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

[Nikolay Sivov]

On 2/4/22 20:33, Esme Povirk (she/they) wrote:
> 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?

It's be a while. The idea is to check a distance from mp[2] point to 
{pt, pt_st} segment (dist_m), and stop recursion if it's small enough.

I haven't verified right now, but expression I believe was meant to get 
that distance as:

sqr(dot(mp - pt, pt_st - pt)) + sqr(dist_m) = sqr(dist(pt_st, pt));

>
> 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)
>>
>>