Move cursor and screen together

Question

I am implementing a smooth scrolling function for <C-u> and <C-d>, which just sleeps for a few milliseconds and then moves the screen up (<C-y>) or down (<C-e>) one line:

function SmoothScroll(up)
    if a:up
        let scrollaction= "\<C-y>"
    else
        let scrollaction="\<C-e>"
    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
    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

The function for time is visualized here: https://www.desmos.com/calculator/of6hhoo1p3

The problem now is that <C-y> and <C-e> move the cursor when the cursor comes closer to the screen edge than scrolloff lines. So when you repeatedly <C-y>, the cursor ends up at least scrolloff lines above the bottom of the screen. And when you repeatedly <C-e> the cursor ends up at least scrolloff lines below the top of the screen. However when I use <C-u> and <C-d> I would like the cursor to stay where it is on the screen.

Is there maybe a way to move both cursor and screen at the same time? I do not want to call both <C-y> and k for example, because if my scrolloff variable was greater than half the lines on my screen (to always keep the cursor centered, which I occasionally want to use), then <C-u> would scroll twice as far.

Answer 1

Not an answer to your question. But thought I'd mention that this exists: https://github.com/terryma/vim-smooth-scroll

Answer 2

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.