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Subject: Units of xpart and ypart of a pair in MetaFun
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Hi,

I have been using xpart and ypart to extract these values from pairs of 
points in a path but I wasn't getting the correct result. I was expecting:

pair (2cm, 11cm) to give xpart 2 and ypart 11

However I was getting:

pair (2cm, 11cm) -> xpart 56.6929 and ypart 311.8096

After much head scratching and reading the MetaPost and MetaFun manuals, 
I realised that the units of xpart or ypart are in Postcript points or 
Big Points (bp), and 1 bp is 1/72 of an inch, and thus to get the values 
of xpart or ypart in cm I would have to use a correction factor. I had 
made the assumption that since the x and ypart in the pair was in cm 
that the result would be in cm, but I see now that this is not the case. 
Will I have to continue doing this or is there some magic within MetaFun 
which takes account of the units in a pair and outputs the result of x 
and ypart in the same units?

The MWE belows shows what I have been doing.

Thanks

Keith McKay

%%% MWE %%%

\setuppapersize [A5, landscape][A4, portrait]

\usecolors[crayola]

\starttext

\startMPpage

StartPage;

width := PaperWidth ; height := PaperHeight ; unit := cm ;

numeric squig;

pair a[]; a0 = (2cm,11cm); a1 = (4cm,10cm); a2 = (6cm,9cm); a3 = (8cm,8cm);

show xpart a[0], ypart a[0]; %Example of result from x and ypart before 
applying correction factor (cf) %

cf := 72/2.54; %Converts points/in to points/cm%

path pp;

for i = 0 step 1 until 3:

pp := ((xpart a[i])/cf*cm, (ypart a[i])/cf*cm);

for squig = 1 step 1 until 15:

xcoord := uniformdeviate(1) - 0.5 + (xpart a[i]/cf);

ycoord := uniformdeviate(1) - 0.5+ (ypart a[i]/cf);

pp := pp .. {curl 100}(xcoord*cm, ycoord*cm);

endfor;

pp := pp --- cycle;

if i < 3 :

pp := pp --- ((xpart a[i+1]/cf)*cm, (ypart a[i+1])/cf*cm);

fi;

f :=((1.4 - 0.6) * uniformdeviate(1)) + 0.8; % Factor to lighten/darken 
colour %

draw pp withpen pencircle xscaled 0.5mm yscaled .1mm rotated 45 
withcolor (f[white,\MPcolor{BurntSienna}]);

endfor;

StopPage;

\stopMPpage

\stoptext

%%%%%%%%%%%%%%


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<html>
  <head>

    <meta http-equiv="content-type" content="text/html; charset=UTF-8">
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  <body>
    <p>Hi,</p>
    <p>I have been using xpart and ypart to extract these values from pairs of points in a path but I wasn't getting the correct result. I was expecting:</p>
    <p>pair (2cm, 11cm) to give xpart 2 and ypart 11</p>
    <p>However I was getting:</p>
    <p>pair (2cm, 11cm) -&gt; xpart 56.6929 and ypart 311.8096</p>
    <p>After much head scratching and reading the MetaPost and MetaFun manuals, I realised that the units of xpart or ypart are in Postcript points or Big Points (bp), and 1 bp is 1/72 of an inch, and thus to get the values of xpart or ypart in cm I would have to use a correction factor. I had made the assumption that since the x and ypart in the pair was in cm that the result would be in cm, but I see now that this is not the case. Will I have to continue doing this or is there some magic within MetaFun which takes account of the units in a pair and outputs the result of x and ypart in the same units?</p>
    <p>The MWE belows shows what I have been doing.</p>
    <p>Thanks</p>
    <p>Keith McKay
</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">%%% MWE %%%</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">\setuppapersize [A5, landscape][A4, portrait]</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">\usecolors[crayola]</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">\starttext</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">\startMPpage</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">StartPage;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">width := PaperWidth ; height := PaperHeight ; unit := cm ;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">numeric squig;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">pair a[]; a0 = (2cm,11cm);  a1 = (4cm,10cm);  a2 = (6cm,9cm);  a3 = (8cm,8cm);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">show xpart a[0], ypart a[0]; %Example of result from x and ypart before applying correction factor (cf) %</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">cf := 72/2.54; %Converts points/in to points/cm%</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">path pp;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">for i = 0 step 1 until 3:</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">	pp := ((xpart a[i])/cf*cm, (ypart a[i])/cf*cm);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">	for squig = 1 step 1 until 15:</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">		xcoord := uniformdeviate(1) - 0.5 + (xpart a[i]/cf);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">		ycoord := uniformdeviate(1) - 0.5+ (ypart a[i]/cf);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">		pp := pp  .. {curl 100}(xcoord*cm, ycoord*cm);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">	endfor;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">	pp := pp --- cycle;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">	if i &lt; 3 :</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">		pp := pp --- ((xpart a[i+1]/cf)*cm, (ypart a[i+1])/cf*cm);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">	fi;	</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">	f :=((1.4 - 0.6) * uniformdeviate(1)) + 0.8; % Factor to lighten/darken colour %</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">	draw pp withpen pencircle xscaled 0.5mm yscaled .1mm rotated 45 withcolor (f[white,\MPcolor{BurntSienna}]);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">endfor;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">StopPage;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">\stopMPpage</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">\stoptext</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">%%%%%%%%%%%%%%</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; line-height:100%;">
</p>
    <p><style type="text/css">
p, li { white-space: pre-wrap; }</style></p>
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