Re: [Devel] 'tension' in splines, Hermite Splines [Re: Rendering (by FreeType) and hinting of Latin small 'a']

[David Turner]

I again Vadim,

Vadim Plessky wrote:
> Further search for Hermite Splines provided several quite interesting links.
> [1] http://www.cubic.org/~submissive/sourcerer/hermite.htm
> [2] http://patrick.wagstrom.net/projects/cs411/prog4/
> [3] 
> http://www.siggraph.org/education/materials/HyperGraph/modeling/splines/hermite.htm
>
> Author of [2] has working sample (sources also available) of program which 
> draws different splines - Hermite, Cardinal, Bezier.
> pre-compiled binary (for RedHat 7.2) runs ok on my Linux-Mandrake 8.2
> Drawing different kinds of splines in that program is a lot of fun :-)

I dont think that Hermite splines have any kind of use in our case. They're
much more complex to process and render than cubic or quadratic beziers, so
forget about real-time processing. And I don't see how we could easily adapt
the hinters to work on them. Finally, we'd still need to import/export bezier
arcs anyway which may introduce some accuracy/rounding problems in certain
ill cases..

Also, I don't think that you can interpolate a Hermite spline by simply
interpolating its control and vector points, so this adds a tremendous
amount of complexity.

That's probably a dangerous path to take. Feel free to study them further
if you feel so however. One never knows, I simply don't have the courage to
try to hint TrueType and Postscript fonts with these..

 >
> I think 'Tension' and 'Continuity' add extra level of semantics to *ordinary* 
> curve, which AA rasterizer so badly needs to preserve original shape of the 
> glyph.

Just to clarify things, the AA rasterizer doesn't need to preserve the shape
of anything, it simply computes pixel converages. It's the hinters that need
to distort the outline in ways that are optimized for certain display modes,
and they mostly work with beziers and linear interpolation

That doesn't mean that Hermite splines wouldn't be a good idea if used as
the basis of vectorial outlines in a new font format; I simply don't see
how we can insert them in the current framework without loosing horrible
amounts of performance..

Regards,

- David Turner
- The FreeType Project  (www.freetype.org)