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Asymptote FAQ - Section 8
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Asymptote FAQ - Section 8 <br>
Questions about differences between Asymptote and
MetaPost
</h1>
<ul>
<li><a href="#interp" rel=subdocument>Q8.1. What is the equivalent of the MetaPost c[a,b] interpolation operator?
</a>
<li><a href="#automaticscaling" rel=subdocument>Q8.2. How does picture scaling differ in Asymptote and
MetaPost?</a>
<li><a href="#manualscaling" rel=subdocument>Q8.3. How can I avoid automatic scaling of a picture?</a>
<li><a href="#mp3dots" rel=subdocument>Q8.4. What is the equivalent of MetaPost ... command?</a>
<li><a href="#mppickup" rel=subdocument>Q8.5. What is the equivalent of the MetaPost pickup
command?</a>
<li><a href="#whatever" rel=subdocument>Q8.6. What is the equivalent of the MetaPost whatever
command?</a>
<li><a href="#lray" rel=subdocument>Q8.7. What is the equivalent for the MetaPost command for
<code>lray - horiz*v - verti*u = whatever*(LightSource -
R)</code>, a system of three linear equations for three unknowns:
<code>horiz, verti, whatever</code>?</a>
<li><a href="#unitsizes" rel=subdocument>Q8.8. In MetaPost, it is possible to have a drawing remain the same size in
different pictures by defining a unit <code>u</code> and explicitly multiply all the coordinates by
<code>u</code>. Is there a better way to do this in Asymptote?</a>
<li><a href="#tiles" rel=subdocument>Q8.9. In MetaPost, one could produce tiling pictures by generating a
picture, and then clipping the picture to a rectangle of fixed
dimensions around the center of the picture. How is that done in
Asymptote?</a>
</ul><hr>
<h2><A name="interp">
Question 8.1. What is the equivalent of the MetaPost c[a,b]
interpolation operator?
</A></h2>
<pre>
interp(a,b,c);
</pre>
<h2><A name="automaticscaling">
Question 8.2. How does picture scaling differ in Asymptote and
MetaPost?
</A></h2>
Asymptote includes an optional facility to do automatic scaling of
pictures to achieve a given overall picture size, whereas Metapost only
supports manual scaling. Asymptote defers drawing of objects drawn to pictures and
distinguishes between true-size objects and objects that should scale
with the picture size. The resulting linear programming problem is solved
via the Simplex method.
<p>
See the <A href="http://asymptote.sourceforge.net/gallery/dimension.asy">http://asymptote.sourceforge.net/gallery/dimension.asy</A> example for an example of how deferred drawing is
used to accomodate both user and true-size (PostScript) coordinates.
<h2><A name="manualscaling">
Question 8.3. How can I avoid automatic scaling of a
picture?
</A></h2>
If you really like Metapost-style manual (hard-wired) scaling either:
<p>
(i) use the default size(0,0) for the entire picture and do all of the
scaling by hand, just like in MetaPost;
<p>
(ii) draw to a separate picture pic and add(pic.fit());
<p>
(iii) use frames.
<h2><A name="mp3dots">
Question 8.4. What is the equivalent of MetaPost ...
command?
</A></h2>
The connector <code>::</code> is a macro for tension atleast 1: <pre>
size(100);
pair z0=(0,0);
pair z1=(1,0.25);
pair z2=(2,0);
draw(z0{up}::z1{right}::z2{down});
</pre>
<h2><A name="mppickup">
Question 8.5. What is the equivalent of the MetaPost pickup
command?
</A></h2>
Just say, for example: <pre>
currentpen=red;
</pre>
<h2><A name="whatever">
Question 8.6. What is the equivalent of the MetaPost whatever
command?
</A></h2>
Asymptote does not implicitly solve linear equations and therefore
does not have the notion of a <code>whatever</code> unknown. Such a facility could certainly be added (perhaps using the notation
<code>?=</code> since <code>=</code> means assignment). However, the most common uses of <code>whatever</code> in MetaPost are covered by functions like <code>extension</code> in <code>math.asy</code>: <pre>
pair extension(pair P, pair Q, pair p, pair q);
</pre>
this returns the intersection point of the extensions of the line
segments <code>PQ</code> and <code>pq</code>. We find using routines like <code>extension</code> more explicit and less confusing to new users. But we
could be persuaded to add something similar if someone can justify the
need. In the meantime, one can always use the explicit built-in linear
solver <code>solve</code> (see <A href="http://asymptote.sourceforge.net/doc/solve.html">http://asymptote.sourceforge.net/doc/solve.html</A>), which uses LU decomposition.
<h2><A name="lray">
Question 8.7. What is the equivalent for the MetaPost command for
<code>lray - horiz*v - verti*u = whatever*(LightSource -
R)</code>, a system of three linear equations for three unknowns:
<code>horiz, verti, whatever</code>?
</A></h2>
Since <code>horiz*v+verti*u</code> spans a plane, you could use <pre>
real intersect(vector P, vector Q, vector n, vector Z);
</pre>
to find the intersection time for the line
<code>lray-whatever*(LightSource - R)</code> and then extract the three desired values from there. (You'll still
need to use the built-in explicit linear solver to solve a 2x2 system to get
<code>horiz</code> and <code>verti</code>.)
<h2><A name="unitsizes">
Question 8.8. In MetaPost, it is possible to have a drawing remain
the same size in different pictures by defining a unit
<code>u</code> and explicitly multiply all the coordinates by
<code>u</code>. Is there a better way to do this in Asymptote?
</A></h2>
Yes, Asymptote has a better way: you definitely don't want to manually
scale all of your coordinates. To make the user coordinates represent
multiples of exactly <code>1cm</code>: <pre>
unitsize(1cm);
draw(unitsquare);
</pre>
One can also specify different x and y unit sizes:
<pre>
unitsize(x=1cm,y=2cm);
draw(unitsquare);
</pre>
Another way is to draw your fixed size object to a frame and add it to
currentpicture like this: <pre>
path p=(0,0)--(1,0);
frame object;
draw(object,scale(100)*p);
add(object);
add(object,(0,-10));
</pre>
To understand the difference between frames and pictures, try this:
<pre>
size(300,300);
path p=(0,0)--(1,0);
picture object;
draw(object,scale(100)*p);
add(object);
add(object,(0,-10)); // Adds truesize object to currentpicture
</pre>
<h2><A name="tiles">
Question 8.9. In MetaPost, one could produce tiling pictures by
generating a picture, and then clipping the picture to a rectangle of
fixed dimensions around the center of the picture. How is that done in
Asymptote?
</A></h2>
If you are using currentpicture the way one would in MetaPost (drawing
in raw PostScript coordinates), you can simply do something like:
<pre>
fill((0,0)--(100,100)--(200,0)--cycle);
pair center(picture pic=currentpicture) {return 0.5*(pic.min()+pic.max());}
real height=100;
real width=100;
pair delta=0.5(width,height);
pair c=center();
clip(box(c-delta,c+delta));
</pre>
However, drawing in PostScript coordinates is often inconvenient.
Here's the Asymptote way of doing the same thing, using deferred drawing:
<pre>
size(200,100);
fill((0,0)--(1,1)--(2,0)--cycle);
void clip(picture pic=currentpicture, real width, real height)
{
pic.clip(new void (frame f, transform) {
pair center=0.5(min(f)+max(f));
pair delta=0.5(width,height);
clip(f,box(center-delta,center+delta));
});
}
clip(100,100);
</pre>
See also the discussion of tilings in the documentation:
<A href="http://asymptote.sourceforge.net/doc/Pens.html">http://asymptote.sourceforge.net/doc/Pens.html</A>. <hr>
Next: <a href="section9.html" rel=precedes>Questions about output</a>.<br>
Back: <a href="section7.html" rev=precedes>Questions about programming</a>.<br>
<a href="index.html" rev=subdocument>Return to contents</a>.<p>
<address>
<A href="http://asymptote.sourceforge.net">Asymptote</A>
- 24 March 2017
</address><br>
Extracted from Asymptote Frequently Asked Questions,
Copyright © 2017 .
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