画一条平行线

Question

我有x1,y1和x2,y2,形成一个线段.如何得到另一条x3,y3-x4,y4,它与图片中的第一行平行.我可以简单地将n添加到x1和x2以获得并行线,但它不是我想要的.我希望线条在图片中平行.

Answer 1

你想要做的是偏移正交方向的坐标.如果您知道向量数学,则将由行的端点之间的距离创建的向量乘以以下矩阵:

[ 0 -1 ]
[ 1  0 ]

说,第一行的点(x1,y1),(x2,y2)与x=x2-x1,y=y2-y1.
我们也有L = sqrt(x*x+y*y),线的长度(原谅表示法).然后下一行应该被偏移

[ 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