sympy's plot_parametric says TypeError: can't convert complex to float

Question

我想画一条实际上是S形的曲线：

画一个圆圈
将半圆的下半部分移动整个直径距离

但代码显示 TypeError: can't convert complex to float。复数在哪里？如何解决？谢谢

import sympy as sp
from sympy.plotting import *

u = sp.Symbol('u', real=True)
R0 = 2
boundLower = 0
boundUpper = 2 * sp.pi

x_u = sp.Piecewise(
    (R0*sp.cos(u)+R0, sp.And(boundLower <= u, u <= boundUpper/2)),
    (R0*sp.cos(u)+3*R0, sp.And(boundUpper/2 < u, u <= boundUpper)),
)

y_u = sp.Piecewise(
    (R0*sp.sin(u), sp.And(boundLower <= u,  u <= boundUpper/2)),
    (R0*sp.sin(u), sp.And(boundUpper/2 < u, u <= boundUpper)),
)

plot_parametric(x_u, y_u, (u, boundLower, boundUpper))

Answer 1

SymPy 的 plot 涉及一些容易出错的操作，旨在提高绘图的性能；它们涉及 complex 数据类型，当涉及不等式时有时会导致错误。在这种情况下减少不等式的数量会有所帮助：

x_u = sp.Piecewise(
    (R0*sp.cos(u)+R0, u <= boundUpper/2),
    (R0*sp.cos(u)+3*R0, u <= boundUpper),
)

y_u = sp.Piecewise(
    (R0*sp.sin(u), u <= boundUpper/2),
    (R0*sp.sin(u), u <= boundUpper),
)

plot_parametric(x_u, y_u, (u, boundLower, boundUpper))

以上是 Piecewise 通常在 SymPy 中的呈现方式：条件按给定的顺序求值，第一个为 True 的结果导致对相应表达式的求值。（u <= boundUpper 可以用 True 代替。）结果：

这仍然不理想。当然，从 0 到 4 的水平线不应该存在 - 这是绘图的产物。此外，此代码显示

UserWarning: The evaluation of the expression is problematic. We are trying a failback method that may still work. Please report this as a bug.

我建议在绘图时避免使用 Piecewise。而是使用 extend 组合片段中的图，如下所示。

x_u1 = R0*sp.cos(u)+R0
x_u2 = R0*sp.cos(u)+3*R0

y_u1 = R0*sp.sin(u)
y_u2 = R0*sp.sin(u)

p = plot_parametric(x_u1, y_u1, (u, boundLower, boundUpper/2), show=False)
p.extend(plot_parametric(x_u2, y_u2, (u, boundUpper/2, boundUpper), show=False))
p.show()

输出（无警告，无伪影）。

sympy's plot_parametric says TypeError: can't convert complex to float

sympy's plot_parametric says TypeError: can't convert complex to float

python

plot

sympy

parametric-equations