如何在给定线段的情况下获取垂直矢量 [英] How to get perpendicular vectors given a line segment

问题描述

如何获取A，B，C和D点?

How to get point A, B , C, and D?

如果AB和CD垂直于p0p1.

if AB and CD are perpendicular to p0p1.

假设p0A，p0B，p1C和p1D具有标准化长度

Assume p0A, p0B, p1C, and p1D have normalized length

推荐答案

线的方向由d = normalize(p1 - p0)给出.要计算垂直向量，我们可以使用与(0, 0, 1)的叉积.结果是:

The direction of the line is given by d = normalize(p1 - p0). To calculate a perpendicular vector we can use the cross product with (0, 0, 1). Which results in:

d_left = (-d.y, d.x)
d_right = (d.y, -d.x)

您还没有说过坐标系统如何对齐，因此d_left可能会变成d_right，反之亦然.

You haven't said how your coordinate system is aligned, so d_left might become d_right and vice versa.

然后使用以下方法获得所需的分数:

You then get the desired points with:

A = p0 + d_left
B = p0 + d_right
C = p1 + d_left
D = p1 + d_right

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