pathbbox

[jdaw1]

Below is code, measuring the height above the baseline of a piece of
text, in user space, which should therefore be independent of
rotation.

%!

/TimesNewRomanPS-BoldMT 15 selectfont

90 5 div 1 add cvi
{
gsave newpath 0 0 moveto
(ABEGHKLNTVWXZ1fhijklt) true charpath flattenpath pathbbox 4 1 roll
pop pop pop =
grestore
5 rotate
} repeat

Mac Distiller 8.1.0, 10/23/06, outputs to the log file:

10.125
25.8882
41.3663
55.9918
69.0431
80.1131
89.0882
95.9074
100.125
101.601
100.273
96.2059
89.5666
80.5308
69.3089
56.2502
41.7149
26.2031
10.17

Please, why aren't these nineteen numbers identical? I'm obviously
making a simple error, but am now blind to it. Thank you.

[Jeffrey H. Coffield]

Page 632 in the Postscipt Language Manual, Third edition says:

"If the user coordinate system is rotated (other than a multiple of 90
degrees) or skewed, the bounding box returned may be larger than expected."

Jeff Coffield

[jdaw1]

Oh, it's that simple, thank you. So I'm going to use the following,
not quite fully debugged.

%!

/TimesNewRomanPS-BoldMT 15 selectfont

% - PathBBox llx lly urx ury
% assesses only parts that will show visibly
/PathBBox
{
21 dict begin

/TrivialDistance 0.0001 def % inconveniently in user space
/MinMaxDefinedX false def
/MinMaxDefinedY false def
/x0y0Defined false def
/MinX /undef def /MaxX /undef def
/MinY /undef def /MaxY /undef def

/SetMinMaxX % takes one parameter
{
1 dict begin
/x exch def
MinMaxDefinedX
{MaxX x lt {/MaxX x store} if MinX x gt {/MinX x store} if}
{/MaxX x store /MinX x store /MinMaxDefinedX true store}
ifelse
end
} def % SetMinMaxX

/SetMinMaxY % takes one parameter
{
1 dict begin
/y exch def
MinMaxDefinedY
{MaxY y lt {/MaxY y store} if MinY y gt {/MinY y store} if}
{/MaxY y store /MinY y store /MinMaxDefinedY true store}
ifelse
end
} def % SetMinMaxY

{ % start move
/y0 exch def /x0 exch def
/x0y0Defined true def
} % end of move
{ % start line
/y1 exch def /x1 exch def
x0 x1 sub abs TrivialDistance ge y0 y1 sub abs TrivialDistance ge
or
{
x0 SetMinMaxX x1 SetMinMaxX
y0 SetMinMaxY y1 SetMinMaxY
} if % non-trivial line segment
/y0 y1 def /x0 x1 def
} % end of line
{ % start curve
/y3 exch def /x3 exch def /y2 exch def /x2 exch def /y1 exch
def /x1 exch def

x0 x1 sub abs TrivialDistance ge x0 x2 sub abs TrivialDistance ge
x0 x3 sub abs TrivialDistance ge or or {true} {
y0 y1 sub abs TrivialDistance ge y0 y2 sub abs TrivialDistance ge
y0 y3 sub abs TrivialDistance ge or or} ifelse
{
x0 SetMinMaxX x3 SetMinMaxX
x1 MaxX gt x1 MinX lt x2 MaxX gt x2 MinX lt or or or
{
% Cubic: a t^3 + b t^2 + c t + x0
/a x0 neg x1 3 mul add x2 3 mul sub x3 add def
/b x0 x1 2 mul sub x2 add 3 mul def
/c x1 x0 sub 3 mul def

a abs 0 gt
{
% Solve first differential for zero
/Discriminant 4 b b mul mul 12 a c mul mul sub def
Discriminant 0 ge
{
/Discriminant Discriminant sqrt def
[ {add} {sub} ]
{
/t -2 b mul Discriminant 4 -1 roll exec 6 a mul div
def
t 0 gt t 1 lt and {a t mul b add t mul c add t mul x0 add
SetMinMaxX} if % if turning point between endpoints
} forall % add, sub
} if % has turning point
} if % a abs 0 gt
} if % x bounds outside MinX to MaxX
y0 SetMinMaxY y3 SetMinMaxY
y1 MaxY gt y1 MinY lt y2 MaxY gt y2 MinY lt or or or
{
/a y0 neg y1 3 mul add y2 3 mul sub y3 add def
/b y0 y1 2 mul sub y2 add 3 mul def
/c y1 y0 sub 3 mul def

a abs 0 gt
{
/Discriminant 4 b b mul mul 12 a c mul mul sub def
Discriminant 0 ge
{
/Discriminant Discriminant sqrt def
[ {add} {sub} ]
{
/t -2 b mul Discriminant 4 -1 roll exec 6 a mul div
def
t 0 gt t 1 lt and {a t mul b add t mul c add t mul y0 add
SetMinMaxY} if % if turning point between endpoints
} forall % add, sub
} if % has turning point
} if % a abs 0 gt
} if % y bounds outside MinY to MaxY
} if % non-trivial curve segment
/y0 y3 def /x0 x3 def
} % end of curve
{ % start close
} % end of close
pathforall

MinMaxDefinedX MinMaxDefinedY and {MinX MinY MaxX MaxY} {x0y0Defined
{x0 y0 2 copy} {PathBBoxEmptyPathError} ifelse} ifelse

end
} def % PathBBox

90 5 div 1 add cvi
{
gsave newpath 0 0 moveto

(ABEGHKLNTVWXZ1fhijklt) true charpath PathBBox 4 1 roll pop pop pop

=
grestore
5 rotate
} repeat

This returns the good enough (but still imperfect)

10.125
10.1755
10.1735
10.1672
10.1696
10.1842
10.1932
10.1873
10.1648
10.1867
10.1876
10.2004
10.1733
10.1746
10.1734
10.1774
10.1771
10.1789
10.17

[Jeffrey H. Coffield]

Without doing a lengthy analysis of your code, it looks like the tests
for TrivialDistance could introduce errors that are large enough to
cause the difference in your output.

Jeff Coffield
www.digitalsynergyinc.com

[jdaw1]

Thank you.

TrivialDistance deleted.
Fixed possible error if cubic was actually a quadratic.

Latest version of PathBBox available within www.jdawiseman.com/papers/placemat/placemat.ps
if you should want it.

[jdaw1]

Code far below outputs stuff immediately below. Still slightly
imperfect: if anyone is willing to wade through the detail,
corrections welcome.

[0 10.125]
[5 10.1755]
[10 10.1735]
[15 10.1672]
[20 10.1696]
[25 10.1842]
[30 10.1931]
[35 10.1872]
[40 10.1648]
[45 10.1867]
[50 10.1876]
[55 10.2004]
[60 10.1733]
[65 10.1746]
[70 10.1733]
[75 10.1774]
[80 10.177]
[85 10.1789]
[90 10.14]

Max - Min =
0.0790844

%!

/TimesNewRomanPS-BoldMT 15 selectfont

% - PathBBox llx lly urx ury
% assesses only parts that will show visibly
/PathBBox
{

22 dict begin

/MinMaxDefinedX false def
/MinMaxDefinedY false def
/x0y0Defined false def
/MinX /undef def /MaxX /undef def
/MinY /undef def /MaxY /undef def

/SetMinMaxX % takes one parameter
{

/z exch def
MinMaxDefinedX
{MaxX z lt {/MaxX z store} {MinX z gt {/MinX z store} if} ifelse}
{/MaxX z store /MinX z store /MinMaxDefinedX true store}
ifelse

} def % SetMinMaxX
/SetMinMaxY % takes one parameter
{

/z exch def
MinMaxDefinedY
{MaxY z lt {/MaxY z store} {MinY z gt {/MinY z store} if} ifelse}
{/MaxY z store /MinY z store /MinMaxDefinedY true store}
ifelse
} def % SetMinMaxY

% First rough bounds from a quick run-through, as doing so can save
doing needless arithmetic in curve routine.

{ % start move
/y0 exch def /x0 exch def
/x0y0Defined true def
} % end of move
{ % start line
/y1 exch def /x1 exch def

x0 SetMinMaxX x1 SetMinMaxX
y0 SetMinMaxY y1 SetMinMaxY

} % end of line
{ % start curve

/y3 exch def /x3 exch def pop pop pop pop
x0 SetMinMaxX x3 SetMinMaxX
y0 SetMinMaxY y3 SetMinMaxY

} % end of curve
{ % start close
} % end of close
pathforall

% Second a slower run-through, not redoing the above, but, where
necessary, thinking hard about curves

{ % start move
/y0 exch def /x0 exch def

} % end of move
{ % start line

/y0 exch def /x0 exch def

} % end of line
{ % start curve
/y3 exch def /x3 exch def /y2 exch def /x2 exch def /y1 exch
def /x1 exch def

x1 MaxX gt x1 MinX lt x2 MaxX gt x2 MinX lt or or or

{
% Cubic: a t^3 + b t^2 + c t + x0
/a x0 neg x1 3 mul add x2 3 mul sub x3 add def
/b x0 x1 2 mul sub x2 add 3 mul def
/c x1 x0 sub 3 mul def

% Solve first differential for zero

a abs 0 gt
{
/Discriminant 4 b b mul mul 12 a c mul mul sub def

Discriminant 0 gt

{
/Discriminant Discriminant sqrt def
[ {add} {sub} ]
{
/t -2 b mul Discriminant 4 -1 roll exec 6 a mul div def
t 0 gt t 1 lt and {a t mul b add t mul c add t mul x0 add
SetMinMaxX} if % if turning point between endpoints
} forall % add, sub

} if % Discriminant 0 gt
}
{
b abs 0 gt
{
/t c -2 div b div def

t 0 gt t 1 lt and {a t mul b add t mul c add t mul x0 add
SetMinMaxX} if % if turning point between endpoints

} if % b abs 0 gt
} ifelse % a abs 0 gt

} if % x bounds outside MinX to MaxX

y1 MaxY gt y1 MinY lt y2 MaxY gt y2 MinY lt or or or

{
/a y0 neg y1 3 mul add y2 3 mul sub y3 add def
/b y0 y1 2 mul sub y2 add 3 mul def
/c y1 y0 sub 3 mul def

a abs 0 gt
{
/Discriminant 4 b b mul mul 12 a c mul mul sub def

Discriminant 0 gt

{
/Discriminant Discriminant sqrt def
[ {add} {sub} ]
{
/t -2 b mul Discriminant 4 -1 roll exec 6 a mul div def
t 0 gt t 1 lt and {a t mul b add t mul c add t mul y0 add
SetMinMaxY} if % if turning point between endpoints
} forall % add, sub

} if % Discriminant 0 gt
}
{
b abs 0 gt
{
/t c -2 div b div def

t 0 gt t 1 lt and {a t mul b add t mul c add t mul y0 add
SetMinMaxY} if % if turning point between endpoints

} if % b abs 0 gt
} ifelse % a abs 0 gt

} if % y bounds outside MinY to MaxY

/y0 y3 def /x0 x3 def
} % end of curve
{ % start close
} % end of close
pathforall

MinMaxDefinedX MinMaxDefinedY and {MinX MinY MaxX MaxY} {x0y0Defined

{x0 y0 2 copy} {nocurrentpoint} ifelse} ifelse

end
} bind def % PathBBox

/sMax 0 def
/sMin 9999999 def

0 1 90
{
/a exch def
gsave a rotate newpath 0 0 moveto

(ABEGHKLNTVWXZ1fhijklt) true charpath PathBBox 4 1 roll pop pop pop

grestore
/s exch def sMax s lt {/sMax s def} if sMin s gt {/sMin s def} if
a 5 mod 0 eq {[a s] ==} if
} for
() = (Max - Min =) = sMax sMin sub ==