[PATCH 2/2] gdiplus: Revise closeness check for bezier curve flattening.

[Esme Povirk (she/they)]

I'm not convinced by this approach. There might be a situation where
the midpoint between the endpoints happens to be close to the midpoint
between the control points, but the control points are further than
the flatness, leaving a possibility that we stop while our
approximation has more error than the flatness.

I feel like we should be testing the distance between the control
points and the line segment (or the distance between the control
points and an endpoint, which should be no less than the distance from
the line segment).

I don't really understand the existing "half of distance between
middle point and a linearized path" test either. Nikolay, can you
explain this?

On Fri, Feb 4, 2022 at 9:59 AM Robert Feuerbach <rjfeuerbach at gmail.com> wrote:
>
> The float equality and flatness calculation in flatten_bezier
> can fail due to the limited precision of the float math.
> The equality test was replaced with a simple check against
> the given flatness tolerance.
>
> Wine-Bug: https://bugs.winehq.org/show_bug.cgi?id=52492
> Signed-off-by: Robert Feuerbach <rjfeuerbach at gmail.com>
> ---
>  dlls/gdiplus/graphicspath.c | 11 ++++++-----
>  1 file changed, 6 insertions(+), 5 deletions(-)
>
> diff --git a/dlls/gdiplus/graphicspath.c b/dlls/gdiplus/graphicspath.c
> index ce2666eedab..c1bdf226e52 100644
> --- a/dlls/gdiplus/graphicspath.c
> +++ b/dlls/gdiplus/graphicspath.c
> @@ -109,7 +109,7 @@ static INT path_list_count(path_list_node_t *node)
>   *  - (x2, y2): first control point;
>   *  - (x3, y3): second control point;
>   *  - end     : pointer to end point node
> - *  - flatness: admissible error of linear approximation.
> + *  - flatness: admissible error of linear approximation in coordinate units.
>   *
>   * Return value:
>   *  TRUE : success
> @@ -142,12 +142,13 @@ static BOOL flatten_bezier(path_list_node_t *start, REAL x2, REAL y2, REAL x3, R
>      mp[2].X = (mp[1].X + mp[3].X) / 2.0;
>      mp[2].Y = (mp[1].Y + mp[3].Y) / 2.0;
>
> -    if ((x2 == mp[0].X && y2 == mp[0].Y && x3 == mp[1].X && y3 == mp[1].Y) ||
> -        (x2 == mp[3].X && y2 == mp[3].Y && x3 == mp[4].X && y3 == mp[4].Y))
> -        return TRUE;
> -
>      pt = end->pt;
>      pt_st = start->pt;
> +    /* test for closely spaced points to avoid limited-precision errors in flatness check */
> +    if((fabs(pt.X - mp[2].X) + fabs(pt.Y - mp[2].Y) +
> +        fabs(pt_st.X - mp[2].X) + fabs(pt_st.Y - mp[2].Y) ) <= flatness)
> +        return TRUE;
> +
>      /* check flatness as a half of distance between middle point and a linearized path */
>      if(fabs(((pt.Y - pt_st.Y)*mp[2].X + (pt_st.X - pt.X)*mp[2].Y +
>          (pt_st.Y*pt.X - pt_st.X*pt.Y))) <=
> --
> 2.32.0 (Apple Git-132)
>
>