计算直线和直线的交点 2维

简介

说来简单，实现难
使用直线的一般式方程 (Ax+By+C=0) 联立方程组求解

TIPS 可以只用 scipy linalg 求解线性方程组

code

# coding=utf-8
from scipy.optimize import fsolve #导入求解方程组的函数 非线性方程组
import numpy as np
from scipy import linalg
class Point2D:
    # AX+BY+C = 0
    # 二维的一般式方程
    def __init__(self, x, y):
        self.x = x
        self.y = y

class Line2D:
    # AX+BY+C = 0
#   # 二维的一般式方程
    def __init__(self, A, B, C):
        self.A = A
        self.B = B
        self.C = C
    def init_from_two_point2d(self, a, b):
        self.A = b.y - a.y
        self.B = a.x - b.x
        self.C = b.x * a.y - a.x * b.y
    def getABC(self):
        return self.A, self.B, self.C

class Point3D:
    def __init__(self, x, y, z):
        self.x = x
        self.y = y
        self.z = z

class Vec3D:
    '''
    向量
    '''
    def __init__(self, x, y, z):
        self.x = x
        self.y = y
        self.z = z


class Line3D:
    # 点向式
    # 二维的一般式方程
    def __init__(self, a, b, c, x_0, y_0, z_0):
        self.a = a
        self.b = b
        self.c = c
        self.x_0 = x_0
        self.y_0 = y_0
        self.z_0 = z_0


def f(x):
    A = x[0]
    B = x[1]
    C = x[2]
    AA = x[3]
    BB = x[4]
    CC = x[5]
    return [A]

def intersection_line2D_line2D(line1, line2):
    A,B,C = line1.getABC()
    D,E,F = line2.getABC()
    AA = np.array([[A, B], [D, E]])
    BB = np.array([-C, -F])
    x = linalg.solve(AA, BB)
    print("[DEBUG] intersection on the point[x,y]", x)

if __name__ == "__main__":
    a = Point2D(0,0)
    b = Point2D(1,1)
    c = Point2D(0,1)
    d = Point2D(1,0)

    l = Line2D(0,0,0)
    l.init_from_two_point2d(a, b)
    n = Line2D(0,0,0)
    n.init_from_two_point2d(c, d)
    intersection_line2D_line2D(l, n)

TIPS2

细心的小伙伴已经发现了，如果是平行的两条2维直线，或者是两条重合的二维直线，那么就会报一个错误 Matrix is singular
需要在程序中排除

def intersection_line2D_line2D(line1, line2):
    A,B,C = line1.getABC()
    D,E,F = line2.getABC()
    # 判断这两条直线是否是重合的 或者平行的
    w = np.array([[A, B, C], [D, E, F]])
    if(np.linalg.matrix_rank(w) != 2):
        print('[ERROR] coincide  重合')
        return
    ww = np.array([[A, B], [D, E]])
    if(np.linalg.matrix_rank(ww) == 1 and C != F):
        print('[ERROR] parallel 平行')
        return
    AA = np.array([[A, B], [D, E]])
    BB = np.array([-C, -F])
    x = linalg.solve(AA, BB)
    print("[DEBUG] intersection on the point[x,y]", x)