问题描述
我有一组线段(不是线),(A1, B1)
,(A2, B2)
,(A3, B3)
,其中A
,B
是线段的终点.每个A
和B
都有(x,y)
坐标.
I have set of line segments (not lines), (A1, B1)
, (A2, B2)
, (A3, B3)
, where A
,B
are ending points of the line segment. Each A
and B
has (x,y)
coordinates.
问题:我需要知道point O
和line segments
之间的最短距离,如代码行中所示的图所示.我真正能理解的代码是伪代码或Python.
QUESTION:I need to know the shortest distance between point O
and line segments
as shown in the shown figure implemented in line of codes. The code I can really understand is either pseudo-code or Python.
代码:很遗憾,我尝试使用此代码解决问题,但该代码无法正常工作.
CODE: I tried to solve the problem with this code, unfortunately, it does not work properly.
def dist(A, B, O):
A_ = complex(*A)
B_ = complex(*B)
O_= complex(*O)
OA = O_ - A_
OB = O_ - B_
return min(OA, OB)
# coordinates are given
A1, B1 = [1, 8], [6,4]
A2, B2 = [3,1], [5,2]
A3, B3 = [2,3], [2, 1]
O = [2, 5]
A = [A1, A2, A3]
B = [B1, B2, B3]
print [ dist(i, j, O) for i, j in zip(A, B)]
谢谢.
推荐答案
以下是答案.该代码属于Malcolm Kesson,来源为此处.我之前只提供了链接本身,但主持人将其删除.我认为这样做的原因是因为没有提供代码(作为答案).
Here is the answer. This code belongs to Malcolm Kesson, the source is here. I provided it before with just link itself and it was deleted by the moderator. I assume that the reason for that is because of not providing the code (as an answer).
import math
def dot(v,w):
x,y,z = v
X,Y,Z = w
return x*X + y*Y + z*Z
def length(v):
x,y,z = v
return math.sqrt(x*x + y*y + z*z)
def vector(b,e):
x,y,z = b
X,Y,Z = e
return (X-x, Y-y, Z-z)
def unit(v):
x,y,z = v
mag = length(v)
return (x/mag, y/mag, z/mag)
def distance(p0,p1):
return length(vector(p0,p1))
def scale(v,sc):
x,y,z = v
return (x * sc, y * sc, z * sc)
def add(v,w):
x,y,z = v
X,Y,Z = w
return (x+X, y+Y, z+Z)
# Given a line with coordinates 'start' and 'end' and the
# coordinates of a point 'pnt' the proc returns the shortest
# distance from pnt to the line and the coordinates of the
# nearest point on the line.
#
# 1 Convert the line segment to a vector ('line_vec').
# 2 Create a vector connecting start to pnt ('pnt_vec').
# 3 Find the length of the line vector ('line_len').
# 4 Convert line_vec to a unit vector ('line_unitvec').
# 5 Scale pnt_vec by line_len ('pnt_vec_scaled').
# 6 Get the dot product of line_unitvec and pnt_vec_scaled ('t').
# 7 Ensure t is in the range 0 to 1.
# 8 Use t to get the nearest location on the line to the end
# of vector pnt_vec_scaled ('nearest').
# 9 Calculate the distance from nearest to pnt_vec_scaled.
# 10 Translate nearest back to the start/end line.
# Malcolm Kesson 16 Dec 2012
def pnt2line(pnt, start, end):
line_vec = vector(start, end)
pnt_vec = vector(start, pnt)
line_len = length(line_vec)
line_unitvec = unit(line_vec)
pnt_vec_scaled = scale(pnt_vec, 1.0/line_len)
t = dot(line_unitvec, pnt_vec_scaled)
if t < 0.0:
t = 0.0
elif t > 1.0:
t = 1.0
nearest = scale(line_vec, t)
dist = distance(nearest, pnt_vec)
nearest = add(nearest, start)
return (dist, nearest)
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