### Re: [NTG-context] Clipping a path to a boundary --- Being more specific

```
Hans et al,

I think I've found something that works. I know ahead of time that
there will only be two crossings of the clipping path boundary (I make
sure of the by the parameters I choose):

beginfig(0);

% initialize a, h, and h for f(x)=ax^2+bx+c=a(x-h)^2+k
numeric a, h, k;
a=-1;
h=-3;
k=2;

% initialize scale
numeric u; 10u=3in;

% draw grid
for k=-5u step 1u until 5u:
draw (-5u,k)--(5u,k) withcolor 0.85white;
draw (k,-5u)--(k,5u) withcolor 0.85white;
endfor;

% draw axes
drawarrow (-5u,0)--(5u,0);
drawarrow (0,-5u)--(0,5u);

% label axes
label.rt(btex \$x\$ etex, (5.2u,0));
label.top(btex \$y\$ etex, (0,5.2.u));
label.bot(btex \$5\$ etex, (5u,0));
label.lft(btex \$5\$ etex, (0,5u));

% define function f(x)=a|x-b|+c
vardef f(expr x)=
a*(x-h)*(x-h)+k
enddef;

% draw line with given point and slope
path F;
F:=(-6,f(-6));
for x=-6 step .1 until 6:
F:=F--(x,f(x));
endfor;

% the line
F:=F scaled 1u;

% clipping path
path cpath;
cpath:=(-5,-5)--(5,-5)--(5,5)--(-5,5)--cycle;
cpath:=cpath scaled 1u;

% clip the path F
pair A, B;
F:=F cutbefore cpath;
F:=reverse F;
F:=F cutbefore cpath;
drawdblarrow F;

endfig;

end.

___
ntg-context mailing list
ntg-context@ntg.nl
http://www.ntg.nl/mailman/listinfo/ntg-context

```

### Re: [NTG-context] Clipping a path to a boundary --- Being more specific

```
Hans et al,

I tried what follows. But as far as I can see, I am not getting back a
path q that is clipped to the cpath.

vardef lastpath (expr p) =
save _p_ ; path _p_ ; _p_ := origin ;
for i within p :
if stroked i : _p_ := pathpart i ; fi ;
endfor ;
_p_
enddef ;

vardef firstpath (expr p) =
save _p_, _b_ ; path _p_ ; _p_ := origin ; boolean _b_ ; _b_ :=
false ;

for i within p :
if not _b_ : if stroked i : _b_ := true ; _p_ := pathpart i
; fi ; fi ;

endfor ;
_p_
enddef ;

beginfig(0);

%initialize a of f(x)=|x-a|
numeric a;
a=-2;

% initialize scale
numeric u; 10u=3in;

%function definition
vardef f(expr x)=
abs(x-a)
enddef;

%path
path F;
F:=(-5,f(-5));
for x=-5 step 1 until 5:
F:=F--(x,f(x));
endfor;

%scale and draw F
F:=F scaled u;
draw F withcolor blue;

%clip path
path cpath;
cpath:=(5,-5)--(5,5)--(-5,5)--(-5,-5)--cycle;
cpath:=cpath scaled u;
clip currentpicture to cpath;

%save and null currentpicture
picture pic;
pic:=currentpicture;
currentpicture:=nullpicture;

%retrieve first path
path q; q:=firstpath(pic);

%draw grid
for k=-5u step 1u until 5u:
draw (-5u,k)--(5u,k) withcolor 0.85white;
draw (k,-5u)--(k,5u) withcolor 0.85white;
endfor;

% draw axes
drawarrow (-5u,0)--(5u,0);
drawarrow (0,-5u)--(0,5u);

% label axes
label.rt(btex \$x\$ etex, (5.2u,0));
label.top(btex \$y\$ etex, (0,5.2.u));
label.bot(btex \$5\$ etex, (5u,0));
label.lft(btex \$5\$ etex, (0,5u));

drawdblarrow q withcolor blue;

endfig;

end.

On Aug 8, 2005, at 6:20 AM, Hans Hagen wrote:

David Arnold wrote:

Hans et al,

Let me try to be more specific. Here is a file which is very typical
of the way I draw graphs for my mathematics classes. When you
compile, you will see the graph of the absolute value of x-1. That
is, it draws the graph of y=|x-1|, but only after clipping it to the
cpath.  What I would like to do is draw the graph with the
drawdblarrow command so that the graph of the absolute value ends in
arrowheads. So, I want to clip the graph to the bounding box, save
the picture, null the picture, then somehow extract the path into the
variable F in its clipped form (not the original path F that extends
outside the clip path) so that I can replace the command draw pic
with drawdblarrow F.

hm, this need some more brainpower than the previous solution,

in mp-tool there is a repathed macro that does most of the job so
let's extend that one a bit:

\starttext

\setupcolors[state=start]

\startMPpage

def restroke  suffix p = p := repathed (21,p) enddef ; % keep
attributes

def reprocess suffix p = p := repathed (22,p) enddef ; % no attributes

vardef repathed (expr mode, p) text t =
begingroup ;
if mode=0 : save withcolor ; remapcolors ; fi ;
save _p_, _pp_, _ppp_, _f_, _b_, _t_ ;
picture _p_, _pp_, _ppp_ ; color _f_ ; path _b_ ; transform _t_ ;
_b_ := boundingbox p ; _p_ := nullpicture ;
for i within p :
_f_ := (redpart i, greenpart i, bluepart i) ;
if bounded i :
_pp_ := repathed(mode,i) t ;
setbounds _pp_ to pathpart i ;
elseif clipped i :
_pp_ := repathed(mode,i) t ;
clip _pp_ to pathpart i ;
elseif stroked i :
if mode=21 :
_ppp_ := i ; % indirectness is needed
addto _p_ also image(scantokens(t   pathpart _ppp_)
dashed dashpart i withpen penpart i
withcolor _f_ ; ) ;
elseif mode=22 :
_ppp_ := i ; % indirectness is needed
addto _p_ also image(scantokens(t   pathpart _ppp_)) ;
else :
dashed dashpart i withpen penpart i
withcolor _f_ % (redpart i, greenpart i, bluepart i)
if mode=2 : t fi ;
fi ;
elseif filled  i :
if mode=11 :
_ppp_ := i ; % indirectness is needed
addto _p_ also image(scantokens(t   pathpart _ppp_)
withcolor _f_ ; ) ;
elseif mode=12 :
_ppp_ := i ; % indirectness is needed
addto _p_ also image(scantokens(t   pathpart _ppp_)) ;
else :
withcolor _f_
if (mode=1) and (_f_refillbackground) : t fi ;
fi ;
elseif textual i : % textpart i   :
if mode  4 :
addto _p_ also i if mode=3 : t fi ;
fi ;
else :
fi ;
endfor ;
setbounds _p_ to _b_ ;
_p_
endgroup
enddef ;

picture pic; pic := image(
draw fullcircle scaled 5cm withpen pencircle scaled 5mm ;
draw fullsquare scaled 2cm withpen pencircle scaled 5mm ;
fill fullcircle scaled 1cm withpen pencircle scaled 5mm ;
) ;

redraw pic withpen pencircle scaled 1mm withcolor red ;
% restroke pic drawdblarrow ;
pic := repathed(21,pic) drawdblarrow ;
pic := repathed(11,pic) drawdblarrow ;
draw pic ;

\stopMPpage

\stoptext

the new restroke variant takes a macro name that itself takes one
argument, i.e. a ```

### Re: [NTG-context] Clipping a path to a boundary --- Being more specific

```
David Arnold wrote:

Hans et al,

Let me try to be more specific. Here is a file which is very typical
of the way I draw graphs for my mathematics classes. When you compile,
you will see the graph of the absolute value of x-1. That is, it draws
the graph of y=|x-1|, but only after clipping it to the cpath.  What I
would like to do is draw the graph with the drawdblarrow command so
that the graph of the absolute value ends in arrowheads. So, I want to
clip the graph to the bounding box, save the picture, null the
picture, then somehow extract the path into the variable F in its
clipped form (not the original path F that extends outside the clip
path) so that I can replace the command draw pic with drawdblarrow F.

hm, this need some more brainpower than the previous solution,

in mp-tool there is a repathed macro that does most of the job so let's
extend that one a bit:

\starttext

\setupcolors[state=start]

\startMPpage

def restroke  suffix p = p := repathed (21,p) enddef ; % keep attributes
def reprocess suffix p = p := repathed (22,p) enddef ; % no attributes

vardef repathed (expr mode, p) text t =
begingroup ;
if mode=0 : save withcolor ; remapcolors ; fi ;
save _p_, _pp_, _ppp_, _f_, _b_, _t_ ;
picture _p_, _pp_, _ppp_ ; color _f_ ; path _b_ ; transform _t_ ;
_b_ := boundingbox p ; _p_ := nullpicture ;
for i within p :
_f_ := (redpart i, greenpart i, bluepart i) ;
if bounded i :
_pp_ := repathed(mode,i) t ;
setbounds _pp_ to pathpart i ;
elseif clipped i :
_pp_ := repathed(mode,i) t ;
clip _pp_ to pathpart i ;
elseif stroked i :
if mode=21 :
_ppp_ := i ; % indirectness is needed
addto _p_ also image(scantokens(t   pathpart _ppp_)
dashed dashpart i withpen penpart i
withcolor _f_ ; ) ;
elseif mode=22 :
_ppp_ := i ; % indirectness is needed
addto _p_ also image(scantokens(t   pathpart _ppp_)) ;
else :
dashed dashpart i withpen penpart i
withcolor _f_ % (redpart i, greenpart i, bluepart i)
if mode=2 : t fi ;
fi ;
elseif filled  i :
if mode=11 :
_ppp_ := i ; % indirectness is needed
addto _p_ also image(scantokens(t   pathpart _ppp_)
withcolor _f_ ; ) ;
elseif mode=12 :
_ppp_ := i ; % indirectness is needed
addto _p_ also image(scantokens(t   pathpart _ppp_)) ;
else :
withcolor _f_
if (mode=1) and (_f_refillbackground) : t fi ;
fi ;
elseif textual i : % textpart i   :
if mode  4 :
addto _p_ also i if mode=3 : t fi ;
fi ;
else :
fi ;
endfor ;
setbounds _p_ to _b_ ;
_p_
endgroup
enddef ;

picture pic; pic := image(
draw fullcircle scaled 5cm withpen pencircle scaled 5mm ;
draw fullsquare scaled 2cm withpen pencircle scaled 5mm ;
fill fullcircle scaled 1cm withpen pencircle scaled 5mm ;
) ;

redraw pic withpen pencircle scaled 1mm withcolor red ;
% restroke pic drawdblarrow ;
pic := repathed(21,pic) drawdblarrow ;
pic := repathed(11,pic) drawdblarrow ;
draw pic ;

\stopMPpage

\stoptext

the new restroke variant takes a macro name that itself takes one argument, i.e. a path, so in order to do more complex things, you need to define those

Hans

-
Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
tel: 038 477 53 69 | fax: 038 477 53 74 | www.pragma-ade.com
| www.pragma-pod.nl
-

___
ntg-context mailing list
ntg-context@ntg.nl
http://www.ntg.nl/mailman/listinfo/ntg-context

```

### [NTG-context] Clipping a path to a boundary --- Being more specific

```
Hans et al,

Let me try to be more specific. Here is a file which is very typical of
the way I draw graphs for my mathematics classes. When you compile, you
will see the graph of the absolute value of x-1. That is, it draws the
graph of y=|x-1|, but only after clipping it to the cpath.  What I
would like to do is draw the graph with the drawdblarrow command so
that the graph of the absolute value ends in arrowheads. So, I want to
clip the graph to the bounding box, save the picture, null the picture,
then somehow extract the path into the variable F in its clipped form
(not the original path F that extends outside the clip path) so that I
can replace the command draw pic with drawdblarrow F.

beginfig(0);

numeric a, c;
a=1;

% define function f(x)=|x-a|
vardef f(expr x)=
abs(x-a)
enddef;

% draw line with given point and slope
path F;
F:=(-5,f(-5));
for x=-5 step 1 until 5:
F:=F--(x,f(x));
endfor;

% initialize scale
numeric u; 10u=3in;

% the line
F:=F scaled 1u;
draw F withcolor blue;

% clipping path
path cpath;
cpath:=(-5,-5)--(5,-5)--(5,5)--(-5,5)--cycle;
cpath:=cpath scaled 1u;

% clip and save current picture
picture pic;
clip currentpicture to cpath;
pic:=currentpicture;
currentpicture:=nullpicture;

% erase currentpicture
currentpicture:=nullpicture;

% draw grid
for k=-5u step 1u until 5u:
draw (-5u,k)--(5u,k) withcolor 0.85white;
draw (k,-5u)--(k,5u) withcolor 0.85white;
endfor;

% draw axes
drawarrow (-5u,0)--(5u,0);
drawarrow (0,-5u)--(0,5u);

% label axes
label.rt(btex \$x\$ etex, (5.2u,0));
label.top(btex \$y\$ etex, (0,5.2.u));
label.bot(btex \$5\$ etex, (5u,0));
label.lft(btex \$5\$ etex, (0,5u));

% redraw line
draw pic;

endfig;

end.

___
ntg-context mailing list
ntg-context@ntg.nl
http://www.ntg.nl/mailman/listinfo/ntg-context

```