Re: [ft-devel] Signed distance fields: distance from any point to the glyph contours

[Behdad Esfahbod]

On 12-10-31 01:16 PM, Alexei Podtelezhnikov wrote:
> On Wed, Oct 31, 2012 at 12:03 PM, Behdad Esfahbod <address@hidden> wrote:
>> On 12-10-31 07:25 AM, Alexei Podtelezhnikov wrote:
>>> On Tue, Oct 30, 2012 at 6:56 AM, Nicolas Rougier
>>> <address@hidden> wrote:
>>>
>>>> My question relates to a more direct way to compute the signed distance 
>>>> and to know if anyone has already coded it by any chance ? Said 
>>>> differently, is there a quick way to compute the shortest signed distance 
>>>> from any point (x,y) to the glyph contours ?
>>>
>>> Quick? I do not think so. A glyph outline is a collection of contours
>>> is a collection of straight segments and Bézier curves.For the
>>> straight segments it is trivial. It is very difficult but surely
>>> doable for the conic and cubic curves. No it is not implemented.
>>
>> Distance to a cubic Bezier involves solving a fifth degree polynomial.
> 
> Ouch! Not doable.
> 
> The Freetype antialiased rendered does not do it either. It splits the
> curves until the curvature is no longer noticeable, then threats all
> segments as straight with trivial solutions as to where they cross
> scanlines. Why don't you adopt a similar approach?

Because I want a size independent representation that remains smooth no matter
how much you zoom in.  Any line approximation will show unsmoothness if you
zoom in enough.  With circular arcs that doesn't happen.