Preview OSX bug (?) converting bezier curve in .eps file to .pdf

Question

I have a small .eps file which uses bezier curves with a thick linewidth to achieve a certain effect. This file displays as I expect it to in gv, but when I convert it to a .pdf (eg with ps2pdf or by opening the file with Preview on a Mac running OSX) it renders some of the curves incorrectly (or at least, not in the way I was expecting); in the middle of the curve, the normals to the curve seem to "flip over", producing a strange artifact.

Here is the .eps file in question, as code:

%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 0 0 750 200
gsave 50 50 scale 1 3 translate

/edge{4 dict begin
/y2 exch def
/x2 exch def
/y1 exch def
/x1 exch def
gsave
1 setgray
1 8 div setlinewidth
newpath
x1 y1 moveto x2 y2 lineto
stroke
0 setgray
1 20 div setlinewidth
newpath
x1 y1 moveto x2 y2 lineto
stroke
x1 y1 0.07 0 360 arc fill stroke
x2 y2 0.07 0 360 arc fill stroke
grestore
end}def

/cur_edge{7 dict begin
/T exch def
/angle2 exch def
/y2 exch def
/x2 exch def
/angle1 exch def
/y1 exch def
/x1 exch def
gsave
1 setgray
1 8 div setlinewidth
newpath
x1 y1 moveto 
x1 angle1 cos T mul add y1 angle1 sin T mul add
x2 angle2 cos T mul add y2 angle2 sin T mul add
x2 y2 curveto
stroke
0 setgray
1 20 div setlinewidth
newpath
x1 y1 moveto 
x1 angle1 cos T mul add y1 angle1 sin T mul add
x2 angle2 cos T mul add y2 angle2 sin T mul add
x2 y2 curveto
stroke
x1 y1 0.07 0 360 arc fill stroke
x2 y2 0.07 0 360 arc fill stroke
grestore
end}def

/fat_edge{7 dict begin
/T exch def
/angle2 exch def
/y2 exch def
/x2 exch def
/angle1 exch def
/y1 exch def
/x1 exch def
gsave
0 setgray
1 4 div setlinewidth
newpath
x1 y1 moveto 
x1 angle1 cos T mul add y1 angle1 sin T mul add
x2 angle2 cos T mul add y2 angle2 sin T mul add
x2 y2 curveto
stroke
0.9 setgray
1 5 div setlinewidth
newpath
x1 y1 moveto 
x1 angle1 cos T mul add y1 angle1 sin T mul add
x2 angle2 cos T mul add y2 angle2 sin T mul add
x2 y2 curveto
stroke
grestore
end}def

/fat_vertex{4 dict begin
/angle exch def
/y exch def
/x exch def
/T 0.14 def
gsave
0.9 setgray
1 5.5 div setlinewidth
newpath
x y moveto
x angle cos T mul add y angle sin T mul add lineto
stroke
grestore
end}def

/extra_fat_vertex{5 dict begin
/y exch def
/x exch def
/w 0.16 def
gsave
1 setgray
newpath
x w sub y w sub moveto
x w add y w sub lineto
x w add y w add lineto
x w sub y w add lineto
closepath
fill
stroke
0 setgray
/v 0.12 def
newpath
x v sub y v sub moveto
x v add y v sub lineto
x v add y v add lineto
x v sub y v add lineto
closepath
fill    
0.9 setgray
/u 0.095 def
newpath
x u sub y u sub moveto
x u add y u sub lineto
x u add y u add lineto
x u sub y u add lineto
closepath
fill    
grestore
end}def

/extra_fat_triangle{5 dict begin
/y exch def
/x exch def
/w 0.16 def
gsave
1 setgray
newpath
x w sub y w sub moveto
x w 1.1 mul add y lineto
x w sub y w add lineto
closepath
fill
stroke
0 setgray
/v 0.12 def
newpath
x v sub y v sub moveto
x v add y lineto
x v sub y v add lineto
closepath
fill    
0.9 setgray
/u 0.095 def
newpath
x u sub y u sub moveto
x u 0.85 mul add y lineto
x u sub y u add lineto
closepath
fill    
grestore
end}def

/extra_fat_triangle_left{5 dict begin
/y exch def
/x exch def
/w 0.16 def
gsave
1 setgray
newpath
x w add y w sub moveto
x w 1.1 mul sub y lineto
x w add y w add lineto
closepath
fill
stroke
0 setgray
/v 0.12 def
newpath
x v add y v sub moveto
x v sub y lineto
x v add y v add lineto
closepath
fill    
0.9 setgray
/u 0.095 def
newpath
x u add y u sub moveto
x u 0.85 mul sub y lineto
x u add y u add lineto
closepath
fill    
grestore
end}def

0 0 90 2 0 270 1 cur_edge
% 0 0 270 2 0 90 1 cur_edge
2 0 90 0 0 270  1 cur_edge
0 0 180 0.5 -2 180 1 cur_edge
0.5 -2 90 1.5 -1.3 180 0.5 cur_edge
1.5 -1.3 270 2.5 -2 270 0.7 cur_edge
2.5 -2 90 0.5 -2 270 1 cur_edge %
2.5 -2 0 3 -0.75 0 1 cur_edge
3 -0.75 270 1.5 -1.3 0 0.7 cur_edge
3 -0.75 180 1.5 -1.3 90 0.7 cur_edge
3 -0.75 90 2 0 0 0.5 cur_edge

5 0 translate
0 0 90 2 0 270 1 fat_edge
% 0 0 270 2 0 90 1 fat_edge
2 0 90 0 0 270  1 fat_edge
0 0 180 0.5 -2 180 1 fat_edge
0.5 -2 90 1.5 -1.3 180 0.5 fat_edge
1.5 -1.3 270 2.5 -2 270 0.7 fat_edge
2.5 -2 90 0.5 -2 270 1 fat_edge
2.5 -2 0 3 -0.75 0 1 fat_edge
3 -0.75 270 1.5 -1.3 0 0.7 fat_edge
3 -0.75 180 1.5 -1.3 90 0.7 fat_edge
3 -0.75 90 2 0 0 0.5 fat_edge

0 0 90 fat_vertex
0 0 180 fat_vertex
0 0 270 fat_vertex
2 0 0 fat_vertex
2 0 90 fat_vertex
2 0 270 fat_vertex
0.5 -2 180 fat_vertex
0.5 -2 90 fat_vertex
2.5 -2 90 fat_vertex
2.5 -2 270 fat_vertex
1.5 -1.3 0 fat_vertex
1.5 -1.3 90 fat_vertex
1.5 -1.3 180 fat_vertex
1.5 -1.3 270 fat_vertex
3 -0.75 0 fat_vertex
3 -0.75 90 fat_vertex
3 -0.75 180 fat_vertex
3 -0.75 270 fat_vertex

5 0 translate
0 0 90 2 0 270 1 fat_edge
% 0 0 270 2 0 90 1 fat_edge
2 0 90 0 0 270  1 fat_edge

0 0 180 0.5 -2 180 1 fat_edge
0.5 -2 90 1.5 -1.3 180 0.5 fat_edge
1.5 -1.3 270 2.5 -2 270 0.7 fat_edge
2.5 -2 90 0.5 -2 270 1 fat_edge
2.5 -2 0 3 -0.75 0 1 fat_edge
3 -0.75 270 1.5 -1.3 0 0.7 fat_edge
3 -0.75 180 1.5 -1.3 90 0.7 fat_edge
3 -0.75 90 2 0 0 0.5 fat_edge

0 0 90 fat_vertex
0 0 180 fat_vertex
0 0 270 fat_vertex
2 0 0 fat_vertex
2 0 90 fat_vertex
2 0 270 fat_vertex
0.5 -2 180 fat_vertex
0.5 -2 90 fat_vertex
2.5 -2 90 fat_vertex
2.5 -2 270 fat_vertex
1.5 -1.3 0 fat_vertex
1.5 -1.3 90 fat_vertex
1.5 -1.3 180 fat_vertex
1.5 -1.3 270 fat_vertex
3 -0.75 0 fat_vertex
3 -0.75 90 fat_vertex
3 -0.75 180 fat_vertex
3 -0.75 270 fat_vertex

0 0 extra_fat_triangle
2 0 extra_fat_triangle_left
0.5 -2 extra_fat_triangle
1.5 -1.3 extra_fat_vertex
2.5 -2 extra_fat_triangle_left
3 -0.75 extra_fat_vertex

grestore
%eof

What is curious is that the .pdf only displays incorrectly when it is resized to certain specific sizes (or: it displays correctly at certain sizes). I don't seem to be able to predict when it will work.

Here is how it displays (part of the image) correctly:

correct image

And here it is resized and displaying incorrectly:

_{(source: dannyc at math.uchicago.edu)}

Note that these images are .jpgs obtained from the .pdf. If you save the code above as an .eps file and open it with Preview on a Mac, I assume it will exhibit the same pathology it did on my computer.

Any advice would be very welcome. I don't know enough (or: anything) about how bezier curves are displayed in .pdf to know what might be the problem here.

Kurt Revis · Accepted Answer · 2013-01-04T06:40:20.890

2

Here's a cut down case that displays the same rendering problem:

%!PS-Adobe-2.0 EPSF-2.0
%%BoundingBox: 0 0 400 200
gsave 50 50 scale 1 3 translate

0 setgray
0.05 setlinewidth
newpath
0 0 moveto 
0 1 2 -1 2 0 curveto
stroke

grestore
%eof

Can't get much simpler than that: a Bezier path with just two points, all with integer values.

It looks like Apple's renderer has some numeric instability around the center of the curve. If you tweak one of the curve control points by a tiny amount, the bug doesn't happen:

0 1.00001 2 -1 2 0 curveto

So there's a workaround: In your original file, add a small fudge factor (a fraction of a degree) to one of the angles in each curve.

I changed each /angle1 exch def to 0.01 add /angle1 exch def, and it worked for me. Here's the EPS file and the resulting PDF file.

(Of course this shouldn't be necessary, but until you file a bug and Apple releases a fix, it may be the most expedient solution.)

edited Jan 04 '13 at 06:40

answered Jan 03 '13 at 06:47

Kurt Revis

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Thanks for the suggestion. I tried it but the bug still seems to persist on my system. Is there any documentation for the algorithm Apple actually uses (or would use if Preview worked correctly)? – Danny Calegari Jan 03 '13 at 14:18
Ha - when I go to try to file a bug report at Apple, I get a login error: "An error has occurred. Please report the error to Apple Inc. by emailing the error detail to devbugs@apple.com." I sense a vicious circle here . . . – Danny Calegari Jan 03 '13 at 14:30
Edited answer to add more details on the workaround, and links to the EPS and PDF files. – Kurt Revis Jan 04 '13 at 06:02

Preview OSX bug (?) converting bezier curve in .eps file to .pdf

1 Answers1