在给定线的另一个点和垂直线上的2个点的情况下，如何找到该点的X坐标? [英] How to find the X coordinate of a point on a line given another point of the line and the 2 points on a perpendicular line?

问题描述

我正在编写一个python应用程序以选择矩形区域，当用户设置2个点(矩形的长度)时，第三点和第四个点在形成矩形时受到限制，其中矩形的宽度已给定通过鼠标光标和最后一个点的Y差.

I'm writing a python app to select rectangular areas, when the user has set 2 points (the length of the rectangle), the third and 4th points are constrained in forming a rectangle, where the width of the rectangle is given by the Y difference of the mouse cursor and the last point.

下面是一张简短的图片，我正在寻找C点的X坐标.

Here's a quick picture to explain, I'm looking for the X coordinate of the point C.

我知道:

• A(2,3)
• B(5,5)
• 角度= 90度
• C的Y坐标为7.

我不确定如何使用向量解决这个问题?我在项目中使用了numpy.

I'm not sure how to tackle this... using vectors ? I'm using numpy in my project.

推荐答案

这不仅仅是数学问题，更是数学问题.

This is more of a math issue than a numpy issue.

(AB)的斜率是(y_a - y_b)/ (a - b).因此，与(AB)垂直的任何斜率都为p=(b-a)/(y_a-y_b)(与原始斜率的倒数相反).

The slope of (AB) is (y_a - y_b)/ (a - b). So the slope of any perpendicular to (AB) is p=(b-a)/(y_a-y_b) (opposite of the inverse of the original slope).

从这里可以轻松确定穿过B的垂直于(AB)的方程:y-y_b=p*(x-x_b).并将y_c替换为y以找到x_c

From here it is easy to determine the equation of the perpendicular to (AB) passing through B : y-y_b=p*(x-x_b). And substitute y_c to y to find x_c

如果(AB)是水平的(0斜率)，则存在一个问题(被零除).在这种情况下，x_c就是x_b((BC)上的所有点都具有相同的x坐标)

There is an issue (division by zero) if (AB) is horizontal (0 slope). In that case, x_c is just x_b (all of the points on (BC) have same x coordinate)

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