Re: [ft-devel] regarding freetype 2 cubic curve flattening
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' we get the permissible height of the control point for the curve not to be split. So should we not be comparing `s = abs(dy * dxi - dx * dyi)' with `s_limit * L' instead of `s' and `s_limit' (because `s' is perpendicular distance of control point multiplied by `L')? It is actually not just cross-product but s = abs(dx * dxi - dx * dyi) / L otherwise the dimensionality is wrong. Some Hain's equations just need to be creatively modified to avoid divisions in the code. After resolving this issue I would be glad if someone could provide a patch which improves the comments in the source code. Werner ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
Re: [ft-devel] regarding freetype 2 cubic curve flattening
On Mon, Oct 31, 2011 at 5:46 AM, Alexei Podtelezhnikov apodt...@gmail.comwrote: 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 height of the control point for the curve not to be split. so should we not be comparing s= abs(dy * dxi - dx * dyi) with s_limit * Linstead of s and s_limit ( because s is perpendicular distance of control point multiplied by L) ? It is actually not just cross-product but s = abs(dx * dxi - dx * dyi) / L otherwise the dimensionality is wrong. Some Hain's equations just need to be creatively modified to avoid divisions in the code. Alexei, I understand the subtle modifications made to avoid division. But I still feel s_limit needs to be multiplied another time by L before making the comparison. 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 control point * L* . but *s_limit* is actual distance, so in order to do the correct comparison (and to avoid division) don't you think we need to multiply *s_limit* once more by *L *? ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
Re: [ft-devel] regarding freetype 2 cubic curve flattening
On Mon, Oct 31, 2011 at 3:22 AM, Vivek Rathod vivekmrat...@gmail.com 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 control point * L . Correct. s_limit is also multiplied by L on line 1065 in ftgrays.c: s_limit = L * (TPos)( ONE_PIXEL / 6 ); I do not see a problem here. but s_limit is actual distance, so in order to do the correct comparison (and to avoid division) don't you think we need to multiply s_limit once more by L ? This is wrong. Look at the actual code. ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
Re: [ft-devel] regarding freetype 2 cubic curve flattening
On Mon, Oct 31, 2011 at 7:43 AM, Vivek Rathod vivekmrat...@gmail.com 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 mentioning comes from this formula. therefore s = (dmax/dnorm) * L; Please correct me if I am wrong about this whole normalization assumption. Stop confusing yourself and everybody else! Do you know what ONE_PIXEL is? Learn that and read the damn code! ONE_PIXEL is an absolute value and does not need any damn normalization. ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
Re: [ft-devel] regarding freetype 2 cubic curve flattening
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 pixel-by-pixel shape. Therefore, we *always* tolerate a constant fraction of ONE_PIXEL no matter how long the arch is. Alexei On Mon, Oct 31, 2011 at 7:51 AM, Alexei Podtelezhnikov apodt...@gmail.com wrote: On Mon, Oct 31, 2011 at 7:43 AM, Vivek Rathod vivekmrat...@gmail.com 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 mentioning comes from this formula. therefore s = (dmax/dnorm) * L; Please correct me if I am wrong about this whole normalization assumption. Stop confusing yourself and everybody else! Do you know what ONE_PIXEL is? Learn that and read the damn code! ONE_PIXEL is an absolute value and does not need any damn normalization. -- Alexei A. Podtelezhnikov, PhD ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
Re: [ft-devel] regarding freetype 2 cubic curve flattening
On Mon, Oct 31, 2011 at 4:45 PM, Alexei Podtelezhnikov apodt...@gmail.com wrote: On Mon, Oct 31, 2011 at 3:22 AM, Vivek Rathod vivekmrat...@gmail.com 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 control point * L . Correct. s_limit is also multiplied by L on line 1065 in ftgrays.c: s_limit = L * (TPos)( ONE_PIXEL / 6 ); I do not see a problem here. 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 mentioning comes from this formula. therefore s = (dmax/dnorm) * L; Please correct me if I am wrong about this whole normalization assumption. but s_limit is actual distance, so in order to do the correct comparison (and to avoid division) don't you think we need to multiply s_limit once more by L ? This is wrong. Look at the actual code. ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
Re: [ft-devel] regarding freetype 2 cubic curve flattening
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. In that case s_limit - calculated as s_limit = L * (TPos)( ONE_PIXEL / 6 ); - is correct for comparing with distance of the control points. Sorry for this confusion. Thanks. On Mon, Oct 31, 2011 at 5:57 PM, Alexei Podtelezhnikov apodt...@gmail.com wrote: 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 pixel-by-pixel shape. Therefore, we *always* tolerate a constant fraction of ONE_PIXEL no matter how long the arch is. Alexei On Mon, Oct 31, 2011 at 7:51 AM, Alexei Podtelezhnikov apodt...@gmail.com wrote: On Mon, Oct 31, 2011 at 7:43 AM, Vivek Rathod vivekmrat...@gmail.com 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 mentioning comes from this formula. therefore s = (dmax/dnorm) * L; Please correct me if I am wrong about this whole normalization assumption. Stop confusing yourself and everybody else! Do you know what ONE_PIXEL is? Learn that and read the damn code! ONE_PIXEL is an absolute value and does not need any damn normalization. -- Alexei A. Podtelezhnikov, PhD ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
Re: [ft-devel] regarding freetype 2 cubic curve flattening
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 David Bevan. Best regards, Graham On 30/10/2011 08:25, Vivek Rathod wrote: Hello Graham, I was looking at the new spline flattening algorithm that you and David worked on. The speed up due to this is fantastic. Great work! I could not understand the part of the code where you compare *s_limit* with *s *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 height of the control point for the curve not to be split. so should we not be comparing *s= abs(dy * dxi - dx * dyi)* with *s_limit * L *instead of *s* and *s_limit* ( because s is perpendicular distance of control point multiplied by L) ? Am I missing something very obvious? * *Thanks, Vivek Rathod ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
Re: [ft-devel] regarding freetype 2 cubic curve flattening
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 height of the control point for the curve not to be split. so should we not be comparing s= abs(dy * dxi - dx * dyi) with s_limit * L instead of s and s_limit ( because s is perpendicular distance of control point multiplied by L) ? It is actually not just cross-product but s = abs(dx * dxi - dx * dyi) / L otherwise the dimensionality is wrong. Some Hain's equations just need to be creatively modified to avoid divisions in the code. ___ Freetype-devel mailing list Freetype-devel@nongnu.org https://lists.nongnu.org/mailman/listinfo/freetype-devel
