画一条平行线

发布于 2024-09-01 09:09:14 字数 250 浏览 8 评论 0原文

我有 x1,y1 和 x2,y2 形成一条线段。如何获得与第一条线平行的另一条线 x3,y3 - x4,y4，如图所示。我可以简单地将 n 添加到 x1 和 x2 以获得平行线，但这不是我想要的。我希望线条在图片中是平行的。

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北凤男飞 2024-09-08 09:09:14

您要做的就是在正交方向上偏移坐标。如果您了解向量数学，请将由直线端点之间的距离创建的向量乘以以下矩阵：

[ 0 -1 ]
[ 1  0 ]

假设第一条线有点 (x1,y1)、(x2 ,y2)，其中 x=x2-x1、y=y2-y1。
我们还有 L = sqrt(x*x+y*y)，即线的长度（请原谅符号）。那么下一行应该偏移

[ 0 -1 ] [x]
[ 1  0 ] [y]

=> dx = -y / L，dy = x / L
这是新行的标准化偏移量。

在类似 C# 的伪代码中：

var x1 = ..., x2 = ..., y1 = ..., y2 = ... // The original line
var L = Math.Sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2))

var offsetPixels = 10.0

// This is the second line
var x1p = x1 + offsetPixels * (y2-y1) / L
var x2p = x2 + offsetPixels * (y2-y1) / L
var y1p = y1 + offsetPixels * (x1-x2) / L
var y2p = y2 + offsetPixels * (x1-x2) / L

g.MoveTo(x1p,y1p) // I don't remember if this is the way
g.LineTo(x2p,y2p) // to draw a line in GDI+ but you get the idea

What you want to do is to offset the coordinates in the orthogonal direction. If you know vector math, multiply the vector created by the distance between the endpoints of the line by the following matrix:

[ 0 -1 ]
[ 1  0 ]

Say that the first line has the points (x1,y1), (x2,y2), with x=x2-x1, y=y2-y1.
We also have L = sqrt(x*x+y*y), the length of the line (pardon the notation). Then the next line should be offset by

[ 0 -1 ] [x]
[ 1  0 ] [y]

=> dx = -y / L, dy = x / L
which is the normalized offset for the new line.

In C#-like pseudocode:

var x1 = ..., x2 = ..., y1 = ..., y2 = ... // The original line
var L = Math.Sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2))

var offsetPixels = 10.0

// This is the second line
var x1p = x1 + offsetPixels * (y2-y1) / L
var x2p = x2 + offsetPixels * (y2-y1) / L
var y1p = y1 + offsetPixels * (x1-x2) / L
var y2p = y2 + offsetPixels * (x1-x2) / L

g.MoveTo(x1p,y1p) // I don't remember if this is the way
g.LineTo(x2p,y2p) // to draw a line in GDI+ but you get the idea

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