Two-dimensional coordinate Inversion

Refer:

Http://zh.wikipedia.org/wiki/%E5%8F%8D%E6%BC%94

Http://sd-invol.github.io/2014/09/29/Hangzhou-2013-D/

Http://wangzhpp.org /? P = 106

Http://www.cnblogs.com/wangsouc/articles/3649201.html

Related Questions: hdu4773

Below:

For two-dimensional inversion, we usually base on a circular α (X α, y α, R α). We call its center as the center of the inversion, the radius is called the inverse radius.

For any two-dimensional point P that is not (X α, y α), we can obtain its inversion point P 'Through inversion '.

The constructor is as follows:OStart RayOPOne point aboveP'Makes |OP|OP'| = Rα 2.

(Here we can set rα to a greater value during calculation, which can reduce the accuracy error .)

There are some good properties after the inversion:

• The line of the midline is still the line of the center. The inverse form of a line that does not pass through the inversion center is the circle that passes through the inversion center.
• The circle that passes through the inversion center is changed to a straight line that does not pass the inversion center. The back of the circle that does not go through the inversion center is still a circle, and the inversion center is the bit-like center of the two opposite circles.

Through the above properties, we can solve some problems for solving Fixed Point Circular coordinate equations. As long as the fixed point is taken as the inversion center, and then a straight line after the inversion is obtained that does not take the center of the inversion, it will surely be the circle at the point after restoration.

Another important feature is:The inverse transformation does not change the tangent of the image.

　

Two-dimensional coordinate Inversion