guide plot(real f(real), real min, real max, int nplotpoints=10, int maxrec=7)

// 使用自适应方法产生 y = f(x) 的图象 guide
guide plot(real f(real), real min, real max, int nplotpoints=10, int maxrec=7)
{
if (nplotpoints < 2)
nplotpoints = 2;
// 描初始的 nplotpoints 个点，并估计函数变化幅度
pair[] fpoints;
real fmax = -infinity, fmin = infinity;
for (int i = 0; i <= nplotpoints; ++i) {
real x = min + i/nplotpoints * (max-min);
pair z = (x, f(x));
fmax = max(fmax, z.y);
fmin = min(fmin, z.y);
fpoints.push(z);
}
// 定义辅助的递归函数：在规定的递归次数之内，在两个样本点之间描新点
// 误差 fuzz 达到函数变化幅度估计值的 1/500 为止
// 这个误差值在一般屏幕显示上只有一两个像素
real fuzz = max(0.002(fmax-fmin), realEpsilon);
guide helper(int nrec, pair a, pair b)
{
if (nrec == 0)
return b;
pair mid = (a+b)/2;
pair z = (mid.x, f(mid.x));
if (abs(z.y-mid.y) < fuzz)
return z -- b;
else
return helper(nrec-1, a, z) -- helper(nrec-1, z, b);
}
// 递归构造 guide
guide g = fpoints[0];
for (int i = 0; i < nplotpoints; ++i)
g = g -- helper(maxrec, fpoints[i], fpoints[i+1]);
return g;
}

//////////////////////////////////////////

real f(real x) {return 2sin(x^3);}
real min = -5.0, max = 5.0;

// 用自适应方法绘制函数 f(x)
guide g = scale(1cm)*plot(f, min, max);
draw(g, red+1pt);
for (int i = 0; i < size(g); ++i) {
draw(point(g,i), blue+2pt);
}
write(size(g));

// 用 graph 模块的默认方法（均匀取点）绘制函数 f(x)
import graph;
guide h = shift(-5cm*I)*scale(1cm)*graph(f, min, max);
draw(h, orange+1pt);
for (int i = 0; i < size(h); ++i) {
draw(point(h,i), blue+2pt);
}
write(size(h));