找到两条线的交点 [英] Finding the intersection of two lines

问题描述

我有两行:

y = -1/3x + 4
y = 3x + 85

交叉点位于 [24.3，12.1] .

我准备了一组坐标:

points = [[1, 3], [4, 8], [25, 10], ... ]
#y = -1/3x + b
m_regr = -1/3
b_regr = 4
m_perp = 3 #(1 / m_regr * -1)    

distances = []
points.each do |pair|
  x1 = pair.first
  y2 = pair.last
  x2 = ((b_perp - b_regr / (m_regr - m_perp))
  y2 = ((m_regr * b_perp) / (m_perp * b_regr))/(m_regr - m_perp)
  distance = Math.hypot((y2 - y1), (x2 - x1))
  distances << distance
end

是否有宝石或更好的方法?

Is there a gem or some better method for this?

注意:上面的方法无效.请参阅我的答案以找到有效的解决方案.

NOTE: THE ABOVE METHOD DOES NOT WORK. See my answer for a solution that works.

推荐答案

在经历了千辛万苦和多次尝试之后，我发现了一种简单的代数方法

After much suffering and many different tries, I found a simple algebraic method here that not only works but is dramatically simplified.

distance = ((y - mx - b).abs / Math.sqrt(m**2 + 1))

其中x和y是已知点的坐标.

where x and y are the coordinates for the known point.

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