如何找到线段上距任意点最近的点？

Question

此函数应接受一个点参数，该参数将用于查找直线段对象上与其最近的点。在示例断言代码中，getClosestPoint(Point())将Point(10, 0)作为参数，并应返回Point(5,5)作为与l1 = Line(Point(5,5), Point(20,35))行上的最接近的点，端点是A Point(5,5), B Point(20,35)，我不知道该如何解决这个问题。我当前的解决方案将返回（4,3），它不在线段上，而是在直线上。在

 from point import Point
 import math
 class Line:
    def __init__(self,aPoint=Point(), bPoint=Point()):
        self.firstPoint = aPoint
        self.secondPoint = bPoint

    def getClosestPoint(self,point=Point()):

        m1 = self.getSlope()
        m2 = -1 / float(m1)
        b1 = self.p1.y - m1 * self.p1.x
        b2 = point.y - m2 * point.x
        x = float(b2 - b1) / float(m1 - m2)
        y = m1 * x + b1
        return Point(x, y)

    if __name__ == "__main__":
         p1 = Point(5,5)
         p2 = Point(20,35)
         l1 = Line(p1,p2)
         assert l1.getClosestPoint(Point(10,0)) == Point(5,5)
         assert l2.getClosestPoint(Point(25/2,25/2)


 class Point: 
    def __init__(self,x=0,y=0):
       self.x = x
       self.y = y

Answer 1

见this nice description by Paul Bourke。

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