Python - 两圆相交求交点坐标
Max.Bai
2016-05-16

Python - 两圆相交求交点坐标

三轴机械臂求坐标问题，其实转化为平面问题就是两圆相交求交点问题，交点算出来就可以用反三角函数算出各个机械臂的夹角。

已知圆1， 半径R， 坐标（x, y)

圆2， 半径S， 坐标（a, b)

求两圆交点x3, y3   x4, y4。

算法一脚本：

# -*- coding: utf-8 -*-import mathdef sq(x):    return float(x * x)# target point on tabletx = float(10)ty = float(10)# hight of tableh0 = float(5)# length of armR = float(10)S = float(8)# arm pointx = float(0)y = float(5)# target point for arma = float(math.sqrt(sq(tx)+ sq(ty)))b = h0print "arm target:", a, bd = math.sqrt(sq(math.fabs(a-x)) + sq(math.fabs(b-y)))print "desitens:", dif d > (R+S) or d < (math.fabs(R-S)):    print "This point can't be rached!"    #return -1    exit    if d == 0 and R==S :    print "Can't rach arm point!"    #return -2    exitA = (sq(R) - sq(S) + sq(d)) / (2 * d)h = math.sqrt(sq(R) - sq(A))x2 = x + A * (a-x)/dy2 = y + A * (b-y)/d#print x2, y2x3 = x2 - h * ( b - y ) / dy3 = y2 + h * ( a - x ) / dx4 = x2 + h * (b - y) / dy4 = y2 - h * (a - x) / dprint "arm middle point:"print x3, y3print x4, y4

已知圆1， 半径L1， 坐标（0, L3)

圆2， 半径L2， 坐标（x, y)

求圆1交点与圆心连线和Y轴的夹角a1，

圆2交点与圆心连线和X轴的夹角a2。

算法二：

# -*- coding: utf-8 -*-import mathL1 = float(10)L2 = float(10)L3 = float(5)x = float(14.1421356237)y = float(5)def sq(x):    return x * xA = float(-2 * x * L1)B = float(2*(y-L3)*L1)C = float(sq(L2) - sq(L1) - sq(x) -sq(y-L3))a1 = float(2*math.atan((B-math.sqrt(sq(B)+sq(A)-sq(C)))/(A+C)))A = float(2 * (y - L3) * L2)B = float(2 * x * L2)C = float(sq(L2) + sq(x) + sq(L3-y) -sq(L1))a2 = float(2* math.atan((B-math.sqrt(sq(B)+sq(A)-sq(C)))/(A+C)))print a1, a2print a1*180/math.pi, a2*180/math.pi