 to 1 in 1D. That is, the returned points are in 1D.

  x = EquidistanceInPoint_Line( order=1 )
  call display( x, "x = " )
  x = EquidistanceInPoint_Line( order=2 )
  call display( x, "x = " )
  x = EquidistanceInPoint_Line( order=3 )
  call display( x, "x = " )

See results

results

x = 
----

  x =  
-------
0.00000

        x =         
--------------------
-0.333333   0.333333

end program main

↢