Mirror a line segment

I have a line segment (x1, y1), (x2, y2) that i need "mirrored" so the new line becomes perpendicular to the first one and passes through its middle.

The lin开发者_Python百科e segment (0,0),(2,2) should return a new line segment (0,2),(2,0)

Can anyone help me with a function/formula to handle this?

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The midpoint is (mx,my) = ((x1+x2)/2,(y1+y2)/2).

To rotate the endpoints 90 degrees about the middle, first compute a vector:

(dx,dy) = (x1-mx),(y1-my)

then rotate it 90 degrees:

dx1 = -dy
dy1 = dx

Then the new point becomes:

x1 = mx+dx1
y1 = my+dy1

Repeat for x2,y2.

You may also combine steps if you're careful.

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It seems you are looking for a symmetry. well, a good way of doing that could be using a scaling matrix.

vx, vy, vz are the coefficient of scaling. px,py,pz are the coordinate of a point. If you multiply the scale matrix for the point coordinate, you will get the scaled coordinates of that point.

A scaling matrix with vx=vy=vz= 1 is an identity transform. For obtain a mirror effect you could simply invert the matrix coefficient of the axis on which you want to perform the symmetry.

For example :

1  0 0|px

0 -1 0|py

0  0 1|pz

will calculate the symmetric point of the given vector respect to y axis.