Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-31 Thread Vivek Rathod
Alexei, I did not mean to talk about the tolerance on deviation. I misunderstood this comment. "/* Max deviation may be as much as (s/L) * 3/4 (if Hain's v = 1). */" Here, I think, the max deviation is in Hain's r s coordinate system( section 3) and s is the actual control point distance limit.

Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-31 Thread Vivek Rathod
On Mon, Oct 31, 2011 at 4:45 PM, Alexei Podtelezhnikov wrote: > On Mon, Oct 31, 2011 at 3:22 AM, Vivek Rathod wrote: >> s is calculated as >> "s = FT_ABS( dy * dx1 - dx * dy1 );"   which means s is the perpendicular >> distance of the control point from chord multiplied by L >> > >> which means c

Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-31 Thread Alexei Podtelezhnikov
Hi All, I finally understand where Vivek is coming from. There is a temptation to tolerate deviations larger than ONE_PIXEL on long arches that may appear with larger font sizes (say, 24 pixels or more). Sure, they'll look smooth (not angular). We are not about smoothness though. We need correct p

Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-31 Thread Alexei Podtelezhnikov
On Mon, Oct 31, 2011 at 7:43 AM, Vivek Rathod wrote: > The formula for deviation ( from Hein's paper). > d = dnorm * s ; here s is normalized --- (1) > so the formula when s is not normalized becomes d = dnorm * (s / L)  ; > -(2) > and I think the L you are mentioni

Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-31 Thread Alexei Podtelezhnikov
On Mon, Oct 31, 2011 at 3:22 AM, Vivek Rathod wrote: > s is calculated as > "s = FT_ABS( dy * dx1 - dx * dy1 );"   which means s is the perpendicular > distance of the control point from chord multiplied by L > > which means currently  s_limit is being compared with perpendicular distance > of co

Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-31 Thread Vivek Rathod
On Mon, Oct 31, 2011 at 5:46 AM, Alexei Podtelezhnikov wrote: > > On 30/10/2011 08:25, Vivek Rathod wrote: > > according to Hain's paper > > dmax = (s/L) * dnorm ; here s is not normalized. dmax is the tolerance > for > > flatness and dnorm is the normalized flatness of the curve. > > > > so s_l

Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-30 Thread Werner LEMBERG
Hello Alexei, hello Vivek! >> according to Hain's paper >> >> dmax = (s/L) * dnorm ; >> >> here `s' is not normalized. `dmax' is the tolerance for flatness >> and `dnorm' is the normalized flatness of the curve. >> >> So >> >> s_limit = (dmax / dnorm) * L ; >> >> by putting `dnorm = 0.75' w

Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-30 Thread Alexei Podtelezhnikov
> On 30/10/2011 08:25, Vivek Rathod wrote: > according to Hain's paper > dmax = (s/L) * dnorm ;  here s  is not normalized. dmax is the tolerance for > flatness and dnorm is the normalized flatness of the curve. > > so s_limit = (dmax / dnorm) * L ; by putting dnorm = 0.75 we get the > permissible

Re: [ft-devel] regarding freetype 2 cubic curve flattening

2011-10-30 Thread Graham Asher
Vivek, in fact the great work is David's, not mine - I made the original attempt, which was buggy, and then supplied a fix, but David wrote a new version which was justified mathematically and based on Hain's paper, as you mention. So I'll have to pass the responsibility for explaining it to