点集之间的平滑线

Question

我希望连接值的线条是平滑的圆线。我试过机智 interp1d 但我似乎没有围绕一维数组要求。

from matplotlib import pyplot as plt

a = int(input("what number?\n"))

X_Values, Y_Values, fibonacci = [0] * a, [0] * a, [0] * a
X_Values[0], Y_Values [0] = 0, 0
X_Values[1], Y_Values[1] = 1, 1
fibonacci[0] = 1
fibonacci[1] = 1
counter = 2

for i in range(2,a):
   fibonacci[i] = fibonacci[i-1] + fibonacci[i-2]
   if counter == 0:
       X_Values[i] = 0
       Y_Values[i] = -fibonacci[i]
       counter += 1
   elif counter == 1:
       X_Values[i] = fibonacci[i]
       Y_Values[i] = 0
       counter += 1
   elif counter == 2:
       X_Values[i] = 0
       Y_Values[i] = fibonacci[i]
       counter += 1
   elif counter == 3:
       X_Values[i] = -fibonacci[i]
       Y_Values[i] = 0
       counter = 0


plt.axhline(y=0, color='k') 
plt.axvline(x=0, color='k')
plt.plot(X_Values, Y_Values, '*-g')
plt.title("Flow Chart of a Fibonacci series with %i elements" %a)
plt.figtext(0.5, 0.025, "The {0}th number of the Fibonacci serie is: {1}".format(a, fibonacci[-1]), ha="center", fontsize=8, bbox={"facecolor":"orange", "alpha":0.5, "pad":5})
print("The ", a, "th Fibonacci number is: ", fibonacci[a-1])
plt.show()

有没有办法缩短 if elif 循环以将坐标分配给 X 和 Y _values？

Answer 1

要创建平滑的插值，您可能可以使用 Bézier splines。您可以通过添加 X[i] 和 X[i+1] 以及 Y[i] 和 Y[i+1].

来计算中间点

使用圆弧效果会更好。起始角度将为 -90, 0, 90, 180, 270, ...。结束角度将是开始角度加上 90。宽度和高度有点棘手，因为它们的角色不断切换。它将是斐波那契数 i 和 i+1，或者相反。 i % 2 和 (i+1) % 2 将负责切换。

为了用更少的代码进行计算，首先请注意不需要 counter，因为它只是 i mod 4。旋转方向可以存储在两个列表中，dir_x 和dir_y。此外，前两个值可以通过 if 测试 (if i < 2) 设置，因此它们可以对 x 和 y 位置使用相同的赋值。

from matplotlib import pyplot as plt
from matplotlib.patches import Arc

a = int(input("what number?\n"))

X_Values, Y_Values, fibonacci = [0] * a, [0] * a, [0] * a

dir_x = [0, 1, 0, -1]
dir_y = [-1, 0, 1, 0]
for i in range(0, a):
    if i < 2:
        fibonacci[i] = 1
    else:
        fibonacci[i] = fibonacci[i - 1] + fibonacci[i - 2]
    X_Values[i] = dir_x[i % 4] * fibonacci[i]
    Y_Values[i] = dir_y[i % 4] * fibonacci[i]

fig, ax = plt.subplots()
for i in range(a - 1):
    ax.add_patch(Arc((0, 0), width=fibonacci[i + (i + 1) % 2] * 2, height=fibonacci[i + i % 2] * 2,
                     theta1=(i - 1) * 90, theta2=i * 90, color='crimson', lw=2))
# ax.relim() # needed to calculate the x and y limits if no lines are added to the plot
# ax.autoscale()
ax.axis('equal') # equal distances on x and on y
ax.axis('off') # hide the surrounding axes

ax.axhline(y=0, color='k')
ax.axvline(x=0, color='k')
ax.plot(X_Values, Y_Values, '*--g', lw=0.5)
ax.set_title("Flow Chart of a Fibonacci series with %i elements" % a)
ax.text(0.5, -0.05, f"The {a}th number of the Fibonacci serie is: {fibonacci[-1]}", ha="center",
        fontsize=8, bbox={"facecolor": "orange", "alpha": 0.5, "pad": 5}, transform=ax.transAxes)
print("The ", a, "th Fibonacci number is: ", fibonacci[a - 1])

plt.tight_layout()
plt.show()

PS：创建圆弧的代码可以使用其 angle 参数进一步简化。 angle 是给圆弧的额外旋转，它消除了交替宽度和高度的需要。

ax.add_patch(Arc((0, 0), width=fibonacci[i] * 2, height=fibonacci[i + 1] * 2,
                 angle=(i - 1) * 90, theta1=0, theta2=90, color='crimson', lw=2))

绘制二次贝塞尔曲线的代码：

from matplotlib.patches import PathPatch, Path

x, y = X_Values, Y_Values
for i in range(a - 1):
    ax.add_patch(PathPatch(
        Path([(x[i], y[i]), (x[i] + x[i + 1], y[i] + y[i + 1]), (x[i + 1], y[i + 1])],
             [Path.MOVETO, Path.CURVE3, Path.CURVE3]),
        fc="none", ec='navy', transform=ax.transData))

点集之间的平滑线

Smooth line between set of points

python

matplotlib

fibonacci