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I have now just checked manually whether the cursor is at the border of scrolloff, i.e. if it would be scrolled by <C-y> for example or not, and if not, then I move it manually at each iteration with j or k:

function SmoothScroll(up)
  if a:up
    let scrollaction= "\<C-y>"
    " now also check how far the cursor is away
    " from the border, including scrolloff
    let offdist = abs((line("w$") - &scrolloff) - line("."))
    if offdist > 0
      let cursormov="k"
    endif
  else
    let scrollaction="\<C-e>"
    let offdist = abs(line(".") - (line("w0") + &scrolloff))
    if offdist > 0
      let cursormov="j"
    endif
  endif
  let s=&scroll " total lines to scroll
  let x=0   " counts from 0 to s
  let T=10 " maximum sleep ms for smoothing
  let a=1 " smoothing amount
  let p=2 " must be at least 2
  let m=s/p " number of lines for which is being smoothed
  while x < s
    let time=T*((x-m)*(x-s+m)*(x+m/a)*(x-s-m/a))/(m*(s-m)*(-m/a)*(s+m/a))
    if time > 0
      exec "sleep ".time."m"
      redraw
    end
    let x+=1
    exec "normal " . scrollaction
    exec "normal " . cursormov
  endwhile
endfunction
nnoremap <C-U> :call SmoothScroll(1)<Enter>
nnoremap <C-D> :call SmoothScroll(0)<Enter>
inoremap <C-U> <Esc>:call SmoothScroll(1)<Enter>i
inoremap <C-D> <Esc>:call SmoothScroll(0)<Enter>i

There may be a more efficient solution though. But this way the cursor also stays in place while smoothly scrolling.

I have now just checked manually whether the cursor is at the border of scrolloff, i.e. if it would be scrolled by <C-y> for example or not, and if not, then I move it manually at each iteration with j or k:

function SmoothScroll(up)
  let cursormov=""
  if a:up
    let scrollaction= "normal \<C-y>"
    " now also check how far the cursor is away
    " from the border, including scrolloff
    let offdist = abs((line("w$") - &scrolloff) - line("."))
    if offdist > 0 || line("w0") < &scroll
      let cursormov="normal k"
    endif
  else
    let scrollaction="normal \<C-e>"
    let offdist = abs(line(".") - (line("w0") + &scrolloff))
    if offdist > 0
      let cursormov="normal j"
    endif
  endif
  let s=&scroll " total lines to scroll
  let x=0   " counts from 0 to s
  let T=2 " maximum sleep ms for smoothing
  let a=2 " smoothing amount
  let p=2 " must be at least 2
  let m=s/p " number of lines for which is being smoothed
  while x < s
    let time=T*((x-m)*(x-s+m)*(x+m/a)*(x-s-m/a))/(m*(s-m)*(-m/a)*(s+m/a))
    if time > 0
      exec "sleep ".time."m"
      redraw
    end
    let x+=1
    exec scrollaction
    exec cursormov
  endwhile
endfunction
nnoremap <C-U> :call SmoothScroll(1)<Enter>
nnoremap <C-D> :call SmoothScroll(0)<Enter>
inoremap <C-U> <Esc>:call SmoothScroll(1)<Enter>i
inoremap <C-D> <Esc>:call SmoothScroll(0)<Enter>i

There may be a more efficient solution though. But this way the cursor also stays in place while smoothly scrolling.

I have now just checked manually whether the cursor is at the border of scrolloff, i.e. if it would be scrolled by <C-y> for example or not, and if not, then I move it manually at each iteration with j or k:

function SmoothScroll(up)
    if a:up
        let scrollaction= "\<C-y>"
        " now also check how far the cursor is away
        " from the border, including scrolloff
        let offdist = (line("w$") - &scrolloff) - line(".")
        let cursormov="k"
    else
        let scrollaction="\<C-e>"
        let offdist = line(".") - (line("w0") + &scrolloff)
        let cursormov="j"
    endif
    let s=&scroll " total lines to scroll
    let x=0   " counts from 0 to s
    let T=10 " maximum sleep ms for smoothing
    let a=3 " smoothing amount
    let p=2 " must be at least 2
    let m=s/p " number of lines for which is being smoothed
    while x < s
      let time=T*((x-m)*(x-s+m)*(x+m/a)*(x-s-m/a))/(m*(s-m)*(-m/a)*(s+m/a))
      if time > 0
        exec "sleep ".time."m"
      end
      let x+=1
      redraw
      exec "normal " . scrollaction
      if offdist > 0  || line("w0") == 1
        exec "normal " . cursormov
      endif
    endwhile
endfunction
nnoremap <C-U> :call SmoothScroll(1)<Enter>
nnoremap <C-D> :call SmoothScroll(0)<Enter>
inoremap <C-U> <Esc>:call SmoothScroll(1)<Enter>i
inoremap <C-D> <Esc>:call SmoothScroll(0)<Enter>i

There may be a more efficient solution though. But this way the cursor also stays in place while smoothly scrolling.

I have now just checked manually whether the cursor is at the border of scrolloff, i.e. if it would be scrolled by <C-y> for example or not, and if not, then I move it manually at each iteration with j or k:

function SmoothScroll(up)
  if a:up
    let scrollaction= "\<C-y>"
    " now also check how far the cursor is away
    " from the border, including scrolloff
    let offdist = abs((line("w$") - &scrolloff) - line("."))
    if offdist > 0
      let cursormov="k"
    endif
  else
    let scrollaction="\<C-e>"
    let offdist = abs(line(".") - (line("w0") + &scrolloff))
    if offdist > 0
      let cursormov="j"
    endif
  endif
  let s=&scroll " total lines to scroll
  let x=0   " counts from 0 to s
  let T=10 " maximum sleep ms for smoothing
  let a=1 " smoothing amount
  let p=2 " must be at least 2
  let m=s/p " number of lines for which is being smoothed
  while x < s
    let time=T*((x-m)*(x-s+m)*(x+m/a)*(x-s-m/a))/(m*(s-m)*(-m/a)*(s+m/a))
    if time > 0
      exec "sleep ".time."m"
      redraw
    end
    let x+=1
    exec "normal " . scrollaction
    exec "normal " . cursormov
  endwhile
endfunction
nnoremap <C-U> :call SmoothScroll(1)<Enter>
nnoremap <C-D> :call SmoothScroll(0)<Enter>
inoremap <C-U> <Esc>:call SmoothScroll(1)<Enter>i
inoremap <C-D> <Esc>:call SmoothScroll(0)<Enter>i

There may be a more efficient solution though. But this way the cursor also stays in place while smoothly scrolling.

I have now just checked manually whether the cursor is at the border of scrolloff, i.e. if it would be scrolled by <C-y> for example or not, and if not, then I move it manually at each iteration with j or k:

function SmoothScroll(up)
    if a:up
        let scrollaction= "\<C-y>"
        " now also check how far the cursor is away
        " from the border, including scrolloff
        let offdist = (line("w$") - &scrolloff) - line(".")
        let cursormov="k"
    else
        let scrollaction="\<C-e>"
        let offdist = line(".") - (line("w0") + &scrolloff)
        let cursormov="j"
    endif
    let s=&scroll " total lines to scroll
    let x=0   " counts from 0 to s
    let T=10 " maximum sleep ms for smoothing
    let a=3 " smoothing amount
    let p=2 " must be at least 2
    let m=s/p " number of lines for which is being smoothed
    while x < s
      let time=T*((x-m)*(x-s+m)*(x+m/a)*(x-s-m/a))/(m*(s-m)*(-m/a)*(s+m/a))
      if time > 0
        exec "sleep ".time."m"
      end
      let x+=1
      redraw
      exec "normal " . scrollaction
      if offdist > 0 
        exec "normal " . cursormov
      endif
    endwhile
endfunction
nnoremap <C-U> :call SmoothScroll(1)<Enter>
nnoremap <C-D> :call SmoothScroll(0)<Enter>
inoremap <C-U> <Esc>:call SmoothScroll(1)<Enter>i
inoremap <C-D> <Esc>:call SmoothScroll(0)<Enter>i

There may be a more efficient solution though. But this way the cursor also stays in place while smoothly scrolling.

I have now just checked manually whether the cursor is at the border of scrolloff, i.e. if it would be scrolled by <C-y> for example or not, and if not, then I move it manually at each iteration with j or k:

function SmoothScroll(up)
    if a:up
        let scrollaction= "\<C-y>"
        " now also check how far the cursor is away
        " from the border, including scrolloff
        let offdist = (line("w$") - &scrolloff) - line(".")
        let cursormov="k"
    else
        let scrollaction="\<C-e>"
        let offdist = line(".") - (line("w0") + &scrolloff)
        let cursormov="j"
    endif
    let s=&scroll " total lines to scroll
    let x=0   " counts from 0 to s
    let T=10 " maximum sleep ms for smoothing
    let a=3 " smoothing amount
    let p=2 " must be at least 2
    let m=s/p " number of lines for which is being smoothed
    while x < s
      let time=T*((x-m)*(x-s+m)*(x+m/a)*(x-s-m/a))/(m*(s-m)*(-m/a)*(s+m/a))
      if time > 0
        exec "sleep ".time."m"
      end
      let x+=1
      redraw
      exec "normal " . scrollaction
      if offdist > 0  || line("w0") == 1
        exec "normal " . cursormov
      endif
    endwhile
endfunction
nnoremap <C-U> :call SmoothScroll(1)<Enter>
nnoremap <C-D> :call SmoothScroll(0)<Enter>
inoremap <C-U> <Esc>:call SmoothScroll(1)<Enter>i
inoremap <C-D> <Esc>:call SmoothScroll(0)<Enter>i

There may be a more efficient solution though. But this way the cursor also stays in place while smoothly scrolling.