FindSpan Function
private pure elemental function FindSpan(me, u) result(span)
This procedure is an elemental function and does a binary search and return the integer :: span value, where lies on. Note that, indexing starts with zero. If , the index is , i.e., , where "nb " is number of control points of the univariate spline basis object.
By a binary search, returns the index of the knot span where lies on.
Implementation Details of Algorithm A2.1
In any given knot span, , at most of the are nonzero, namely the functions . On the only nonzero zeroth-degree function is . Hence, the only cubic functions not zero on are . This property is illustrated here
So, we can decrease the computation time by focusing only non-zero functions and their derivatives.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(basis), | intent(in) | :: | me | |||
| real(kind=wp), | intent(in) | :: | u | Given value |
Return Value integer
Knot span index of value
Calls
Source Code
pure elemental function FindSpan(me,u) result (span)
class(basis), intent(in) :: me
real(wp), intent(in) :: u !< Given \( u \) value
integer :: span !< Knot span index of \( u \) value
!locals
integer :: low, high !< indices for binary search
associate( p => me%p, Ui => me%kv, n => me%n ) !get rid of % signs
!/* Special cases */
if (u >= Ui(n+1)) then
span = me%n
return
end if
if (u <= Ui(p)) then
span = p
return
end if
!/* Do binary search */
low = p; high = n+1
span = (low + high) / 2
do while (u < Ui(span) .or. u >= Ui(span+1))
if (u < Ui(span)) then
high = span
else
low = span
end if
span = (low + high) / 2
end do
end associate
end function FindSpan