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如何将此 Asymptote 代码渲染成图像?

[英]How do I render this Asymptote code into an image?

I don't know anything about asymptote, I asked an AI to generate the code based this geometry problem,我对渐近线一无所知,我请人工智能根据这个几何问题生成代码,

Prove that in a triangle ABC, if the altitudes AD, BE and CF to sides AB, AC and BC respectively, are concurrent, then the triangle is an isosceles triangle.

Here is the Asymptote code it generated,这是它生成的渐近线代码,

pointpen = black;
pathpen = black+linewidth(0.7);
size(180);
pair A=(0,0),B=(1,0),C=IP(CR(A,3),CR(B,2)),D=foot(A,B,C),E=foot(B,A,C),F=foot(C,A,B);
D(MP("A",A,SW)--MP("B",B,SE)--MP("C",C,N)--cycle);
D(A--MP("D",D,S)--B);
D(B--MP("E",E,S)--C);
D(C--MP("F",F,S)--A);
D(D);D(E);
D(F);
D(circumcircle(A,B,C));
D(incircle(A,B,C));

I found this renderer online, http://asymptote.ualberta.ca/ .我在网上找到了这个渲染器, http://asymptote.ualberta.ca/ When I enter this into the renderer I get this error,当我将其输入渲染器时出现此错误,

pointpen = black;
^
workspace_1.asy: 1.1: no matching variable 'pointpen'

Update: OK on further investigation seems like the AI may be using some sort of short-hand mapping or making assumptions about pre-existing variables.更新:好的,进一步调查似乎 AI 可能正在使用某种速记映射或对预先存在的变量做出假设。 I think variables like pointpen don't really exist, and maybe this D stands for draw() .我认为像pointpen这样的变量并不存在,也许这个D代表draw() Will keep trying.会继续努力的。

I am looking at Asymptote's tutorial here ( https://asymptote.sourceforge.io/asymptote_tutorial.pdf ), and I can't find any of these things like pointpen , pathpen , or these D things here, so this isn't standard Asymptote code?我在这里查看 Asymptote 的教程 ( https://asymptote.sourceforge.io/asymptote_tutorial.pdf ),我在这里找不到pointpenpathpen或这些D东西,所以这不是标准的渐近线代码? Searched high & low can't really figure out what this is or how to visualize it.搜索高低无法真正弄清楚这是什么或如何形象化它。 Any help would be appreciated thanks!任何帮助将不胜感激谢谢!

OK finally figured this out.好的,终于想通了。 I think the AI was using some older (or alternative version) of Asymptote.我认为 AI 使用的是一些较旧(或替代版本)的 Asymptote。

I think the modern equivalent of the code it generated looks like this,我认为它生成的代码的现代版本看起来像这样,

size(180); 
pair A=(0,0),B=(1,0),C=(0.5,sqrt(3)/2),D=(A+B)/2,E=(B+C)/2,F=(A+C)/2;
draw(A--B--C--cycle);
draw(A--D); draw(B--E); draw(C--F);
dot("$A$",A,SW); dot("$B$",B,SE); dot("$C$",C,N); dot("$D$",D,S); 
dot("$E$",E,S); dot("$F$",F,S);

Of course I can't be 100% sure this is what the AI intended (does it have intentions?) but this graphic looks like it fits what the geometry problem is asking.当然,我不能 100% 确定这就是 AI 的意图(它有意图吗?),但这张图看起来很符合几何问题的要求。

Sorry my original question was super vague.抱歉,我原来的问题非常模糊。

渐近线生成的几何图形

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