如何找到用于绘制给定两点的垂直线的点 [英] How to Find points for draw a Perpendicular line of given two points

问题描述

我有两个点（x1，y1）和（x2，y2），这是一条直线。现在我想通过与主线垂直的终点绘制两条线。



附加图片你可以看到我需要的东西。



Pointsfind.png - Google云端硬盘 [ ^ ]







如果有人知道该怎么办请帮助

先谢谢。

解决方案

垂直于（a，b）的向量是（-b，a）。这个可以通过标量积（也称为点积）的帮助来证明。



在你的情况下（a，b）=（x2，y2） - （x1，y1）。现在，使用这个（-b，a）向量，可以很容易地分别计算出四个（？，？）向量的代表（抱歉，我找不到正确的英文单词）。



因为（？，？）未指定更精确，我个人会使用上面提到的计算。另一种方法是使用单位矢量（-b，a），但是在图形的情况下，必须注意，不要失去精确度。



对不起对于我糟糕的英语，我希望它有所帮助。



它是简单的向量计算。即使其他人认为它更多。

感谢所有人的回复。

i使用以下代码做同样的事情



dx = x1-x2

dy = y1-y2

dist = sqrt（dx * dx + dy * dy）

dx / = dist

dy / = dist

x3 = x1 +（N / 2）* dy //其中N是行的长度抽奖。

y3 = y1 - （N / 2）* dx

x4 = x1 - （N / 2）* dy

y4 = y1 +（N / 2）* dx





和我发现x5，y5和x6 y6的方式相同。

Hi,
I have two point (x1,y1) and (x2,y2) which makes a straight line. Now I want to draw two lines through the terminal points which will be perpendicular to the main line.

in attached image you can see what i need.

Pointsfind.png - Google Drive[^]



if anyone know how to do please help
Thanks in Advance.

解决方案

A vector perpendicular to (a,b) is (-b,a). This one can prove by the help of scalar product (also named dot product).

In your case (a,b)= (x2,y2)-(x1,y1). Now, with this (-b,a) vector one can easily calculate the four (?,?) vectors respectively their "representants" (sorry I do not find the right word in English).

Because (?,?) is not specified more precise, I personally would use the above mentioned calculations. Another way is to use "unit vector" for (-b,a), but in case of graphics one has to pay attention, not to lose precisions.

Sorry for my bad English, I hope it helps.

It is simple vector computation. Even if others here think it is more.

Thanks to all for your reply.
i did the same by using the following code

dx = x1-x2
dy = y1-y2
dist = sqrt(dx*dx + dy*dy)
dx /= dist
dy /= dist
x3 = x1 + (N/2)*dy // where N is the length of line to be draw.
y3 = y1 - (N/2)*dx
x4 = x1 - (N/2)*dy
y4 = y1 + (N/2)*dx


and same way i found the x5,y5 and x6 y6.

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