问题描述
假设您有一个二维平面，上面有 2 个点(称为 a 和 b)，每个点用一个 x 整数和一个 y 整数表示.
Let's say you have a two dimensional plane with 2 points (called a and b) on it represented by an x integer and a y integer for each point.
如何确定另一个点 c 是否在 a 和 b 定义的线段上?
How can you determine if another point c is on the line segment defined by a and b?
我最常使用 python，但任何语言的示例都会有所帮助.
I use python most, but examples in any language would be helpful.
推荐答案
检查 (ba) 和 (ca) 的 叉积 是否为 0，正如 Darius Bacon 所说，告诉您积分是否a、b 和 c 对齐.
Check if the cross product of (b-a) and (c-a) is 0, as tells Darius Bacon, tells you if the points a, b and c are aligned.
但是，由于您想知道 c 是否介于 a 和 b 之间，您还必须检查 (ba) 和 (ca) 的 点积 是否正 并且小于 a 和 b 之间距离的平方.
But, as you want to know if c is between a and b, you also have to check that the dot product of (b-a) and (c-a) is positive and is less than the square of the distance between a and b.
在未优化的伪代码中:
def isBetween(a, b, c):
crossproduct = (c.y - a.y) * (b.x - a.x) - (c.x - a.x) * (b.y - a.y)
# compare versus epsilon for floating point values, or != 0 if using integers
if abs(crossproduct) > epsilon:
return False
dotproduct = (c.x - a.x) * (b.x - a.x) + (c.y - a.y)*(b.y - a.y)
if dotproduct < 0:
return False
squaredlengthba = (b.x - a.x)*(b.x - a.x) + (b.y - a.y)*(b.y - a.y)
if dotproduct > squaredlengthba:
return False
return True
这篇关于您如何确定一个点位于线段上的其他两个点之间?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持跟版网！