Blowup of a plane at a point

The following image illustrates the blowup of a plane at a point–an important construction in algebraic geometry.

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\documentclass[border=10pt]{standalone}
\usepackage[inline]{asymptote}
\begin{document}
\begin{asy}[width=\the\linewidth,inline=true]
settings.outformat="pdf";
settings.render=0;
settings.prc=false;
usepackage("lmodern");
usepackage("fontenc","T1");
usepackage("amssymb");  // for the \mathbb command
defaultpen(fontsize(10pt));
import graph3;
size(400,400);
currentprojection=orthographic(5,-10,4);
real R=8;
struct scaler {
    private real factor;
    void operator init(real factor) {
        this.factor = factor;
    }
    real scale(real t) {return factor*atan(tan(t)/factor);}
    real invert(real t) {return tan(atan(t)*factor)/factor;}
}
scaler theScaler = scaler(6);
triple f(pair t) {
    real r = t.x;
    real theta = 2 * atan(t.y*2/pi);
//  real theta = -t.y;
    return (r*cos(theta),r*sin(theta),theScaler.scale(theta));
}
int resolution = 10;
real epsilon = .01;
 
 
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Source: TeX.SE
Author: Charles Staats (License)