【python】Draw a straight line

根据直线方程画直线是一个比较直观且容易实现的方法，那么如何画线段呢？ 也即，如何根据两个端点来画线段呢？这就是本篇博客要介绍的内容之一，其次，由线段围成的封闭区域面积应该如何计算呢？

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1 画线段

参考博客 matplotlib画直线

from matplotlib.lines import Line2D
import matplotlib.pyplot as plt

figure, ax = plt.subplots()
# 设置x，y值域
ax.set_xlim(left=0, right=4)
ax.set_ylim(bottom=0, top=4)
# 两条line的数据
line1 = [(1, 1), (2, 2)]
line2 = [(3, 3), (4, 4)]
(line1_xs, line1_ys) = zip(*line1)
(line2_xs, line2_ys) = zip(*line2)
# 创建两条线，并添加
ax.add_line(Line2D(line1_xs, line1_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line2_xs, line2_ys, linewidth=1, color='red'))
# 展示
plt.plot()
plt.show()

2 计算多边形面积

《宫颐癌细胞计算机自动识别系统研究与设计》论文中有如下描述

对于 $\begin{vmatrix} x_1 & x_2\\ y_1 & y_2 \end{vmatrix}$∣∣∣∣​x1​y1​​x2​y2​​∣∣∣∣​ 具体的计算方法作者没有进一步阐述，脑海里第一反应是 det (determinant)，二阶的容易嘛 $\begin{vmatrix} A & B\\ C & D \end{vmatrix} = AD-BC$∣∣∣∣​AC​BD​∣∣∣∣​=AD−BC，coding 试了试，并不正确 (づ╥﹏╥)づ

在 如何计算封闭曲线的面积？ [问题点数：40分，结帖人OnlyVB] 这个论坛中找到了解决方案！

也即论文中 $\begin{vmatrix} x_1 & x_2\\ y_1 & y_2 \end{vmatrix}$∣∣∣∣​x1​y1​​x2​y2​​∣∣∣∣​ 的计算形式如下：$(x_1-x_2)*(y_1+y_2)$(x1​−x2​)∗(y1​+y2​)，coding 后发现 $(x_2-x_1)*(y_1+y_2)$(x2​−x1​)∗(y1​+y2​) 为正确结果（两者差一个负号）

总结公式如下：
$S = \frac{1}{2}\sum_{i=1}^{n}\left ( x_{i+1} - x_i \right )\left ( y_{i+1}+y_{i} \right )$S=21​i=1∑n​(xi+1​−xi​)(yi+1​+yi​)
当 $i = n$i=n时，$x_{i+1} = x_1, y_{i+1} = y_1$xi+1​=x1​,yi+1​=y1​

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用第一节的画法来画个图，然后测试下公式
线段比较多，打印下代码，哈哈哈

for i in range(1,13):
    #print("line{a} = [A{a},A{b}]".format(a=i,b=i+1))
    #print("(line{a}_xs, line{a}_ys) = zip(*line{a})".format(a=i))
    print("ax.add_line(Line2D(line{a}_xs, line{a}_ys, linewidth=1, color='blue'))".format(a=i))

设置好端点

A1 = (0,1)
A2 = (1,2)
A3 = (0,3)
A4 = (1,4)
A5 = (2,3)
A6 = (3,4)
A7 = (4,3)
A8 = (3,2)
A9 = (4,1)
A10 = (3,0)
A11 = (2,1)
A12 = (1,0)

画一下图（方法比较笨，仅提供一种配合打印代码的使用方法）

from matplotlib.lines import Line2D
import matplotlib.pyplot as plt

figure, ax = plt.subplots()
# 设置x，y值域
ax.set_xlim(left=0, right=4)
ax.set_ylim(bottom=0, top=4)
# 两条line的数据
line1 = [A1,A2]
line2 = [A2,A3]
line3 = [A3,A4]
line4 = [A4,A5]
line5 = [A5,A6]
line6 = [A6,A7]
line7 = [A7,A8]
line8 = [A8,A9]
line9 = [A9,A10]
line10 = [A10,A11]
line11 = [A11,A12]
line12 = [A12,A1]
(line1_xs, line1_ys) = zip(*line1)
(line2_xs, line2_ys) = zip(*line2)
(line3_xs, line3_ys) = zip(*line3)
(line4_xs, line4_ys) = zip(*line4)
(line5_xs, line5_ys) = zip(*line5)
(line6_xs, line6_ys) = zip(*line6)
(line7_xs, line7_ys) = zip(*line7)
(line8_xs, line8_ys) = zip(*line8)
(line9_xs, line9_ys) = zip(*line9)
(line10_xs, line10_ys) = zip(*line10)
(line11_xs, line11_ys) = zip(*line11)
(line12_xs, line12_ys) = zip(*line12)
# 创建两条线，并添加
ax.add_line(Line2D(line1_xs, line1_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line2_xs, line2_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line3_xs, line3_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line4_xs, line4_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line5_xs, line5_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line6_xs, line6_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line7_xs, line7_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line8_xs, line8_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line9_xs, line9_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line10_xs, line10_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line11_xs, line11_ys, linewidth=1, color='blue'))
ax.add_line(Line2D(line12_xs, line12_ys, linewidth=1, color='blue'))
# 展示
plt.plot()
plt.savefig('1.png')
plt.show()

我们可以计算出该多边形的面积为 $\sqrt{2}*\sqrt{2}*5=10$2​∗2​∗5=10

用公式计算下面积 $(x_2-x_1)*(y_1+y_2)$(x2​−x1​)∗(y1​+y2​)

def det(A,B):
    x1,y1 = A[0],A[1]
    x2,y2 = B[0],B[1]
    return (x2-x1)*(y1+y2)

代入端点

S = 1/2*(det(A1,A2)+det(A2,A3)+det(A3,A4)+det(A4,A5)+det(A5,A6)+det(A6,A7)+
         det(A7,A8)+det(A8,A9)+det(A9,A10)+det(A10,A11)+det(A11,A12)+det(A12,A1))
S

output

10.0

OK，大功告成